Numerical Tribute to Achievement of Euler

Science.gov (United States)

Figueroa-Navarro, Carlos; Molinar-Tabares, Martín Eduardo; Castro-Arce, Lamberto; Campos-García, Julio Cesar

2014-03-01

This work aims to make a tribute to one of the world's brightest personalities as it was the mathematical physicist Leonhard Euler (1707-1783). Some results where the influence of Euler persists with the novelty of applying numerical analysis using Matlab are here exposed. A first analysis was done with the series that defines Euler numbers and polynomials of Frobenius-Euler; another result is the characterization of the functions that carry to Euler-Macheroni constant. In hydrodynamics is also feasible to evaluate graphically the relationship between dimensions in diameter and the exit angle of the height of Euler for turbomachines. In differential equations of Cauchy-Euler solutions for the cases of distinct real roots and complex roots are generated. Furthermore we report the generation of the Fourier series and the Fourier transform calculated by using Direct Commands of Matlab. In variational calculus it is possible to obtain plots from a problem of the Euler Lagrange equations. Finally, the Euler function is analyzed. Our purpose is to present a tribute to this giant of science also it could be an excuse to study his legacy by utilizing modern computational techniques.

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-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....

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.

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.

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

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....

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

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.

Explicit integration of some integrable systems of classical mechanics

OpenAIRE

Basak Gancheva, Inna

2011-01-01

The main objective of the thesis is the analytical and geometrical study of several integrable finite-dimentional dynamical systems of classical mechanics, which are closely related, namely: - the classical generalization of the Euler top: the Zhukovski-Volterra (ZV) system describing the free motion of a gyrostat, i.e., a rigid body carrying a symmetric rotator whose axis is fixed in the body; - the Steklov-Lyapunov integrable case of the Kirchhoff equations describing the motio...

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

Science.gov (United States)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

Science.gov (United States)

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

The accuracy of dynamic attitude propagation

Science.gov (United States)

Harvie, E.; Chu, D.; Woodard, M.

1990-01-01

Propagating attitude by integrating Euler's equation for rigid body motion has long been suggested for the Earth Radiation Budget Satellite (ERBS) but until now has not been implemented. Because of limited Sun visibility, propagation is necessary for yaw determination. With the deterioration of the gyros, dynamic propagation has become more attractive. Angular rates are derived from integrating Euler's equation with a stepsize of 1 second, using torques computed from telemetered control system data. The environmental torque model was quite basic. It included gravity gradient and unshadowed aerodynamic torques. Knowledge of control torques is critical to the accuracy of dynamic modeling. Due to their coarseness and sparsity, control actuator telemetry were smoothed before integration. The dynamic model was incorporated into existing ERBS attitude determination software. Modeled rates were then used for attitude propagation in the standard ERBS fine-attitude algorithm. In spite of the simplicity of the approach, the dynamically propagated attitude matched the attitude propagated with good gyros well for roll and yaw but diverged up to 3 degrees for pitch because of the very low resolution in pitch momentum wheel telemetry. When control anomalies significantly perturb the nominal attitude, the effect of telemetry granularity is reduced and the dynamically propagated attitudes are accurate on all three axes.

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.

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.

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

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.

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

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,.

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.

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.

Drawing Euler Diagrams with Circles

OpenAIRE

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

2010-01-01

Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis. As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of manual data analysis and the subsequent task of drawing an appropriate diagram. Various methods have emerged that automatically dra...

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…

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...

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

Improving Euler computations at low Mach numbers

NARCIS (Netherlands)

Koren, B.; Leer, van B.; Deconinck, H.; Koren, B.

1997-01-01

The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of

Improving Euler computations at low Mach numbers

NARCIS (Netherlands)

Koren, B.

1996-01-01

This paper consists of two parts, both dealing with conditioning techniques for low-Mach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized linearized 1-D Euler equations, the smoothing behavior of

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.

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

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.

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

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.

Flow fields in the supersonic through-flow fan. Comparison of the solutions of the linear potential theory and the numerical solution of the Euler equations; Choonsoku tsukaryu fan nai no nagareba. Senkei potential rironkai to Euler hoteishiki no suchikai no hikaku

Energy Technology Data Exchange (ETDEWEB)

Yamasaki, N; Nanba, M; Tashiro, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1996-03-27

Comparison study between solutions of a linear potential theory and numerical solution of Euler equations was made for flow in a supersonic through-flow fan. In numerical fluid dynamic technique, Euler equations are solved by finite difference method under the assumption of air and perfect gas fluid, and neglected viscosity and thermal conductivity of fluid. As a result, in a linear potential theory, expansion wave was regarded as equipotential discontinuous surface, while in Euler numerical solution, it was regarded as finite pressure gradient where a wave front fans out toward downstream. The latter reflection point of shock wave on a wing existed upstream as compared with the former reflection point. The shock wave angle was dominated by Euler equations, and different from the Mach line of a linear potential theory in both angle and discontinuous quantities in front and behind. Both calculated solutions well agreed with each other until the first reflection point of the Mach line, however, thereafter the difference between them increased toward downstream. 5 refs., 5 figs., 1 tab.

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.

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.

Euler deconvolution and spectral analysis of regional aeromagnetic ...

African Journals Online (AJOL)

Existing regional aeromagnetic data from the south-central Zimbabwe craton has been analysed using 3D Euler deconvolution and spectral analysis to obtain quantitative information on the geological units and structures for depth constraints on the geotectonic interpretation of the region. The Euler solution maps confirm ...

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).

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

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

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

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.

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.

Störmer problem restricted to a spherical surface and the Euler and Lagrange tops

International Nuclear Information System (INIS)

Piña, Eduardo; Cortés, Emilio

2016-01-01

In a recent work, Cortés and Poza (2015 Eur. J. Phys. 36 055009) analysed, in full, the dynamics of a charged particle in the field of a magnetic dipole restricted to a spherical surface with the dipole at its centre. This model can be considered as the classical non-relativistic Störmer problem on a sphere. Here, we started from a Lagrangian approach: we derived the Hamilton equations of motion and observed that in this restricted case the equations can be reduced to quadratures, and they were integrated numerically. From the Hamiltonian function we found, for the polar angle, an equivalent one-dimensional system of a particle in the presence of an effective potential. In the present work we start from a change of variable to the cosine of the polar angle. In terms of this variable we obtain an equation that turns out to be the same as the one of a particle in a quartic potential. Then, we can actually solve the equations of motion for the polar angle using Jacobi elliptic functions, and for the azimuthal angle we use the same integrals which were expressed by Jacobi in terms of theta functions, both in the Euler and Lagrange tops. In this restricted Störmer problem, the student at undergraduate or graduate level will have a good example of an integrable nonlinear physical system in which, after analysis of its complex dynamics, one can obtain an analytical solution by means of some special functions of mathematical physics. Additionally, one discovers that the equations of motion of this restricted case of a charge in a magnetic dipole field have the same mathematical structure as the corresponding equations of other well known integrable classical dynamical systems. (paper)

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...

Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Pt. 1

Energy Technology Data Exchange (ETDEWEB)

Gonzalez, Ivan [Valparaiso Univ. (Chile). Inst. de Fisica y Astronomia; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Dept. de Ciencias Basicas; Notte-Cuello, Eduardo A. [La Serena Univ. (Chile). Dept. de Matematicas; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica; Rojas-Medar, Marko A. [Univ. de Tarapaca, Arica (Chile). Inst. de Alta Investigacion

2016-12-15

In this paper we proceed to study properties of Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions. In our previous papers [Nuclear Physics B 870 (2013) 243], [Nuclear Physics B 876 (2013) 322] we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms and that the higher-order UD functions were obtained in terms of a differential operator by applying it to a slightly modified first UD function. The result is valid in d=4 dimensions and its analog in d=4-2ε dimensions exits too [Theoretical and Mathematical Physics 177 (2013) 1515]. In [Nuclear Physics B 870 (2013) 243] the chain of recurrent relations for analytically regularized UD functions was obtained implicitly by comparing the left hand side and the right hand side of the diagrammatic relations between the diagrams with different loop orders. In turn, these diagrammatic relations were obtained due to the method of loop reductions for the triangle ladder diagrams proposed in 1983 by Belokurov and Usyukina. Here we reproduce these recurrent relations by calculating explicitly via Barnes lemmas the contour integrals produced by the left hand sides of the diagrammatic relations. In such a way we explicitly calculate a family of multi-fold contour integrals of certain ratios of Euler gamma functions. We make a conjecture that similar results for the contour integrals are valid for a wider family of smooth functions which includes the MB transforms of UD functions.

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.

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.

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

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.

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.

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 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.

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.

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.

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...

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.

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.

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.

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.

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

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 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

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…

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

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

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.

Nonlinear dynamics non-integrable systems and chaotic dynamics

CERN Document Server

Borisov, Alexander

2017-01-01

This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

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.

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.

Dynamics of a nonlinear dipole vortex

DEFF Research Database (Denmark)

Hesthaven, J.S.; Lynov, Jens-Peter; Nielsen, A.H.

1995-01-01

A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganiz...

Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations

Directory of Open Access Journals (Sweden)

Guanfeng Li

2014-01-01

Full Text Available We introduce a class of variational integrals whose Euler equations are nonhomogeneous -harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous -harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.

Lagrangian structures, integrability and chaos for 3D dynamical equations

International Nuclear Information System (INIS)

Bustamante, Miguel D; Hojman, Sergio A

2003-01-01

In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion

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...

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

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

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...

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.

Adaptive Integration of Nonsmooth Dynamical Systems

Science.gov (United States)

2017-10-11

2017 W911NF-12-R-0012-03: Adaptive Integration of Nonsmooth Dynamical Systems The views, opinions and/or findings contained in this report are those of...Integration of Nonsmooth Dynamical Systems Report Term: 0-Other Email: drum@gwu.edu Distribution Statement: 1-Approved for public release; distribution is...classdrake_1_1systems_1_1_integrator_base.html ; 3) a solver for dynamical systems with arbitrary unilateral and bilateral constraints (the key component of the time stepping systems )- see

Development of an Output-based Adaptive Method for Multi-Dimensional Euler and Navier-Stokes Simulations

Science.gov (United States)

Darmofal, David L.

2003-01-01

The use of computational simulations in the prediction of complex aerodynamic flows is becoming increasingly prevalent in the design process within the aerospace industry. Continuing advancements in both computing technology and algorithmic development are ultimately leading to attempts at simulating ever-larger, more complex problems. However, by increasing the reliance on computational simulations in the design cycle, we must also increase the accuracy of these simulations in order to maintain or improve the reliability arid safety of the resulting aircraft. At the same time, large-scale computational simulations must be made more affordable so that their potential benefits can be fully realized within the design cycle. Thus, a continuing need exists for increasing the accuracy and efficiency of computational algorithms such that computational fluid dynamics can become a viable tool in the design of more reliable, safer aircraft. The objective of this research was the development of an error estimation and grid adaptive strategy for reducing simulation errors in integral outputs (functionals) such as lift or drag from from multi-dimensional Euler and Navier-Stokes simulations. In this final report, we summarize our work during this grant.

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.

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…

Influence of foundation mass and surface roughness on dynamic response of beam on dynamic foundation subjected to the moving load

Science.gov (United States)

Tran Quoc, Tinh; Khong Trong, Toan; Luong Van, Hai

2018-04-01

In this paper, Improved Moving Element Method (IMEM) is used to analyze the dynamic response of Euler-Bernoulli beam structures on the dynamic foundation model subjected to the moving load. The effects of characteristic foundation model parameters such as Winkler stiffness, shear layer based on the Pasternak model, viscoelastic dashpot and characteristic parameter of mass on foundation. Beams are modeled by moving elements while the load is fixed. Based on the principle of the publicly virtual balancing and the theory of moving element method, the motion differential equation of the system is established and solved by means of the numerical integration based on the Newmark algorithm. The influence of mass on foundation and the roughness of the beam surface on the dynamic response of beam are examined in details.

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)

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.

Dynamic planar embeddings of dynamic graphs

DEFF Research Database (Denmark)

Holm, Jacob; Rotenberg, Eva

2015-01-01

-flip-linkable(u, v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler, exploiting...... that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour....

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.

A general treatment of dynamic integrity constraints

NARCIS (Netherlands)

de Brock, EO

This paper introduces a general, set-theoretic model for expressing dynamic integrity constraints, i.e., integrity constraints on the state changes that are allowed in a given state space. In a managerial context, such dynamic integrity constraints can be seen as representations of "real world"

Cone Algorithm of Spinning Vehicles under Dynamic Coning Environment

Directory of Open Access Journals (Sweden)

Shuang-biao Zhang

2015-01-01

Full Text Available Due to the fact that attitude error of vehicles has an intense trend of divergence when vehicles undergo worsening coning environment, in this paper, the model of dynamic coning environment is derived firstly. Then, through investigation of the effect on Euler attitude algorithm for the equivalency of traditional attitude algorithm, it is found that attitude error is actually the roll angle error including drifting error and oscillating error, which is induced directly by dynamic coning environment and further affects the pitch angle and yaw angle through transferring. Based on definition of the cone frame and cone attitude, a cone algorithm is proposed by rotation relationship to calculate cone attitude, and the relationship between cone attitude and Euler attitude of spinning vehicle is established. Through numerical simulations with different conditions of dynamic coning environment, it is shown that the induced error of Euler attitude fluctuates by the variation of precession and nutation, especially by that of nutation, and the oscillating frequency of roll angle error is twice that of pitch angle error and yaw angle error. In addition, the rotation angle is more competent to describe the spinning process of vehicles under coning environment than Euler angle gamma, and the real pitch angle and yaw angle are calculated finally.

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.

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"

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

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

Science.gov (United States)

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

Directory of Open Access Journals (Sweden)

Ling Zhang

2017-10-01

Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Integrability of dynamical systems algebra and analysis

CERN Document Server

Zhang, Xiang

2017-01-01

This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

Parallel processors and nonlinear structural dynamics algorithms and software

Science.gov (United States)

Belytschko, Ted

1989-01-01

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Functional integral approach to classical statistical dynamics

International Nuclear Information System (INIS)

Jensen, R.V.

1980-04-01

A functional integral method is developed for the statistical solution of nonlinear stochastic differential equations which arise in classical dynamics. The functional integral approach provides a very natural and elegant derivation of the statistical dynamical equations that have been derived using the operator formalism of Martin, Siggia, and Rose

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.

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-05

Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-01

Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

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

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry I.

2017-12-08

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry; Kasimov, Aslan R.

2018-01-01

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

KAUST Repository

Kabanov, Dmitry

2018-03-20

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

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 { \

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.

DYNAMIC SOCIAL INTEGRATION: SOCIAL INTEGRATION OF RELIGIOUS FOLLOWERS IN AMBON

Directory of Open Access Journals (Sweden)

Saidin Ernas

2015-12-01

Full Text Available The social dynamics in post-conflict Ambon, Maluku, 1999-2004, indicated that even though people were segregated in the ​​Islamic-Christian areas, gradually social integration began to occur naturally. The process of integration that occurred also gave birth to new values ​​and inclusive views that give hope to future peace building. Using the theory of social integration of dynamic adaptation of the Parsonian structural-functional classic paradigm and combined with a qualitative research model, this study successfully formulated several important findings. First, social integration occurred in the city of Ambon could run naturally through economic interactions, consensus on political balance and inclusive religious spirit. In addition, the presence of public spaces such as offices, schools, malls and coffee shops served as a natural integration medium that is increasingly important in the dynamics of the society. Second, the new social integration has created an increasingly important meaning that leads to a model of active harmony characterized by a process of the increasingly active social interaction between different religions, as well as strengthening pluralism and multiculturalism insight due to campaign by educational institutions and civil society groups. Third, this study also reminds us that although there has been a process of the increasingly positive social integration in Ambon city, people still need to be aware of the growth of radical religious ideologies at a certain level, and also of strengthening identity politics in the long run that will potentially give birth to primordial and ethnocentric attitudes that are harmful to the development of peace.

Equivariance, Variational Principles, and the Feynman Integral

Directory of Open Access Journals (Sweden)

George Svetlichny

2008-03-01

Full Text Available We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman's integral.

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.

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

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.

Stability Analysis and Variational Integrator for Real-Time Formation Based on Potential Field

Directory of Open Access Journals (Sweden)

Shengqing Yang

2014-01-01

Full Text Available This paper investigates a framework of real-time formation of autonomous vehicles by using potential field and variational integrator. Real-time formation requires vehicles to have coordinated motion and efficient computation. Interactions described by potential field can meet the former requirement which results in a nonlinear system. Stability analysis of such nonlinear system is difficult. Our methodology of stability analysis is discussed in error dynamic system. Transformation of coordinates from inertial frame to body frame can help the stability analysis focus on the structure instead of particular coordinates. Then, the Jacobian of reduced system can be calculated. It can be proved that the formation is stable at the equilibrium point of error dynamic system with the effect of damping force. For consideration of calculation, variational integrator is introduced. It is equivalent to solving algebraic equations. Forced Euler-Lagrange equation in discrete expression is used to construct a forced variational integrator for vehicles in potential field and obstacle environment. By applying forced variational integrator on computation of vehicles' motion, real-time formation of vehicles in obstacle environment can be implemented. Algorithm based on forced variational integrator is designed for a leader-follower formation.

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.

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Directory of Open Access Journals (Sweden)

Pengcheng HAN

2017-12-01

Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.

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

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

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.

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

A non-linear multigrid method for the steady Euler equations

NARCIS (Netherlands)

Hemker, P.W.; Koren, B.; Dervieux, A.; Leer, van B.; Periaux, J.; Rizzi, A.

1989-01-01

Higher-order accurate Euler-flow solutions are presented for some airfoil test cases. Second-order accurate solutions are computed by an Iterative Defect Correction process. For two test cases even higher accuracy is obtained by the additional use of a ~xtrapolation technique. Finite volume

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

A conceptual design of multidisciplinary-integrated C.F.D. simulation on parallel computers

International Nuclear Information System (INIS)

Onishi, Ryoichi; Ohta, Takashi; Kimura, Toshiya.

1996-11-01

A design of a parallel aeroelastic code for aircraft integrated simulations is conducted. The method for integrating aerodynamics and structural dynamics software on parallel computers is devised by using the Euler/Navier-Stokes equations coupled with wing-box finite element structures. A synthesis of modern aircraft requires the optimizations of aerodynamics, structures, controls, operabilities, or other design disciplines, and the R and D efforts to implement Multidisciplinary Design Optimization environments using high performance computers are made especially among the U.S. aerospace industries. This report describes a Multiple Program Multiple Data (MPMD) parallelization of aerodynamics and structural dynamics codes with a dynamic deformation grid. A three-dimensional computation of a flowfield with dynamic deformation caused by a structural deformation is performed, and a pressure data calculated is used for a computation of the structural deformation which is input again to a fluid dynamics code. This process is repeated exchanging the computed data of pressures and deformations between flowfield grids and structural elements. It enables to simulate the structure movements which take into account of the interaction of fluid and structure. The conceptual design for achieving the aforementioned various functions is reported. Also the future extensions to incorporate control systems, which enable to simulate a realistic aircraft configuration to be a major tool for Aircraft Integrated Simulation, are investigated. (author)

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.

Dynamic Enforcement of the Strict Integrity Policy

Institute of Scientific and Technical Information of China (English)

ZHANGXiangfeng; LIANGHongliang; SUNYufang

2005-01-01

The Strict integrity policy (SIP) in Biba's integrity model is widely used in protecting information integrity, but the static integrity labels of both subjects and objects increase compatibility cost of applications and might prevent some operations that are indeed harmless.In order to improve compatibility, Dynamic enforcement of the Strict integrity policy (DESIP) is put forward. The current integrity label attribute of a subject in SIP is replaced with two attributes in DESIP, which are used to confine dynamically the range of objects a subject could be allowed to access. The new rules of access control in DESIP are given for each kind of access mode (observe,modify and invoke) together with the proofs of their valid-ity. Comparison between SIP and DESIP shows that after a sequence of operations, a subject controlled by DESIP tends to behave in a similar way as it is controlled by SIP and DESIP is more compatible than SIP.

A Lagrangian dynamic subgrid-scale model turbulence

Science.gov (United States)

Meneveau, C.; Lund, T. S.; Cabot, W.

1994-01-01

A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Dynamic instability in the hook-flagellum system that triggers bacterial flicks

Science.gov (United States)

Jabbarzadeh, Mehdi; Fu, Henry Chien

2018-01-01

Dynamical bending, buckling, and polymorphic transformations of the flagellum are known to affect bacterial motility, but run-reverse-flick motility of monotrichous bacteria also involves the even more flexible hook connecting the flagellum to its rotary motor. Although flick initiation has been hypothesized to involve either static Euler buckling or dynamic bending of the hook, the precise mechanism of flick initiation remains unknown. Here, we find that flicks initiate via a dynamic instability requiring flexibility in both the hook and flagellum. We obtain accurate estimates of forces and torques on the hook that suggest that flicks occur for stresses below the (static) Euler buckling criterion, then provide a mechanistic model for flick initiation that requires combined bending of the hook and flagellum. We calculate the triggering torque-stiffness ratio and find that our predicted onset of dynamic instability corresponds well with experimental observations.

High effective inverse dynamics modelling for dual-arm robot

Science.gov (United States)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Dynamic Gust Load Analysis for Rotors

Directory of Open Access Journals (Sweden)

Yuting Dai

2016-01-01

Full Text Available Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

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.

Some New Integrable Equations from the Self-Dual Yang-Mills Equations

International Nuclear Information System (INIS)

Ivanova, T.A.; Popov, A.D.

1994-01-01

Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

Integrated framework for dynamic safety analysis

International Nuclear Information System (INIS)

Kim, Tae Wan; Karanki, Durga R.

2012-01-01

In the conventional PSA (Probabilistic Safety Assessment), detailed plant simulations by independent thermal hydraulic (TH) codes are used in the development of accident sequence models. Typical accidents in a NPP involve complex interactions among process, safety systems, and operator actions. As independent TH codes do not have the models of operator actions and full safety systems, they cannot literally simulate the integrated and dynamic interactions of process, safety systems, and operator responses. Offline simulation with pre decided states and time delays may not model the accident sequences properly. Moreover, when stochastic variability in responses of accident models is considered, defining all the combinations for simulations will be cumbersome task. To overcome some of these limitations of conventional safety analysis approach, TH models are coupled with the stochastic models in the dynamic event tree (DET) framework, which provides flexibility to model the integrated response due to better communication as all the accident elements are in the same model. The advantages of this framework also include: Realistic modeling in dynamic scenarios, comprehensive results, integrated approach (both deterministic and probabilistic models), and support for HRA (Human Reliability Analysis)

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

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

Complexified dynamical systems

International Nuclear Information System (INIS)

Bender, Carl M; Holm, Darryl D; Hook, Daniel W

2007-01-01

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)

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.

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.

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.

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

Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics

KAUST Repository

Giesselmann, Jan

2016-10-26

For an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The latter, when applied to specific energies, yields relative energy identities for the Euler-Korteweg, the Euler-Poisson, the Quantum Hydrodynamics system, and low order approximations of the Euler-Korteweg system. For the Euler-Korteweg system we prove a stability theorem between a weak and a strong solution and an associated weak-strong uniqueness theorem. In the second part we focus on the Navier-Stokes-Korteweg system (NSK) with non-monotone pressure laws: we prove stability for the NSK system via a modified relative energy approach. We prove continuous dependence of solutions on initial data and convergence of solutions of a low order model to solutions of the NSK system. The last two results provide physically meaningful examples of how higher order regularization terms enable the use of the relative energy framework for models with energies which are not poly- or quasi-convex, but compensating via higher-order gradients.

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

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.

Dynamical Investigation of Asteroid 66391 (1999 KW4)

Science.gov (United States)

Scheeres, Daniel J.; Fahnestock, E. G.; Ostro, S. J.; Margot, J. L.; Benner, L. A.; Broschart, S. B.; Bellerose, J.; Giorgini, J. D.; Nolan, M. C.; Magri, C.; Pravec, P.; Scheirich, P.; Rose, R.; Jurgens, R. F.; Suzuki, S.; DeJong, E. M.

2006-09-01

Radar imaging and simulation of the binary near-Earth asteroid 66391 (1999 KW4) reveals a system with highly unusual physical and dynamical properties (Ostro et al., DPS 2006). Classical treatments and previous analyses of binary-system dynamics have made assumptions about the component shapes that are not valid for the KW4 system. We have explored the full dynamics of the KW4 system via numerical simulations that solve the equations of motion for the coupled evolution of orbit and rotation, using radar-derived physical models, and using dynamical constraints from the observations to guide our initial conditions. Our simulations model the translational (or orbital) dynamics as the relative motion between the body centers of mass and model the rotational dynamics using the Euler equations and attitude kinematic equations for each body. All the equations are driven by the mutual gravitational potential, which is an explicit function of the relative position and attitude of the two bodies. Propagation of the system's dynamical evolution over time spans of months has been made tractable by using a novel variational integrator that requires only one evaluation per time step but conserves the symplectic properties of the dynamical system, and by implementing the evaluations on a parallel computer, using up to 256 processors. Our simulations use the component shapes, masses, and average orbit as initial conditions for integrations of the components' spins and mutual orbit, taking into consideration the actual gravitational potentials produced by the model shapes and the coupling between the components' motions. Our results reveal this NEA to have extraordinary physical and dynamical properties, which suggest intriguing possibilities for formation and evolution mechanisms.

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.

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

Science.gov (United States)

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

2018-05-01

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration." Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

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 topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid

International Nuclear Information System (INIS)

Nikolaenko, S S

2014-01-01

The paper is concerned with the topological analysis of the Chaplygin integrable case in the dynamics of a rigid body in a fluid. A full list of the topological types of Chaplygin systems in their dependence on the energy level is compiled on the basis of the Fomenko-Zieschang theory. An effective description of the topology of the Liouville foliation in terms of natural coordinate variables is also presented, which opens a direct way to calculating topological invariants. It turns out that on all nonsingular energy levels Chaplygin systems are Liouville equivalent to the well-known Euler case in the dynamics of a rigid body with fixed point. Bibliography: 23 titles

Feature extraction for dynamic integration of classifiers

NARCIS (Netherlands)

Pechenizkiy, M.; Tsymbal, A.; Puuronen, S.; Patterson, D.W.

2007-01-01

Recent research has shown the integration of multiple classifiers to be one of the most important directions in machine learning and data mining. In this paper, we present an algorithm for the dynamic integration of classifiers in the space of extracted features (FEDIC). It is based on the technique

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.

Low level constraints on dynamic contour path integration.

Directory of Open Access Journals (Sweden)

Sophie Hall

Full Text Available Contour integration is a fundamental visual process. The constraints on integrating discrete contour elements and the associated neural mechanisms have typically been investigated using static contour paths. However, in our dynamic natural environment objects and scenes vary over space and time. With the aim of investigating the parameters affecting spatiotemporal contour path integration, we measured human contrast detection performance of a briefly presented foveal target embedded in dynamic collinear stimulus sequences (comprising five short 'predictor' bars appearing consecutively towards the fovea, followed by the 'target' bar in four experiments. The data showed that participants' target detection performance was relatively unchanged when individual contour elements were separated by up to 2° spatial gap or 200 ms temporal gap. Randomising the luminance contrast or colour of the predictors, on the other hand, had similar detrimental effect on grouping dynamic contour path and subsequent target detection performance. Randomising the orientation of the predictors reduced target detection performance greater than introducing misalignment relative to the contour path. The results suggest that the visual system integrates dynamic path elements to bias target detection even when the continuity of path is disrupted in terms of spatial (2°, temporal (200 ms, colour (over 10 colours and luminance (-25% to 25% information. We discuss how the findings can be largely reconciled within the functioning of V1 horizontal connections.

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.

Geometry and dynamics of integrable systems

CERN Document Server

Matveev, Vladimir

2016-01-01

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...

Lagrangian structures, integrability and chaos for 3D dynamical equations 45.20.Jj Lagrangian and Hamiltonian mechanics; 02.30.Ik Integrable systems; 05.45.Ac Low-dimensional chaos;

CERN Document Server

Bustamante, M D

2003-01-01

In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, w...

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)

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

Lagrangian structures, integrability and chaos for 3D dynamical equations[45.20.Jj Lagrangian and Hamiltonian mechanics; 02.30.Ik Integrable systems; 05.45.Ac Low-dimensional chaos;

Energy Technology Data Exchange (ETDEWEB)

Bustamante, Miguel D [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile); Hojman, Sergio A [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile)

2003-01-10

In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion.

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

Dynamic Reactive Power Compensation of Large Scale Wind Integrated Power System

DEFF Research Database (Denmark)

Rather, Zakir Hussain; Chen, Zhe; Thøgersen, Paul

2015-01-01

wind turbines especially wind farms with additional grid support functionalities like dynamic support (e,g dynamic reactive power support etc.) and ii) refurbishment of existing conventional central power plants to synchronous condensers could be one of the efficient, reliable and cost effective option......Due to progressive displacement of conventional power plants by wind turbines, dynamic security of large scale wind integrated power systems gets significantly compromised. In this paper we first highlight the importance of dynamic reactive power support/voltage security in large scale wind...... integrated power systems with least presence of conventional power plants. Then we propose a mixed integer dynamic optimization based method for optimal dynamic reactive power allocation in large scale wind integrated power systems. One of the important aspects of the proposed methodology is that unlike...

A dynamic integrated fault diagnosis method for power transformers.

Science.gov (United States)

Gao, Wensheng; Bai, Cuifen; Liu, Tong

2015-01-01

In order to diagnose transformer fault efficiently and accurately, a dynamic integrated fault diagnosis method based on Bayesian network is proposed in this paper. First, an integrated fault diagnosis model is established based on the causal relationship among abnormal working conditions, failure modes, and failure symptoms of transformers, aimed at obtaining the most possible failure mode. And then considering the evidence input into the diagnosis model is gradually acquired and the fault diagnosis process in reality is multistep, a dynamic fault diagnosis mechanism is proposed based on the integrated fault diagnosis model. Different from the existing one-step diagnosis mechanism, it includes a multistep evidence-selection process, which gives the most effective diagnostic test to be performed in next step. Therefore, it can reduce unnecessary diagnostic tests and improve the accuracy and efficiency of diagnosis. Finally, the dynamic integrated fault diagnosis method is applied to actual cases, and the validity of this method is verified.

A Dynamic Integrated Fault Diagnosis Method for Power Transformers

Science.gov (United States)

Gao, Wensheng; Liu, Tong

2015-01-01

In order to diagnose transformer fault efficiently and accurately, a dynamic integrated fault diagnosis method based on Bayesian network is proposed in this paper. First, an integrated fault diagnosis model is established based on the causal relationship among abnormal working conditions, failure modes, and failure symptoms of transformers, aimed at obtaining the most possible failure mode. And then considering the evidence input into the diagnosis model is gradually acquired and the fault diagnosis process in reality is multistep, a dynamic fault diagnosis mechanism is proposed based on the integrated fault diagnosis model. Different from the existing one-step diagnosis mechanism, it includes a multistep evidence-selection process, which gives the most effective diagnostic test to be performed in next step. Therefore, it can reduce unnecessary diagnostic tests and improve the accuracy and efficiency of diagnosis. Finally, the dynamic integrated fault diagnosis method is applied to actual cases, and the validity of this method is verified. PMID:25685841

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.

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.

Dynamical Intention: Integrated Intelligence Modeling for Goal-directed Embodied Agents

Directory of Open Access Journals (Sweden)

Eric Aaron

2016-11-01

Full Text Available Intelligent embodied robots are integrated systems: As they move continuously through their environments, executing behaviors and carrying out tasks, components for low-level and high-level intelligence are integrated in the robot's cognitive system, and cognitive and physical processes combine to create their behavior. For a modeling framework to enable the design and analysis of such integrated intelligence, the underlying representations in the design of the robot should be dynamically sensitive, capable of reflecting both continuous motion and micro-cognitive influences, while also directly representing the necessary beliefs and intentions for goal-directed behavior. In this paper, a dynamical intention-based modeling framework is presented that satisfies these criteria, along with a hybrid dynamical cognitive agent (HDCA framework for employing dynamical intentions in embodied agents. This dynamical intention-HDCA (DI-HDCA modeling framework is a fusion of concepts from spreading activation networks, hybrid dynamical system models, and the BDI (belief-desire-intention theory of goal-directed reasoning, adapted and employed unconventionally to meet entailments of environment and embodiment. The paper presents two kinds of autonomous agent learning results that demonstrate dynamical intentions and the multi-faceted integration they enable in embodied robots: with a simulated service robot in a grid-world office environment, reactive-level learning minimizes reliance on deliberative-level intelligence, enabling task sequencing and action selection to be distributed over both deliberative and reactive levels; and with a simulated game of Tag, the cognitive-physical integration of an autonomous agent enables the straightforward learning of a user-specified strategy during gameplay, without interruption to the game. In addition, the paper argues that dynamical intentions are consistent with cognitive theory underlying goal-directed behavior, and

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

NARCIS (Netherlands)

Koren, B.; Leer, van B.

1995-01-01

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in

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

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.

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.

Calculations of the electromechanical transfer processes using implicit methods of numerical integration

Energy Technology Data Exchange (ETDEWEB)

Pogosyan, T A

1983-01-01

The article is dedicated to the solution of systems of differential equations which describe the transfer processes in an electric power system (EES) by implicit methods of numerical integration. The distinguishing feature of the implicit methods (Euler's reverse method and the trapeze method) is their absolute stability and, consequently, the relatively small accumulation of errors in each step of integration. Therefore, they are found to be very convenient for solving problems of electric power engineering, when the transfer processes are described by a rigid system of differential equations. The rigidity is associated with the range of values of the time constants considered. The advantage of the implicit methods over explicit are shown in a specific example (calculation of the dynamic stability of the simplest electric power system), along with the field of use of the implicit methods and the expedience of their use in power engineering problems.

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...

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

Science.gov (United States)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

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

DYNAMIC OPTIMAL BUDGET ALLOCATION FOR INTEGRATED MARKETING CONSIDERING PERSISTENCE

OpenAIRE

SHIZHONG AI; RONG DU; QIYING HU

2010-01-01

Aiming at forming dynamic optimal integrated marketing policies, we build a budget allocation model considering both current effects and sustained ones. The model includes multiple time periods and multiple marketing tools which interact through a common resource pool as well as through delayed cross influences on each other's sales, reflecting the nature of "integrated marketing" and its dynamics. In our study, marginal analysis is used to illuminate the structure of optimal policy. We deriv...

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.

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.

A global first integral for certain dynamical systems and related remarks

International Nuclear Information System (INIS)

Gonzalez-Gascon, F.

1977-01-01

A global first integral for certain dynamical systems and the related remarks are presented. In particular, it is shown that for these dynamical systems by introducing the (intrinsic) definition of the divergence of a vector field defined on an orientable differentiable manifold, the first integral, i.e. the (intrinsic) divergence of a vector field is now, automatically, a global first integral. (author)

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

Dynamics of 3D Timoshenko gyroelastic beams with large attitude changes for the gyros

Science.gov (United States)

Hassanpour, Soroosh; Heppler, G. R.

2016-01-01

This work is concerned with the theoretical development of dynamic equations for undamped gyroelastic beams which are dynamic systems with continuous inertia, elasticity, and gyricity. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing generalized Hooke's law, Duleau torsion theory, and Timoshenko bending theory, the energy expressions and equations of motion for the gyroelastic beams in three-dimensional space are derived. The so-obtained comprehensive gyroelastic beam model is compared against earlier gyroelastic beam models developed using Euler-Bernoulli beam models and is used to study the dynamics of gyroelastic beams through numerical examples. It is shown that there are significant differences between the developed unrestricted Timoshenko gyroelastic beam model and the previously derived zero-order restricted Euler-Bernoulli gyroelastic beam models. These differences are more pronounced in the short beam and transverse gyricity cases.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.

2017-08-29

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.

2017-01-01

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

Science.gov (United States)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

Co-simulation of dynamic systems in parallel and serial model configurations

International Nuclear Information System (INIS)

Sweafford, Trevor; Yoon, Hwan Sik

2013-01-01

Recent advancement in simulation software and computation hardware make it realizable to simulate complex dynamic systems comprised of multiple submodels developed in different modeling languages. The so-called co-simulation enables one to study various aspects of a complex dynamic system with heterogeneous submodels in a cost-effective manner. Among several different model configurations for co-simulation, synchronized parallel configuration is regarded to expedite the simulation process by simulation multiple sub models concurrently on a multi core processor. In this paper, computational accuracies as well as computation time are studied for three different co-simulation frameworks : integrated, serial, and parallel. for this purpose, analytical evaluations of the three different methods are made using the explicit Euler method and then they are applied to two-DOF mass-spring systems. The result show that while the parallel simulation configuration produces the same accurate results as the integrated configuration, results of the serial configuration, results of the serial configuration show a slight deviation. it is also shown that the computation time can be reduced by running simulation in the parallel configuration. Therefore, it can be concluded that the synchronized parallel simulation methodology is the best for both simulation accuracy and time efficiency.

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

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

Science.gov (United States)

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

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.

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.

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.))

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.

A Multi-Actor Dynamic Integrated Assessment Model (MADIAM)

OpenAIRE

Weber, Michael

2004-01-01

The interactions between climate and the socio-economic system are investigated with a Multi-Actor Dynamic Integrated Assessment Model (MADIAM) obtained by coupling a nonlinear impulse response model of the climate sub-system (NICCS) to a multi-actor dynamic economic model (MADEM). The main goal is to initiate a model development that is able to treat the dynamics of the coupled climate socio-economic system, including endogenous technological change, in a non-equilibrium situation, thereby o...

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 ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.

Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

CERN Document Server

2016-01-01

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

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, ∞).

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

Homological Perturbation Theory for Nonperturbative Integrals

Science.gov (United States)

Johnson-Freyd, Theo

2015-11-01

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.

A study on the evaluation for dynamic fracture mechanics parameters of viscoelastic materials by impact bending

International Nuclear Information System (INIS)

Sim, Jae Ki; Cho, Kyu Jac

1988-01-01

In this paper We derived simple formulas for the dynamic strain intensity factor by means of the Timoshenko's beam theory including the influence of rotary inertia and shear deformation on the three-point viscoelastic bend specimen. Also the contact force between the specimen and the impactor is estimated by appling the nonlinear integral equation and the Hertz's theory to the local deformation near the contact point. The results obtained from this study are as follow : 1. Analysis results of this paper, base on Timoshenko's beam theory, were more accuracy than that of Euler-Bernouli beam theory and it can be confirmed by comparsion the results with experimental results. 2. Hertz's contact thepry is static one, but it is proved that by the solution of dynamic strain intensity factor it can be applied for the case of dynamic one. 3. It is founded that the fracture mechanics paraments are overestimatimated if the effects of rotary inertia and transverse shear deformation of specimen are negleted. (Author)

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.

Overview of Dynamics Integration Research (DIR) program at Langley Research Center

Science.gov (United States)

Sliwa, Steven M.; Abel, Irving

1989-01-01

Research goals and objectives for an ongoing activity at Langley Research Center (LaRC) are described. The activity is aimed principally at dynamics optimization for aircraft. The effort involves active participation by the Flight Systems, Structures, and Electronics directorates at LaRC. The Functional Integration Technology (FIT) team has been pursuing related goals since 1985. A prime goal has been the integration and optimization of vehicle dynamics through collaboration at the basic principles or equation level. Some significant technical progress has been accomplished since then and is reflected here. An augmentation for this activity, Dynamics Integration Research (DIR), has been proposed to NASA Headquarters and is being considered for funding in FY 1990 or FY 1991.

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.

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...

Path integral methods for the dynamics of stochastic and disordered systems

International Nuclear Information System (INIS)

Hertz, John A; Roudi, Yasser; Sollich, Peter

2017-01-01

We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models. (topical review)

“Coupled processes” as dynamic capabilities in systems integration

Directory of Open Access Journals (Sweden)

Milton de Freitas Chagas Jr.

2017-05-01

Full Text Available The dynamics of innovation in complex systems industries is becoming an independent research stream. Apart from conventional uncertainties related to commerce and technology, complex-system industries must cope with systemic uncertainty. This paper’s objective is to analyze evolving technological paths from one product generation to the next through two case studies in the Brazilian aerospace indus­try, considering systems integration as an empirical instantiation of dynamic capabilities. A proposed “coupled processes” model intertwines two organizational processes regarded as two levels of dynamic capabilities: new product and technological developments. The model addresses the role of emergent properties in shaping a firm’s technological base. Moreover, it uses a technology readiness level to unveil systems integration business tricks and as a decision-making yardstick. The “coupled processes” model is revealed as a set of dynamic capabilities presenting ambidexterity in complex systems indus­tries, a finding that may be relevant for newly industrialized economies.

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.

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.

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)

One-way spatial integration of hyperbolic equations

Science.gov (United States)

Towne, Aaron; Colonius, Tim

2015-11-01

In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.

Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics

KAUST Repository

Giesselmann, Jan; Lattanzio, Corrado; Tzavaras, Athanasios

2016-01-01

For an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The latter, when applied to specific energies, yields relative energy

Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method

DEFF Research Database (Denmark)

Zhang, Xuping; Sørensen, Rasmus; RahbekIversen, Mathias

2018-01-01

This paper presents a novel and computationally efficient modeling method for the dynamics of flexible-link robot manipulators. In this method, a robot manipulator is decomposed into components/elements. The component/element dynamics is established using Newton–Euler equations, and then is linea......This paper presents a novel and computationally efficient modeling method for the dynamics of flexible-link robot manipulators. In this method, a robot manipulator is decomposed into components/elements. The component/element dynamics is established using Newton–Euler equations......, and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size...... manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies....

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.

"COUPLED PROCESSES" AS DYNAMIC CAPABILITIES IN SYSTEMS INTEGRATION

OpenAIRE

Chagas Jr, Milton de Freitas; Leite, Dinah Eluze Sales; Jesus, Gabriel Torres de

2017-01-01

ABSTRACT The dynamics of innovation in complex systems industries is becoming an independent research stream. Apart from conventional uncertainties related to commerce and technology, complex-system industries must cope with systemic uncertainty. This paper's objective is to analyze evolving technological paths from one product generation to the next through two case studies in the Brazilian aerospace industry, considering systems integration as an empirical instantiation of dynamic capabilit...

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.

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.

Introduction to dynamics

CERN Document Server

Pfeiffer, Friedrich

2015-01-01

This concise textbook for students preferably of a postgraduate level, but also for engineers in practice, contains the basic kinematical and kinetic structures of dynamics together with carefully selected applications. The book is a condensed introduction to the fundamental laws of kinematics and kinetics, on the most important principles of mechanics and presents the equations of motion in the form of Lagrange and Newton-Euler. Selected problems of linear and nonlinear dynamics are treated, as well as problems of vibration formation. The presented selection of topics gives a useful basis for stepping into more advanced problems of dynamics. The contents of this book represent the result of a regularly revised course, which has been and still is given for masters students at the Technische Universität München. .

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)

Seeing the System: Dynamics and Complexity of Technology Integration in Secondary Schools

Science.gov (United States)

Howard, Sarah K.; Thompson, Kate

2016-01-01

This paper introduces system dynamics modeling to understand, visualize and explore technology integration in schools, through the development of a theoretical model of technology-related change in teachers' practice. Technology integration is a dynamic social practice, within the social system of education. It is difficult, if not nearly…

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.

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.)

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.

A modelling of robot manipulator dynamics based on Newton-Euler's equations

International Nuclear Information System (INIS)

Sasaki, Shinobu

1990-09-01

In this paper is presented an algorithm for solving the inverse dynamics of robot manipulators. In comparison with the dynamical equations derived from the Lagrange's mechanics, the relations to be treated are of simple forms due to recursive expressions of relative link motions. A computer simulation for applying the algorithm to a six-link manipulator indicated that the present method might be most appropriate among the existing approaches from the viewpoint of computational efficiency. In particular, it is noted that the increase of the number of links has hardly great effect on the intricacy of calculation. (author)

An Integrated Platform for Dynamic Software Updating and its Application in Self-* systems

DEFF Research Database (Denmark)

Gregersen, Allan Raundahl; Jørgensen, Bo Nørregaard; Hadaytullah

2012-01-01

Practical dynamic updating of modern Java applications requires tool support to become an integral part of the software development and maintenance lifecycle. In this paper we present Javeleon, an easy-to-use tool for dynamic updates of Java applications. To support integration with specific...... frameworks, component systems and application servers, Javeleon currently provides tight integration with the NetBeans Platform, facilitating dynamic updating for applications built on top of the NetBeans Platform in an unconstrained manner. Javeleon supports state-preserving unanticipated runtime evolution...

Simulation of quantum dynamics with integrated photonics

Science.gov (United States)

Sansoni, Linda; Sciarrino, Fabio; Mataloni, Paolo; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

2012-12-01

In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.

An Integrated Dynamic Weighing System Based on SCADA

Directory of Open Access Journals (Sweden)

Piotr Bazydło

2015-01-01

Full Text Available A prototyped dynamic weighing system has been presented which integrates together three advanced software environments: MATLAB, LabVIEW and iFIX SCADA. They were used for advanced signal processing, data acquisition, as well as visualization and process control. Dynamic weighing is a constantly developing field of metrology. Because of the highly complicated structure of any electronic weighing module, it is vulnerable to many sources of environmental disturbances. For this reason, there is a lot of research concerned with weighing signal processing, mechanical matters and functionality of the system. In the paper, some issues connected with dynamic weighing have been presented, and the necessity of implementing signal processing methods has been discussed. Implementation of this feature is impossible in the majority of SCADA systems. The integration of the three environments mentioned above is an attempt to create an industrial system with capabilities to deal with major dynamic weighing problems. It is innovative because it connects the industrial SCADA, laboratory/industrial product LabVIEW and MATLAB. In addition, the algorithms responsible for process control and data exchange are presented. The paper includes a description of the capabilities, performance tests, as well as benefits and drawbacks, of the system. The outcome of the research is a prototyped system and evaluation of its usefulness. (original abstract

Dual Quaternion Variational Integrator for Rigid Body Dynamic Simulation

OpenAIRE

Xu, Jiafeng; Halse, Karl Henning

2016-01-01

In rigid body dynamic simulations, often the algorithm is required to deal with general situations where both reference point and inertia matrix are arbitrarily de- fined. We introduce a novel Lie group variational integrator using dual quaternion for simulating rigid body dynamics in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group method is used to derive dynamic equations. The combination of these two becomes the first Lie group ...

New integrable problems in a rigid body dynamics with cubic integral in velocities

Science.gov (United States)

Elmandouh, A. A.

2018-03-01

We introduce a new family of the 2D integrable mechanical system possessing an additional integral of the third degree in velocities. This system contains 20 arbitrary parameters. We also clarify that the majority of the previous systems with a cubic integral can be reconstructed from it as a special version for certain values of those parameters. The applications of this system are extended to include the problem of motion of a particle and rigid body about its fixed point. We announce new integrable problems describing the motion of a particle in the plane, pseudosphere, and surfaces of variable curvature. We also present a new integrable problem in a rigid body dynamics and this problem generalizes some of the previous results for Sokolov-Tsiganov, Yehia, Stretensky, and Goriachev.

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)

Dynamic planar embeddings of dynamic graphs

DEFF Research Database (Denmark)

Holm, Jacob; Rotenberg, Eva

2017-01-01

query, one-flip- linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We support all updates and queries in O(log 2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler......, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common...

Integrating microbial diversity in soil carbon dynamic models parameters

Science.gov (United States)

Louis, Benjamin; Menasseri-Aubry, Safya; Leterme, Philippe; Maron, Pierre-Alain; Viaud, Valérie

2015-04-01

Faced with the numerous concerns about soil carbon dynamic, a large quantity of carbon dynamic models has been developed during the last century. These models are mainly in the form of deterministic compartment models with carbon fluxes between compartments represented by ordinary differential equations. Nowadays, lots of them consider the microbial biomass as a compartment of the soil organic matter (carbon quantity). But the amount of microbial carbon is rarely used in the differential equations of the models as a limiting factor. Additionally, microbial diversity and community composition are mostly missing, although last advances in soil microbial analytical methods during the two past decades have shown that these characteristics play also a significant role in soil carbon dynamic. As soil microorganisms are essential drivers of soil carbon dynamic, the question about explicitly integrating their role have become a key issue in soil carbon dynamic models development. Some interesting attempts can be found and are dominated by the incorporation of several compartments of different groups of microbial biomass in terms of functional traits and/or biogeochemical compositions to integrate microbial diversity. However, these models are basically heuristic models in the sense that they are used to test hypotheses through simulations. They have rarely been confronted to real data and thus cannot be used to predict realistic situations. The objective of this work was to empirically integrate microbial diversity in a simple model of carbon dynamic through statistical modelling of the model parameters. This work is based on available experimental results coming from a French National Research Agency program called DIMIMOS. Briefly, 13C-labelled wheat residue has been incorporated into soils with different pedological characteristics and land use history. Then, the soils have been incubated during 104 days and labelled and non-labelled CO2 fluxes have been measured at ten

Modeling and Experimental Tests of a Mechatronic Device to Measure Road Profiles Considering Impact Dynamics

DEFF Research Database (Denmark)

Souza, A.; Santos, Ilmar

2002-01-01

dynamics is led with help of a set of non-linear equations of motion obtained using Newton-Euler-Jourdain´s Method. Such a set of equation is numerically solved and the theoretical results are compared with experimental carried out with a laboratory prototype. Comparisons show that the theoretical model...... predicts well the mechanism movements. However it was also experimentally observed that the contact between the wheels and the road profile is not permanent. To analyze the non-contact between the wheels and the road, the Newton-Euler´s Method is used to calculate forces and moments of reactions between...

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 computational procedure for the dynamics of flexible beams within multibody systems. Ph.D. Thesis Final Technical Report

Science.gov (United States)

Downer, Janice Diane

1990-01-01

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

A geometrical method towards first integrals for dynamical systems

International Nuclear Information System (INIS)

Labrunie, S.; Conte, R.

1996-01-01

We develop a method, based on Darboux close-quote s and Liouville close-quote s works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements close-quote forms. We apply it to three dynamical systems: Lotka endash Volterra, Lorenz and Rikitake. copyright 1996 American Institute of Physics

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…

Consequence Based Design. An approach for integrating computational collaborative models (Integrated Dynamic Models) in the building design phase

DEFF Research Database (Denmark)

Negendahl, Kristoffer

relies on various advancements in the area of integrated dynamic models. It also relies on the application and test of the approach in practice to evaluate the Consequence based design and the use of integrated dynamic models. As a result, the Consequence based design approach has been applied in five...... and define new ways to implement integrated dynamic models for the following project. In parallel, seven different developments of new methods, tools and algorithms have been performed to support the application of the approach. The developments concern: Decision diagrams – to clarify goals and the ability...... affect the design process and collaboration between building designers and simulationists. Within the limits of applying the approach of Consequence based design to five case studies, followed by documentation based on interviews, surveys and project related documentations derived from internal reports...

Proposed Robot Scheme with 5 DoF and Dynamic Modelling Using Maple Software

Directory of Open Access Journals (Sweden)

Shala Ahmet

2017-11-01

Full Text Available In this paper is represented Dynamical Modelling of robots which is commonly first important step of Modelling, Analysis and Control of robotic systems. This paper is focused on using Denavit-Hartenberg (DH convention for kinematics and Newton-Euler Formulations for dynamic modelling of 5 DoF - Degree of Freedom of 3D robot. The process of deriving of dynamical model is done using Software Maple. Derived Dynamical Model of 5 DoF robot is converted for Matlab use for future analysis, control and simulations.

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,

Causal dissipation for the relativistic dynamics of ideal gases.

Science.gov (United States)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

The simulation research for the dynamic performance of integrated PWR

International Nuclear Information System (INIS)

Yuan Jiandong; Xia Guoqing; Fu Mingyu

2005-01-01

The mathematical model of the reactor core of integrated PWR has been studied and simplified properly. With the lumped parameter method, authors have established the mathematical model of the reactor core, including the neutron dynamic equation, the feedback reactivities model and the thermo-hydraulic model of the reactor. Based on the above equations and models, the incremental transfer functions of the reactor core model have been built. By simulation experimentation, authors have compared the dynamic characteristics of the integrated PWR with the traditional dispersed PWR. The simulation results show that the mathematical models and equations are correct. (authors)

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

Towards better integrators for dissipative particle dynamics simulations

DEFF Research Database (Denmark)

Besold, Gerhard; Vattulainen, Ilpo Tapio; Karttunen, Mikko

2000-01-01

Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to pronounced artifacts in physical quantities such as the com...

On the Use of Linearized Euler Equations in the Prediction of Jet Noise

Science.gov (United States)

Mankbadi, Reda R.; Hixon, R.; Shih, S.-H.; Povinelli, L. A.

1995-01-01

Linearized Euler equations are used to simulate supersonic jet noise generation and propagation. Special attention is given to boundary treatment. The resulting solution is stable and nearly free from boundary reflections without the need for artificial dissipation, filtering, or a sponge layer. The computed solution is in good agreement with theory and observation and is much less CPU-intensive as compared to large-eddy simulations.

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.

Quantifying chaotic dynamics from integrate-and-fire processes

Energy Technology Data Exchange (ETDEWEB)

Pavlov, A. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov (Russian Federation); Pavlova, O. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Mohammad, Y. K. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit (Iraq); Kurths, J. [Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam (Germany); Institute of Physics, Humboldt University Berlin, 12489 Berlin (Germany)

2015-01-15

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.

Integrability and chaos in quantum systems (as viewed from geometry and dynamical symmetry)

International Nuclear Information System (INIS)

Zhang, Wei-Min.

1989-01-01

It is known that the development and deep understanding of modern interaction theory and classical mechanics are made through geometry and symmetry. Yet, quantum mechanics which was regarded to be the microscopic theory of classical mechanics and achieved the crowning success in interpreting the entire microscopic world was developed purely from algebraic methods. In this thesis, the author will study the geometry and dynamical symmetry in quantum systems, from which the question of integrability and chaos are explicitly addressed. First of all, the quantum dynamical degrees of freedom and quantum integrability are precisely defined and the inherent geometrical structure of quantum systems is explored from the fundamental structure of quantum theory. Such a geometrical structure can provide a framework to simultaneously build quantum and classical mechanics. The quantum-classical correspondence is then explicitly deduced. The dynamics of quantum system before it reaches the classical limit is formulated. Thus, the classical chaos is proven to be a special limiting phenomena of quantum systems and the dynamics before the system reaches its classical chaos is explored. The latter is the first step to seek the quantum manifestation of chaos. The relationship between integrability and dynamical symmetry are studied and some universal properties are discovered: a dynamical system (both quantum and classical) in integrable if it possesses a dynamical symmetry. Chaos will occur if the system undergoes a dynamical symmetry breaking and is accompanied by a structural phase transition. Thus, the concept of dynamical symmetry can be used to predict the general behaviors of a system. The theoretical underpinnings developed in this thesis are verified by many basic quantum mechanical examples

Integrating atomistic molecular dynamics simulations, experiments, and network analysis to study protein dynamics

DEFF Research Database (Denmark)

Papaleo, Elena

2015-01-01

that we observe and the functional properties of these important cellular machines. To make progresses in this direction, we need to improve the physical models used to describe proteins and solvent in molecular dynamics, as well as to strengthen the integration of experiments and simulations to overcome...... with the possibility to validate simulation methods and physical models against a broad range of experimental observables. On the other side, it also allows a complementary and comprehensive view on protein structure and dynamics. What is needed now is a better understanding of the link between the dynamic properties...... simulations with attention to the effects that can be propagated over long distances and are often associated to important biological functions. In this context, approaches inspired by network analysis can make an important contribution to the analysis of molecular dynamics simulations....

Three-Dimensional Crane Modelling and Control Using Euler-Lagrange State-Space Approach and Anti-Swing Fuzzy Logic

Directory of Open Access Journals (Sweden)

Aksjonov Andrei

2015-12-01

Full Text Available The mathematical model of the three-dimensional crane using the Euler-Lagrange approach is derived. A state-space representation of the derived model is proposed and explored in the Simulink® environment and on the laboratory stand. The obtained control design was simulated, analyzed and compared with existing encoder-based system provided by the three-dimensional (3D Crane manufacturer Inteco®. As well, an anti-swing fuzzy logic control has been developed, simulated, and analyzed. Obtained control algorithm is compared with the existing anti-swing proportional-integral controller designed by the 3D crane manufacturer Inteco®. 5-degree of freedom (5DOF control schemes are designed, examined and compared with the various load masses. The topicality of the problem is due to the wide usage of gantry cranes in industry. The solution is proposed for the future research in sensorless and intelligent control of complex motor driven application.

Dynamic Complexity Study of Nuclear Reactor and Process Heat Application Integration

International Nuclear Information System (INIS)

Taylor, J'Tia Patrice; Shropshire, David E.

2009-01-01

This paper describes the key obstacles and challenges facing the integration of nuclear reactors with process heat applications as they relate to dynamic issues. The paper also presents capabilities of current modeling and analysis tools available to investigate these issues. A pragmatic approach to an analysis is developed with the ultimate objective of improving the viability of nuclear energy as a heat source for process industries. The extension of nuclear energy to process heat industries would improve energy security and aid in reduction of carbon emissions by reducing demands for foreign derived fossil fuels. The paper begins with an overview of nuclear reactors and process application for potential use in an integrated system. Reactors are evaluated against specific characteristics that determine their compatibility with process applications such as heat outlet temperature. The reactor system categories include light water, heavy water, small to medium, near term high-temperature, and far term high temperature reactors. Low temperature process systems include desalination, district heating, and tar sands and shale oil recovery. High temperature processes that support hydrogen production include steam reforming, steam cracking, hydrogen production by electrolysis, and far-term applications such as the sulfur iodine chemical process and high-temperature electrolysis. A simple static matching between complementary systems is performed; however, to gain a true appreciation for system integration complexity, time dependent dynamic analysis is required. The paper identifies critical issues arising from dynamic complexity associated with integration of systems. Operational issues include scheduling conflicts and resource allocation for heat and electricity. Additionally, economic and safety considerations that could impact the successful integration of these systems are considered. Economic issues include the cost differential arising due to an integrated system

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

Evaluation of Dynamic Characteristics of the Footbridge with Integral Abutments

Science.gov (United States)

Pańtak, Marek; Jarek, Bogusław

2017-09-01

The paper presents the results of dynamic field tests and numerical analysis of the footbridge designed as a three-span composite structure with integral abutments. The adopted design solution which has allowed to achieve a high resistance of the structure to dynamic loads and to meet the requirements of the criteria of comfort of use with a large reserve has been characterized. For comparative purposes, numerical analyzes of three construction variants of the footbridge were presented: F-1 - construction with integral abutments (realized variant), F-2 - construction with girders anchored in the abutments by means of tension rocker bearings, F-3 - construction with concrete side spans.

Evaluation of Dynamic Characteristics of the Footbridge with Integral Abutments

Directory of Open Access Journals (Sweden)

Pańtak Marek

2017-09-01

Full Text Available The paper presents the results of dynamic field tests and numerical analysis of the footbridge designed as a three-span composite structure with integral abutments. The adopted design solution which has allowed to achieve a high resistance of the structure to dynamic loads and to meet the requirements of the criteria of comfort of use with a large reserve has been characterized. For comparative purposes, numerical analyzes of three construction variants of the footbridge were presented: F-1 - construction with integral abutments (realized variant, F-2 - construction with girders anchored in the abutments by means of tension rocker bearings, F-3 - construction with concrete side spans.

On the Dynamics of the Furuta Pendulum

Directory of Open Access Journals (Sweden)

Benjamin Seth Cazzolato

2011-01-01

Full Text Available The Furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of nonlinear control laws. Despite the popularity of the platform, there are very few papers which employ the correct dynamics and only one that derives the full system dynamics. In this paper, the full dynamics of the Furuta pendulum are derived using two methods: a Lagrangian formulation and an iterative Newton-Euler formulation. Approximations are made to the full dynamics which converge to the more commonly presented expressions. The system dynamics are then linearised using a Jacobian. To illustrate the influence the commonly neglected inertia terms have on the system dynamics, a brief example is offered.

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.

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

Science.gov (United States)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Integrable topological billiards and equivalent dynamical systems

Science.gov (United States)

Vedyushkina, V. V.; Fomenko, A. T.

2017-08-01

We consider several topological integrable billiards and prove that they are Liouville equivalent to many systems of rigid body dynamics. The proof uses the Fomenko-Zieschang theory of invariants of integrable systems. We study billiards bounded by arcs of confocal quadrics and their generalizations, generalized billiards, where the motion occurs on a locally planar surface obtained by gluing several planar domains isometrically along their boundaries, which are arcs of confocal quadrics. We describe two new classes of integrable billiards bounded by arcs of confocal quadrics, namely, non-compact billiards and generalized billiards obtained by gluing planar billiards along non-convex parts of their boundaries. We completely classify non-compact billiards bounded by arcs of confocal quadrics and study their topology using the Fomenko invariants that describe the bifurcations of singular leaves of the additional integral. We study the topology of isoenergy surfaces for some non-convex generalized billiards. It turns out that they possess exotic Liouville foliations: the integral trajectories of the billiard that lie on some singular leaves admit no continuous extension. Such billiards appear to be leafwise equivalent to billiards bounded by arcs of confocal quadrics in the Minkowski metric.

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.

Topological classification of the Goryachev integrable case in rigid body dynamics

International Nuclear Information System (INIS)

Nikolaenko, S S

2016-01-01

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles

Stability Results, Almost Global Generalized Beltrami Fields and Applications to Vortex Structures in the Euler Equations

Science.gov (United States)

Enciso, Alberto; Poyato, David; Soler, Juan

2018-05-01

Strong Beltrami fields, that is, vector fields in three dimensions whose curl is the product of the field itself by a constant factor, have long played a key role in fluid mechanics and magnetohydrodynamics. In particular, they are the kind of stationary solutions of the Euler equations where one has been able to show the existence of vortex structures (vortex tubes and vortex lines) of arbitrarily complicated topology. On the contrary, there are very few results about the existence of generalized Beltrami fields, that is, divergence-free fields whose curl is the field times a non-constant function. In fact, generalized Beltrami fields (which are also stationary solutions to the Euler equations) have been recently shown to be rare, in the sense that for "most" proportionality factors there are no nontrivial Beltrami fields of high enough regularity (e.g., of class {C^{6,α}}), not even locally. Our objective in this work is to show that, nevertheless, there are "many" Beltrami fields with non-constant factor, even realizing arbitrarily complicated vortex structures. This fact is relevant in the study of turbulent configurations. The core results are an "almost global" stability theorem for strong Beltrami fields, which ensures that a global strong Beltrami field with suitable decay at infinity can be perturbed to get "many" Beltrami fields with non-constant factor of arbitrarily high regularity and defined in the exterior of an arbitrarily small ball, and a "local" stability theorem for generalized Beltrami fields, which is an analogous perturbative result which is valid for any kind of Beltrami field (not just with a constant factor) but only applies to small enough domains. The proof relies on an iterative scheme of Grad-Rubin type. For this purpose, we study the Neumann problem for the inhomogeneous Beltrami equation in exterior domains via a boundary integral equation method and we obtain Hölder estimates, a sharp decay at infinity and some compactness

Prototype development and demonstration for integrated dynamic transit operations.

Science.gov (United States)

2016-01-01

This document serves as the Final Report specific to the Integrated Dynamic Transit Operations (IDTO) Prototype Development and Deployment Project, hereafter referred to as IDTO Prototype Deployment or IDTO PD project. This project was performed unde...

Interchanging parameters and integrals in dynamical systems: the mapping case

Energy Technology Data Exchange (ETDEWEB)

Roberts, John A.G. [Department of Mathematics, La Trobe University, Bundoora, VIC (Australia) and School of Mathematics, University of New South Wales, Sydney, NSW (Australia)]. E-mail: jagr@maths.unsw.edu.au; Apostolos, Iatrou; Quispel, G.R.W. [Department of Mathematics, La Trobe University, Bundoora, VIC (Australia)]. E-mails: A.Iatrou@latrobe.edu.au; R.Quispel@latrobe.edu.au

2002-03-08

We consider dynamical systems with discrete time (maps) that possess one or more integrals depending upon parameters. We show that integrals can be used to replace parameters in the original map so as to construct a different map with different integrals. We also highlight a process of reparametrization that can be used to increase the number of parameters in the original map prior to using integrals to replace them. Properties of the original map and the new map are compared. The theory is motivated by, and illustrated with, examples of a three-dimensional trace map and some four-dimensional maps previously shown to be integrable. (author)

Path integral methods for the dynamics of stochastic and disordered systems

DEFF Research Database (Denmark)

Hertz, John A.; Roudi, Yasser; Sollich, Peter

2017-01-01

We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...

DECREASING OF MECHANISMS DYNAMIC LOADING AT THE TRANSIENT STATE

Directory of Open Access Journals (Sweden)

V. S. Loveikin

2015-11-01

Full Text Available Purpose. It is necessary to select modes of motion to reduce the dynamic loads in the mechanisms. This choice should be made on optimization basis. The purpose of research is to study methods of synthesis regimes of mechanisms and machines motion that provide optimal modes of movement for terminal and integral criteria. Methodology. For research the one-mass dynamic model of the mechanism has been used. As optimization criteria the terminal and comprehensive integral criteria were used. The stated optimization problem has been solved using dynamic programming and variational calculation. The direct variation method, which allowed finding only approximate solution of the original problem of optimal control, has been used as well. Findings. The ways of ensuring the absolute minimum of terminal criterion have been set for each method of problem solving. The stated characteristics show softness changes of kinematic functions during braking of mechanism. They point to the absolute minimum of adopted terminal criterion in the calculation. Originality. It is necessary to introduce new variables in the system equations during the solving of optimal control problems using dynamic programming to achieve an absolute minimum of terminal criteria. In general, to achieve a minimum of n-order terminal criterion an optimization problem should find relatively (n+1-th order function. When optimization problems is solving by variational calculation in order to ensure a minimization of n-th order terminal criterion by selecting the appropriate boundary conditions, it is necessary to solve the Euler-Poisson 2(n+1-th order equation (subject to symmetric setting boundary conditions. It is a necessary condition for an extremum of the functional with the (n+1-th order integrant. Practical value. Minimizing of adopted terminal criterion in the calculation allows eliminate the brunt in kinematic gearing of mechanisms, which increases their operational life. In addition

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.

Co-Simulation Control of Robot Arm Dynamics in ADAMS and MATLAB

OpenAIRE

Luo Haitao; Liu Yuwang; Chen Zhengcang; Leng Yuquan

2013-01-01

The main objective of this study is how to quickly establish the virtual prototyping model of robot arm system and effectively solve trajectory tracking control for a given signal. Taking the 2-DOF robot arm as an example, a co-simulation control method is introduced to research multi-body dynamics. Using Newton-Euler and Lagrange method, respectively establish the dynamics model of robot arm and verify the correctness of equations. Firstly, the physical model of robot arm was built by PROE a...

The role of emotion in dynamic audiovisual integration of faces and voices.

Science.gov (United States)

Kokinous, Jenny; Kotz, Sonja A; Tavano, Alessandro; Schröger, Erich

2015-05-01

We used human electroencephalogram to study early audiovisual integration of dynamic angry and neutral expressions. An auditory-only condition served as a baseline for the interpretation of integration effects. In the audiovisual conditions, the validity of visual information was manipulated using facial expressions that were either emotionally congruent or incongruent with the vocal expressions. First, we report an N1 suppression effect for angry compared with neutral vocalizations in the auditory-only condition. Second, we confirm early integration of congruent visual and auditory information as indexed by a suppression of the auditory N1 and P2 components in the audiovisual compared with the auditory-only condition. Third, audiovisual N1 suppression was modulated by audiovisual congruency in interaction with emotion: for neutral vocalizations, there was N1 suppression in both the congruent and the incongruent audiovisual conditions. For angry vocalizations, there was N1 suppression only in the congruent but not in the incongruent condition. Extending previous findings of dynamic audiovisual integration, the current results suggest that audiovisual N1 suppression is congruency- and emotion-specific and indicate that dynamic emotional expressions compared with non-emotional expressions are preferentially processed in early audiovisual integration. © The Author (2014). Published by Oxford University Press. For Permissions, please email: journals.permissions@oup.com.

Distributed Energy Resources and Dynamic Microgrid: An Integrated Assessment

Science.gov (United States)

Shang, Duo Rick

The overall goal of this thesis is to improve understanding in terms of the benefit of DERs to both utility and to electricity end-users when integrated in power distribution system. To achieve this goal, a series of two studies was conducted to assess the value of DERs when integrated with new power paradigms. First, the arbitrage value of DERs was examined in markets with time-variant electricity pricing rates (e.g., time of use, real time pricing) under a smart grid distribution paradigm. This study uses a stochastic optimization model to estimate the potential profit from electricity price arbitrage over a five-year period. The optimization process involves two types of PHEVs (PHEV-10, and PHEV-40) under three scenarios with different assumptions on technology performance, electricity market and PHEV owner types. The simulation results indicate that expected arbitrage profit is not a viable option to engage PHEVs in dispatching and in providing ancillary services without more favorable policy and PHEV battery technologies. Subsidy or change in electricity tariff or both are needed. Second, it examined the concept of dynamic microgrid as a measure to improve distribution resilience, and estimates the prices of this emerging service. An economic load dispatch (ELD) model is developed to estimate the market-clearing price in a hypothetical community with single bid auction electricity market. The results show that the electricity market clearing price on the dynamic microgrid is predominantly decided by power output and cost of electricity of each type of DGs. At circumstances where CHP is the only source, the electricity market clearing price in the island is even cheaper than the on-grid electricity price at normal times. Integration of PHEVs in the dynamic microgrid will increase electricity market clearing prices. It demonstrates that dynamic microgrid is an economically viable alternative to enhance grid resilience.

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.

Dynamic Complexity Study of Nuclear Reactor and Process Heat Application Integration

Energy Technology Data Exchange (ETDEWEB)

J' Tia Patrice Taylor; David E. Shropshire

2009-09-01

Abstract This paper describes the key obstacles and challenges facing the integration of nuclear reactors with process heat applications as they relate to dynamic issues. The paper also presents capabilities of current modeling and analysis tools available to investigate these issues. A pragmatic approach to an analysis is developed with the ultimate objective of improving the viability of nuclear energy as a heat source for process industries. The extension of nuclear energy to process heat industries would improve energy security and aid in reduction of carbon emissions by reducing demands for foreign derived fossil fuels. The paper begins with an overview of nuclear reactors and process application for potential use in an integrated system. Reactors are evaluated against specific characteristics that determine their compatibility with process applications such as heat outlet temperature. The reactor system categories include light water, heavy water, small to medium, near term high-temperature, and far term high temperature reactors. Low temperature process systems include desalination, district heating, and tar sands and shale oil recovery. High temperature processes that support hydrogen production include steam reforming, steam cracking, hydrogen production by electrolysis, and far-term applications such as the sulfur iodine chemical process and high-temperature electrolysis. A simple static matching between complementary systems is performed; however, to gain a true appreciation for system integration complexity, time dependent dynamic analysis is required. The paper identifies critical issues arising from dynamic complexity associated with integration of systems. Operational issues include scheduling conflicts and resource allocation for heat and electricity. Additionally, economic and safety considerations that could impact the successful integration of these systems are considered. Economic issues include the cost differential arising due to an integrated

Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics

DEFF Research Database (Denmark)

Bordbar, Aarash; Yurkovich, James T.; Paglia, Giuseppe

2017-01-01

The increasing availability of metabolomics data necessitates novel methods for deeper data analysis and interpretation. We present a flux balance analysis method that allows for the computation of dynamic intracellular metabolic changes at the cellular scale through integration of time-course ab......The increasing availability of metabolomics data necessitates novel methods for deeper data analysis and interpretation. We present a flux balance analysis method that allows for the computation of dynamic intracellular metabolic changes at the cellular scale through integration of time...

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.

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.

BMS3 invariant fluid dynamics at null infinity

Science.gov (United States)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

Science.gov (United States)

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Reminimization of energy integral and stability limit for non-ideal MHD (magnetohydrodynamic) plasma

International Nuclear Information System (INIS)

Kondoh, Y.

1988-03-01

The stability condition of relaxed states is derived from the energy principle for the non-ideal MHD plasma. An Euler equation for the reminimization of energy integral is derived and shown to give the marginal stable, non-singular perturbations for the stability condition. An extended stability limit for the β = 0 relaxed states is derived from the stability condition, with use of the eigenvalue analysis for the Euler equation. By using the perturbation method, the extended stability limit is solved in the 1st order approximation to explain the deviation of the experimental stability limit from the idealized stability limit by Taylor. A procedure to get overall stability limit against both the non-singular and the singular perturbations is discussed. 25 refs

Improved Integral Attacks on SIMON32 and SIMON48 with Dynamic Key-Guessing Techniques

Directory of Open Access Journals (Sweden)

Zhihui Chu

2018-01-01

Full Text Available Dynamic key-guessing techniques, which exploit the property of AND operation, could improve the differential and linear cryptanalytic results by reducing the number of guessed subkey bits and lead to good cryptanalytic results for SIMON. They have only been applied in differential and linear attacks as far as we know. In this paper, dynamic key-guessing techniques are first introduced in integral cryptanalysis. According to the features of integral cryptanalysis, we extend dynamic key-guessing techniques and get better integral cryptanalysis results than before. As a result, we present integral attacks on 24-round SIMON32, 24-round SIMON48/72, and 25-round SIMON48/96. In terms of the number of attacked rounds, our attack on SIMON32 is better than any previously known attacks, and our attacks on SIMON48 are the same as the best attacks.

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…

Analysis of time integration methods for the compressible two-fluid model for pipe flow simulations

NARCIS (Netherlands)

B. Sanderse (Benjamin); I. Eskerud Smith (Ivar); M.H.W. Hendrix (Maurice)

2017-01-01

textabstractIn this paper we analyse different time integration methods for the two-fluid model and propose the BDF2 method as the preferred choice to simulate transient compressible multiphase flow in pipelines. Compared to the prevailing Backward Euler method, the BDF2 scheme has a significantly

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.

Signatures of chaos and non-integrability in two-dimensional gravity with dynamical boundary

Directory of Open Access Journals (Sweden)

Fitkevich Maxim

2016-01-01

Full Text Available We propose a model of two-dimensional dilaton gravity with a boundary. In the bulk our model coincides with the classically integrable CGHS model; the dynamical boundary cuts of the CGHS strong-coupling region. As a result, classical dynamics in our model reminds that in the spherically-symmetric gravity: wave packets of matter fields either reflect from the boundary or form black holes. We find large integrable sector of multisoliton solutions in this model. At the same time, we argue that the model is globally non-integrable because solutions at the verge of black hole formation display chaotic properties.

The maximal kinematical invariance group of fluid dynamics and explosion-implosion duality

International Nuclear Information System (INIS)

O'Raifeartaigh, L.; Sreedhar, V.V.

2001-01-01

It has recently been found that supernova explosions can be simulated in the laboratory by implosions induced in a plasma by intense lasers. A theoretical explanation is that the inversion transformation, (Σ:t→-1/t, x→x/t), leaves the Euler equations of fluid dynamics, with standard polytropic exponent, invariant. This implies that the kinematical invariance group of the Euler equations is larger than the Galilei group. In this paper we determine, in a systematic manner, the maximal invariance group G of general fluid dynamics and show that it is a semi-direct product G=SL(2, R) three G, where the SL(2, R) group contains the time-translations, dilations, and the inversion Σ, and G is the static (nine-parameter) Galilei group. A subtle aspect of the inclusion of viscosity fields is discussed and it is shown that the Navier-Stokes assumption of constant viscosity breaks the SL(2, R) group to a two-parameter group of time translations and dilations in a tensorial way. The 12-parameter group G is also known to be the maximal invariance group of the free Schroedinger equation. It originates in the free Hamilton-Jacobi equation which is central to both fluid dynamics and the Schroedinger equation

The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

International Nuclear Information System (INIS)

Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

2007-05-01

The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

Integrated vehicle dynamics control using State Dependent Riccati Equations

NARCIS (Netherlands)

Bonsen, B.; Mansvelders, R.; Vermeer, E.

2010-01-01

In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this

Dynamic Design of Ground Transport With the Help of Computational Experiment

Directory of Open Access Journals (Sweden)

Kravets Victor

2015-05-01

Full Text Available Objectives of ground transport (motor transport vehicle have been considered. Mathematical model of nonlinear dynamics in spatial motion of asymmetric carriage in the form of Euler-Lagrange equations represented as symmetrical block structure in quaternion matrices has been developed. Kinematic equations and partition matrices of external action in which Rodrigues-Hamilton parameters have been applied describe quaternionic matrices.

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.

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.

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).

Numerical integration of some new unified plasticity-creep formulations

International Nuclear Information System (INIS)

Krieg, R.D.

1977-01-01

The unified formulations seem to lead to very non-linear systems of equations which are very well behaved in some regions and very stiff in other regions where the word 'stiff' is used in the mathematical sense. Simple conventional methods of integrating incremental constitutive equations are observed to be totally inadequate. A method of numerically integrating the equations is presented. Automatic step size determination based on accuracy and stability is a necessary expense. In the region where accuracy is the limiting condition the equations can be integrated directly. A forward Euler predictor with a trapezoidal corrector is used in the paper. In the region where stability is the limiting condition, direct integration methods become inefficient and an implicit integrator which is suited to stiff equations must be used. A backward Euler method is used in the paper. It is implemented with a Picard iteration method in which a Newton method is used to predict inelastic strainrate and speed convergence in a Newton-Raphson manner. This allows an analytic expression for the Jacobian to be used, where a full Newton-Raphson would require a numerical approximation to the Jacobian. The starting procedure for the iteration is an adaptation of time independent plasticity ideas. Because of the inherent capability of the unified plasticity-creep formulations, it is felt that these theories will become accepted in the metallurgical community. Structural analysts will then be required to incorporate these formulations and must be prepared to face the difficult implementation inherent in these models. This paper is an attempt to shed some light on the difficulties and expenses involved

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).

Integrated 6-DOF Orbit-Attitude Dynamical Modeling and Control Using Geometric Mechanics

Directory of Open Access Journals (Sweden)

Ling Jiang

2017-01-01

Full Text Available The integrated 6-DOF orbit-attitude dynamical modeling and control have shown great importance in various missions, for example, formation flying and proximity operations. The integrated approach yields better performances than the separate one in terms of accuracy, efficiency, and agility. One challenge in the integrated approach is to find a unified representation for the 6-DOF motion with configuration space SE(3. Recently, exponential coordinates of SE(3 have been used in dynamics and control of the 6-DOF motion, however, only on the kinematical level. In this paper, we will improve the current method by adopting exponential coordinates on the dynamical level, by giving the relation between the second-order derivative of exponential coordinates and spacecraft’s accelerations. In this way, the 6-DOF motion in terms of exponential coordinates can be written as a second-order system with a quite compact form, to which a broader range of control theories, such as higher-order sliding modes, can be applied. For a demonstration purpose, a simple asymptotic tracking control law with almost global convergence is designed. Finally, the integrated modeling and control are applied to the body-fixed hovering over an asteroid and verified by a simulation, in which absolute motions of the spacecraft and asteroid are simulated separately.

Generalizing the classical fixed-centres problem in a non-Hamiltonian way

International Nuclear Information System (INIS)

Albouy, A; Stuchi, T J

2004-01-01

The problem of two gravitational (or Coulombian) fixed centres is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. We introduce some straightforward generalizations of the problem that still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations showing the main features of their dynamics. In the domain of bounded orbits the behaviour of these a priori non-Hamiltonian systems is very similar to the behaviour of usual near-integrable systems

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

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

International Nuclear Information System (INIS)

Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.

2010-12-01

A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)

Conservative fourth-order time integration of non-linear dynamic systems

DEFF Research Database (Denmark)

Krenk, Steen

2015-01-01

An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

Combination of dynamic and integral methods for generating reproducible functional CBF images

International Nuclear Information System (INIS)

Lammertsma, A.A.; Cunningham, V.J.; Deiber, M.P.; Heather, J.D.; Bloomfield, P.M.; Nutt, J.; Frackowiak, R.S.; Jones, T.

1990-01-01

A new method to measure regional CBF is presented, applying both dynamic and integral analyses to a dynamic sequence of positron emission tomographic scans collected during and following the administration of H2(15)O (inhalation of C15O2). The dynamic analysis is used to correct continuously monitored arterial whole-blood activity for delay and dispersion relative to tissue scans. An integral analysis including corrections for this delay and dispersion is then used to calculate CBF on a pixel-by-pixel basis. Normal values and reproducibility over a 2-h period are presented, together with the results of validation and simulation studies. The results indicate that the single-tissue compartment model adequately describes the distribution of H2(15)O in the brain, without recourse to postulating a nonexchanging water pool

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Simulation of sensory integration dysfunction in autism with dynamic neural fields model

NARCIS (Netherlands)

Chonnaparamutt, W.; Barakova, E.I.; Rutkowski, L.; Taseusiewicz, R.

2008-01-01

This paper applies dynamic neural fields model [1,23,7] to multimodal interaction of sensory cues obtained from a mobile robot, and shows the impact of different temporal aspects of the integration to the precision of movements. We speculate that temporally uncoordinated sensory integration might be

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)

Double light-cone dynamics establish thermal states in integrable 1D Bose gases

Science.gov (United States)

Langen, T.; Schweigler, T.; Demler, E.; Schmiedmayer, J.

2018-02-01

We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.

The dynamics of multimodal integration: The averaging diffusion model.

Science.gov (United States)

Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James

2017-12-01

We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.

On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Directory of Open Access Journals (Sweden)

Koh Kim Jie

2017-01-01

Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach for contaminated sites management

Energy Technology Data Exchange (ETDEWEB)

Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu, E-mail: liyuxx8@hotmail.com

2013-10-15

Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management.

A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach for contaminated sites management

International Nuclear Information System (INIS)

Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu

2013-01-01

Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management

Dynamic hysteretic sensing model of bending-mode Galfenol transducer

International Nuclear Information System (INIS)

Cao, Shuying; Zheng, Jiaju; Sang, Jie; Zhang, Pengfei; Wang, Bowen; Huang, Wenmei

2015-01-01

A dynamic hysteretic sensing model has been developed to predict the dynamic responses of the magnetic induction, the stress, and the output voltage for a bending-mode Galfenol unimorph transducer subjected simultaneously to acceleration and bias magnetic field. This model is obtained by coupling the hysteretic Armstrong model and the structural dynamic model of the Galfenol unimorph beam. The structural dynamic model of the beam is founded based on the Euler-Bernouli beam theory, the nonlinear constitutive equations, and the Faraday law of electromagnetic induction. Comparisons between the calculated and measured results show the model can describe dynamic nonlinear voltage characteristics of the device, and can predict hysteretic behaviors between the magnetic induction and the stress. Moreover, the model can effectively analyze the effects of the bias magnetic field, the acceleration amplitude, and frequency on the root mean square voltage of the device

Dynamic hysteretic sensing model of bending-mode Galfenol transducer

Energy Technology Data Exchange (ETDEWEB)

Cao, Shuying, E-mail: shuying-cao@hebut.edu.cn; Zheng, Jiaju; Sang, Jie; Zhang, Pengfei; Wang, Bowen; Huang, Wenmei [Province-Ministry Joint Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability, Hebei University of Technology, Tianjin 300130 (China)

2015-05-07

A dynamic hysteretic sensing model has been developed to predict the dynamic responses of the magnetic induction, the stress, and the output voltage for a bending-mode Galfenol unimorph transducer subjected simultaneously to acceleration and bias magnetic field. This model is obtained by coupling the hysteretic Armstrong model and the structural dynamic model of the Galfenol unimorph beam. The structural dynamic model of the beam is founded based on the Euler-Bernouli beam theory, the nonlinear constitutive equations, and the Faraday law of electromagnetic induction. Comparisons between the calculated and measured results show the model can describe dynamic nonlinear voltage characteristics of the device, and can predict hysteretic behaviors between the magnetic induction and the stress. Moreover, the model can effectively analyze the effects of the bias magnetic field, the acceleration amplitude, and frequency on the root mean square voltage of the device.

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems

Energy Technology Data Exchange (ETDEWEB)

EL-Nabulsi, Ahmad Rami [Department of Nuclear and Energy Engineering, Cheju National University, Ara-dong 1, Jeju 690-756 (Korea, Republic of)], E-mail: nabulsiahmadrami@yahoo.fr

2009-10-15

We communicate through this work the fractional calculus of variations and its corresponding Euler-Lagrange equations in 1D constrained holonomic, non-holonomic, and semi-holonomic dissipative dynamical system. The extension of the laws obtained to the 2D space state is done. Some interesting consequences are revealed.

Poisson structure of dynamical systems with three degrees of freedom

Science.gov (United States)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

Multistability in an electrically actuated carbon nanotube: A dynamical integrity perspective

KAUST Repository

Ruzziconi, Laura

2013-07-12

This study deals with a slacked carbon nanotube, which is electrostatically and electrodynamically actuated. After introducing a reduced-order model, we investigate the overall scenario of the device response when both the frequency and the electrodynamic voltage are varied. Extensive numerical simulations are performed. The nanostructure exhibits several competing attractors with different characteristics. We examine the multistability in detail, based on numerical integration of the equation of motion in time, since it leads to a considerable versatility of behavior, which may be desirable in applications. Nevertheless, these results do not take into account the presence of disturbances, which are unavoidable under realistic conditions. To extend them to the practical case where disturbances exist, we develop a dynamical integrity analysis. This is performed via the combined use of several dynamical integrity tools. Analyzing the potential well, we observe that the device may be vulnerable to pull-in considerably before the theoretical inevitable escape. Focusing on the safe range, the main attractors are examined to investigate the practical probability to catch them and the practical disappearance of the main ones. Special attention is devoted to the practical final response, to detect where the safe jump to another attractor may be ensured and where instead dynamic pull-in may arise. We build the integrity charts, which are able to illustrate if and in which parameter range the theoretical predictions can be guaranteed in practice. They may be used to establish safety factors to effectively operate the device according to the desired outcome, depending on the expected disturbances. © 2013 Springer Science+Business Media Dordrecht.

Shock structure in continuum models of gas dynamics: stability and bifurcation analysis

International Nuclear Information System (INIS)

Simić, Srboljub S

2009-01-01

The problem of shock structure in gas dynamics is analysed through a comparative study of two continuum models: the parabolic Navier–Stokes–Fourier model and the hyperbolic system of 13 moments equations modeling viscous, heat-conducting monatomic gases within the context of extended thermodynamics. When dissipative phenomena are neglected these models both reduce to classical Euler's equations of gas dynamics. The shock profile solution, assumed in the form of a planar travelling wave, reduces the problem to a system of ordinary differential equations, and equilibrium states appear to be stationary points of the system. It is shown that in both models an upstream equilibrium state suffers an exchange of stability when the shock speed crosses the critical value which coincides with the highest characteristic speed of the Euler's system. At the same time a downstream equilibrium state could be seen as a steady bifurcating solution, while the shock profile represents a heteroclinic orbit connecting the two stationary points. Using centre manifold reduction it is demonstrated that both models, although mathematically different, obey the same transcritical bifurcation pattern in the neighbourhood of the bifurcation point corresponding to the critical value of shock speed, the speed of sound

High-precision numerical integration of equations in dynamics

Science.gov (United States)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.

Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion

Science.gov (United States)

Ohkitani, Koji

2018-02-01

After surveying analyses of the 3D Euler equations using the Clebsch potentials scattered over the literature, we report some preliminary new results. 1. Assuming that flow fields are free from nulls of the impulse and the vorticity fields, we study how constraints imposed by the Clebsch potentials lead to a degenerate geometrical structure, typically in the form of depletion of nonlinearity. We consider a vorticity surface spanned by \\boldsymbol ω and another material vector \\boldsymbol {W} such that \\boldsymbol γ=\\boldsymbol ω× \\boldsymbol {W}, where \\boldsymbol γ is the impulse variable in geometric gauge. We identify dual mechanism for geometric depletion and show that at least of one them is acting if \\boldsymbol {W} does not develop a null. This suggests that formation of singularity in flows endowed with Clebsch potentials is less likely to happen than in more general flows. Some arguments are given towards exclusion of ‘type I’ blowup. A mathematical challenge remains to rule out singularity formation for flows which have Clebsch potentials everywhere. 2. We exploit classical differential geometry kinematically to write down the Gauss-Weingarten equations for the vorticity surface of the Clebsch potential in terms of fluid dynamical variables, as are the first, second and third fundamental forms. In particular, we derive a constraint on the size of the Gaussian curvature near the point of a possible singularity. On the other hand, an application of the Gauss-Bonnet theorem reveals that the tangential curvature of the surface becomes large in the neighborhood of near-singularity. 3. Using spatially-periodic flows with highly-symmetry, i.e. initial conditions of the Taylor-Green vortex and the Kida-Pelz flow, we present explicit formulas of the Clebsch potentials with exceptional singular surfaces where the Clebsch potentials are undefined. This is done by connecting the known expressions with the solenoidal impulse variable (i.e. the

An integrated ball projection technology for the study of dynamic interceptive actions.

Science.gov (United States)

Stone, J A; Panchuk, D; Davids, K; North, J S; Fairweather, I; Maynard, I W

2014-12-01

Dynamic interceptive actions, such as catching or hitting a ball, are important task vehicles for investigating the complex relationship between cognition, perception, and action in performance environments. Representative experimental designs have become more important recently, highlighting the need for research methods to ensure that the coupling of information and movement is faithfully maintained. However, retaining representative design while ensuring systematic control of experimental variables is challenging, due to the traditional tendency to employ methods that typically involve use of reductionist motor responses such as buttonpressing or micromovements. Here, we outline the methodology behind a custom-built, integrated ball projection technology that allows images of advanced visual information to be synchronized with ball projection. This integrated technology supports the controlled presentation of visual information to participants while they perform dynamic interceptive actions. We discuss theoretical ideas behind the integration of hardware and software, along with practical issues resolved in technological design, and emphasize how the system can be integrated with emerging developments such as mixed reality environments. We conclude by considering future developments and applications of the integrated projection technology for research in human movement behaviors.

Dynamic state estimation for distribution networks with renewable energy integration

NARCIS (Netherlands)

Nguyen, P.H.; Venayagamoorthy, G.K.; Kling, W.L.; Ribeiro, P.F.

2013-01-01

The massive integration of variable and unpredictable Renewable Energy Sources (RES) and new types of load consumptions increases the dynamic and uncertain nature of the electricity grid. Emerging interests have focused on improving the monitoring capabilities of network operators so that they can

Spatial integration and cortical dynamics.

Science.gov (United States)

Gilbert, C D; Das, A; Ito, M; Kapadia, M; Westheimer, G

1996-01-23

Cells in adult primary visual cortex are capable of integrating information over much larger portions of the visual field than was originally thought. Moreover, their receptive field properties can be altered by the context within which local features are presented and by changes in visual experience. The substrate for both spatial integration and cortical plasticity is likely to be found in a plexus of long-range horizontal connections, formed by cortical pyramidal cells, which link cells within each cortical area over distances of 6-8 mm. The relationship between horizontal connections and cortical functional architecture suggests a role in visual segmentation and spatial integration. The distribution of lateral interactions within striate cortex was visualized with optical recording, and their functional consequences were explored by using comparable stimuli in human psychophysical experiments and in recordings from alert monkeys. They may represent the substrate for perceptual phenomena such as illusory contours, surface fill-in, and contour saliency. The dynamic nature of receptive field properties and cortical architecture has been seen over time scales ranging from seconds to months. One can induce a remapping of the topography of visual cortex by making focal binocular retinal lesions. Shorter-term plasticity of cortical receptive fields was observed following brief periods of visual stimulation. The mechanisms involved entailed, for the short-term changes, altering the effectiveness of existing cortical connections, and for the long-term changes, sprouting of axon collaterals and synaptogenesis. The mutability of cortical function implies a continual process of calibration and normalization of the perception of visual attributes that is dependent on sensory experience throughout adulthood and might further represent the mechanism of perceptual learning.

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

Numerical methods for engine-airframe integration

International Nuclear Information System (INIS)

Murthy, S.N.B.; Paynter, G.C.

1986-01-01

Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment

Some thoughts on the pressure integration requirements of the Navier–Stokes equations

International Nuclear Information System (INIS)

Saad, Tony; Majdalani, Joseph

2012-01-01

The Navier–Stokes formulation represents a uniquely challenging system of partial differential equations that continues to influence modern applied science and engineering. In its simplest form, the system can be used to prescribe the motion of a viscous incompressible fluid with constant properties. It consists of four equations in three-dimensional space that account for both the kinematic and dynamic conditions that a fluid element senses. In this work, we investigate the pressure integration rules and restrictions that affect the resolution of the scalar pressure field. We begin our analysis by exploring the integration properties of Euler's equations in two dimensions while making use of Clairaut's theorem on the commutativity of mixed partial derivatives. We then extend our findings to three-dimensional space. This process gives rise to a theorem and four corollaries that help to clarify the conditions needed to obtain exact or asymptotic solutions for the pressure distribution. Consequently, we identify the fundamental conditions under which the Navier–Stokes equations can be properly integrated to arrive at an analytic expression for the pressure field, namely, one that is continuous and twice differentiable. In closing, several configurations are used to test the theorem and showcase its connection with the pressure formulation. These include potential flows for which the pressure can be obtained unconditionally, and inviscid rotational motions of the Taylor–Culick type with and without headwall injection. (paper)

Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro

2011-01-01

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)

Microscopic study of nuclear 'pasta' by quantum molecular dynamics

International Nuclear Information System (INIS)

Watanabe, Gentaro; Sato, Katsuhiko; Yasuoka, Kenji; Ebisuzaki, Toshikazu

2002-01-01

Structure of cold dense matter at subnuclear densities is investigated by quantum molecular dynamics (QMD) simulations. We succeeded in showing that the phases with slab-like and rod-like nuclei etc. and be formed dynamically from hot uniform nuclear matter without any assumptions on nuclear shape. We also observe intermediate phases, which has complicated nuclear shapes. Geometrical structures of matter are analyzed with Minkowski functionals, and it is found out that intermediate phases can be characterized as ones with negative Euler characteristic. Our result suggests the existence of these kinds of phases in addition to the simple 'pasta' phases in neutron star crusts. (author)

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.

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.

Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

Science.gov (United States)

Maiti, Soumyabrata; Bandyopadhyay, Ritwik; Chatterjee, Anindya

2018-01-01

We study free and harmonically forced vibrations of an Euler-Bernoulli beam with rate-independent hysteretic dissipation. The dissipation follows a model proposed elsewhere for materials with randomly dispersed frictional microcracks. The virtual work of distributed dissipative moments is approximated using Gaussian quadrature, yielding a few discrete internal hysteretic states. Lagrange's equations are obtained for the modal coordinates. Differential equations for the modal coordinates and internal states are integrated together. Free vibrations decay exponentially when a single mode dominates. With multiple modes active, higher modes initially decay rapidly while lower modes decay relatively slowly. Subsequently, lower modes show their own characteristic modal damping, while small amplitude higher modes show more erratic decay. Large dissipation, for the adopted model, leads mathematically to fast and damped oscillations in the limit, unlike viscously overdamped systems. Next, harmonically forced, lightly damped responses of the beam are studied using both a slow frequency sweep and a shooting-method based search for periodic solutions along with numerical continuation. Shooting method and frequency sweep results match for large ranges of frequency. The shooting method struggles near resonances, where internal states collapse into lower dimensional behavior and Newton-Raphson iterations fail. Near the primary resonances, simple numerically-aided harmonic balance gives excellent results. Insights are also obtained into the harmonic content of secondary resonances.

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

Science.gov (United States)

Sharma, Atul Kumar; Arora, Nitesh; Joglekar, M. M.

2018-03-01

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler-Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

Integrated dynamic modeling and management system mission analysis

Energy Technology Data Exchange (ETDEWEB)

Lee, A.K.

1994-12-28

This document summarizes the mission analysis performed on the Integrated Dynamic Modeling and Management System (IDMMS). The IDMMS will be developed to provide the modeling and analysis capability required to understand the TWRS system behavior in terms of the identified TWRS performance measures. The IDMMS will be used to demonstrate in a verified and validated manner the satisfactory performance of the TWRS system configuration and assurance that the requirements have been satisfied.

Dynamics on the group manifolds and path integral

International Nuclear Information System (INIS)

Marinov, M.S.; Terentyev, M.V.

1979-01-01

Classical and quantum dynamics onn the compact simple Lie group and on the sphere of arbitrary dimensionality are considered. The accuracy of the semiclassical approximation for Green functions is discussed. Various path integral representations of the Green functions are presented. The special features of these representations due to the compactness and curvature are analysed. Basic results of the theory of Lie algebras and Lie groups used in the main text are presented

Integrated dynamic modeling and management system mission analysis

International Nuclear Information System (INIS)

Lee, A.K.

1994-01-01

This document summarizes the mission analysis performed on the Integrated Dynamic Modeling and Management System (IDMMS). The IDMMS will be developed to provide the modeling and analysis capability required to understand the TWRS system behavior in terms of the identified TWRS performance measures. The IDMMS will be used to demonstrate in a verified and validated manner the satisfactory performance of the TWRS system configuration and assurance that the requirements have been satisfied

Analyzing the non-smooth dynamics induced by a split-path nonlinear integral controller

NARCIS (Netherlands)

Hunnekens, B.G.B.; van Loon, S.J.L.M.; van de Wouw, N.; Heemels, W.P.M.H.; Nijmeijer, H.; Ecker, Horst; Steindl, Alois; Jakubek, Stefan

2014-01-01

In this paper, we introduce a novel non-smooth integral controller, which aims at achieving a better transient response in terms of overshoot of a feedback controlled dynamical system. The resulting closed-loop system can be represented as a non-smooth system with different continuous dynamics being

Exploring the dynamic and complex integration of sustainability performance measurement into product development

DEFF Research Database (Denmark)

Rodrigues, Vinicius Picanco; Morioka, S.; Pigosso, Daniela Cristina Antelmi

2016-01-01

In order to deal with the complex and dynamic nature of sustainability integration into the product development process, this research explore the use of a qualitative System Dynamics approach by using the causal loop diagram (CLD) tool. A literature analysis was followed by a case study, aiming ...

Exact solution for the quench dynamics of a nested integrable system

Science.gov (United States)

Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale

2017-08-01

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Integrative Analysis of Metabolic Models – from Structure to Dynamics

Energy Technology Data Exchange (ETDEWEB)

Hartmann, Anja, E-mail: hartmann@ipk-gatersleben.de [Leibniz Institute of Plant Genetics and Crop Plant Research (IPK), Gatersleben (Germany); Schreiber, Falk [Monash University, Melbourne, VIC (Australia); Martin-Luther-University Halle-Wittenberg, Halle (Germany)

2015-01-26

The characterization of biological systems with respect to their behavior and functionality based on versatile biochemical interactions is a major challenge. To understand these complex mechanisms at systems level modeling approaches are investigated. Different modeling formalisms allow metabolic models to be analyzed depending on the question to be solved, the biochemical knowledge and the availability of experimental data. Here, we describe a method for an integrative analysis of the structure and dynamics represented by qualitative and quantitative metabolic models. Using various formalisms, the metabolic model is analyzed from different perspectives. Determined structural and dynamic properties are visualized in the context of the metabolic model. Interaction techniques allow the exploration and visual analysis thereby leading to a broader understanding of the behavior and functionality of the underlying biological system. The System Biology Metabolic Model Framework (SBM{sup 2} – Framework) implements the developed method and, as an example, is applied for the integrative analysis of the crop plant potato.

DyNAMiC Workbench: an integrated development environment for dynamic DNA nanotechnology.

Science.gov (United States)

Grun, Casey; Werfel, Justin; Zhang, David Yu; Yin, Peng

2015-10-06

Dynamic DNA nanotechnology provides a promising avenue for implementing sophisticated assembly processes, mechanical behaviours, sensing and computation at the nanoscale. However, design of these systems is complex and error-prone, because the need to control the kinetic pathway of a system greatly increases the number of design constraints and possible failure modes for the system. Previous tools have automated some parts of the design workflow, but an integrated solution is lacking. Here, we present software implementing a three 'tier' design process: a high-level visual programming language is used to describe systems, a molecular compiler builds a DNA implementation and nucleotide sequences are generated and optimized. Additionally, our software includes tools for analysing and 'debugging' the designs in silico, and for importing/exporting designs to other commonly used software systems. The software we present is built on many existing pieces of software, but is integrated into a single package—accessible using a Web-based interface at http://molecular-systems.net/workbench. We hope that the deep integration between tools and the flexibility of this design process will lead to better experimental results, fewer experimental design iterations and the development of more complex DNA nanosystems. © 2015 The Authors.

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)

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.

Integrals of the Ising class

International Nuclear Information System (INIS)

Bailey, D H; Borwein, J M; Crandall, R E

2006-01-01

From an experimental-mathematical perspective we analyse 'Ising-class' integrals. These are structurally related n-dimensional integrals we call C n , D n , E n , where D n is a magnetic susceptibility integral central to the Ising theory of solid-state physics. We first analyse C n := 4/(n factorial) ∫ 0 ∞ ... ∫ 0 ∞ 1/(Σ j=1 n (u j + 1/u j )) 2 du 1 /u 1 ... du n /u n . We had conjectured-on the basis of extreme-precision numerical quadrature-that C n has a finite large-n limit, namely C ∞ = 2 e -2γ , with γ being the Euler constant. On such a numerological clue we are able to prove the conjecture. We then show that integrals D n and E n both decay exponentially with n, in a certain rigorous sense. While C n , D n remain unresolved for n ≥ 5, we were able to conjecture a closed form for E 5 . Our experimental results involved extreme-precision, multidimensional quadrature on intricate integrands; thus, a highly parallel computation was required

Integrated information in discrete dynamical systems: motivation and theoretical framework.

Directory of Open Access Journals (Sweden)

David Balduzzi

2008-06-01

Full Text Available This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks

Integrated information in discrete dynamical systems: motivation and theoretical framework.

Science.gov (United States)

Balduzzi, David; Tononi, Giulio

2008-06-13

This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv) In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks are optimized

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.

Dynamic behavior and functional integrity tests on RC shear walls

International Nuclear Information System (INIS)

Akino, Kinji; Nasuda, Toshiaki; Shibata, Akenori.

1991-01-01

A project consisting of seven subprojects has been conducted to study the dynamic behavior and functional integrity of reinforced concrete (RC) shear walls in reactor buildings. The objective of this project is to obtain the data to improve and prepare the seismic analysis code regarding the nonlinear structural behavior and integrity of reactor buildings during and after earthquakes. The project started in April, 1986, and will end in March, 1994. Seven subprojects are strain rate test, damping characteristic test, ultimate state response test and the verification test for the test of restoring force characteristics regarding dynamic restoring force characteristics and damping performance; the restoring force characteristic test on the shear walls with openings; and pull-out strength test and the test on air leakage through concrete cracks regarding the functional integrity. The objectives of respective subprojects, the test models and the interim results are reported. Three subprojects have been completed by March, 1990. The results of these projects will be used for the overall evaluation. The strain rate test showed that the ultimate strength of shear walls increased with strain rate. A formula for estimating air flow through the cracks in walls was given by the leakage test. (K.I.)

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

An integrated dynamic model for probabilistic risk assessments

International Nuclear Information System (INIS)

Hsueh, K.-S.; Wang Kong

2004-01-01

The purpose of this dissertation is to develop a simulation based accident sequence analysis program (ADS) for large scale dynamic accident sequence simulation. Human operators, front-line and support systems as well as plant thermal-hydraulic behavior are explicitly modeled as integrated active parts in the development of accident scenarios. To overcome the model size, the proposed methodology employs several techniques including use of 'initial state vector' which decouples time-dependent and time-independent factors, and a depth first integration method in which the computation memory demand increases in a linear order. The computer implementation of the method is capable of simulating up to 500 branch points in sequence development, models system failure during operation, allows for recovery from operator errors and hardware failures, and implements a simple model for operator system interactions. (author)

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

Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion

International Nuclear Information System (INIS)

Braden, H W; Enolski, V Z; Fedorov, Yu N

2013-01-01

We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve. (paper)

Locomotion Dynamics for Bio-inspired Robots with Soft Appendages: Application to Flapping Flight and Passive Swimming

Science.gov (United States)

Boyer, Frédéric; Porez, Mathieu; Morsli, Ferhat; Morel, Yannick

2017-08-01

In animal locomotion, either in fish or flying insects, the use of flexible terminal organs or appendages greatly improves the performance of locomotion (thrust and lift). In this article, we propose a general unified framework for modeling and simulating the (bio-inspired) locomotion of robots using soft organs. The proposed approach is based on the model of Mobile Multibody Systems (MMS). The distributed flexibilities are modeled according to two major approaches: the Floating Frame Approach (FFA) and the Geometrically Exact Approach (GEA). Encompassing these two approaches in the Newton-Euler modeling formalism of robotics, this article proposes a unique modeling framework suited to the fast numerical integration of the dynamics of a MMS in both the FFA and the GEA. This general framework is applied on two illustrative examples drawn from bio-inspired locomotion: the passive swimming in von Karman Vortex Street, and the hovering flight with flexible flapping wings.

Computational package for the dynamic analysis of synchronous generators and their controls; Paquete computacional para el analisis de generadores sincronos y sus controles

Energy Technology Data Exchange (ETDEWEB)

Perez Guillen, Jesus Artemio

1997-12-31

This thesis presents a computational package for the dynamic analysis of synchronous generators and their controls in a machine - infinite bus system. The package is integrated by a graphic interface for Windows environment and several models for the different components of the generation system. The development of the graphic interface was carried out with object oriented programming under Windows environment, available from Borland C++, which generates a group of menus that integrates an environment of interactive and versatile simulation. The package contains mathematical models of third, fourth, fifth and sixth order for synchronous generators of round and salient poles. Several mathematical models for the excitation systems DC1A, AC1A and ST1A, according to the IEEE classification, are included. Models for thermal and hydraulic turbines with governor of speed are also included, as well as a mathematical model for the power system stabilizer and magnetic saturation on synchronous generators. Numerical methods like Euler, Modified Euler and Runge Kutta of second and fourth order are used to solve the characteristics differential equations of the system under study. Algorithms for graphic generation includes phasor diagram, capability and saturation curves for synchronous machine. Computer models are validated and sensitivity analysis is carried out in order to assess the ef ect of type of model for synchronous machine, excitation systems, power system stabilizer, magnetic saturation in the synchronous generator and different numerical methods of integration. The computational package is useful in teaching and research on the dynamic response of synchronous machines and their controls. [Espanol] En este trabajo se presenta el desarrollo de un paquete computacional para el analisis dinamico de generadores sincronos y sus controles en el esquema de una unidad de generacion - bus infinito. El paquete esta integrado por una interfaz grafica para ambiente Windows y un

Flight Dynamics Simulation Modeling and Control of a Large Flexible Tiltrotor Aircraft

Science.gov (United States)

2014-09-01

analyses as it retains a momentum theory type rotor system. Later, CAMRAD, a comprehensive aeromechanics and dynamics model capa- ble of multi-rotor and...isotropic, linearly elastic material. 8. All blades are identical. 9. Euler- Bernoulli beam theory is used, implying plane cross sections remain plane and...aircraft could be improved to achieve a higher fidelity structural response. Currently, flexible wings are modeled as Bernoulli beams. Actual aircraft

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.

Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

Energy Technology Data Exchange (ETDEWEB)

Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic)

2012-06-04

In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.

Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

International Nuclear Information System (INIS)

Sergyeyev, Artur

2012-01-01

In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.

A System Dynamics Model for Integrated Decision Making ...

Science.gov (United States)

EPA’s Sustainable and Healthy Communities Research Program (SHC) is conducting transdisciplinary research to inform and empower decision-makers. EPA tools and approaches are being developed to enable communities to effectively weigh and integrate human health, socioeconomic, environmental, and ecological factors into their decisions to promote community sustainability. To help achieve this goal, EPA researchers have developed systems approaches to account for the linkages among resources, assets, and outcomes managed by a community. System dynamics (SD) is a member of the family of systems approaches and provides a framework for dynamic modeling that can assist with assessing and understanding complex issues across multiple dimensions. To test the utility of such tools when applied to a real-world situation, the EPA has developed a prototype SD model for community sustainability using the proposed Durham-Orange Light Rail Project (D-O LRP) as a case study.The EPA D-O LRP SD modeling team chose the proposed D-O LRP to demonstrate that an integrated modeling approach could represent the multitude of related cross-sectoral decisions that would be made and the cascading impacts that could result from a light rail transit system connecting Durham and Chapel Hill, NC. In keeping with the SHC vision described above, the proposal for the light rail is a starting point solution for the more intractable problems of population growth, unsustainable land use, environmenta

The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram

Science.gov (United States)

Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.

2016-09-01

The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).

Two-Dimensional Self-Propelled Fish Motion in Medium: An Integrated Method for Deforming Body Dynamics and Unsteady Fluid Dynamics

International Nuclear Information System (INIS)

Yan, Yang; Yong-Liang, Yu; Bing-Gang, Tong; Guan-Hao, Wu

2008-01-01

We present (1) the dynamical equations of deforming body and (2) an integrated method for deforming body dynamics and unsteady fluid dynamics, to investigate a modelled freely self-propelled fish. The theoretical model and practical method is applicable for studies on the general mechanics of animal locomotion such as flying in air and swimming in water, particularly of free self-propulsion. The present results behave more credibly than the previous numerical studies and are close to the experimental results, and the aligned vortices pattern is discovered in cruising swimming

Calculating effective diffusivities in the limit of vanishing molecular diffusion

International Nuclear Information System (INIS)

Pavliotis, G.A.; Stuart, A.M.; Zygalakis, K.C.

2009-01-01

In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the limit of vanishing molecular diffusion. In this limit traditional numerical methods typically fail, since they do not represent accurately the geometry of the underlying deterministic dynamics. We propose a stochastic splitting method that takes into account the volume-preserving property of the equations of motion in the absence of noise, and when inertial effects can be neglected. An extension of the method is then proposed for the cases where the noise has a non-trivial time-correlation structure and when inertial effects cannot be neglected. The method of modified equations is used to explain failings of Euler-based methods. The new stochastic geometric integrators are shown to outperform standard Euler-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

Science.gov (United States)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Hybrid Approximate Dynamic Programming Approach for Dynamic Optimal Energy Flow in the Integrated Gas and Power Systems

DEFF Research Database (Denmark)

Shuai, Hang; Ai, Xiaomeng; Wen, Jinyu

2017-01-01

This paper proposes a hybrid approximate dynamic programming (ADP) approach for the multiple time-period optimal power flow in integrated gas and power systems. ADP successively solves Bellman's equation to make decisions according to the current state of the system. So, the updated near future...

Options of system integrated environment modelling in the predicated dynamic cyberspace

International Nuclear Information System (INIS)

Janková, Martina; Dvořák, Jiří

2015-01-01

In this article there are briefly mentioned some selected options of contemporary conception of cybernetic system models in the corresponding and possible integratable environment with modern system dynamics thinking and all this in the cyberspace of possible projecting of predicted system characteristics. The key to new capabilities of system integration modelling in the considered cyberspace is mainly the ability to improve the environment and the system integration options, all this with the aim of modern control in the hierarchically arranged dynamic cyberspace, e.g. in the currently desired electronic business with information. The aim of this article is to assess generally the trends in the use of modern modelling methods considering the cybernetics applications verified in practice, modern concept of project management and also the potential integration of artificial intelligence in the new projecting and project management of integratable and intelligent models, e.g. with the optimal structures and adaptable behaviour.The article results from the solution of a specific research partial task at the faculty; especially the moments proving that the new economics will be based more and more on information, knowledge system defined cyberspace of modern management, are stressed in the text

Options of system integrated environment modelling in the predicated dynamic cyberspace

Energy Technology Data Exchange (ETDEWEB)

Janková, Martina; Dvořák, Jiří [Institute of Informatics, Faculty of Business and Management, Brno University of Technology, Brno (Czech Republic)

2015-03-10

In this article there are briefly mentioned some selected options of contemporary conception of cybernetic system models in the corresponding and possible integratable environment with modern system dynamics thinking and all this in the cyberspace of possible projecting of predicted system characteristics. The key to new capabilities of system integration modelling in the considered cyberspace is mainly the ability to improve the environment and the system integration options, all this with the aim of modern control in the hierarchically arranged dynamic cyberspace, e.g. in the currently desired electronic business with information. The aim of this article is to assess generally the trends in the use of modern modelling methods considering the cybernetics applications verified in practice, modern concept of project management and also the potential integration of artificial intelligence in the new projecting and project management of integratable and intelligent models, e.g. with the optimal structures and adaptable behaviour.The article results from the solution of a specific research partial task at the faculty; especially the moments proving that the new economics will be based more and more on information, knowledge system defined cyberspace of modern management, are stressed in the text.

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.)

Arnold tongues and the Devil's Staircase in a discrete-time Hindmarsh–Rose neuron model

Energy Technology Data Exchange (ETDEWEB)

Felicio, Carolini C., E-mail: carolini.cf@gmail.com; Rech, Paulo C., E-mail: paulo.rech@udesc.br

2015-11-06

We investigate a three-dimensional discrete-time dynamical system, described by a three-dimensional map derived from a continuous-time Hindmarsh–Rose neuron model by the forward Euler method. For a fixed integration step size, we report a two-dimensional parameter-space for this system, where periodic structures, the so-called Arnold tongues, can be seen with periods organized in a Farey tree sequence. We also report possible modifications in this parameter-space, as a function of the integration step size. - Highlights: • We investigate the parameter-space of a particular 3D map. • Periodic structures, namely Arnold tongues, can be seen there. • They are organized in a Farey tree sequence. • The map was derived from a continuous-time Hindmarsh–Rose neuron model. • The forward Euler method was used for such purpose.

Arnold tongues and the Devil's Staircase in a discrete-time Hindmarsh–Rose neuron model

International Nuclear Information System (INIS)

Felicio, Carolini C.; Rech, Paulo C.

2015-01-01

We investigate a three-dimensional discrete-time dynamical system, described by a three-dimensional map derived from a continuous-time Hindmarsh–Rose neuron model by the forward Euler method. For a fixed integration step size, we report a two-dimensional parameter-space for this system, where periodic structures, the so-called Arnold tongues, can be seen with periods organized in a Farey tree sequence. We also report possible modifications in this parameter-space, as a function of the integration step size. - Highlights: • We investigate the parameter-space of a particular 3D map. • Periodic structures, namely Arnold tongues, can be seen there. • They are organized in a Farey tree sequence. • The map was derived from a continuous-time Hindmarsh–Rose neuron model. • The forward Euler method was used for such purpose.

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.

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.

Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics.

Science.gov (United States)

D'Onofrio, Giuseppe; Pirozzi, Enrica

2017-05-01

We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.

Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots

Directory of Open Access Journals (Sweden)

Ching-Long Shih

2012-08-01

Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on-line numerical computations. Based on the decomposition approach and cross-product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on-line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed-chain robot systems.

Static and dynamic pile testing of reinforced concrete piles with structure integrated fibre optic strain sensors

Science.gov (United States)

Schilder, Constanze; Kohlhoff, Harald; Hofmann, Detlef; Basedau, Frank; Habel, Wolfgang R.; Baeßler, Matthias; Niederleithinger, Ernst; Georgi, Steven; Herten, Markus

2013-05-01

Static and dynamic pile tests are carried out to determine the load bearing capacity and the quality of reinforced concrete piles. As part of a round robin test to evaluate dynamic load tests, structure integrated fibre optic strain sensors were used to receive more detailed information about the strains along the pile length compared to conventional measurements at the pile head. This paper shows the instrumentation of the pile with extrinsic Fabry-Perot interferometers sensors and fibre Bragg gratings sensors together with the results of the conducted static load test as well as the dynamic load tests and pile integrity tests.

Integrating GIS and ABM to Explore Spatiotemporal Dynamics

Science.gov (United States)

Sun, M.; Jiang, Y.; Yang, C.

2013-12-01

Agent-based modeling as a methodology for the bottom-up exploration with the account of adaptive behavior and heterogeneity of system components can help discover the development and pattern of the complex social and environmental system. However, ABM is a computationally intensive process especially when the number of system components becomes large and the agent-agent/agent-environmental interaction is modeled very complex. Most of traditional ABM frameworks developed based on CPU do not have a satisfying computing capacity. To address the problem and as the emergence of advanced techniques, GPU computing with CUDA can provide powerful parallel structure to enable the complex simulation of spatiotemporal dynamics. In this study, we first develop a GPU-based ABM system. Secondly, in order to visualize the dynamics generated from the movement of agent and the change of agent/environmental attributes during the simulation, we integrate GIS into the ABM system. Advanced geovisualization technologies can be utilized for representing the spatiotemporal change events, such as proper 2D/3D maps with state-of-the-art symbols, space-time cube and multiple layers each of which presents pattern in one time-stamp, etc. Thirdly, visual analytics which include interactive tools (e.g. grouping, filtering, linking, etc.) is included in our ABM-GIS system to help users conduct real-time data exploration during the progress of simulation. Analysis like flow analysis and spatial cluster analysis can be integrated according to the geographical problem we want to explore.

Integrating atomistic molecular dynamics simulations, experiments and network analysis to study protein dynamics: strength in unity

Directory of Open Access Journals (Sweden)

Elena ePapaleo

2015-05-01

Full Text Available In the last years, we have been observing remarkable improvements in the field of protein dynamics. Indeed, we can now study protein dynamics in atomistic details over several timescales with a rich portfolio of experimental and computational techniques. On one side, this provides us with the possibility to validate simulation methods and physical models against a broad range of experimental observables. On the other side, it also allows a complementary and comprehensive view on protein structure and dynamics. What is needed now is a better understanding of the link between the dynamic properties that we observe and the functional properties of these important cellular machines. To make progresses in this direction, we need to improve the physical models used to describe proteins and solvent in molecular dynamics, as well as to strengthen the integration of experiments and simulations to overcome their own limitations. Moreover, now that we have the means to study protein dynamics in great details, we need new tools to understand the information embedded in the protein ensembles and in their dynamic signature. With this aim in mind, we should enrich the current tools for analysis of biomolecular simulations with attention to the effects that can be propagated over long distances and are often associated to important biological functions. In this context, approaches inspired by network analysis can make an important contribution to the analysis of molecular dynamics simulations.

Determining integral density distribution in the mach reflection of shock waves

Science.gov (United States)

Shevchenko, A. M.; Golubev, M. P.; Pavlov, A. A.; Pavlov, Al. A.; Khotyanovsky, D. V.; Shmakov, A. S.

2017-05-01

We present a method for and results of determination of the field of integral density in the structure of flow corresponding to the Mach interaction of shock waves at Mach number M = 3. The optical diagnostics of flow was performed using an interference technique based on self-adjusting Zernike filters (SA-AVT method). Numerical simulations were carried out using the CFS3D program package for solving the Euler and Navier-Stokes equations. Quantitative data on the distribution of integral density on the path of probing radiation in one direction of 3D flow transillumination in the region of Mach interaction of shock waves were obtained for the first time.

An integrated methodology for the dynamic performance and reliability evaluation of fault-tolerant systems

International Nuclear Information System (INIS)

Dominguez-Garcia, Alejandro D.; Kassakian, John G.; Schindall, Joel E.; Zinchuk, Jeffrey J.

2008-01-01

We propose an integrated methodology for the reliability and dynamic performance analysis of fault-tolerant systems. This methodology uses a behavioral model of the system dynamics, similar to the ones used by control engineers to design the control system, but also incorporates artifacts to model the failure behavior of each component. These artifacts include component failure modes (and associated failure rates) and how those failure modes affect the dynamic behavior of the component. The methodology bases the system evaluation on the analysis of the dynamics of the different configurations the system can reach after component failures occur. For each of the possible system configurations, a performance evaluation of its dynamic behavior is carried out to check whether its properties, e.g., accuracy, overshoot, or settling time, which are called performance metrics, meet system requirements. Markov chains are used to model the stochastic process associated with the different configurations that a system can adopt when failures occur. This methodology not only enables an integrated framework for evaluating dynamic performance and reliability of fault-tolerant systems, but also enables a method for guiding the system design process, and further optimization. To illustrate the methodology, we present a case-study of a lateral-directional flight control system for a fighter aircraft

Nonlinear Dynamical Analysis for a Plain Bearing

Directory of Open Access Journals (Sweden)

Ali Belhamra

2014-03-01

Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.

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.

Global format for energy-momentum based time integration in nonlinear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

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

A mathematical perspective on flight dynamics and control

CERN Document Server

L'Afflitto, Andrea

2017-01-01

This brief presents several aspects of flight dynamics, which are usually omitted or briefly mentioned in textbooks, in a concise, self-contained, and rigorous manner. The kinematic and dynamic equations of an aircraft are derived starting from the notion of the derivative of a vector and then thoroughly analysed, interpreting their deep meaning from a mathematical standpoint and without relying on physical intuition. Moreover, some classic and advanced control design techniques are presented and illustrated with meaningful examples. Distinguishing features that characterize this brief include a definition of angular velocity, which leaves no room for ambiguities, an improvement on traditional definitions based on infinitesimal variations. Quaternion algebra, Euler parameters, and their role in capturing the dynamics of an aircraft are discussed in great detail. After having analyzed the longitudinal- and lateral-directional modes of an aircraft, the linear-quadratic regulator, the linear-quadratic Gaussian r...

From gas dynamics with large friction to gradient flows describing diffusion theories

KAUST Repository

Lattanzio, Corrado

2016-12-09

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.

From gas dynamics with large friction to gradient flows describing diffusion theories

KAUST Repository

Lattanzio, Corrado; Tzavaras, Athanasios

2016-01-01

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.

An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

Directory of Open Access Journals (Sweden)

Pål Johan From

2012-04-01

Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methods

International Nuclear Information System (INIS)

Gray, S.K.; Noid, D.W.; Sumpter, B.G.

1994-01-01

We test the suitability of a variety of explicit symplectic integrators for molecular dynamics calculations on Hamiltonian systems. These integrators are extremely simple algorithms with low memory requirements, and appear to be well suited for large scale simulations. We first apply all the methods to a simple test case using the ideas of Berendsen and van Gunsteren. We then use the integrators to generate long time trajectories of a 1000 unit polyethylene chain. Calculations are also performed with two popular but nonsymplectic integrators. The most efficient integrators of the set investigated are deduced. We also discuss certain variations on the basic symplectic integration technique

Variational formulation for dissipative continua and an incremental J-integral

Science.gov (United States)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Chaos in integrate-and-fire dynamical systems

International Nuclear Information System (INIS)

Coombes, S.

2000-01-01

Integrate-and-fire (IF) mechanisms are often studied within the context of neural dynamics. From a mathematical perspective they represent a minimal yet biologically realistic model of a spiking neuron. The non-smooth nature of the dynamics leads to extremely rich spike train behavior capable of explaining a variety of biological phenomenon including phase-locked states, mode-locking, bursting and pattern formation. The conditions under which chaotic spike trains may be generated in synaptically interacting networks of neural oscillators is an important open question. Using techniques originally introduced for the study of impact oscillators we develop the notion of a Liapunov exponent for IF systems. In the strong coupling regime a network may undergo a discrete Turing-Hopf bifurcation of the firing times from a synchronous state to a state with periodic or quasiperiodic variations of the interspike intervals on closed orbits. Away from the bifurcation point these invariant circles may break up. We establish numerically that in this case the largest IF Liapunov exponent becomes positive. Hence, one route to chaos in networks of synaptically coupled IF neurons is via the breakup of invariant circles

Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

Science.gov (United States)

Vanicat, Matthieu

2018-04-01

We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

Science.gov (United States)

Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

1990-12-01

Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

Science.gov (United States)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).

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

An electrically actuated imperfect microbeam: Dynamical integrity for interpreting and predicting the device response

KAUST Repository

Ruzziconi, Laura

2013-02-20

In this study we deal with a microelectromechanical system (MEMS) and develop a dynamical integrity analysis to interpret and predict the experimental response. The device consists of a clamped-clamped polysilicon microbeam, which is electrostatically and electrodynamically actuated. It has non-negligible imperfections, which are a typical consequence of the microfabrication process. A single-mode reduced-order model is derived and extensive numerical simulations are performed in a neighborhood of the first symmetric natural frequency, via frequency response diagrams and behavior chart. The typical softening behavior is observed and the overall scenario is explored, when both the frequency and the electrodynamic voltage are varied. We show that simulations based on direct numerical integration of the equation of motion in time yield satisfactory agreement with the experimental data. Nevertheless, these theoretical predictions are not completely fulfilled in some aspects. In particular, the range of existence of each attractor is smaller in practice than in the simulations. This is because these theoretical curves represent the ideal limit case where disturbances are absent, which never occurs under realistic conditions. A reliable prediction of the actual (and not only theoretical) range of existence of each attractor is essential in applications. To overcome this discrepancy and extend the results to the practical case where disturbances exist, a dynamical integrity analysis is developed. After introducing dynamical integrity concepts, integrity profiles and integrity charts are drawn. They are able to describe if each attractor is robust enough to tolerate the disturbances. Moreover, they detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable, i.e. they provide valuable information to operate the device in safe conditions according to the desired outcome and depending on the expected disturbances

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

Science.gov (United States)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

Exactly integrable two-dimensional dynamical systems related with supersymmetric algebras

International Nuclear Information System (INIS)

Leznov, A.N.

1983-01-01

A wide class of exactly integrable dynamical systems in two-dimensional space related with superalgebras, which generalize supersymmetric Liouville equation, is constructed. The equations can be interpretated as nonlinearly interacting Bose and Fermi fields belonging within classical limit to even and odd parts of the Grassman space. Explicit expressions for the solutions of the constructed systems are obtained on the basis of standard perturbation theory

Implicit Unstructured Computational Aerodynamics on Many-Integrated Core Architecture

KAUST Repository

Al Farhan, Mohammed A.

2014-05-04

This research aims to understand the performance of PETSc-FUN3D, a fully nonlinear implicit unstructured grid incompressible or compressible Euler code with origins at NASA and the U.S. DOE, on many-integrated core architecture and how a hybridprogramming paradigm (MPI+OpenMP) can exploit Intel Xeon Phi hardware with upwards of 60 cores per node and 4 threads per core. For the current contribution, we focus on strong scaling with many-integrated core hardware. In most implicit PDE-based codes, while the linear algebraic kernel is limited by the bottleneck of memory bandwidth, the flux kernel arising in control volume discretization of the conservation law residuals and the preconditioner for the Jacobian exploits the Phi hardware well.

Efficient stochastic thermostatting of path integral molecular dynamics.

Science.gov (United States)

Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E

2010-09-28

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

Numerical Investigations of Post-Newtonian Hamiltonian Dynamics for Spinning Compact Binaries

Science.gov (United States)

Zhong, S. Y.

2012-03-01

Spinning compact binaries, consisting of neutron stars or black holes, not only have rich dynamic phenomena of resonance and chaos, but also are the most promising source for detecting gravitational waves. There should be a certain relation between the dynamics of the gravitational bodies and the gravitational waveforms. Based on the least-squares correction, several manifold correction schemes like the single-scaling method and the dual-scaling method are designed to suppress numerical errors from 6 integrals of motion in a conservative post-Newtonian (PN) Hamiltonian of spinning compact binaries. Taking a fifth order Runge-Kutta algorithm as a basic integrator, we wonder whether the PN contributions, the spin effects, and the classification of orbits exert some influences on these correction schemes and the Nacozy's approach. It is found that they are almost the same in correcting the integrals for the pure Kepler problem. Once the third-order PN contributions are added to the pure orbital part, there are explicit differences of correction effectiveness among these methods. As an interesting case, the efficiency of correction is better for chaotic eccentric orbits than for quasicircular regular ones. In all cases tested, the new momentum-position dual-scaling scheme does always have the optimal performance. It costs a little but not much expensive additional computational cost when the spin effects exist, and several time-saving techniques are used. The corrected numerical results are more accurate than the uncorrected ones, so that chaos from the numerical errors can be avoided. See Phys. Rev. D 81, 104037 (2010) for more details. Lubich et al. (Phys. Rev. D 81, 104025 (2010)) presented a noncanonically symplectic integrator for the PN Hamiltonian of a spinning compact binary. However, the Euler mixed integrator is problematic because of its bad numerical stability.We improved the work by constructing the second-order and the fourth-order fixed symplectic

Comparison of two integration methods for dynamic causal modeling of electrophysiological data.

Science.gov (United States)

Lemaréchal, Jean-Didier; George, Nathalie; David, Olivier

2018-06-01

Dynamic causal modeling (DCM) is a methodological approach to study effective connectivity among brain regions. Based on a set of observations and a biophysical model of brain interactions, DCM uses a Bayesian framework to estimate the posterior distribution of the free parameters of the model (e.g. modulation of connectivity) and infer architectural properties of the most plausible model (i.e. model selection). When modeling electrophysiological event-related responses, the estimation of the model relies on the integration of the system of delay differential equations (DDEs) that describe the dynamics of the system. In this technical note, we compared two numerical schemes for the integration of DDEs. The first, and standard, scheme approximates the DDEs (more precisely, the state of the system, with respect to conduction delays among brain regions) using ordinary differential equations (ODEs) and solves it with a fixed step size. The second scheme uses a dedicated DDEs solver with adaptive step sizes to control error, making it theoretically more accurate. To highlight the effects of the approximation used by the first integration scheme in regard to parameter estimation and Bayesian model selection, we performed simulations of local field potentials using first, a simple model comprising 2 regions and second, a more complex model comprising 6 regions. In these simulations, the second integration scheme served as the standard to which the first one was compared. Then, the performances of the two integration schemes were directly compared by fitting a public mismatch negativity EEG dataset with different models. The simulations revealed that the use of the standard DCM integration scheme was acceptable for Bayesian model selection but underestimated the connectivity parameters and did not allow an accurate estimation of conduction delays. Fitting to empirical data showed that the models systematically obtained an increased accuracy when using the second

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.

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

Science.gov (United States)

Nguyen, Nhan; Ting, Eric

2018-01-01

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

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.

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.

Localization and diagonalization. A review of functional integral techniques for low-dimensional gauge theories and topological field theories

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1995-01-01

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs

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.

Boundary-value problems in cosmological dynamics

Science.gov (United States)

Nusser, Adi

2008-08-01

The dynamics of cosmological gravitating system is governed by the Euler and the Poisson equations. Tiny fluctuations near the big bang singularity are amplified by gravitational instability into the observed structure today. Given the current distribution of galaxies and assuming initial homogeneity, dynamic reconstruction methods have been developed to derive the cosmic density and velocity fields back in time. The reconstruction method described here is based on a least action principle formulation of the dynamics of collisionless particles (representing galaxies). Two observational data sets will be considered. The first is the distribution of galaxies which is assumed to be an fair tracer of the mass density field of the dark matter. The second set is measurements of the peculiar velocities (deviations from pure Hubble flow) of galaxies. Given the first data set, the reconstruction method recovers the associated velocity field which can then be compared with the second data set. This comparison constrains the nature of the dark matter and the relation between mass and light in the Universe.

Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane

International Nuclear Information System (INIS)

Liu, Jian; Zhang, Zhijun

2016-01-01

Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems

CEASEMT system: the TEDEL code. Pipings - Plasticity - Dynamics - Statics - Buckling - Thermoplasticity - Creep - Large displacements - FLUIDS - SEISMS - ASME

International Nuclear Information System (INIS)

Hoffmann, Alain; Jeanpierre, Francoise; Axisa, Francois; Chevalier, Gerard; Lepareux, Michel.

1977-01-01

The TEDEL code is intended for elastic and plastic computation of three-dimensional pipes and frames with possible junction to shells. The structures are described with using assemblies of beam elements, or piping elements such as, curved pipes, 90 0 elbows, tees, any elements, the stiffness properties of which are given to TEDEL. TEDEL allows the dynamic computation of the structures: search of eigenfrequencies and eigenmodes of vibration, time response to any time-dependent canvassing. This response can be obtained either from recombining a number of eigenmodes, or from a direct numerical integration of the dynamics equation. In these last two cases TEDEL accounts for some possible damping. A TEDEL option allows critical buckling loads to be computed (Euler). The structures can offer any shapes comprising any number of materials. The data are readout without any format, and distributed in optional commands with a precise physical meaning: GEOMETRY, MATERIALS, LOAD, COMPUTATION, END. A dynamical memory control allows the size of the routine to be adapted to the problem to be treated. For pipings, an option is intended for an automatic checking of the stress level with regard to the limiting values of the ASME. Geometrical data, node positions, element numbering are given by COCO which also delivers perspective drawings for the structure to be studied. The results on magnetic tapes can be treated by the subroutines ESPACE-VISU-TEMPS [fr

Parametric design and analysis framework with integrated dynamic models

DEFF Research Database (Denmark)

Negendahl, Kristoffer

2014-01-01

of building energy and indoor environment, are generally confined to late in the design process. Consequence based design is a framework intended for the early design stage. It involves interdisciplinary expertise that secures validity and quality assurance with a simulationist while sustaining autonomous...... control with the building designer. Consequence based design is defined by the specific use of integrated dynamic modeling, which includes the parametric capabilities of a scripting tool and building simulation features of a building performance simulation tool. The framework can lead to enhanced...

Social Group Dynamics and Patterns of Latin American Integration Processes

Directory of Open Access Journals (Sweden)

Sébastien Dubé

2017-04-01

Full Text Available This article proposes to incorporate social psychology elements with mainstream political science and international relations theories to help understand the contradictions related to the integration processes in Latin America. Through a theoretical analysis, it contributes to the challenge proposed by Dabène (2009 to explain the “resilience” of the Latin American regional integration process in spite of its “instability and crises.” Our main proposition calls for considering Latin America as a community and its regional organizations as “social groups.” In conclusion, three phenomena from the field of social psychology and particularly social group dynamics shed light on these contradictory patterns: the value of the group and the emotional bond, groupthink, and cognitive dissonance.

Complexified quantum field theory and 'mass without mass' from multidimensional fractional actionlike variational approach with dynamical fractional exponents

International Nuclear Information System (INIS)

El-Nabulsi, Ahmad Rami

2009-01-01

Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.

Positivity-preserving dual time stepping schemes for gas dynamics

Science.gov (United States)

Parent, Bernard

2018-05-01

A new approach at discretizing the temporal derivative of the Euler equations is here presented which can be used with dual time stepping. The temporal discretization stencil is derived along the lines of the Cauchy-Kowalevski procedure resulting in cross differences in spacetime but with some novel modifications which ensure the positivity of the discretization coefficients. It is then shown that the so-obtained spacetime cross differences result in changes to the wave speeds and can thus be incorporated within Roe or Steger-Warming schemes (with and without reconstruction-evolution) simply by altering the eigenvalues. The proposed approach is advantaged over alternatives in that it is positivity-preserving for the Euler equations. Further, it yields monotone solutions near discontinuities while exhibiting a truncation error in smooth regions less than the one of the second- or third-order accurate backward-difference-formula (BDF) for either small or large time steps. The high resolution and positivity preservation of the proposed discretization stencils are independent of the convergence acceleration technique which can be set to multigrid, preconditioning, Jacobian-free Newton-Krylov, block-implicit, etc. Thus, the current paper also offers the first implicit integration of the time-accurate Euler equations that is positivity-preserving in the strict sense (that is, the density and temperature are guaranteed to remain positive). This is in contrast to all previous positivity-preserving implicit methods which only guaranteed the positivity of the density, not of the temperature or pressure. Several stringent reacting and inert test cases confirm the positivity-preserving property of the proposed method as well as its higher resolution and higher computational efficiency over other second-order and third-order implicit temporal discretization strategies.

Incorporating Cutting Edge Scientific Results from the Margins-Geoprisms Program into the Undergraduate Curriculum, Rupturing Continental Lithosphere Part II: Introducing Euler Poles Using Baja-North America Relative Plate Motion Across the Gulf of California

Science.gov (United States)

Loveless, J. P.; Bennett, S. E. K.; Cashman, S. M.; Dorsey, R. J.; Goodliffe, A. M.; Lamb, M. A.

2014-12-01

The NSF-MARGINS Program funded a decade of research on continental margin processes. The NSF-GeoPRISMS Mini-lesson Project, funded by NSF-TUES, is designed to integrate the significant findings from the MARGINS program into open-source college-level curriculum. The Gulf of California (GOC) served as the focus site for the Rupturing Continental Lithosphere (RCL) initiative, which addressed several scientific questions: What forces drive rift initiation, localization, propagation and evolution? How does deformation vary in time and space, and why? How does crust evolve, physically and chemically, as rifting proceeds to sea-floor spreading? What is the role of sedimentation and magmatism in continental extension? We developed two weeks of curriculum, including lectures, labs, and in-class activities that can be used as a whole or individually. This component of the curriculum introduces students to the Euler pole description of relative plate motion (RPM) by examining the tectonic interactions of the Baja California microplate and North American plate. The plate boundary varies in rift obliquity along strike, from highly oblique and strike-slip dominated in the south to slightly less oblique and with a larger extensional component in the north. This Google Earth-based exercise provides students with a visualization of RPM using small circle contours of the local direction and magnitude of Baja-North America movement on a spherical Earth. Students use RPM to calculate the fault slip rates on transform, normal, and oblique-slip faults and examine how the varying faulting styles combine to accommodate RPM. MARGINS results are integrated via comparison of rift obliquity with the structural style of rift-related faults around the GOC. We find this exercise to fit naturally into courses about plate tectonics, geophysics, and especially structural geology, given the similarity between Euler pole rotations and stereonet-based rotations of structural data.

Integration agent-based models and GIS as a virtual urban dynamic laboratory

Science.gov (United States)

Chen, Peng; Liu, Miaolong

2007-06-01

Based on the Agent-based Model and spatial data model, a tight-coupling integrating method of GIS and Agent-based Model (ABM) is to be discussed in this paper. The use of object-orientation for both spatial data and spatial process models facilitates their integration, which can allow exploration and explanation of spatial-temporal phenomena such as urban dynamic. In order to better understand how tight coupling might proceed and to evaluate the possible functional and efficiency gains from such a tight coupling, the agent-based model and spatial data model are discussed, and then the relationships affecting spatial data model and agent-based process models interaction. After that, a realistic crowd flow simulation experiment is presented. Using some tools provided by general GIS systems and a few specific programming languages, a new software system integrating GIS and MAS as a virtual laboratory applicable for simulating pedestrian flows in a crowd activity centre has been developed successfully. Under the environment supported by the software system, as an applicable case, a dynamic evolution process of the pedestrian's flows (dispersed process for the spectators) in a crowds' activity center - The Shanghai Stadium has been simulated successfully. At the end of the paper, some new research problems have been pointed out for the future.

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...

Nonlinear Dynamics: Integrability, Chaos and Patterns

International Nuclear Information System (INIS)

Grammaticos, B

2004-01-01

When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like 'verify the relation 14.81'. Others are less so, such as 'prepare a write-up on a) frequency-locking and b) devil

Nonlinear Dynamics: Integrability, Chaos and Patterns

Energy Technology Data Exchange (ETDEWEB)

Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)

2004-02-06

When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like 'verify the relation 14.81'. Others are less so, such as 'prepare a write-up on a) frequency

A dynamic probabilistic safety margin characterization approach in support of Integrated Deterministic and Probabilistic Safety Analysis

International Nuclear Information System (INIS)

Di Maio, Francesco; Rai, Ajit; Zio, Enrico

2016-01-01

The challenge of Risk-Informed Safety Margin Characterization (RISMC) is to develop a methodology for estimating system safety margins in the presence of stochastic and epistemic uncertainties affecting the system dynamic behavior. This is useful to support decision-making for licensing purposes. In the present work, safety margin uncertainties are handled by Order Statistics (OS) (with both Bracketing and Coverage approaches) to jointly estimate percentiles of the distributions of the safety parameter and of the time required for it to reach these percentiles values during its dynamic evolution. The novelty of the proposed approach consists in the integration of dynamic aspects (i.e., timing of events) into the definition of a dynamic safety margin for a probabilistic Quantification of Margin and Uncertainties (QMU). The system here considered for demonstration purposes is the Lead–Bismuth Eutectic- eXperimental Accelerator Driven System (LBE-XADS). - Highlights: • We integrate dynamic aspects into the definition of a safety margins. • We consider stochastic and epistemic uncertainties affecting the system dynamics. • Uncertainties are handled by Order Statistics (OS). • We estimate the system grace time during accidental scenarios. • We apply the approach to an LBE-XADS accidental scenario.

Global aspects of classical integrable systems

CERN Document Server

Cushman, Richard H

2015-01-01

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

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)

Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions

International Nuclear Information System (INIS)

Celledoni, E; Saefstroem, N

2006-01-01

If the three moments of inertia are distinct, the solution to the Euler equations for the free rigid body is given in terms of Jacobi elliptic functions. Using the arithmetic-geometric mean algorithm (Abramowitz and Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)), these functions can be calculated efficiently and accurately. Compared to standard numerical ODE and Lie-Poisson solvers, the overall approach yields a faster and more accurate numerical solution to the Euler equations. This approach is designed for mass asymmetric rigid bodies. In the case of symmetric bodies, the exact solution is available in terms of trigonometric functions, see Dullweber et al (1997 J. Chem. Phys. 107 5840-51), Reich (1996 Fields Inst. Commun. 10 181-91) and Benettin et al (2001 SIAM J. Sci. Comp. 23 1189-203) for details. In this paper, we consider the case of asymmetric rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in Reich (1996 Fields Inst. Commun. 10 181-91) and Dullweber et al (1997 J. Chem. Phys. 107 5840-51). The method proposed here is time-symmetric. We decompose the vector field of our problem into a free rigid body (FRB) problem and another completely integrable vector field. The FRB problem consists of the Euler equations and a differential equation for the 3 x 3 orientation matrix. The Euler equations are integrated exactly while the matrix equation is approximated using a truncated Magnus series. In our experiments, we observe that the overall numerical solution benefits greatly from the very accurate solution of the Euler equations. We apply the method to the heavy top and the simulation of artificial satellite attitude dynamics

Bayesian integration of position and orientation cues in perception of biological and non-biological dynamic forms

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Steven Matthew Thurman

2014-02-01

Full Text Available Visual form analysis is fundamental to shape perception and likely plays a central role in perception of more complex dynamic shapes, such as moving objects or biological motion. Two primary form-based cues serve to represent the overall shape of an object: the spatial position and the orientation of locations along the boundary of the object. However, it is unclear how the visual system integrates these two sources of information in dynamic form analysis, and in particular how the brain resolves ambiguities due to sensory uncertainty and/or cue conflict. In the current study, we created animations of sparsely-sampled dynamic objects (human walkers or rotating squares comprised of oriented Gabor patches in which orientation could either coincide or conflict with information provided by position cues. When the cues were incongruent, we found a characteristic trade-off between position and orientation information whereby position cues increasingly dominated perception as the relative uncertainty of orientation increased and vice versa. Furthermore, we found no evidence for differences in the visual processing of biological and non-biological objects, casting doubt on the claim that biological motion may be specialized in the human brain, at least in specific terms of form analysis. To explain these behavioral results quantitatively, we adopt a probabilistic template-matching model that uses Bayesian inference within local modules to estimate object shape separately from either spatial position or orientation signals. The outputs of the two modules are integrated with weights that reflect individual estimates of subjective cue reliability, and integrated over time to produce a decision about the perceived dynamics of the input data. Results of this model provided a close fit to the behavioral data, suggesting a mechanism in the human visual system that approximates rational Bayesian inference to integrate position and orientation signals in dynamic

Integral transform solutions of dynamic response of a clamped–clamped pipe conveying fluid

International Nuclear Information System (INIS)

Gu Jijun; An Chen; Duan Menglan; Levi, Carlos; Su Jian

2013-01-01

Highlights: ► Dynamic response of pipe conveying fluid was studied numerically. ► The generalized integral transform technique (GITT) was applied. ► Numerical solutions with automatic global accuracy control were obtained. ► Excellent convergence behavior was shown. ► Modal separation analysis was carried out and the influence of mass ratio was analyzed. - Abstract: Analysis of dynamic response of pipe conveying fluid is an important aspect in nuclear power plant design. In the present paper, dynamic response of a clamped–clamped pipe conveying fluid was solved by the generalized integral transform technique (GITT). The governing partial differential equation was transformed into a set of second-order ordinary differential equations which is then numerically solved by making use of the subroutine DIVPAG from IMSL Library. A thorough convergence analysis was performed to yield sets of reference results of the transverse deflection at different time and spanwise position. We found good agreement between the computed natural frequencies at mode 1–3 and those obtained by previous theoretical study. Besides, modal separation analysis was carried out and the influence of mass ratio on deflection and natural frequencies was qualitatively and quantitatively assessed.

On a non-local gas dynamics like integrable hierarchy

International Nuclear Information System (INIS)

Brunelli, Jose Carlos; Das, Ashok

2004-01-01

We study a new hierarchy of equations derived from the system of isentropic gas dynamics equations where the pressure is a non-local function of the density. We show that the hierarchy of equations is integrable. We construct the two compatible Hamiltonian structures and show that the first structure has three distinct Casimirs while the second has one. The existence of Casimirs allows us to extend the flows to local ones. We construct an infinite series of commuting local Hamiltonians as well as three infinite series (related to the three Casimirs) of non-local charges. We discuss the zero curvature formulation of the system where we obtain a simple expression for the non-local conserved charges, which also clarifies the existence of the three series from a Lie algebraic point of view. We point out that the non-local hierarchy of Hunter-Zheng equations can be obtained from our non-local flows when the dynamical variables are properly constrained. (author)

Optimal Control via Integrating the Dynamics of Magnetorheological Dampers and Structures

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Amir Fayezioghani

2015-03-01

Full Text Available Magnetorheological (MR dampers have the advantage of being tuned by low voltages. This has attracted many researchers to develop semi-active control of structures in theory and practice. Most of the control strategies first obtain the desired forces of dampers without taking their dynamics into consideration and then determine the input voltages according to those forces. As a result, these strategies may face situations where the desired forces cannot be produced by the dampers. In this article, by integrating the equations of the dynamics of MR dampers and the structural motion, and solving them in one set, a more concise semi-active optimal control strategy is presented, so as to bypass the aforementioned drawback. Next, a strong database that can be utilized to form a controller for more realistic implementations is produced. As an illustrative example, the optimal voltages of the dampers of a six-storey shear building are obtained under the scaled El-Centro earthquake and used to train a set of integrated analysis-adaptive neuro-fuzzy inference systems (ANFISs as a controller. Results show that the overall performance of the proposed strategy is higher than most of the other conventional methods.

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

Institute of Scientific and Technical Information of China (English)

WANG Dian-Fu; SONG He-Shan; MI Dong

2004-01-01

In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.

Neuronal integration of dynamic sources: Bayesian learning and Bayesian inference.

Science.gov (United States)

Siegelmann, Hava T; Holzman, Lars E

2010-09-01

One of the brain's most basic functions is integrating sensory data from diverse sources. This ability causes us to question whether the neural system is computationally capable of intelligently integrating data, not only when sources have known, fixed relative dependencies but also when it must determine such relative weightings based on dynamic conditions, and then use these learned weightings to accurately infer information about the world. We suggest that the brain is, in fact, fully capable of computing this parallel task in a single network and describe a neural inspired circuit with this property. Our implementation suggests the possibility that evidence learning requires a more complex organization of the network than was previously assumed, where neurons have different specialties, whose emergence brings the desired adaptivity seen in human online inference.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

International Nuclear Information System (INIS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.

2017-01-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

Energy Technology Data Exchange (ETDEWEB)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

2017-04-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

DYNAMIC TRENDS OF WAGE IN UKRAINE: PROSPECTS OF EUROPEAN INTEGRATION

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Ganna KATARANCHUK

2016-07-01

Full Text Available We analyze the main trends of the national economy and the dynamics of wages in Ukraine and other postsocialist countries in terms of the prospects of Ukraine's integration into the European economic and social space. The estimation of the impact of the wage indices for the welfare of citizens. The basic factors of Ukraine’s backlog in terms of wages from other countries and the possibilities and prospects of solving this problem are determined

Seamless variation of isometric and anisometric dynamical integrity measures in basins's erosion

Science.gov (United States)

Belardinelli, P.; Lenci, S.; Rega, G.

2018-03-01

Anisometric integrity measures defined as improvement and generalization of two existing measures (LIM, local integrity measure, and IF, integrity factor) of the extent and compactness of basins of attraction are introduced. Non-equidistant measures make it possible to account for inhomogeneous sensitivities of the state space variables to perturbations, thus permitting a more confident and targeted identification of the safe regions. All four measures are used for a global dynamics analysis of the twin-well Duffing oscillator, which is performed by considering a nearly continuous variation of a governing control parameter, thanks to the use of parallel computation allowing reasonable CPU time. This improves literature results based on finite (and commonly large) variations of the parameter, due to computational constraints. The seamless evolution of key integrity measures highlights the fine aspects of the erosion of the safe domain with respect to the increasing forcing amplitude.

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

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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.

Internationalisation of construction business and e-commerce: Innovation, integration and dynamic capabilities

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Thayaparan Gajendran

2013-06-01

Full Text Available Despite the role of internet and web based applications in delivering competitive advantage through e-business process is widely acknowledged, little is done by way of research to use the dynamic capability framework, in exploring the role of ecommerce in the construction business internationalisation. The aim of this paper is to present a literature based theoretical exploration using dynamic capability view to discuss internationalising construction businesses through electronic commerce (e-commerce platforms. This paper contextualises the opportunities for internationalising construction, using a mix of supply chain paradigms, embedded with e-commerce platforms. The paper concludes by identifying the potential of dynamic capabilities of a firm, exploiting the innovation and integration potential of different e-business systems, in contributing to the internationalisation of construction businesses. It proposes that contracting firms with developed dynamic capabilities, has the potential to exploit e-commerce platforms to channel upstream activities to an international destination, and also offers the firm’s products/services to international markets.

Metro-access integrated network based on optical OFDMA with dynamic sub-carrier allocation and power distribution.

Science.gov (United States)

Zhang, Chongfu; Zhang, Qiongli; Chen, Chen; Jiang, Ning; Liu, Deming; Qiu, Kun; Liu, Shuang; Wu, Baojian

2013-01-28

We propose and demonstrate a novel optical orthogonal frequency-division multiple access (OFDMA)-based metro-access integrated network with dynamic resource allocation. It consists of a single fiber OFDMA ring and many single fiber OFDMA trees, which transparently integrates metropolitan area networks with optical access networks. The single fiber OFDMA ring connects the core network and the central nodes (CNs), the CNs are on demand reconfigurable and use multiple orthogonal sub-carriers to realize parallel data transmission and dynamic resource allocation, meanwhile, they can also implement flexible power distribution. The remote nodes (RNs) distributed in the user side are connected by the single fiber OFDMA trees with the corresponding CN. The obtained results indicate that our proposed metro-access integrated network is feasible and the power distribution is agile.

Entanglement dynamics after quantum quenches in generic integrable systems

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Vincenzo Alba, Pasquale Calabrese

2018-03-01

Full Text Available The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

Numerical simulation of the fluid-structure interaction between air blast waves and soil structure

Science.gov (United States)

Umar, S.; Risby, M. S.; Albert, A. Luthfi; Norazman, M.; Ariffin, I.; Alias, Y. Muhamad

2014-03-01

Normally, an explosion threat on free field especially from high explosives is very dangerous due to the ground shocks generated that have high impulsive load. Nowadays, explosion threats do not only occur in the battlefield, but also in industries and urban areas. In industries such as oil and gas, explosion threats may occur on logistic transportation, maintenance, production, and distribution pipeline that are located underground to supply crude oil. Therefore, the appropriate blast resistances are a priority requirement that can be obtained through an assessment on the structural response, material strength and impact pattern of material due to ground shock. A highly impulsive load from ground shocks is a dynamic load due to its loading time which is faster than ground response time. Of late, almost all blast studies consider and analyze the ground shock in the fluid-structure interaction (FSI) because of its influence on the propagation and interaction of ground shock. Furthermore, analysis in the FSI integrates action of ground shock and reaction of ground on calculations of velocity, pressure and force. Therefore, this integration of the FSI has the capability to deliver the ground shock analysis on simulation to be closer to experimental investigation results. In this study, the FSI was implemented on AUTODYN computer code by using Euler-Godunov and the arbitrary Lagrangian-Eulerian (ALE). Euler-Godunov has the capability to deliver a structural computation on a 3D analysis, while ALE delivers an arbitrary calculation that is appropriate for a FSI analysis. In addition, ALE scheme delivers fine approach on little deformation analysis with an arbitrary motion, while the Euler-Godunov scheme delivers fine approach on a large deformation analysis. An integrated scheme based on Euler-Godunov and the arbitrary Lagrangian-Eulerian allows us to analyze the blast propagation waves and structural interaction simultaneously.

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

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Science.gov (United States)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

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

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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

Mathematical aspects of vortex dynamics; Proceedings of the Workshop, Leesburg, VA, Apr. 25-27, 1988

International Nuclear Information System (INIS)

Caflisch, R.E.

1989-01-01

Various papers on the mathematical aspects of vortex dynamics are presented. Individual topics addressed include: mathematical analysis of vortex dynamics, improved vortex methods for three-dimensional flows, the relation between thin vortex layer and vortex sheets, computations of broadband instabilities in a class of closed-streamline flows, vortex-sheet dynamics and hyperfunction theory, free surface vortex method with weak viscous effects, iterative method for computing steady vortex flow systems, invariant measures for the two-dimensional Euler flow, similarity flows containing two-branched vortex sheets, strain-induced vortex stripping, convergence of the vortex method for vortex sheets, boundary conditions and deterministic vortex methods for the Navier-Stokes equations, vorticity creation boundary conditions, vortex dynamics of stratified flows, vortex breakdown, numerical studies of vortex reconnection, vortex lattices in theory and practice, dynamics of vortex structures in the wall region of a turbulent boundary layer, and energy of a vortex lattice configuration

Integrating human behaviour dynamics into flood disaster risk assessment

Science.gov (United States)

Aerts, J. C. J. H.; Botzen, W. J.; Clarke, K. C.; Cutter, S. L.; Hall, J. W.; Merz, B.; Michel-Kerjan, E.; Mysiak, J.; Surminski, S.; Kunreuther, H.

2018-03-01

The behaviour of individuals, businesses, and government entities before, during, and immediately after a disaster can dramatically affect the impact and recovery time. However, existing risk-assessment methods rarely include this critical factor. In this Perspective, we show why this is a concern, and demonstrate that although initial efforts have inevitably represented human behaviour in limited terms, innovations in flood-risk assessment that integrate societal behaviour and behavioural adaptation dynamics into such quantifications may lead to more accurate characterization of risks and improved assessment of the effectiveness of risk-management strategies and investments. Such multidisciplinary approaches can inform flood-risk management policy development.