Harmonic oscillators in the Nosé-Hoover environment

Golo, V. L.; Salnikov, Vl. N.; Шайтан, К. В.

doi:10.1103/physreve.70.046130

Cited by 19 publications

(16 citation statements)

References 9 publications

(8 reference statements)

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“…These types of intersections will be described after each algorithm; an illustration of each of them can also be seen in the Appendix 1 (Figs. 16,17,18,19,20,21,22,23,24,25,26,27,28,29). …”

Section: Intersection Conditionsmentioning

confidence: 97%

“…15,16,17,18,19,20,21,22,23,24,25,26,27,28, 29 represent typical intersections of spheres and cylinders and the result of application of the relaxation procedure to them. The Tables (2, 3 , 4, 5, 6) show the dependence of time of construction of the RVEs following the algorithm 5 on various parameters of them: volume fractions f s , f c , number of inclusions, their geometry.…”

Section: Appendix 1 Validation Of Dynamicsmentioning

confidence: 99%

“…The Figs. (15,16,17,18,19,20,21,22,23,24,25,26,27,28,29) in the Appendix 7 show typical intersections of couples of spheres and cylinders and their configuration after the relaxation process governed by the Eq. (6).…”

Section: Time Driven Molecular Dynamicsmentioning

confidence: 99%

See 2 more Smart Citations

On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

2014

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In this paper we describe efficient methods of generation of representative volume elements (RVEs) suitable for producing the samples for analysis of effective properties of composite materials via and for stochastic homogenization. We are interested in composites reinforced by a mixture of spherical and cylindrical inclusions. For these geometries we give explicit conditions of intersection in a convenient form for verification. Based on those conditions we present two methods to generate RVEs: one is based on the random sequential adsorption scheme, the other one on the time driven molecular dynamics. We test the efficiency of these methods and show that the first one is extremely powerful for low volume fraction of inclusions, while the second one allows us to construct denser configurations. All the algorithms are given explicitly so they can be implemented directly.

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“…These types of intersections will be described after each algorithm; an illustration of each of them can also be seen in the Appendix 1 (Figs. 16,17,18,19,20,21,22,23,24,25,26,27,28,29). …”

Section: Intersection Conditionsmentioning

confidence: 97%

Section: Appendix 1 Validation Of Dynamicsmentioning

confidence: 99%

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On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

2014

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“…The first step of generating non-intersecting inclusions corresponds to placing them into the matrix, while "puffing up" in a simplified way mimics various external forces applied to the samples to ensure contacts. This qualitative logic is in some sense inspired by [12], where some analysis of differential equations related to molecular dynamics is performed.…”

Section: Stochastic Part -Sample Generationmentioning

confidence: 99%

Computation of effective electrical conductivity of composite materials: A novel approach based on analysis of graphs

Salnikov

Choi

Karamian-Surville

2018

Composite Structures

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In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic part is due to averaging over some series of samples, and the fact that these samples fit into the concept of RVE (Representative Volume Element) in order to reduce the variance effect.In this article, we present a novel method for computation of effective electric properties of composites -it is based on the analysis of the connectivity graph (and the respective adjacency matrix) for each sample of a composite material. We describe how this matrix is constructed in order to take into account complex microscopic geometry. We also explain what we mean by homogenization procedure for electrical conductivity, and how the constructed matrix is related to the problem. The developed method is applied to a test study of the influence of micromorphology of composites materials on their conductivity.

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“…To see how much these techniques are appreciated nowadays, it is enough to cite the chemistry Nobel Prize 2013 1 : the work is related to the method of Molecular Dynamics -an approach to modelling the condensed matter, popular since the eighties. 2 One can also mention some very concrete problems coming from mechanics: fluid-structure interaction in engineering (e.g. studying off-shore wind turbines, stability, resonances and fatigue of dock structures and bridges, 3 phenomena related to counters in petrol pipelines, the construction of thermal reactors, medical applications), the development and implementation of constraints in robotics; and this list is in no case exhaustive… One can even talk about open systems, where considering the dissipation of energy is a very subtle question.…”

Section: Introduction/motivationmentioning

confidence: 99%

From modelling of systems with constraints to generalized geometry and back to numerics

Salnikov

Hamdouni

2019

Z Angew Math Mech

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In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints -we recall the mathematical construction in the context of so called implicit Lagrangian systems. We explain how they can be used to produce new numerical methods, that we call Dirac integrators.On a test example of a simple pendulum in a gravity field we compare the Dirac integrators with classical explicit and implicit methods, we pay special attention to conservation of constrains. Then, on a more advanced example of the Ziegler-type system we show that the choice of numerical methods can indeed affect the conclusions of qualitative analysis of the dynamics of mechanical systems. We also tell why we think that Dirac integrators are appropriate for this kind of systems by explaining the relation with the notions of geometric degree of non-conservativity and kinematic structural stability. K E Y W O R D SDirac structures, geometric integrators, systems with constraints

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Harmonic oscillators in the Nosé-Hoover environment

Cited by 19 publications

References 9 publications

On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

Computation of effective electrical conductivity of composite materials: A novel approach based on analysis of graphs

From modelling of systems with constraints to generalized geometry and back to numerics

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