Numerische Simulation in der Moleküldynamik

Griebel, Michael; Knapek, Stephan; Zumbusch, Gerhard; Caglar, Attila

doi:10.1007/978-3-642-18779-7

Cited by 117 publications

(158 citation statements)

References 0 publications

Supporting

Mentioning

145

Contrasting

Unclassified

Order By: Relevance

“…The time-independent operator H := H(R, r) in the case of negligible relativistic effects [19] is given by…”

Section: Discussionmentioning

confidence: 99%

“…with weights c k = ψ k (R, r) Ψ (R, r, 0) dR dr. Now we apply the so-called single configuration ansatz as presented in [19]. For that we define the decomposition H = H e + H K with H e := T e + V ee + V eK + V KK = T e + V e and V e := V ee + V eK + V KK .…”

Section: Discussionmentioning

confidence: 99%

“…2 We make use of the equivalent so-called scalar product definition γ ijkl := π ± arccos r ij − r ij r kj /r kj r kj r lk − r lk r kj /r kj r kj , since it leads to more efficient computations [19]. Note that in both cases, the sign is determined by sgn(det(r ij , r jk , r kl )) = sgn r ij r jk ∧ r kl .…”

Section: Bonded and Non-bonded Potentialsmentioning

confidence: 99%

See 2 more Smart Citations

A semi-analytical approach to molecular dynamics

Michels

Desbrun

2015

Journal of Computational Physics

View full text Add to dashboard Cite

Despite numerous computational advances over the last few decades, molecular dynamics still favors explicit (and thus easily-parallelizable) time integrators for large scale numerical simulation. As a consequence, computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size. In this paper, we present a semianalytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes. By efficiently approximating the exact integration of the strong (harmonic) forces of covalent bonds through matrix functions, far improved stability with respect to time step size is achieved without sacrificing the explicit, symplectic, time-reversible, or fine-grained parallelizable nature of the integration scheme. We demonstrate the efficiency and scalability of our integrator on simulations ranging from DNA strand unbinding and protein folding to nanotube resonators.

show abstract

“…The time-independent operator H := H(R, r) in the case of negligible relativistic effects [19] is given by…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A semi-analytical approach to molecular dynamics

Michels

Desbrun

2015

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…The second order differential equations above are numerically solved by rewriting them as a system of two first order differential equations. A leapfrog method then computes particle positions, velocities and forces between the particles alternatingly (therefore "leaping") [4]. In the first part of the leapfrog scheme, at the time t n+ 1 2 , the velocities v i are updated based on the forces from the previous step.…”

Section: Methodsmentioning

confidence: 99%

Dynamic simulation of particle‐filled hollow spheres

Steinle

Vrabec

Walther

2011

Proc Appl Math and Mech

View full text Add to dashboard Cite

We are simulating a new lightweight material that could potentially be used in several technical applications, such as machine casings to rapidly damp vibrations, reducing wear and tear. This is achieved by employing embedded hollow spheres that are filled with a granular material, such as a ceramic powder. Energy is dissipated via friction caused by the interaction of particles with each other and with the sphere wall. The present dynamic simulation is based on a leapfrog algorithm, a time integration method used in molecular dynamics. Modifications, such as reflecting boundary conditions, are introduced to adapt the scheme to the field of granular materials. Motivation and Technical ApplicationsLimited fossil fuel supply and increasing awareness of climate change has led to a raise in demand of highly efficient means of transportation and industrial equipment. These can be constructed to be more efficient, e.g. by reducing their mass. The Fraunhofer Institute for Advanced Manufacturing Technology in Dresden, Germany is developing a new type of lightweight material that uses particle filled hollow spheres that are embedded within technical structures [1]. While the particles add to the overall weight, the material still shows a highly desirable dampening-to-weight ratio. When the structure is vibrating, e.g. due to engine operation, the particles can help to suppress these vibrations by quickly converting kinetic energy to heat through friction arising from collisions of the particles with each other and with the hull of the sphere [2]. This new material could be deployed in machine casings to reduce wear and tear. The benefits include lower maintenance cost and noise reductions. Computational MethodsTo simulate the dynamics of a large number of particles inside a hollow sphere, discrete element methods can be used. This allows to track each individual particle with respect to its position, velocity and rotational state. Modern molecular dynamics (MD) methods are capable of simulating large numbers of particles. Starting from a typical MD code that is aimed at the thermodynamic behavior of macroscopic fluid phases, some adaptations are required. For instance, MD usually considers periodic boundary conditions for the simulation volume. In the present scenario, the particles must interact with the boundary of the simulation volume to allow for energy transfer by vibration and particle impact. Additionally, most implementations only allow for a limited number of shapes for the simulation volume, such as a cuboid. We based our algorithm on a MD code co-developed at the Chair of Thermodynamics and Energy Technology, University of Paderborn [3]. Newton's equations of motion are at the core of the computations. For the equation of translational motion and the equation of rigid body rotational motion we considerHere, F i , m i , a i and x i are the forces acting on a particle i, the particle mass, the acceleration and position, while θ i , τ i , I i and α i are the angular orientation, torque, moment of inertia tensor...

show abstract

“…According to the Born-Oppenheimer approximation [24,25], atomic nuclei are treated as point particles, because they are much heavier than surrounding electrons. Therefore, classical MD consists in driving N particles with the following Newtonian equation of motion:…”

Section: Modeling Techniques Of Contact At Nanoscalementioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

View full text Add to dashboard Cite

Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

show abstract

Numerische Simulation in der Moleküldynamik

Cited by 117 publications

References 0 publications

A semi-analytical approach to molecular dynamics

A semi-analytical approach to molecular dynamics

Dynamic simulation of particle‐filled hollow spheres

MD/FE Multiscale Modeling of Contact

Contact Info

Product

Resources

About