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Register a new userThree Balls Problem Revisited - On the Limitations of Event-Driven Modeling
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If a tennis ball is held above a basket ball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimplification, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different final velocity as compared with the velocity resulting from the oversimplified model.
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Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noethers theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct statement of potentials is necessary. An important consequence is that gauge transformations are severely limited when conservation conditions must be satisfied. When transverse and longitudinal fields are present concurrently, the only practical gauge is the radiation gauge.
The dynamics of dissipative soft-sphere gases obeys Newtons equation of motion which are commonly solved numerically by (force-based) Molecular Dynamics schemes. With the assumption of instantaneous, pairwise collisions, the simulation can be accelerated considerably using event-driven Molecular Dynamics, where the coefficient of restitution is derived from the interaction force between particles. Recently it was shown, however, that this approach may fail dramatically, that is, the obtained trajectories deviate significantly from the ones predicted by Newtons equations. In this paper, we generalize the concept of the coefficient of restitution and derive a numerical scheme which, in the case of dilute systems and frictionless interaction, allows us to perform highly efficient event-driven Molecular Dynamics simulations even for non-instantaneous collisions. We show that the particle trajectories predicted by the new scheme agree perfectly with the corresponding (force-based) Molecular Dynamics, except for a short transient period whose duration corresponds to the duration of the contact. Thus, the new algorithm solves Newtons equations of motion like force-based MD while preserving the advantages of event-driven simulations.
Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $nge 7$. We also make a conjecture that would imply that $ngeq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature.
DNA is structurally and mechanically altered by the binding of intercalator molecules. Intercalation strongly affects the force-extension behavior of DNA, in particular the overstretching transition. We present a statistical model that captures all relevant findings of recent force-extension experiments. Two predictions from our model are presented. The first suggests the existence of a novel hyper-stretching regime in the presence of intercalators and the second, a linear dependence of the overstretching force on intercalator concentration, is verified by re-analyzing available experimental data. Our model pins down the physical principles that govern intercalated DNA mechanics, providing a predictive understanding of its limitations and possibilities.
CEA-Gramat studies the sensitivity of energetic materials to enhance their security and reliability. The conditions leading to the initiation of an explosive must be understood to control its sensitivity. According to the hot spots theory, the shock initiation of heterogeneous explosives is related to their microstructure: the shock interacts with the heterogeneities of the microstructure (pores and inclusions, morphology of grains and fragments, debonding, etc.) and creates local deposits of energy. To describe these hot spots, energetic materials have to be modeled at a scale allowing the discretization of their microstructure: the mesoscale. Micro-computed tomographies of energetic materials are done at CEA-Gramat and analyzed to build geometric models used in finite element simulations. Two kinds of models are studied:-Real models are directly built on the real microstructures extracted from micro-computed tomographies.-Virtual models are based on the same microstructures but simplified to study independently the effects of microstructural parameters (granulometry, porosity, filler content{ldots}) on the creation of hot spots. Compositions based on different kind of RDX particles in an inert binder are studied through numerical simulation. The influence of particle shape on the inert shock response is investigated at the mesoscale. Local heterogeneities of pressure and temperature fields appear intimately related to the morphological properties of the microstructures. Particles with sharp edges create more hot spots than spherical particles.
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