How do plastic balls break?Fragmentation phenomena are ubiquitous in nature and play a crucial
role in numerous industrial processes related to mining and ore
processing. The most interesting feature of
fragmenting systems is that the size/mass distribution of pieces
exhibits a surprising universality, i.e. power law distributions are
obtained independent of materials' details and of the way of energy
input. Detailed laboratory experiments on the breakup of disordered
solids have revealed that mainly the effective dimensionality of the
system determines the value of the exponent, according to which
universality classes of fragmentation phenomena can be distinguished.
The breakup of heterogeneous brittle materials (rocks, concrete,
ceramics, glass,...) is very well understood by today, however, hardly anything
is known about the fragmentation of materials with more complicated
rheological behaviors such as plastic. In order to
understand how plastic materials fragment, we accelerated
polypropylene balls of a few millimeter diameter and impacted them
against a hard wall. In the experiments we found
again a power law distribution of fragment masses; however, the value
of the exponent 1.2 is astonishingly small compared to any known
exponents 1.9-2.4 of bulk materials. To understand the physical origin
of this novel behavior we worked out a discrete model
of plastic and performed computer simulations of the impact process of
balls. The simulations reproduce both the large permanent deformation
of plastic during impact, and the novel value of the mass distribution
exponent. We demonstrated that the dominance of shear in the crack
formation and the plastic material response are the key
features which give rise to the emergence of the novel universality
class of fragmentation phenomena.
Attached figure:
Final states of impact at low impact velocities in the experiment
(a) and in the simulation (b). In the contact area with the hard
wall large permanent deformations occur due to compression, while
above it vertical cracks are formed due to tensile stresses.
The simulations are in very good agreement with the measurements.
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EL10508
Order and Chaos in the Slashdot Body ProblemClick image for animation
A novel analysis highlights the fascinating mix of simplicity and complexity in the orbits of a slash and a dot. A massive line segment or slash (/) and a massive point or dot (.) interact gravitationally to form a slashdot (/.) system. The resulting dynamics is especially beautiful, balancing order with chaos. Online movies and three dimensional strobed animations communicate the graceful pirouettes of this pas de deux. [http://www3.wooster.edu/Physics/Lindner/Research/SlashdotTrailsLarge.mov] The extension of the slash provides an extra degree of freedom that enables the interplay between rotation and revolution, which characterize actual planets, natural and artificial satellites, but not the interaction of idealized points. The International Space Station and a docking space shuttle form an extended million-pound system that is definitely not well-approximated by two points. The asteroid Ida and its moonlet Dactyl form a natural slashdot body system. The slashdot body problem is an instructive semi-solvable model problem in the vicinity of the famous two and three body problems that anchor celestial mechanics.
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LC12642B
Thermal rectifiers; from nano-electronic devices to energy-saving buildings
Generally, rectification is a transport process that is faster in one direction than in the opposite. This phenomenon is well-known for the current of charges; diodes are electric rectifiers. Thermal rectification, i.e., the non-equivalence of the heat transport in two opposite directions, however, has been detected only recently. Thermal rectification phenomena can be used to create thermal diodes and hence lead to a revolution in the nano/micro devices. Moreover, based on this phenomenon, in macroscopic world, special walls and windows for the energy efficiency of buildings can be designed. Using molecular dynamics simulations, we have demonstrated that thermal rectification can be forced in mass-graded systems (i.e., via isotope substitution), via a gradient in the force-constant (i.e., via impurity doping), or in special designed topologies.
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AH10518
Classical structures smaller than Planck constant do influence Quantum Mechanics.
It is a commonly held belief that dynamical classical structures smaller than Planck constant can not be "see" by quantum wave-functions and therefore have no effect on their evolution in time. This paper shows that this is not true in general: a correspondence is found between classical resonances (the ratio of two frequencies of the system being equal to the ratio of two integer numbers) and a number of quantum resonances (interactions between energy levels). In the system studied, the resonant quantum states reproduce the underlying resonant classical structures in phase space, even when these structures are smaller than Planck constant. Classical related quantum resonances are present only when the distance between two levels allows them to interact through the classical resonance itself. Varying one of the system parameters, several quantum levels can get close enough to enter resonances related to small classical structures, leading to significant population transfer. In the case studied in this paper, this results in to a remarkable agreement between classical, quantum, and experimental results. Studies of small classical structures could be used to improve methods for the transfer of population among quantum states.
