3,681 research outputs found
Green's Relations in Finite Transformation Semigroups
We consider the complexity of Green's relations when the semigroup is given
by transformations on a finite set. Green's relations can be defined by
reachability in the (right/left/two-sided) Cayley graph. The equivalence
classes then correspond to the strongly connected components. It is not
difficult to show that, in the worst case, the number of equivalence classes is
in the same order of magnitude as the number of elements. Another important
parameter is the maximal length of a chain of components. Our main contribution
is an exponential lower bound for this parameter. There is a simple
construction for an arbitrary set of generators. However, the proof for
constant alphabet is rather involved. Our results also apply to automata and
their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1
Melting-freezing cycles in a relatively sheared pair of crystalline monolayers
The nonequilibrium dynamical behaviour that arises when two ordered
two-dimensional monolayers of particles are sheared over each other is studied
in Brownian dynamics simulations. A curious sequence of nonequilibrium states
is observed as the driving rate is increased, the most striking of which is a
sliding state with irregular alternation between disordered and ordered states.
We comment on possible mechanisms underlying these cycles, and experiments that
could observe them.Comment: 7 pages, 8 figures, minor changes in text and figures, references
adde
Complex Periodic Orbits and Tunnelling in Chaotic Potentials
We derive a trace formula for the splitting-weighted density of states
suitable for chaotic potentials with isolated symmetric wells. This formula is
based on complex orbits which tunnel through classically forbidden barriers.
The theory is applicable whenever the tunnelling is dominated by isolated
orbits, a situation which applies to chaotic systems but also to certain
near-integrable ones. It is used to analyse a specific two-dimensional
potential with chaotic dynamics. Mean behaviour of the splittings is predicted
by an orbit with imaginary action. Oscillations around this mean are obtained
from a collection of related orbits whose actions have nonzero real part
Jamming under tension in polymer crazes
Molecular dynamics simulations are used to study a unique expanded jammed
state. Tension transforms many glassy polymers from a dense glass to a network
of fibrils and voids called a craze. Entanglements between polymers and
interchain friction jam the system after a fixed increase in volume. As in
dense jammed systems, the distribution of forces is exponential, but they are
tensile rather than compressive. The broad distribution of forces has important
implications for fibril breakdown and the ultimate strength of crazes.Comment: 4 pages, 4 figure
Enhanced Learnability of Flight Techniques Through the Introduction of Targeted Observation Flights with Ab-Initio through Advanced Flight Training Candidates
Flight training paradigms exist to provide a framework for instructors to relay both technical and applied knowledge to students in the most efficient way possible. Traditional methods imply the use of pre/post flight briefings coincident with flight in either an actual or simulated environments. The demonstration of maneuvers may be accomplished by the instructor followed by the student or solely by the student. In this phase, aeronautical knowledge, procedural knowledge, and performance metrics are usually assessed. With regard to enhanced learnability, the study of effectiveness becomes critical to the application of new methods that could significantly lower the amount of flight time required to meet objectives or performance criteria for a given lesson. As industry continues to evolve with the use of automation, efficient pathways from initial to advanced flight training must be assessed in order to ensure students are receiving the most out of each activity. The direct observation of flights as an in-flight observer may improve performance and enhance the learnability of certain aspects of flight training, therefore reducing the number of flight hours necessary to achieve flight training landmarks. An experiential assessment of this technique will provide insight into the use of observation flights and how they may be correlated to improvement in student retention and performance
Contact of Single Asperities with Varying Adhesion: Comparing Continuum Mechanics to Atomistic Simulations
Atomistic simulations are used to test the equations of continuum contact
mechanics in nanometer scale contacts. Nominally spherical tips, made by
bending crystals or cutting crystalline or amorphous solids, are pressed into a
flat, elastic substrate. The normal displacement, contact radius, stress
distribution, friction and lateral stiffness are examined as a function of load
and adhesion. The atomic scale roughness present on any tip made of discrete
atoms is shown to have profound effects on the results. Contact areas, local
stresses, and the work of adhesion change by factors of two to four, and the
friction and lateral stiffness vary by orders of magnitude. The microscopic
factors responsible for these changes are discussed. The results are also used
to test methods for analyzing experimental data with continuum theory to
determine information, such as contact area, that can not be measured directly
in nanometer scale contacts. Even when the data appear to be fit by continuum
theory, extracted quantities can differ substantially from their true values
Friction Laws for Elastic Nano-Scale Contacts
The effect of surface curvature on the law relating frictional forces F with
normal load L is investigated by molecular dynamics simulations as a function
of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry,
commensurate surfaces show a linear dependency, F proportional to L, similar to
dry flat commensurate or amorphous surfaces and macroscopic surfaces. In
contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to
L^(2/3) similar to friction force microscopes. In our model, adhesive effects
are most adequately described by the Hertz plus offset model, as the
simulations are confined to small contact radii. Curved lubricated or
contaminated surfaces show again different behavior; details depend on how much
of the contaminant gets squeezed out of the contact. Also, it is seen that the
friction force in the lubricated case is mainly due to atoms at the entrance of
the tip.Comment: 7 pages, 5 figures, submitted to Europhys. Let
Controlling Microscopic Friction through Mechanical Oscillations
We study in detail the recent suggestions by Tshiprut et al. [Phys. Rev.
Lett. 95, 016101 (2005)] to tune tribological properties at the nanoscale by
subjecting a substrate to periodic mechanical oscillations. We show that both
in stick-slip and sliding regimes of motion friction can be tuned and reduced
by controlling the frequency and amplitude of the imposed substrate lateral
excitations. We demonstrate that the mechanisms of oscillation-induced
reduction of friction are different for stick-slip and sliding dynamics. In the
first regime the effect results from a giant enhancement of surface diffusion,
while in the second regime it is due to the interplay between washboard and
oscillation frequencies that leads to the occurrence of parametric resonances.
Moreover we show that for particular set of parameters it is possible to
sustain the motion with the only oscillations
- …