618,918 research outputs found
Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas
We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at
low density. The positive Lyapunov exponent may be obtained either by a direct
analysis of the dynamics, or by the use of kinetic theory methods. To leading
orders in the density of scatterers it is of the form
, where and are
known constants and is the number density of scatterers expressed
in dimensionless units. In this paper, we find that through order
, the positive Lyapunov exponent is of the form
. Explicit numerical values of the new constants
and are obtained by means of a systematic analysis. This takes into
account, up to , the effects of {\it all\/} possible
trajectories in two versions of the model; in one version overlapping scatterer
configurations are allowed and in the other they are not.Comment: 12 pages, 9 figures, minor changes in this version, to appear in J.
Stat. Phy
Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
A kinetic approach is adopted to describe the exponential growth of a small
deviation of the initial phase space point, measured by the largest Lyapunov
exponent, for a dilute system of hard disks, both in equilibrium and in a
uniform shear flow. We derive a generalized Boltzmann equation for an extended
one-particle distribution that includes deviations from the reference phase
space point. The equation is valid for very low densities n, and requires an
unusual expansion in powers of 1/|ln n|. It reproduces and extends results from
the earlier, more heuristic clock model and may be interpreted as describing a
front propagating into an unstable state. The asymptotic speed of propagation
of the front is proportional to the largest Lyapunov exponent of the system.
Its value may be found by applying the standard front speed selection mechanism
for pulled fronts to the case at hand. For the equilibrium case, an explicit
expression for the largest Lyapunov exponent is given and for sheared systems
we give explicit expressions that may be evaluated numerically to obtain the
shear rate dependence of the largest Lyapunov exponent.Comment: 26 pages REVTeX, 1 eps figure. Added remarks, a reference and
corrected some typo
Protocol-Safe Workflow Support for Santa Claus
Practical software analysis techniques exploit a form a process description, mostly in some \ud
avour of state diagram. Unlike typing information, these process structures are usually not passed down to the implementation level, and neither are they exploited in any form of consistency check. It is our belief that the information in most designs suffices to perform all sorts of consistency checks. This workshop paper studies a simple case where work\ud
ow processes interact with `actual' objects at the implementation level, and demonstrates how useful protocol checking can be in making and keeping these processes consistent with each other
Measurement of the inelastic proton-proton cross section at = 13 TeV
A measurement of the inelastic proton-proton cross section at a
centre-of-mass energy of = 13 TeV is presented. The analysis is
performed using the CMS detector, in particular with information from forward
calorimetry at pseudorapidities of 3.0 < {\eta} < 5.2 and -6.6 < {\eta} < -3.0.
A visible cross section is measured in two different detector acceptances and
finally extrapolated to the full inelastic phase space domain. The results are
compared with those of other experiments, and with models used to describe
high-energy hadronic interactions.Comment: 5 pages, 2 figures, proceedings of the XXIV International Workshop on
Deep-Inelastic Scattering and Related Subjects, 11-15 April 2016, DESY
Hamburg, German
On Practical Verification of Processes
The integration of a formal process theory with a practically usable notation is not straightforward, but it is necessary for practical verification of process specifications. Given such an intermediate language, a verification process that gives useful feedback is not trivial either: Model checkers are not powerful enough to deal with object models, and theorem provers provide insu#cient feedback and are not certain to find a proof
Non-abelian Littlewood-Offord inequalities
In 1943, Littlewood and Offord proved the first anti-concentration result for
sums of independent random variables. Their result has since then been
strengthened and generalized by generations of researchers, with applications
in several areas of mathematics.
In this paper, we present the first non-abelian analogue of Littlewood-Offord
result, a sharp anti-concentration inequality for products of independent
random variables.Comment: 14 pages Second version. Dependence of the upper bound on the matrix
size in the main results has been remove
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