3,640 research outputs found
State Complexity of Reversals of Deterministic Finite Automata with Output
We investigate the worst-case state complexity of reversals of deterministic
finite automata with output (DFAOs). In these automata, each state is assigned
some output value, rather than simply being labelled final or non-final. This
directly generalizes the well-studied problem of determining the worst-case
state complexity of reversals of ordinary deterministic finite automata. If a
DFAO has states and possible output values, there is a known upper
bound of for the state complexity of reversal. We show this bound can be
reached with a ternary input alphabet. We conjecture it cannot be reached with
a binary input alphabet except when , and give a lower bound for the
case . We prove that the state complexity of reversal depends
solely on the transition monoid of the DFAO and the mapping that assigns output
values to states.Comment: 18 pages, 3 tables. Added missing affiliation/funding informatio
The Magic Number Problem for Subregular Language Families
We investigate the magic number problem, that is, the question whether there
exists a minimal n-state nondeterministic finite automaton (NFA) whose
equivalent minimal deterministic finite automaton (DFA) has alpha states, for
all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n).
A number alpha not satisfying this condition is called a magic number (for n).
It was shown in [11] that no magic numbers exist for general regular languages,
while in [5] trivial and non-trivial magic numbers for unary regular languages
were identified. We obtain similar results for automata accepting subregular
languages like, for example, combinational languages, star-free, prefix-,
suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free
languages, showing that there are only trivial magic numbers, when they exist.
For finite languages we obtain some partial results showing that certain
numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127
A study of waves in the earth's bow shock
The perturbation vectors of waves up and downstream from the region of maximum compression in the bow shock were examined on OGO-5 under particularly steady solar wind conditions. The polarization of the upstream waves was RH, circular and of the downstream waves LH, elliptical in the spacecraft frame. By observing that the polarization of the waves remained unchanged as the shock motion swept the wave structure back and forth across the satellite three times in eight minutes, it was found that the waves were not stationary in the shock frame. A study of the methods of determining the shock normal indicates that the normal estimated from a shock model should be superior to one based upon magnetic coplanarity. The propagation vectors of the waves examined did not coincide with the shock model normal, the average magnetic field, or the plasma flow velocity. However, the major axis of the polarization ellipse of the downstream wave was nearly parallel to the upstream propagation vector
Particles held by springs in a linear shear flow exhibit oscillatory motion
The dynamics of small spheres, which are held by linear springs in a low
Reynolds number shear flow at neighboring locations is investigated. The flow
elongates the beads and the interplay of the shear gradient with the nonlinear
behavior of the hydrodynamic interaction among the spheres causes in a large
range of parameters a bifurcation to a surprising oscillatory bead motion. The
parameter ranges, wherein this bifurcation is either super- or subcritical, are
determined.Comment: 4 pages, 5 figure
Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference
We derive an exact solution for the total kinetic energy of noninteracting
spinless electrons at half-filling in two-dimensional bipartite lattices. We
employ a conceptually novel approach that maps this problem exactly into a
Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic
study of the sum of magnetic phase factors on closed paths. We compare our
results with the ones obtained through numerical calculations.Comment: 5 pages, RevTe
Direct measurement of shear-induced cross-correlations of Brownian motion
Shear-induced cross-correlations of particle fluctuations perpendicular and
along stream-lines are investigated experimentally and theoretically. Direct
measurements of the Brownian motion of micron-sized beads, held by optical
tweezers in a shear-flow cell, show a strong time-asymmetry in the
cross-correlation, which is caused by the non-normal amplification of
fluctuations. Complementary measurements on the single particle probability
distribution substantiate this behavior and both results are consistent with a
Langevin model. In addition, a shear-induced anti-correlation between
orthogonal random-displacements of two trapped and hydrodynamically interacting
particles is detected, having one or two extrema in time, depending on the
positions of the particles.Comment: 4 pages, 4 figure
Decay of scalar turbulence revisited
We demonstrate that at long times the rate of passive scalar decay in a
turbulent, or simply chaotic, flow is dominated by regions (in real space or in
inverse space) where mixing is less efficient. We examine two situations. The
first is of a spatially homogeneous stationary turbulent flow with both viscous
and inertial scales present. It is shown that at large times scalar
fluctuations decay algebraically in time at all spatial scales (particularly in
the viscous range, where the velocity is smooth). The second example explains
chaotic stationary flow in a disk/pipe. The boundary region of the flow
controls the long-time decay, which is algebraic at some transient times, but
becomes exponential, with the decay rate dependent on the scalar diffusion
coefficient, at longer times.Comment: 4 pages, no figure
Dynamics of a trapped Brownian particle in shear flows
The Brownian motion of a particle in a harmonic potential, which is
simultaneously exposed either to a linear shear flow or to a plane Poiseuille
flow is investigated. In the shear plane of both flows the probability
distribution of the particle becomes anisotropic and the dynamics is changed in
a characteristic manner compared to a trapped particle in a quiescent fluid.
The particle distribution takes either an elliptical or a parachute shape or a
superposition of both depending on the mean particle position in the shear
plane. Simultaneously, shear-induced cross-correlations between particle
fluctuations along orthogonal directions in the shear plane are found. They are
asymmetric in time. In Poiseuille flow thermal particle fluctuations
perpendicular to the flow direction in the shear plane induce a shift of the
particle's mean position away from the potential minimum. Two complementary
methods are suggested to measure shear-induced cross-correlations between
particle fluctuations along orthogonal directions.Comment: 14 pages, 7 figure
Measurements of heavy ion beam losses from collimation
The collimation efficiency for Pb ion beams in the LHC is predicted to be
lower than requirements. Nuclear fragmentation and electromagnetic dissociation
in the primary collimators create fragments with a wide range of Z/A ratios,
which are not intercepted by the secondary collimators but lost where the
dispersion has grown sufficiently large. In this article we present
measurements and simulations of loss patterns generated by a prototype LHC
collimator in the CERN SPS. Measurements were performed at two different
energies and angles of the collimator. We also compare with proton loss maps
and find a qualitative difference between Pb ions and protons, with the maximum
loss rate observed at different places in the ring. This behavior was predicted
by simulations and provides a valuable benchmark of our understanding of ion
beam losses caused by collimation.Comment: 12 pages, 20 figure
Phase Rotation, Cooling And Acceleration Of Muon Beams: A Comparison Of Different Approaches
Experimental and theoretical activities are underway at CERN with the aim of
examining the feasibility of a very-high-flux neutrino source. In the present
scheme, a high-power proton beam (some 4 MW) bombards a target where pions are
produced. The pions are collected and decay to muons under controlled optical
condition. The muons are cooled and accelerated to a final energy of 50 GeV
before being injected into a decay ring where they decay under well-defined
conditions of energy and emittance.
We present the most challenging parts of the whole scenario, the muon
capture, the ionisation-cooling and the first stage of the muon acceleration.
Different schemes, their performance and the technical challenges are compared.Comment: LINAC 2000 CONFERENCE, paper ID No. THC1
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