967 research outputs found
Minimal Brownian Ratchet: An Exactly Solvable Model
We develop an exactly-solvable three-state discrete-time minimal Brownian
ratchet (MBR), where the transition probabilities between states are
asymmetric. By solving the master equations we obtain the steady-state
probabilities. Generally the steady-state solution does not display detailed
balance, giving rise to an induced directional motion in the MBR. For a reduced
two-dimensional parameter space we find the null-curve on which the net current
vanishes and detailed balance holds. A system on this curve is said to be
balanced. On the null-curve, an additional source of external random noise is
introduced to show that a directional motion can be induced under the zero
overall driving force. We also indicate the off-balance behavior with biased
random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be
appeared in Phys. Rev. Let
New paradoxical games based on Brownian ratchets
Based on Brownian ratchets, a counter-intuitive phenomenon has recently
emerged -- namely, that two losing games can yield, when combined, a
paradoxical tendency to win. A restriction of this phenomenon is that the rules
depend on the current capital of the player. Here we present new games where
all the rules depend only on the history of the game and not on the capital.
This new history-dependent structure significantly increases the parameter
space for which the effect operates.Comment: 4 pages, 3 eps figures, revte
Brownian ratchets and Parrondo's games
Parrondo's games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player's current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of "noise" that is rectified by game B to produce overall positive drift-as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo's games is that they are physically motivated and were originally derived by considering a Brownian ratchet-the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research. (c) 2001 American Institute of Physics.Gregory P. Harmer, Derek Abbott, Peter G. Taylor, and Juan M. R. Parrond
Spectral simplicity and asymptotic separation of variables
We describe a method for comparing the real analytic eigenbranches of two
families of quadratic forms that degenerate as t tends to zero. One of the
families is assumed to be amenable to `separation of variables' and the other
one not. With certain additional assumptions, we show that if the families are
asymptotic at first order as t tends to 0, then the generic spectral simplicity
of the separable family implies that the eigenbranches of the second family are
also generically one-dimensional. As an application, we prove that for the
generic triangle (simplex) in Euclidean space (constant curvature space form)
each eigenspace of the Laplacian is one-dimensional. We also show that for all
but countably many t, the geodesic triangle in the hyperbolic plane with
interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure
Optical and Infrared Spectroscopy of the type IIn SN 1998S : Days 3-127
We present contemporary infrared and optical spectroscopic observations of
the type IIn SN 1998S for the period between 3 and 127 days after discovery. In
the first week the spectra are characterised by prominent broad emission lines
with narrow peaks superimposed on a very blue continuum(T~24000K). In the
following two weeks broad, blueshifted absorption components appeared in the
spectra and the temperature dropped. By day 44, broad emission components in H
and He reappeared in the spectra. These persisted to 100-130d, becoming
increasingly asymmetric. We agree with Leonard et al. (2000) that the broad
emission lines indicate interaction between the ejecta and circumstellar
material (CSM) and deduce that progenitor of SN 1998S appears to have gone
through at least two phases of mass loss, giving rise to two CSM zones.
Examination of the spectra indicates that the inner zone extended to <90AU,
while the outer CSM extended from 185AU to over 1800AU. Analysis of high
resolution spectra shows that the outer CSM had a velocity of 40-50 km/s.
Assuming a constant velocity, we can infer that the outer CSM wind commenced
more than 170 years ago, and ceased about 20 years ago, while the inner CSM
wind may have commenced less than 9 years ago. During the era of the outer CSM
wind the outflow was high, >2x10^{-5}M_{\odot}/yr corresponding to a mass loss
of at least 0.003M_{\odot} and suggesting a massive progenitor. We also model
the CO emission observed in SN 1998S. We deduce a CO mass of ~10^{-3} M_{\odot}
moving at ~2200km/s, and infer a mixed metal/He core of ~4M_{\odot}, again
indicating a massive progenitor.Comment: 22 pages, 14 figures, accepted in MNRA
Quantum ergodicity for graphs related to interval maps
We prove quantum ergodicity for a family of graphs that are obtained from
ergodic one-dimensional maps of an interval using a procedure introduced by
Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take
the L^2 functions on the interval. The proof is based on the periodic orbit
expansion of a majorant of the quantum variance. Specifically, given a
one-dimensional, Lebesgue-measure-preserving map of an interval, we consider an
increasingly refined sequence of partitions of the interval. To this sequence
we associate a sequence of graphs, whose directed edges correspond to elements
of the partitions and on which the classical dynamics approximates the
Perron-Frobenius operator corresponding to the map. We show that, except
possibly for subsequences of density 0, the eigenstates of the quantum graphs
equidistribute in the limit of large graphs. For a smaller class of observables
we also show that the Egorov property, a correspondence between classical and
quantum evolution in the semiclassical limit, holds for the quantum graphs in
question.Comment: 20 pages, 1 figur
Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching
We propose a new mechanism for pattern formation based on the global
alternation of two dynamics neither of which exhibits patterns. When driven by
either one of the separate dynamics, the system goes to a spatially homogeneous
state associated with that dynamics. However, when the two dynamics are
globally alternated sufficiently rapidly, the system exhibits stationary
spatial patterns. Somewhat slower switching leads to oscillatory patterns. We
support our findings by numerical simulations and discuss the results in terms
of the symmetries of the system and the ratio of two relevant characteristic
times, the switching period and the relaxation time to a homogeneous state in
each separate dynamics.Comment: REVTEX preprint: 12 pages including 1 (B&W) + 3 (COLOR) figures (to
appear in Physical Review Letters
Parrondo's paradoxical games and the discrete Brownian ratchet
Gregory P. Harmer, Derek Abbott, Peter G. Taylor and Juan M. R. Parrond
Quantum random walks with history dependence
We introduce a multi-coin discrete quantum random walk where the amplitude
for a coin flip depends upon previous tosses. Although the corresponding
classical random walk is unbiased, a bias can be introduced into the quantum
walk by varying the history dependence. By mixing the biased random walk with
an unbiased one, the direction of the bias can be reversed leading to a new
quantum version of Parrondo's paradox.Comment: 8 pages, 6 figures, RevTe
On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions
Courant theorem provides an upper bound for the number of nodal domains of
eigenfunctions of a wide class of Laplacian-type operators. In particular, it
holds for generic eigenfunctions of quantum graph. The theorem stipulates that,
after ordering the eigenvalues as a non decreasing sequence, the number of
nodal domains of the -th eigenfunction satisfies . Here,
we provide a new interpretation for the Courant nodal deficiency in the case of quantum graphs. It equals the Morse index --- at a
critical point --- of an energy functional on a suitably defined space of graph
partitions. Thus, the nodal deficiency assumes a previously unknown and
profound meaning --- it is the number of unstable directions in the vicinity of
the critical point corresponding to the -th eigenfunction. To demonstrate
this connection, the space of graph partitions and the energy functional are
defined and the corresponding critical partitions are studied in detail.Comment: 22 pages, 6 figure
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