50,142 research outputs found
Long delay times in reaction rates increase intrinsic fluctuations
In spatially distributed cellular systems, it is often convenient to
represent complicated auxiliary pathways and spatial transport by time-delayed
reaction rates. Furthermore, many of the reactants appear in low numbers
necessitating a probabilistic description. The coupling of delayed rates with
stochastic dynamics leads to a probability conservation equation characterizing
a non-Markovian process. A systematic approximation is derived that
incorporates the effect of delayed rates on the characterization of molecular
noise, valid in the limit of long delay time. By way of a simple example, we
show that delayed reaction dynamics can only increase intrinsic fluctuations
about the steady-state. The method is general enough to accommodate nonlinear
transition rates, allowing characterization of fluctuations around a
delay-induced limit cycle.Comment: 8 pages, 3 figures, to be published in Physical Review
Examining the inherent variability in ΔR: New methods of presenting ΔR values and implications for MRE studies
Topology of the polarization field in ferroelectric nanowires from first principles
The behaviour of the cross-sectional polarization field is explored for thin
nanowires of barium titanate from first-principles calculations. Topological
defects of different winding numbers have been obtained, beyond the known
textures in ferroelectric nanostructures. They result from the inward
accommodation of the polarization patterns imposed at the surface of the wire
by surface and edge effects. Close to a topological defect the polarization
field orients out of the basal plane in some cases, maintaining a close to
constant magnitude, whereas it virtually vanishes in other cases.Comment: 4 pages, 3 figure
Photoionization cross sections of O II, O III, O IV, and O V: benchmarking R-matrix theory and experiments
For crucial tests between theory and experiment, ab initio close coupling
calculations are carried out for photoionization of O II, O III, O IV, O V. The
relativistic fine structure and resonance effects are studied using the
R-matrix and its relativistic variant the Breit Pauli R-matrix (BPRM)
approximation. Detailed comparison is made with high resolution experimental
measurements carried out in three different set-ups: Advanced Light Source at
Berkeley, and synchrotron radiation experiments at University of Aarhus and
University of Paris-Sud. The comparisons illustrate physical effects in
photoionization such as (i) fine structure, (ii) resolution, and (iii)
metastable components. Photoionization cross sections sigma{PI} of the ground
and a few low lying excited states of these ions obtained in the experimental
spectrum include combined features of these states. Theoretically calculated
resonances need to be resolved with extremely fine energy mesh for precise
comparison. In addition, prominent resonant features are observed in the
measured spectra from transitions allowed with relativistic fine structure, but
not in LS coupling. The sigma_{PI} are obtained for ground and metastable (i)
2s^22p^3(^4S^o, ^2D^o, ^2P^o) states of O II, (ii) 2s^22p^2(^3P,^1D,^1S) and
2s2p^3(^5S^o) states of O III, (iii) 2s^22p(^2P^o_J) and 2s2p^2(^4P_J) levels
of O IV, and (iv) 2s^2(^1S) and 2s2p(^3P^o,^1P^o) states of O V. It is found
that resonances in ground and metastable cross sections can be a diagnostic of
experimental beam composition, with potential ap plications to astrophysical
and laboratory plasma environments.Comment: 27 pages, 7 figs., submitted to Phys. Rev. A., text with high
resolution figures at http://www.astronomy.ohio-state.edu/~pradhan/Oions.p
Robust and fragile PT-symmetric phases in a tight-binding chain
We study the phase-diagram of a parity and time-reversal (PT) symmetric
tight-binding chain with sites and hopping energy , in the presence of
two impurities with imaginary potentials located at arbitrary
(P-symmetric) positions on the chain where . We
find that except in the two special cases where impurities are either the
farthest or the closest, the PT-symmetric region - defined as the region in
which all energy eigenvalues are real - is algebraically fragile. We
analytically and numerically obtain the critical impurity potential
and show that as
except in the two special cases. When the PT symmetry is
spontaneously broken, we find that the maximum number of complex eigenvalues is
given by . When the two impurities are the closest, we show that the
critical impurity strength in the limit
approaches () provided that is even (odd). For an even the PT
symmetry is maximally broken whereas for an odd , it is sequentially broken.
Our results show that the phase-diagram of a PT-symmetric tight-binding chain
is extremely rich and that, in the continuum limit, this model may give rise to
new PT-symmetric Hamiltonians.Comment: 10 pages, 4 figure
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