4,506 research outputs found
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
We introduce a new method, allowing to describe slowly time-dependent
Langevin equations through the behaviour of individual paths. This approach
yields considerably more information than the computation of the probability
density. The main idea is to show that for sufficiently small noise intensity
and slow time dependence, the vast majority of paths remain in small space-time
sets, typically in the neighbourhood of potential wells. The size of these sets
often has a power-law dependence on the small parameters, with universal
exponents. The overall probability of exceptional paths is exponentially small,
with an exponent also showing power-law behaviour. The results cover time spans
up to the maximal Kramers time of the system. We apply our method to three
phenomena characteristic for bistable systems: stochastic resonance, dynamical
hysteresis and bifurcation delay, where it yields precise bounds on transition
probabilities, and the distribution of hysteresis areas and first-exit times.
We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure
Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory
It has been suggested that the observed value of the cosmological constant is
related to the supersymmetry breaking scale M_{susy} through the formula Lambda
\sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally
arises in the codimension two solutions of warped space-time varying
compactifications of string theory in which non-isotropic stringy moduli induce
a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map
between deSitter and global cosmic brane solutions clarified, supersymmetry
breaking discussion improved and references adde
Phase-Dependent Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates
The spontaneous spin polarization and bifurcation delay in two-component
Bose-Einstein condensates coupled with laser or/and radio-frequency pulses are
investigated. We find that the bifurcation and the spontaneous spin
polarization are determined by both physical parameters and relative phase
between two condensates. Through bifurcations, the system enters into the
spontaneous spin polarization regime from the Rabi regime. We also find that
bifurcation delay appears when the parameter is swept through a static
bifurcation point. This bifurcation delay is responsible for metastability
leading to hysteresis.Comment: Improved version for cond-mat/021157
Green and Fire Resistant Nanocellulose/Hemicellulose/Clay Foams
Lightweight polymer foams from synthetic polymers are commonly used in a wide-spread spectrum of application fields. Their intrinsic flammability coupled with restrictions on flame retardant chemicals poses a severe threat to safety. Here, fire resistant foams comprising biobased components capable of replacing petroleum-based foams are investigated. Cellulose nanofibers are combined with 2D montmorillonite nanoplatelets and a native xyloglucan hemicellulose binder, using a water-based freeze casting approach. Due to the silicate nanoplatelets, these lightweight foams self-extinguish the flame during flammability tests. The limiting oxygen index is as high as 31.5% and in the same range as the best fire-retardant synthetic foams available. In cone calorimetry, the foams display extremely low combustion rates. Smoke release is near the detection limit of the instrument. In addition, the foams are withstanding the penetration of a flame torch focused on one side of the specimen (T on surface 800 °C) and structural integrity is maintained. At the same time, the unexposed side is insulated, as demonstrated by a through-thickness temperature drop of 680 °C cm−1. The results represent a tremendous opportunity for the development of fire-safe foams combining excellent sustainability with multifunctional performance
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of
neuronal action potentials, in parameter regimes characterised by mixed-mode
oscillations. The interspike time interval is related to the random number of
small-amplitude oscillations separating consecutive spikes. We prove that this
number has an asymptotically geometric distribution, whose parameter is related
to the principal eigenvalue of a substochastic Markov chain. We provide
rigorous bounds on this eigenvalue in the small-noise regime, and derive an
approximation of its dependence on the system's parameters for a large range of
noise intensities. This yields a precise description of the probability
distribution of observed mixed-mode patterns and interspike intervals.Comment: 36 page
A repulsive trap for two electrons in a magnetic field
We study numerically and analytically the dynamics of two classical electrons
with Coulomb interaction in a two dimensional antidot superlattice potential in
the presence of crossed electric and magnetic fields. It is found that near one
antidot the electron pair can be trapped for a long time and the escape rate
from such a trap is proportional to the square of a weak electric field. This
is qualitatively different from the case of noninteracting electrons which are
trapped forever by the antidot. For the pair propagation in the antidot
superlattice we found a broad parameter regime for which the pair is stable and
where two repulsive electrons propagate together on an enormously large
distance.Comment: revtex, 5 pages, 6 figure
Evaluating matrix elements relevant to some Lorenz violating operators
Carlson, Carone and Lebed have derived the Feynman rules for a consistent
formulation of noncommutative QCD. The results they obtained were used to
constrain the noncommutativity parameter in Lorentz violating noncommutative
field theories. However, their constraint depended upon an estimate of the
matrix element of the quark level operator (gamma.p - m) in a nucleon. In this
paper we calculate the matrix element of (gamma.p - m), using a variety of
confinement potential models. Our results are within an order of magnitude
agreement with the estimate made by Carlson et al. The constraints placed on
the noncommutativity parameter were very strong, and are still quite severe
even if weakened by an order of magnitude.Comment: 4 pages, 3 figures, RevTex, minor change
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio
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