4,474 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
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable orbit modes
By combining detailed imaging measurements at different tilt angles with
simulations of ray emission from prolate deformed lasing micro-droplets, we
conclude that the probability density for the lasing modes in a
three-dimensional dielectric microcavity must reside in the chaotic region of
the ray phase space. In particular, maximum emission from such chaotic lasing
modes is not from tangent rays emerging from the highest curvature part of the
rim. The laser emission is observed and calculated to be non-tangent and
displaced from the highest curvature due to the presence of stable orbits. In
this Letter we present the first experimental evidence for this phenomenon of
``dynamical eclipsing''.Comment: 4 figure
Criminal Law: Customerâs Permanent Exclusion From Retail Store Due to Prior Shoplifting Arrests Held Enforceable Under Criminal Trespass Statute
In interpretive research, trustworthiness has developed to become an important alternative for measuring the value of research and its effects, as well as leading the way of providing for rigour in the research process. The article develops the argument that trustworthiness plays an important role in not only effecting change in a research projectâs original setting, but also that trustworthy research contributes toward building a body of knowledge that can play an important role in societal change. An essential aspect in the development of this trustworthiness is its relationship to context. To deal with the multiplicity of meanings of context, we distinguish between contexts at different levels of the research project: the domains of the researcher, the collective, and the individual participant. Furthermore, we argue that depending on the primary purpose associated with the collective learning potential, critical potential, or performative potential of phenomenographic research, developing trustworthiness may take different forms and is related to aspects of pedagogical legitimacy, social legitimacy, and epistemological legitimacy. Trustworthiness in phenomenographic research is further analysed by distinguishing between the internal horizon â the constitution of trustworthiness as it takes place within the research project â and the external horizon, which points to the impact of the phenomenographic project in the world mediated by trustworthiness
Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma
models on toric Calabi-Yau manifolds. We derive and solve new constraint
equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on
the physical data of dual linear sigma models. In Calabi-Yau threefolds case,
we consider two examples. First, we give the mirror symmetry of the canonical
line bundle over the Hirzebruch surfaces . Second, we find a special
geometry with the affine so(8) Lie algebra toric data extending the geometry of
elliptically fibered K3. This geometry leads to a pure N=1 six dimensional
SO(8) gauge model from the F-theory compactification. For Calabi-Yau fourfolds,
we give a new algebraic realization for ADE hypersurfaces.Comment: 27 pages, latex. To appear in Journal of Physics A: Mathematical and
Genera
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
Construction of an evidence-based integrated morphology cleavage embryo score for implantation potential of embryos scored and transferred on day 2 after oocyte retrieval
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Measurement with Persons: A European Network
The European âMeasuring the Impossibleâ Network MINET promotes new research activities in measurement dependent on human perception and/or interpretation. This includes the perceived attributes of products and services, such as quality or desirability, and societal parameters such as security and well-being. Work has aimed at consensus about four âgenericâ metrological issues: (1) Measurement Concepts & Terminology; (2) Measurement Techniques: (3) Measurement Uncertainty; and (4) Decision-making & Impact Assessment, and how these can be applied specificallyto the âMeasurement of Personsâ in terms of âMan as a Measurement Instrumentâ and âMeasuring Man.â Some of the main achievements of MINET include a research repository with glossary; training course; book; series of workshops;think tanks and study visits, which have brought together a unique constellation of researchers from physics, metrology,physiology, psychophysics, psychology and sociology. Metrology (quality-assured measurement) in this area is relativelyunderdeveloped, despite great potential for innovation, and extends beyond traditional physiological metrology in thatit also deals with measurement with all human senses as well as mental and behavioral processes. This is particularlyrelevant in applications where humans are an important component of critical systems, where for instance health andsafety are at stake
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
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