582 research outputs found
The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth
I review the excursion set theory (EST) of dark matter halo formation and
clustering. I recount the Press-Schechter argument for the mass function of
bound objects and review the derivation of the Press-Schechter mass function in
EST. The EST formalism is powerful and can be applied to numerous problems. I
review the EST of halo bias and the properties of void regions. I spend
considerable time reviewing halo growth in the EST. This section culminates
with descriptions of two Monte Carlo methods for generating halo mass accretion
histories. In the final section, I emphasize that the standard EST approach is
the result of several simplifying assumptions. Dropping these assumptions can
lead to more faithful predictions and a more versatile formalism. One such
assumption is the constant height of the barrier for nonlinear collapse. I
review implementations of the excursion set approach with arbitrary barrier
shapes. An application of this is the now well-known improvement to standard
EST that follows from the ellipsoidal-collapse barrier. Additionally, I
emphasize that the statement that halo accretion histories are independent of
halo environments is a simplifying assumption, rather than a prediction of the
theory. I review the method for constructing correlated random walks of the
density field in more general cases. I construct a simple toy model with
correlated walks and I show that excursion set theory makes a qualitatively
simple and general prediction for the relation between halo accretion histories
and halo environments: regions of high density preferentially contain
late-forming halos and conversely for regions of low density. I conclude with a
brief discussion of this prediction in the context of recent numerical studies
of the environmental dependence of halo properties. (Abridged)Comment: 62 pages, 19 figures. Review article based on lectures given at the
Sixth Summer School of the Helmholtz Institute for Supercomputational
Physics. Accepted for Publication in IJMPD. Comments Welcom
Penetration depth of low-coherence enhanced backscattered light in sub-diffusion regime
The mechanisms of photon propagation in random media in the diffusive
multiple scattering regime have been previously studied using diffusion
approximation. However, similar understanding in the low-order (sub-diffusion)
scattering regime is not complete due to difficulties in tracking photons that
undergo very few scatterings events. Recent developments in low-coherence
enhanced backscattering (LEBS) overcome these difficulties and enable probing
photons that travel very short distances and undergo only a few scattering
events. In LEBS, enhanced backscattering is observed under illumination with
spatial coherence length L_sc less than the scattering mean free path l_s. In
order to understand the mechanisms of photon propagation in LEBS in the
subdiffusion regime, it is imperative to develop analytical and numerical
models that describe the statistical properties of photon trajectories. Here we
derive the probability distribution of penetration depth of LEBS photons and
report Monte Carlo numerical simulations to support our analytical results. Our
results demonstrate that, surprisingly, the transport of photons that undergo
low-order scattering events has only weak dependence on the optical properties
of the medium (l_s and anisotropy factor g) and strong dependence on the
spatial coherence length of illumination, L_sc, relative to those in the
diffusion regime. More importantly, these low order scattering photons
typically penetrate less than l_s into the medium due to low spatial coherence
length of illumination and their penetration depth is proportional to the
one-third power of the coherence volume (i.e. [l_s \pi L_sc^2 ]^1/3).Comment: 32 pages(including 7 figures), modified version to appear in Phys.
Rev.
Measured quantum probability distribution functions for Brownian motion
The quantum analog of the joint probability distributions describing a
classical stochastic process is introduced. A prescription is given for
constructing the quantum distribution associated with a sequence of
measurements. For the case of quantum Brownian motion this prescription is
illustrated with a number of explicit examples. In particular it is shown how
the prescription can be extended in the form of a general formula for the
Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres
Linear systems with adiabatic fluctuations
We consider a dynamical system subjected to weak but adiabatically slow
fluctuations of external origin. Based on the ``adiabatic following''
approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the
strength of fluctuations and 1/|\mu| refers to the time scale of evolution of
the unperturbed system to obtain a linear differential equation for the average
solution. The theory is applied to the problems of a damped harmonic oscillator
and diffusion in a turbulent fluid. The result is the realization of
`renormalized' diffusion constant or damping constant for the respective
problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page
The influence of charge detection on counting statistics
We consider the counting statistics of electron transport through a double
quantum dot with special emphasis on the dephasing induced by a nearby charge
detector. The double dot is embedded in a dissipative enviroment, and the
presence of electrons on the double dot is detected with a nearby quantum point
contact. Charge transport through the double dot is governed by a non-Markovian
generalized master equation. We describe how the cumulants of the current can
be obtained for such problems, and investigate the difference between the
dephasing mechanisms induced by the quantum point contact and the coupling to
the external heat bath. Finally, we consider various open questions of
relevance to future research.Comment: 15 pages, 2 figures, Contribution to 5-th International Conference on
Unsolved Problems on Noise, Lyon, France, June 2-6, 200
Brownian Simulations and Uni-Directional Flux in Diffusion
Brownian dynamics simulations require the connection of a small discrete
simulation volume to large baths that are maintained at fixed concentrations
and voltages. The continuum baths are connected to the simulation through
interfaces, located in the baths sufficiently far from the channel. Average
boundary concentrations have to be maintained at their values in the baths by
injecting and removing particles at the interfaces. The particles injected into
the simulation volume represent a unidirectional diffusion flux, while the
outgoing particles represent the unidirectional flux in the opposite direction.
The classical diffusion equation defines net diffusion flux, but not
unidirectional fluxes. The stochastic formulation of classical diffusion in
terms of the Wiener process leads to a Wiener path integral, which can split
the net flux into unidirectional fluxes. These unidirectional fluxes are
infinite, though the net flux is finite and agrees with classical theory. We
find that the infinite unidirectional flux is an artifact caused by replacing
the Langevin dynamics with its Smoluchowski approximation, which is classical
diffusion. The Smoluchowski approximation fails on time scales shorter than the
relaxation time of the Langevin equation. We find the unidirectional
flux (source strength) needed to maintain average boundary concentrations in a
manner consistent with the physics of Brownian particles. This unidirectional
flux is proportional to the concentration and inversely proportional to
to leading order. We develop a BD simulation that maintains
fixed average boundary concentrations in a manner consistent with the actual
physics of the interface and without creating spurious boundary layers
Algorithm for normal random numbers
We propose a simple algorithm for generating normally distributed pseudo
random numbers. The algorithm simulates N molecules that exchange energy among
themselves following a simple stochastic rule. We prove that the system is
ergodic, and that a Maxwell like distribution that may be used as a source of
normally distributed random deviates follows when N tends to infinity. The
algorithm passes various performance tests, including Monte Carlo simulation of
a finite 2D Ising model using Wolff's algorithm. It only requires four simple
lines of computer code, and is approximately ten times faster than the
Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to
Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf
Theory of Adiabatic fluctuations : third-order noise
We consider the response of a dynamical system driven by external adiabatic
fluctuations. Based on the `adiabatic following approximation' we have made a
systematic separation of time-scales to carry out an expansion in , where is the strength of fluctuations and is the
damping rate. We show that probability distribution functions obey the
differential equations of motion which contain third order terms (beyond the
usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of
adiabatic fluctuations in velocity space which is the counterpart of Brownian
motion for fast fluctuations, has been solved exactly. The characteristic
function and the associated probability distribution function are shown to be
of stable form. The linear dissipation leads to a steady state which is stable
and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.
How Stands Collapse II
I review ten problems associated with the dynamical wave function collapse
program, which were described in the first of these two papers. Five of these,
the \textit{interaction, preferred basis, trigger, symmetry} and
\textit{superluminal} problems, were discussed as resolved there. In this
volume in honor of Abner Shimony, I discuss the five remaining problems,
\textit{tails, conservation law, experimental, relativity, legitimization}.
Particular emphasis is given to the tails problem, first raised by Abner. The
discussion of legitimization contains a new argument, that the energy density
of the fluctuating field which causes collapse should exert a gravitational
force. This force can be repulsive, since this energy density can be negative.
Speculative illustrations of cosmological implications are offered.Comment: 37 page
A web of stakeholders and strategies: A case of broadband diffusion in South Korea
When a new technology is launched, its diffusion becomes an issue of importance. There are various stakeholders that influence diffusion. The question that remains to be determined is their identification and roles. This paper outlines how the strategies pursued by a government acting as the key stakeholder affected the diffusion of a new technology. The analysis is based on a theoretical framework derived from innovation diffusion and stakeholder theories. The empirical evidence comes from a study of broadband development in South Korea. A web of stakeholders and strategies is drawn in order to identify the major stakeholders involved and highlight their relations. The case of South Korea offers implications for other countries that are pursuing broadband diffusion strategies
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