3,914 research outputs found
Multispeckle diffusing-wave spectroscopy: a tool to study slow relaxation and time-dependent dynamics
A multispeckle technique for efficiently measuring correctly
ensemble-averaged intensity autocorrelation functions of scattered light from
non-ergodic and/or non-stationary systems is described.
The method employs a CCD camera as a multispeckle light detector and a
computer-based correlator, and permits the simultaneous calculation of up to
500 correlation functions, where each correlation function is started at a
different time.
The correlation functions are calculated in real time and are referenced to a
unique starting time.
The multispeckle nature of the CCD camera detector means that a true ensemble
average is calculated; no time averaging is necessary.
The technique thus provides a "snapshot" of the dynamics, making it
particularly useful for non-stationary systems where the dynamics are changing
with time.
Delay times spanning the range from 1 ms to 1000 s are readily achieved with
this method.
The technique is demonstrated in the multiple scattering limit where
diffusing-wave spectroscopy theory applies.
The technique can also be combined with a recently-developed two-cell
technique that can measure faster decay times.
The combined technique can measure delay times from 10 ns to 1000 s.
The method is peculiarly well suited for studying aging processes in soft
glassy materials, which exhibit both short and long relaxation times,
non-ergodic dynamics, and slowly-evolving transient behavior.Comment: 11 pages 13 figures Accepted in Review of Scientific Instrument (june
02
Unravelling intermittent features in single particle trajectories by a local convex hull method
We propose a new model-free method to detect change points between distinct
phases in a single random trajectory of an intermittent stochastic process. The
local convex hull (LCH) is constructed for each trajectory point, while its
geometric properties (e.g., the diameter or the volume) are used as
discriminators between phases. The efficiency of the LCH method is validated
for six models of intermittent motion, including Brownian motion with different
diffusivities or drifts, fractional Brownian motion with different Hurst
exponents, and surface-mediated diffusion. We discuss potential applications of
the method for detection of active and passive phases in the intracellular
transport, temporal trapping or binding of diffusing molecules, alternating
bulk and surface diffusion, run and tumble (or search) phases in the motion of
bacteria and foraging animals, and instantaneous firing rates in neurons
Long-Term Dependence Characteristics of European Stock Indices
In this paper we show the degrees of persistence of the time series if eight European stock market indices are measured, after their lack of ergodicity and stationarity has been established. The proper identification of the nature of the persistence of financial time series forms a crucial step in deciding whether econometric modeling of such series might provide meaningful results. Testing for ergodicity and stationarity must be the first step in deciding whether the assumptions of numerous time series models are met. Our results indicate that ergodicity and stationarity are very difficult to establish in daily observations of these market indexes and thus various time-series models cannot be successfully identified. However, the measured degrees of persistence point to the existence of certain dependencies, most likely of a nonlinear nature, which, perhaps can be used in the identification of proper empirical econometric models of such dynamic time paths of the European stock market indexes. The paper computes and analyzes the long- term dependence of the equity index data as measured by global Hurst exponents, which are computed from wavelet multi-resolution analysis. For example, the FTSE turns out to be an ultra-efficient market with abnormally fast mean-reversion, faster than theoretically postulated by a Geometric Brownian Motion. Various methodologies appear to produce non-unique empirical measurement results and it is very difficult to obtain definite conclusions regarding the presence or absence of long term dependence phenomena like persistence or anti-persistence based on the global or homogeneous Hurst exponent. More powerful methods, such as the computation of the multifractal spectra of financial time series may be required. However, the visualization of the wavelet resonance coefficients and their power spectrograms in the form of localized scalograms and average scalegrams, forcefully assist with the detection and measurement of several nonlinear types of market price diffusion.Long-Term Dependence, European Stock Indices
Breakdown of the Onsager principle as a sign of aging
We discuss the problem of the equivalence between Continuous Time Random Walk
(CTRW) and Generalized Master Equation (GME). The walker, making instantaneous
jumps from one site of the lattice to another, resides in each site for
extended times. The sojourn times have a distribution psi(t) that is assumed to
be an inverse power law. We assume that the Onsager principle is fulfilled, and
we use this assumption to establish a complete equivalence between GME and the
Montroll-Weiss CTRW. We prove that this equivalence is confined to the case
when psi(t) is an exponential. We argue that is so because the Montroll-Weiss
CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101
(2003)], is non-stationary, thereby implying aging, while the Onsager
principle, is valid only in the case of fully aged systems. We consider the
case of a dichotomous fluctuation, and we prove that the Onsager principle is
fulfilled for any form of regression to equilibrium provided that the
stationary condition holds true. We set the stationary condition on both the
CTRW and the GME, thereby creating a condition of total equivalence, regardless
the nature of the waiting time distribution. As a consequence of this procedure
we create a GME that it is a "bona fide" master equation, in spite of being
non-Markovian. We note that the memory kernel of the GME affords information on
the interaction between system of interest and its bath. The Poisson case
yields a bath with infinitely fast fluctuations. We argue that departing from
the Poisson form has the effect of creating a condition of infinite memory and
that these results might be useful to shed light into the problem of how to
unravel non-Markovian master equations.Comment: one file .tex, revtex4 style, 11 page
Meaning of the wave function
We investigate the meaning of the wave function by analyzing the mass and
charge density distributions of a quantum system. According to protective
measurement, a charged quantum system has mass and charge density distributing
in space, proportional to the modulus square of its wave function. In a
realistic interpretation, the wave function of a quantum system can be taken as
a description of either a physical field or the ergodic motion of a particle.
If the wave function is a physical field, then the mass and charge density will
be distributed throughout space at a given time for a charged quantum system,
and thus there will exist gravitational and electrostatic self-interactions of
its wave function. This not only violates the superposition principle of
quantum mechanics but also contradicts experimental observations. Thus the wave
function cannot be a description of a physical field but a description of the
ergodic motion of a particle. For the later there is only a localized particle
with mass and charge at every instant, and thus there will not exist any
self-interaction for the wave function. It is further argued that the classical
ergodic models, which assume continuous motion of particles, cannot be
consistent with quantum mechanics. Based on the negative result, we suggest
that the wave function is a description of the quantum motion of particles,
which is random and discontinuous in nature. On this interpretation, the
modulus square of the wave function not only gives the density of probability
of the particle being found in certain locations, but also gives the density of
objective probability of the particle being there. We show that this new
interpretation of the wave function provides a natural realistic alternative to
the orthodox interpretation, and its implications for other realistic
interpretations of quantum mechanics are also briefly discussed.Comment: 22 page
Hyperbolic Covariant Coherent Structures in two dimensional flows
A new method to describe hyperbolic patterns in two dimensional flows is
proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which
have the properties to be covariant with the dynamics, and thus being mapped by
the tangent linear operator into another CLVs basis, they are norm independent,
invariant under time reversal and can be not orthonormal. CLVs can thus give a
more detailed information on the expansion and contraction directions of the
flow than the Lyapunov Vector bases, that are instead always orthogonal. We
suggest a definition of Hyperbolic Covariant Coherent Structures (HCCSs), that
can be defined on the scalar field representing the angle between the CLVs.
HCCSs can be defined for every time instant and could be useful to understand
the long term behaviour of particle tracers.
We consider three examples: a simple autonomous Hamiltonian system, as well
as the non-autonomous "double gyre" and Bickley jet, to see how well the angle
is able to describe particular patterns and barriers. We compare the results
from the HCCSs with other coherent patterns defined on finite time by the
Finite Time Lyapunov Exponents (FTLEs), to see how the behaviour of these
structures change asymptotically
Anomalous transport in the crowded world of biological cells
A ubiquitous observation in cell biology is that diffusion of macromolecules
and organelles is anomalous, and a description simply based on the conventional
diffusion equation with diffusion constants measured in dilute solution fails.
This is commonly attributed to macromolecular crowding in the interior of cells
and in cellular membranes, summarising their densely packed and heterogeneous
structures. The most familiar phenomenon is a power-law increase of the MSD,
but there are other manifestations like strongly reduced and time-dependent
diffusion coefficients, persistent correlations, non-gaussian distributions of
the displacements, heterogeneous diffusion, and immobile particles. After a
general introduction to the statistical description of slow, anomalous
transport, we summarise some widely used theoretical models: gaussian models
like FBM and Langevin equations for visco-elastic media, the CTRW model, and
the Lorentz model describing obstructed transport in a heterogeneous
environment. Emphasis is put on the spatio-temporal properties of the transport
in terms of 2-point correlation functions, dynamic scaling behaviour, and how
the models are distinguished by their propagators even for identical MSDs.
Then, we review the theory underlying common experimental techniques in the
presence of anomalous transport: single-particle tracking, FCS, and FRAP. We
report on the large body of recent experimental evidence for anomalous
transport in crowded biological media: in cyto- and nucleoplasm as well as in
cellular membranes, complemented by in vitro experiments where model systems
mimic physiological crowding conditions. Finally, computer simulations play an
important role in testing the theoretical models and corroborating the
experimental findings. The review is completed by a synthesis of the
theoretical and experimental progress identifying open questions for future
investigation.Comment: review article, to appear in Rep. Prog. Phy
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