1,567 research outputs found
Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
The one-dimensional coagulation-diffusion process describes the strongly
fluctuating dynamics of particles, freely hopping between the nearest-neighbour
sites of a chain such that one of them disappears with probability 1 if two
particles meet. The exact two-time correlation and response function in the
one-dimensional coagulation-diffusion process are derived from the
empty-interval-particle method. The main quantity is the conditional
probability of finding an empty interval of n consecutive sites, if at distance
d a site is occupied by a particle. Closed equations of motion are derived such
that the probabilities needed for the calculation of correlators and responses,
respectively, are distinguished by different initial and boundary conditions.
In this way, the dynamical scaling of these two-time observables is analysed in
the longtime ageing regime. A new generalised fluctuation-dissipation ratio
with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec
Accurate Spectral Algorithms for Solving Variable-order Fractional Percolation Equations
A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented and compared with the results in literature, which reveals wonderful results
Multiscale simulations of porous media flows in flow-based coordinate system
In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system
Anomalous transport resolved in space and time by fluorescence correlation spectroscopy
A ubiquitous observation in crowded cell membranes is that molecular
transport does not follow Fickian diffusion but exhibits subdiffusion. The
microscopic origin of such a behaviour is not understood and highly debated.
Here we discuss the spatio-temporal dynamics for two models of subdiffusion:
fractional Brownian motion and hindered motion due to immobile obstacles. We
show that the different microscopic mechanisms can be distinguished using
fluorescence correlation spectroscopy (FCS) by systematic variation of the
confocal detection area. We provide a theoretical framework for space-resolved
FCS by generalising FCS theory beyond the common assumption of spatially
Gaussian transport. We derive a master formula for the FCS autocorrelation
function, from which it is evident that the beam waist of an FCS experiment is
a similarly important parameter as the wavenumber of scattering experiments.
These results lead to scaling properties of the FCS correlation for both
models, which are tested by in silico experiments. Further, our scaling
prediction is compatible with the FCS half-value times reported by Wawrezinieck
et al. [Biophys. J. 89, 4029 (2005)] for in vivo experiments on a transmembrane
protein.Comment: accepted for publication in Soft Matte
Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields
We apply the Minkowski Tensor statistics to two dimensional slices of the
three dimensional density field. The Minkowski Tensors are a set of functions
that are sensitive to directionally dependent signals in the data, and
furthermore can be used to quantify the mean shape of density peaks. We begin
by introducing our algorithm for constructing bounding perimeters around
subsets of a two dimensional field, and reviewing the definition of Minkowski
Tensors. Focusing on the translational invariant statistic - a matrix - we calculate its eigenvalues for both the entire excursion
set () and for individual connected regions and holes
within the set (). The ratio of eigenvalues
informs us of the presence of global anisotropies in
the data, and is a measure of the
mean shape of peaks and troughs in the density field. We study these quantities
for a Gaussian field, then consider how they are modified by the effect of
gravitational collapse using the latest Horizon Run 4 cosmological simulation.
We find are essentially independent of gravitational collapse,
as the process maintains statistical isotropy. However, the mean shape of peaks
is modified significantly - overdensities become relatively more circular
compared to underdensities of the same area. When applying the statistic to a
redshift space distorted density field, we find a significant signal in the
eigenvalues , suggesting that they can be used to probe the
large-scale velocity field.Comment: 17 pages, accepted for publication in AP
Non-coincidence of Quenched and Annealed Connective Constants on the supercritical planar percolation cluster
In this paper, we study the abundance of self-avoiding paths of a given
length on a supercritical percolation cluster on \bbZ^d. More precisely, we
count the number of self-avoiding paths of length on the infinite
cluster, starting from the origin (that we condition to be in the cluster). We
are interested in estimating the upper growth rate of , , that we call the connective constant of the dilute lattice.
After proving that this connective constant is a.s.\ non-random, we focus on
the two-dimensional case and show that for every percolation parameter , almost surely, grows exponentially slower than its expected
value. In other word we prove that \limsup_{N\to \infty} (Z_N)^{1/N}
<\lim_{N\to \infty} \bbE[Z_N]^{1/N} where expectation is taken with respect to
the percolation process. This result can be considered as a first mathematical
attempt to understand the influence of disorder for self-avoiding walk on a
(quenched) dilute lattice. Our method, which combines change of measure and
coarse graining arguments, does not rely on specifics of percolation on
\bbZ^2, so that our result can be extended to a large family of two
dimensional models including general self-avoiding walk in random environment.Comment: 25 pages. Version accepted for publication in PTR
Persistence and First-Passage Properties in Non-equilibrium Systems
In this review we discuss the persistence and the related first-passage
properties in extended many-body nonequilibrium systems. Starting with simple
systems with one or few degrees of freedom, such as random walk and random
acceleration problems, we progressively discuss the persistence properties in
systems with many degrees of freedom. These systems include spins models
undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces
etc. Persistence properties are nontrivial in these systems as the effective
underlying stochastic process is non-Markovian. Several exact and approximate
methods have been developed to compute the persistence of such non-Markov
processes over the last two decades, as reviewed in this article. We also
discuss various generalisations of the local site persistence probability.
Persistence in systems with quenched disorder is discussed briefly. Although
the main emphasis of this review is on the theoretical developments on
persistence, we briefly touch upon various experimental systems as well.Comment: Review article submitted to Advances in Physics: 149 pages, 21
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The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model
Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales
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