246 research outputs found
The development and application of time resolved PIV at the University of Strathclyde
This paper describes the development of time resolved particle image velocimetry (PIV) within the Department of Mechanical Engineering at the University of Strathclyde. The Department's first PIV systems were developed on a limited budget and used existing and second hand equipment. The original technique which, employed 16mm high speed cinematography, is described. The introduction and development of low cost systems employing high speed digital video (HSDV) is discussed and, finally, the Department's new time resolved PIV system, supplied by Dantec Dynamics, is introduced. For each of the PIV systems that have been developed a critical analysis of their functionality is given and samples of the data that they have been produced are shown. Data are presented from systems such as de-rotated centrifugal impellers, air bubbles growing in columns of water, pulsatile jets and vortex shedding
A crossing probability for critical percolation in two dimensions
Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in
their extensive numerical investigations of critical percolation in two
dimensions. Cardy was able to find the exact form of pi_h by treating it as a
correlation function of boundary operators in the Q goes to 1 limit of the Q
state Potts model. We extend his results to find an analogous formula for
pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo
changed
Fractional chemotaxis diffusion equations
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles
Fractional Chemotaxis Diffusion Equations
We introduce mesoscopic and macroscopic model equations of chemotaxis with
anomalous subdiffusion for modelling chemically directed transport of
biological organisms in changing chemical environments with diffusion hindered
by traps or macro-molecular crowding. The mesoscopic models are formulated
using Continuous Time Random Walk master equations and the macroscopic models
are formulated with fractional order differential equations. Different models
are proposed depending on the timing of the chemotactic forcing.
Generalizations of the models to include linear reaction dynamics are also
derived. Finally a Monte Carlo method for simulating anomalous subdiffusion
with chemotaxis is introduced and simulation results are compared with
numerical solutions of the model equations. The model equations developed here
could be used to replace Keller-Segel type equations in biological systems with
transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page
Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
We have derived a fractional Fokker-Planck equation for subdiffusion in a
general space-and- time-dependent force field from power law waiting time
continuous time random walks biased by Boltzmann weights. The governing
equation is derived from a generalized master equation and is shown to be
equivalent to a subordinated stochastic Langevin equation.Comment: 5 page
Deformed strings in the Heisenberg model
We investigate solutions to the Bethe equations for the isotropic S = 1/2
Heisenberg chain involving complex, string-like rapidity configurations of
arbitrary length. Going beyond the traditional string hypothesis of undeformed
strings, we describe a general procedure to construct eigenstates including
strings with generic deformations, discuss general features of these solutions,
and provide a number of explicit examples including complete solutions for all
wavefunctions of short chains. We finally investigate some singular cases and
show from simple symmetry arguments that their contribution to zero-temperature
correlation functions vanishes.Comment: 34 pages, 13 figure
Mesoscopic description of reactions under anomalous diffusion: A case study
Reaction-diffusion equations deliver a versatile tool for the description of
reactions in inhomogeneous systems under the assumption that the characteristic
reaction scales and the scales of the inhomogeneities in the reactant
concentrations separate. In the present work we discuss the possibilities of a
generalization of reaction-diffusion equations to the case of anomalous
diffusion described by continuous-time random walks with decoupled step length
and waiting time probability densities, the first being Gaussian or Levy, the
second one being an exponential or a power-law lacking the first moment. We
consider a special case of an irreversible or reversible A ->B conversion and
show that only in the Markovian case of an exponential waiting time
distribution the diffusion- and the reaction-term can be decoupled. In all
other cases, the properties of the reaction affect the transport operator, so
that the form of the corresponding reaction-anomalous diffusion equations does
not closely follow the form of the usual reaction-diffusion equations
An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations
In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using Von-Neumann stability analysis. We have proved the method is unconditionally stable when and , and demonstrated the method is also stable numerically in the case and . The accuracy and convergence of the scheme was also investigated and found to be of order in time and in space. To confirm the accuracy and stability of the proposed method we provide three examples with one including a linear reaction term
Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
Extensive Monte-Carlo simulations were performed to evaluate the excess
number of clusters and the crossing probability function for three-dimensional
percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and
body-centered cubic (b.c.c.) lattices. Systems L x L x L' with L' >> L were
studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The
excess number of clusters per unit length was confirmed to be a
universal quantity with a value . Likewise, the
critical crossing probability in the L' direction, with periodic boundary
conditions in the L x L plane, was found to follow a universal exponential
decay as a function of r = L'/L for large r. Simulations were also carried out
to find new precise values of the critical thresholds for site percolation on
the f.c.c. and b.c.c. lattices, yielding , .Comment: 14 pages, 7 figures, LaTeX, submitted to J. Phys. A: Math. Gen, added
references, corrected typo
- …