13 research outputs found
Discrete cilia modelling with singularity distributions
We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous âsingularity modelsâ is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a âposterior tilt,â and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 ÎŒm/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this technique to various other biological problems, particularly in the reproductive system
Effective interaction between helical bio-molecules
The effective interaction between two parallel strands of helical
bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using
computer simulations of the "primitive" model of electrolytes. In particular we
study a simple model for B-DNA incorporating explicitly its charge pattern as a
double-helix structure. The effective force and the effective torque exerted
onto the molecules depend on the central distance and on the relative
orientation. The contributions of nonlinear screening by monovalent counterions
to these forces and torques are analyzed and calculated for different salt
concentrations. As a result, we find that the sign of the force depends
sensitively on the relative orientation. For intermolecular distances smaller
than it can be both attractive and repulsive. Furthermore we report a
nonmonotonic behaviour of the effective force for increasing salt
concentration. Both features cannot be described within linear screening
theories. For large distances, on the other hand, the results agree with linear
screening theories provided the charge of the bio-molecules is suitably
renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog
Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emerge
Coalescence-fragmentation problems are of great interest across the physical,
biological, and recently social sciences. They are typically studied from the
perspective of the rate equations, at the heart of such models are the rules
used for coalescence and fragmentation. Here we discuss how changes in these
microscopic rules affect the macroscopic cluster-size distribution which
emerges from the solution to the rate equation. More generally, our work
elucidates the crucial role that the fragmentation rule can play in such
dynamical grouping models. We focus on two well-known models whose
fragmentation rules lie at opposite extremes setting the models within the
broader context of binary coalescence-fragmentation models. Further, we provide
a range of generalizations and new analytic results for a well-known model of
social group formation [V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett.
85, 5659 (2000)]. We develop analytic perturbation treatment of the original
model, and extend the mathematical to the treatment of growing and declining
populations
WORKFARE IN THE 1980s: SUCCESSES AND LIMITS
Between 1981 and 1987 twenty-eight states experimented with workfare programs. By requiring mandatory community service from welfare recipients, the states hoped to reduce welfare caseloads as well as increase community service. Based in part on those program experiences, Congress included the first national workfare requirement in the 1988 welfare reform package (the Family Support Act). This study is the first to attempt to evaluate the implementation and impact of workfare on a national basis. A pooled, cross-section, longitudinal model is used to estimate the effect of workfare on AFDC caseloads. Despite the low level of state-level implementation, the evidence suggests that workfare may have contributed to welfare caseload reductions in the 1980s. Copyright 1990 by The Policy Studies Organization.