46 research outputs found
Two-dimensional perturbations in a scalar model for shear banding
We present an analytical study of a toy model for shear banding, without
normal stresses, which uses a piecewise linear approximation to the flow curve
(shear stress as a function of shear rate). This model exhibits multiple
stationary states, one of which is linearly stable against general
two-dimensional perturbations. This is in contrast to analogous results for the
Johnson-Segalman model, which includes normal stresses, and which has been
reported to be linearly unstable for general two-dimensional perturbations.
This strongly suggests that the linear instabilities found in the
Johnson-Segalman can be attributed to normal stress effects.Comment: 16 pages, 10 figures, to appear in EPJE, available online first,
click DOI or http://www.springerlink.com/content/q1q0187385017628
Driven translocation of a polymer: role of pore friction and crowding
Force-driven translocation of a macromolecule through a nanopore is
investigated by taking into account the monomer-pore friction as well as the
"crowding" of monomers on the {\it trans} - side of the membrane which
counterbalance the driving force acting in the pore. The set of governing
differential-algebraic equations for the translocation dynamics is derived and
solved numerically. The analysis of this solution shows that the crowding of
monomers on the trans side hardly affects the dynamics, but the monomer-pore
friction can substantially slow down the translocation process. Moreover, the
translocation exponent in the translocation time - vs. - chain length
scaling law, , becomes smaller when monomer-pore
friction coefficient increases. This is most noticeable for relatively strong
forces. Our findings may explain the variety of values which were
found in experiments and computer simulations.Comment: 12 page
Terminal sliding mode control for continuous stirred tank reactor
© 2014 The Institution of Chemical Engineers. A continuous stirred tank reactor (CSTR) is a typical example of chemical industrial equipment, whose dynamics represent an extensive class of second order nonlinear systems. It has been witnessed that designing a good control algorithm for the CSTR is very challenging due to the high complexity. The two difficult issues in CSTR control are state estimation and external disturbance attenuation. In general, in industrial process control a fast and robust response is essential. Driven by these challenging issues and desired performance, this paper proposes an output feedback terminal sliding mode control (TSMC) framework which is developed for CSTR, and can estimate the system states and stabilize the system output tracking error to zero in a finite time. The corresponding stability analysis is presented in terms of the Lyapunov method. Illustrative examples are demonstrated by using Matlab simulations to validate the effectiveness of the proposed approach
Interspecific competition shapes the structural stability of mutualistic networks
Mutualistic networks have attracted increasing attention in the ecological
literature in the last decades as they play a key role in the maintenance of
biodiversity. Here, we develop an analytical framework to study the structural
stability of these networks including both mutualistic and competitive
interactions. Analytical and numerical analyses show that the structure of the
competitive network fundamentally alters the necessary conditions for species
coexistence in communities. Using 50 real mutualistic networks, we show that
when the relative importance of shared partners is incorporated via weighted
competition, the feasibility area in the parameter space is highly correlated
with May's stability criteria and can be predicted by a functional relationship
between the number of species, the network connectance and the average
interaction strength in the community. Our work reopens a decade-long debate
about the complexity-stability relationship in ecological communities, and
highlights the role of the relative structures of different interaction types.Comment: 33 pages including main text, supplementary material and figures.
Submitted for publicatio