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 $\alpha$ in the translocation time - vs. - chain length scaling law, $\tau \propto N^{\alpha}$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $\alpha$ 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