The mean velocity of two-state models of molecular motor

The motion of molecular motor is essential to the biophysical functioning of living cells. In principle, this motion can be regraded as a multiple chemical states process. In which, the molecular motor can jump between different chemical states, and in each chemical state, the motor moves forward or backward in a corresponding potential. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping models or by several coupled Fokker-Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest cases: in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, we find that the mean velocity of molecular motor might be nonzero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is energy input to the molecular motor. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two states, but also on the transition rates between the two chemical states

Increasing safe design practice within the engineering curriculum

CONTEXT The Australian Work Health and Safety Strategy 2012-2022 contains two national Action Areas of direct relevance to Engineering Educators: Healthy and safe by design and Health and safety capabilities. The need for designs to be safe, and for student engineers to develop competencies in this area, is not new. However, poor design of machinery plant and powered tools continues to kill and injure Australian workers. Safe Work Australia (2014) reports that between 2006 and 2011, 63 workrelated deaths were determined to be caused by the unsafe design of machinery plant and power tools, or design-related factors contributed to the fatality. A further 125 fatalities were considered as possibly design-related. It is sad fact that many of these deaths were preventable with existing design solutions. Good design can eliminate (or minimise the impact of) the major physical, biomechanical and psychosocial hazards associated with work. From an engineering education perspective it is necessary to increase awareness amongst educators and students of these processes such that consideration of safe design is inherent to the engineering design process and not simply an added regulatory requirement. PURPOSE Safe design is not a separate activity or series of activities, but is integral to the engineering process regardless of sector or discipline. This paper reviews the role of engineering educators in understanding, promoting and embedding safe design principles within the engineering curricula. APPROACH The paper explores how safe design has been incorporated into engineering education since the early 1990s, and assesses the effectiveness of available resources and teaching practice. Changes to the legislative environment throughout this time are also described, to provide context and articulate implications for engineering educators. RESULTS The importance of safe design is recognised and resources do exist to support engineering educators to embed safe design principles within curriculum. The paper provides a series of recommendations to mainstream the available resources, highlights characteristics of effective practice and identifies areas for further professional development of engineering educators who are not familiar with safe design principles. CONCLUSIONS In order to develop graduates who are safe design practitioners, the model of engineering design introduced within the engineering curriculum must demonstrate that safe design is an inherent user requirement for all projects. This requires engineering educators to be familiar with human centred engineering design and how this impacts traditional technical design outcomes.Bernadette Foley, Prue Howard, Yvonne Toft and Mike Hur

Density classification on infinite lattices and trees

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations

Direct Simulation of the Sedimentation of Elliptic Particles in Oldroyd-B Fluids

Cross stream migration and stable orientations of elliptic particles falling in an Oldroyd-B fluid in a channel are studied. We show that the normal component of the extra stress on a rigid body vanishes; lateral forces and torques are determined by the pressure. Inertia turns the longside of the ellipse across the stream and elasticity turns it along the stream; tilted off-center falling is unstable. There are two critical numbers; elasticity and Mach numbers. When the elasticity number is smaller than critical the fluid is essentially Newtonian with broadside-on falling at the centerline of the channel. For larger elasticity numbers the settling turns the longside of the particle along the stream in the channel center for all velocities below a critical one, identified with a critical Mach number of order one. For larger Mach numbers the ellipse flips into broadside-on falling again. The critical numbers are functions of the channel blockage ratio, the particle aspect ratio and the retardation/relaxation time ratio of the fluid. Two ellipses falling nearby, attract, line-up and straighten-out in a long chain of ellipses with longside vertical, all in a row. Stable, off-center tilting is found for ellipses falling in shear thinning fluids and for cylinders with flat ends in which particles tend align their longest diameter with gravity

Generic phase diagram of active polar films

We study theoretically the phase diagram of compressible active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations, we perform a linear stability analysis of the uniform states in the case of an infinite bidimensional active gel to obtain the dynamic phase diagram of active polar films. We predict in particular modulated flowing phases, and a macroscopic phase separation at high activity. This qualitatively accounts for experimental observations of various active systems, such as acto-myosin gels, microtubules and kinesins in vitro solutions, or swimming bacterial colonies.Comment: 4 pages, 1 figur

Direct Simulation of the Motion of Solid Particles in Couette and Poiseuille Flows of Viscoelastic Fluids

This paper reports the results of direct numerical simulation of the motion of a two-dimensional circular cylinder in Couette flow and in Poiseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and non-neutrally buoyant cylinders are considered. The cylinder\u27s motion and the mechanisms which cause the cylinders to migrate are studied. The stable equilibrium position of neutrally buoyant particles varies with inertia, elasticity, shear thinning and the blockage ratio of the channel in both shear flows. Shear thinning promotes the migration of the cylinder to the wall while inertia causes the cylinder to migrate away from the wall. The cylinder moves closer to the wall in a narrower channel. In a Poiseuille flow, the effect of elastic normal stresses is manifested by an attraction toward the nearby wall if the blockage is strong. If the blockage is weak, the normal stresses act through the curvature of the inflow velocity profile and generate a lateral force that points to the centreline. In both cases, the migration of particles is controlled by elastic normal stresses which in the limit of slow flow in two dimensions are compressive and proportional to the square of the shear rate on the body. A slightly buoyant cylinder in Couette flow migrates to an equilibrium position nearer the centreline of the channel in a viscoelastic fluid than in a Newtonian fluid. On the other hand, the same slightly buoyant cylinder in Poiseuille flow moves to a stable position farther away from the centreline of the channel in a viscoelastic fluid than in a Newtonian fluid. Marked effects of shear thinning are documented and discussed

Atomic scale engines: Cars and wheels

We introduce a new approach to build microscopic engines on the atomic scale that move translationally or rotationally and can perform useful functions such as pulling of a cargo. Characteristic of these engines is the possibility to determine dynamically the directionality of the motion. The approach is based on the transformation of the fed energy to directed motion through a dynamical competition between the intrinsic lengths of the moving object and the supporting carrier.Comment: 4 pages, 3 figures (2 in color), Phys. Rev. Lett. (in print

The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase transition will appear at zero branching rate limit belonging to the same universality class as that of the dynamical two-offspring (2-BARW2) model. This class persists even if the branching is biased towards one of the species. If the two systems are not coupled by branching but hard-core interaction is allowed only the transition will occur at finite branching rate belonging to the usual 1+1 dimensional directed percolation class.Comment: 3 pages, 3 figures include