4,232 research outputs found
Dynamics of Patterns
Patterns and nonlinear waves arise in many applications. Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle systems, time-delayed systems, and numerical analysis. This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction
Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
Steady states and traveling waves play a fundamental role in understanding
hydrodynamic problems. Even when unstable, these states provide the
bifurcation-theoretic explanation for the origin of the observed states. In
turbulent wall-bounded shear flows, these states have been hypothesized to be
saddle points organizing the trajectories within a chaotic attractor. These
states must be computed with Newton's method or one of its generalizations,
since time-integration cannot converge to unstable equilibria. The bottleneck
is the solution of linear systems involving the Jacobian of the Navier-Stokes
or Boussinesq equations. Originally such computations were carried out by
constructing and directly inverting the Jacobian, but this is unfeasible for
the matrices arising from three-dimensional hydrodynamic configurations in
large domains. A popular method is to seek states that are invariant under
numerical time integration. Surprisingly, equilibria may also be found by
seeking flows that are invariant under a single very large Backwards-Euler
Forwards-Euler timestep. We show that this method, called Stokes
preconditioning, is 10 to 50 times faster at computing steady states in plane
Couette flow and traveling waves in pipe flow. Moreover, it can be carried out
using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes
to these popular spectral codes. We explain the convergence rate as a function
of the integration period and Reynolds number by computing the full spectra of
the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid
Dynamics, ed. Alexander Gelfgat (Springer, 2018
Statistical Physics of Vehicular Traffic and Some Related Systems
In the so-called "microscopic" models of vehicular traffic, attention is paid
explicitly to each individual vehicle each of which is represented by a
"particle"; the nature of the "interactions" among these particles is
determined by the way the vehicles influence each others' movement. Therefore,
vehicular traffic, modeled as a system of interacting "particles" driven far
from equilibrium, offers the possibility to study various fundamental aspects
of truly nonequilibrium systems which are of current interest in statistical
physics. Analytical as well as numerical techniques of statistical physics are
being used to study these models to understand rich variety of physical
phenomena exhibited by vehicular traffic. Some of these phenomena, observed in
vehicular traffic under different circumstances, include transitions from one
dynamical phase to another, criticality and self-organized criticality,
metastability and hysteresis, phase-segregation, etc. In this critical review,
written from the perspective of statistical physics, we explain the guiding
principles behind all the main theoretical approaches. But we present detailed
discussions on the results obtained mainly from the so-called
"particle-hopping" models, particularly emphasizing those which have been
formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include
A Methodology Towards Comprehensive Evaluation of Shape Memory Alloy Actuators for Prosthetic Finger Design
Presently, DC motors are the actuator of choice within intelligent upper limb prostheses. However, the weight and dimensions associated with suitable DC motors are not always compatible with the geometric restrictions of a prosthetic hand; reducing available degrees of freedom and ultimately rendering the prosthesis uncomfortable for the end-user. As a result, the search is on-going to find a more appropriate actuation solution that is lightweight, noiseless, strong and cheap. Shape memory alloy (SMA) actuators offer the potential to meet these requirements. To date, no viable upper limb prosthesis using SMA actuators has been developed. The primary reasons lie in low force generation as a result of unsuitable actuator designs, and significant difficulties in control owing to the highly nonlinear response of SMAs when subjected to joule heating. This work presents a novel and comprehensive methodology to facilitate evaluation of SMA bundle actuators for prosthetic finger design. SMA bundle actuators feature multiple SMA wires in parallel. This allows for increased force generation without compromising on dynamic performance. The SMA bundle actuator is tasked with reproducing the typical forces and contractions associated with the human finger in a prosthetic finger design, whilst maintaining a high degree of energy efficiency. A novel approach to SMA control is employed, whereby an adaptive controller is developed and tuned using the underlying thermo-mechanical principles of operation of SMA wires. A mathematical simulation of the kinematics and dynamics of motion provides a platform for designing, optimizing and evaluating suitable SMA bundle actuators offline. This significantly reduces the time and cost involved in implementing an appropriate actuation solution. Experimental results show iii that the performance of SMA bundle actuators is favourable for prosthesis applications. Phalangeal tip forces are shown to improve significantly through bundling of SMA wire actuators, while dynamic performance is maintained owing to the design and implementation of the selected control strategy. The work is intended to serve as a roadmap for fellow researchers seeking to design, implement and control SMA bundle actuators in a prosthesis design. Furthermore, the methodology can also be adopted to serve as a guide in the evaluation of other non-conventional actuation technologies in alternative applications
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