10,851 research outputs found
The power dissipation method and kinematic reducibility of multiple-model robotic systems
This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems
High-order myopic coronagraphic phase diversity (COFFEE) for wave-front control in high-contrast imaging systems
The estimation and compensation of quasi-static aberrations is mandatory to
reach the ultimate performance of high-contrast imaging systems. COFFEE is a
focal plane wave-front sensing method that consists in the extension of phase
diversity to high-contrast imaging systems. Based on a Bayesian approach, it
estimates the quasi-static aberrations from two focal plane images recorded
from the scientific camera itself. In this paper, we present COFFEE's extension
which allows an estimation of low and high order aberrations with nanometric
precision for any coronagraphic device. The performance is evaluated by
realistic simulations, performed in the SPHERE instrument framework. We develop
a myopic estimation that allows us to take into account an imperfect knowledge
on the used diversity phase. Lastly, we evaluate COFFEE's performance in a
compensation process, to optimize the contrast on the detector, and show it
allows one to reach the 10^-6 contrast required by SPHERE at a few resolution
elements from the star. Notably, we present a non-linear energy minimization
method which can be used to reach very high contrast levels (better than 10^-7
in a SPHERE-like context)Comment: Accepted in Optics Expres
A simple and efficient BEM implementation of quasistatic linear visco-elasticity
A simple, yet efficient procedure to solve quasistatic problems of special
linear visco-elastic solids at small strains with equal rheological response in
all tensorial components, utilizing boundary element method (BEM), is
introduced. This procedure is based on the implicit discretisation in time (the
so-called Rothe method) combined with a simple "algebraic" transformation of
variables, leading to a numerically stable procedure (proved explicitly by
discrete energy estimates), which can be easily implemented in a BEM code to
solve initial-boundary value visco-elastic problems by using the Kelvin
elastostatic fundamental solution only. It is worth mentioning that no inverse
Laplace transform is required here. The formulation is straightforward for both
2D and 3D problems involving unilateral frictionless contact. Although the
focus is to the simplest Kelvin-Voigt rheology, a generalization to Maxwell,
Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and
implemented in the BEM code too. A few 2D and 3D initial-boundary value
problems, one of them with unilateral frictionless contact, are solved
numerically
Quantitative analysis of Clausius inequality
In the context of driven diffusive systems, for thermodynamic transformations
over a large but finite time window, we derive an expansion of the energy
balance. In particular, we characterize the transformations which minimize the
energy dissipation and describe the optimal correction to the quasi-static
limit. Surprisingly, in the case of transformations between homogeneous
equilibrium states of an ideal gas, the optimal transformation is a sequence of
inhomogeneous equilibrium states.Comment: arXiv admin note: text overlap with arXiv:1404.646
The maximum efficiency of nano heat engines depends on more than temperature
Sadi Carnot's theorem regarding the maximum efficiency of heat engines is
considered to be of fundamental importance in thermodynamics. This theorem
famously states that the maximum efficiency depends only on the temperature of
the heat baths used by the engine, but not on the specific structure of baths.
Here, we show that when the heat baths are finite in size, and when the engine
operates in the quantum nanoregime, a revision to this statement is required.
We show that one may still achieve the Carnot efficiency, when certain
conditions on the bath structure are satisfied; however if that is not the
case, then the maximum achievable efficiency can reduce to a value which is
strictly less than Carnot. We derive the maximum efficiency for the case when
one of the baths is composed of qubits. Furthermore, we show that the maximum
efficiency is determined by either the standard second law of thermodynamics,
analogously to the macroscopic case, or by the non increase of the max relative
entropy, which is a quantity previously associated with the single shot regime
in many quantum protocols. This relative entropic quantity emerges as a
consequence of additional constraints, called generalized free energies, that
govern thermodynamical transitions in the nanoregime. Our findings imply that
in order to maximize efficiency, further considerations in choosing bath
Hamiltonians should be made, when explicitly constructing quantum heat engines
in the future. This understanding of thermodynamics has implications for
nanoscale engineering aiming to construct small thermal machines.Comment: Main text 14 pages. Appendix 60 pages. Accepted in Journal Quantu
High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
Phase-field approaches to fracture based on energy minimization principles
have been rapidly gaining popularity in recent years, and are particularly
well-suited for simulating crack initiation and growth in complex fracture
networks. In the phase-field framework, the surface energy associated with
crack formation is calculated by evaluating a functional defined in terms of a
scalar order parameter and its gradients, which in turn describe the fractures
in a diffuse sense following a prescribed regularization length scale. Imposing
stationarity of the total energy leads to a coupled system of partial
differential equations, one enforcing stress equilibrium and another governing
phase-field evolution. The two equations are coupled through an energy
degradation function that models the loss of stiffness in the bulk material as
it undergoes damage. In the present work, we introduce a new parametric family
of degradation functions aimed at increasing the accuracy of phase-field models
in predicting critical loads associated with crack nucleation as well as the
propagation of existing fractures. An additional goal is the preservation of
linear elastic response in the bulk material prior to fracture. Through the
analysis of several numerical examples, we demonstrate the superiority of the
proposed family of functions to the classical quadratic degradation function
that is used most often in the literature.Comment: 33 pages, 30 figure
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