456,587 research outputs found
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
Small-scale spatial structure in plankton distributions
International audienceThe observed filamental nature of plankton populations suggests that stirring plays an important role in determining their spatial structure. If diffusive mixing is neglected, the various interacting biological species within a fluid parcel are determined by the parcel time history. The induced spatial structure has been shown to be a result of competition between the time evolution of the biological processes involved and the stirring induced by the flow as measured, for example, by the rate of divergence of the distance of neighbouring fluid parcels. In the work presented here we examine a simple biological model based on delay-differential equations, previously seen in Abraham (1998) including nutrients, phytoplankton and zooplankton, coupled to a strain flow. Previous theoretical investigations made on a differential equation model (Hernández-Garcia et al., 2002) imply that the latter two should share the same small-scale structure. The generalization from differential equations to delay-differential equations, associated with the addition of a maturation time to the zooplankton growth, should not make a difference, provided sufficiently small spatial scales are considered. However, this theoretical prediction is in contradiction with the results of Abraham (1998) where the phytoplankton and zooplankton structures remain uncorrelated at all length scales. A new set of numerical experiments is performed here which show that these two regimes coexist. On larger scales , there is a decoupling of the spatial structure of the zooplankton distribution on the one hand, and the phytoplankton and nutrient on the other. On the other hand, at small enough length scales, the phytoplankton and zooplankton share the same spatial structure as expected by the theory involving no maturation time
Scale relativity and fractal space-time: theory and applications
In the first part of this contribution, we review the development of the
theory of scale relativity and its geometric framework constructed in terms of
a fractal and nondifferentiable continuous space-time. This theory leads (i) to
a generalization of possible physically relevant fractal laws, written as
partial differential equation acting in the space of scales, and (ii) to a new
geometric foundation of quantum mechanics and gauge field theories and their
possible generalisations. In the second part, we discuss some examples of
application of the theory to various sciences, in particular in cases when the
theoretical predictions have been validated by new or updated observational and
experimental data. This includes predictions in physics and cosmology (value of
the QCD coupling and of the cosmological constant), to astrophysics and
gravitational structure formation (distances of extrasolar planets to their
stars, of Kuiper belt objects, value of solar and solar-like star cycles), to
sciences of life (log-periodic law for species punctuated evolution, human
development and society evolution), to Earth sciences (log-periodic
deceleration of the rate of California earthquakes and of Sichuan earthquake
replicas, critical law for the arctic sea ice extent) and tentative
applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the
Evolution and Development of the Universe,8th - 9th October 2008, Paris,
Franc
Interacting Dark Energy and the Cosmic Coincidence Problem
The introduction of an interaction for dark energy to the standard cosmology
offers a potential solution to the cosmic coincidence problem. We examine the
conditions on the dark energy density that must be satisfied for this scenario
to be realized. Under some general conditions we find a stable attractor for
the evolution of the Universe in the future. Holographic conjectures for the
dark energy offer some specific examples of models with the desired properties.Comment: 8 pages, 3 figures, Phys. Rev. D versio
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