Steady flow in a deformable porous medium

A nonlinear model for a steady flow in a deformable porous medium is considered. The flow is governed by the poroelasticity system consisting of an elasticity equation for the displacement of the porous medium and Darcy's equation for the pressure in the fluid. This poroelasticity system is nonlinear when the permeability in Darcy's equation is assumed to depend on the dilatation of the porous medium. Existence and uniqueness of a weak solution of this poroelasticity system is established under rather weak assumptions on the regularity of the data. Convergence of a finite element approximation is proved and verified through numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite state bilaterally deterministic strongly mixing processes

Triviality of the two-sided tail field of a stationary process is not an invariant property under factorization ([4]). In this paper we give an example of a bilaterally deterministic process with finitely many states which is strongly mixing. This extends and complements a result of Bradley ([1]).     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Many symmetrically indivisible structures

A structure in a first‐order language is indivisible if for every colouring of its universe M in two colours, there is a monochromatic such that . Additionally, we say that is symmetrically indivisible if can be chosen to be symmetrically embedded in (that is, every automorphism of can be extended to an automorphism of ). In the following paper we give a general method for constructing new symmetrically indivisible structures out of existing ones. Using this method, we construct many non‐isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from 6 : Let be a symmetrically indivisible structure in a language . Let . Is symmetrically indivisible?     

Sortin1-hypersensitive mutants link vacuolar-trafficking defects and flavonoid metabolism in Arabidopsis vegetative tissues

Sortin1 is a chemical genetic-hit molecule that causes specific mislocalization of plant and yeast-soluble and membrane vacuolar markers. To better understand its mode of action, we designed a Sortin1-hypersensitive screen and identified several Sortin1-hypersensitive and flavonoid-defective mutants. Mechanistically, Sortin1 mimics the effect of the glutathione inhibitor buthionine sulfoximine and alters the vacuolar accumulation of flavonoids, likely blocking their transport through vacuole-localized ABC transporters. Structure-activity relationship studies conducted in Arabidopsis revealed the structural requirements for Sortin1 bioactivity and demonstrated that overlapping Sortin1 substructures can be used to discriminate between vacuolar-flavonoid accumulations and vacuolar-biogenesis defects. We conclude that Sortin1 is a valuable probe for dissecting novel links among flavonoid transport, vacuolar integrity, and the trafficking of vacuolar targeted cargoes in Arabidopsis.     

Data compression and prediction in neural networks

We study the relationship between data compression and prediction in single-layer neural networks of limited complexity. Quantifying the intuitive notion of Occam's razor using Rissanen's minimum complexity framework, we investigate the model-selection criterion advocated by this principle. While we find that the criterion works well for large sample sizes (as it must for consistency), the behavior for finite sample sizes is rather complex, depending intricately on the relationship between the complexity of the hypothesis space and the target space. We also show that the limited networks studied perform efficient data compression, even in the error full regime.     

Processes with no standard extension

Using an example of A. Vershik, a class of processes is introduced with the property that they do not admit astandard extension. This provides a simple proof that Vershik's example process does not admit a standard extension. Supported in part by The Israel Science Foundation.     

Adaptive optics for airborne platforms—Part 1: modeling

Adaptive optics systems mitigate the atmospheric turbulence-induced distortion of a propagating light wavefront. The use of adaptive optics entails the design of a feedback controller, which requires the development of a model of the plant to be controlled. In adaptive optics, the plant consists of the atmosphere through which light is traveling. Moreover, a distinct feature of the adaptive optics control application is the presence of random signals in the plant. In optics, Zernike orthonormal polynomials are commonly used as a basis set for the expansion of wavefront phase distortions. Due to the atmospheric turbulence-induced random nature of the underlying physical process, the spatial-temporal correlation functions of the Zernike polynomial phase distortion expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In Part 1 of this paper, these correlation functions are developed using a layered atmospheric model and calculations for the first few low-order Zernike modes are performed. Using these correlation functions, an underlying stochastic linear dynamical system, which is adequate for control design, is synthesized. This system models the plant and, in turn, provides the basis for the employment of advanced model-based control and estimation concepts in an adaptive optics system for an airborne platform application.     

On random mapping patterns

Random mapping patterns may be represented by unlabelled directed graphs in which each point has out-degree one. We determine the asymptotic behaviour of various parameters associated with such graphs, such as the expected number of points belonging to cycles and the expected number of components. Dedicated to Paul Erdős on his seventieth birthday