Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

A classification methodology for the risk of weed infestation using fuzzy logic

Despite modern weed control practices, weeds continue to be a threat to agricultural production. Considering the variability of weeds, a classification methodology for the risk of infestation in agricultural zones using fuzzy logic is proposed. The inputs for the classification are attributes extracted from estimated maps for weed seed production and weed coverage using kriging and map analysis and from the percentage of surface infested by grass weeds, in order to account for the presence of weed species with a high rate of development and proliferation. The output for the classification predicts the risk of infestation of regions of the field for the next crop. The risk classification methodology described in this paper integrates analysis techniques which may help to reduce costs and improve weed control practices. Results for the risk classification of the infestation in a maize crop field are presented. To illustrate the effectiveness of the proposed system, the risk of infestation over the entire field is checked against the yield loss map estimated by kriging and also with the average yield loss estimated from a hyperbolic model.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

The critical power function is dependent on the duration of the predictive exercise tests chosen

The linear relationship between work accomplished (W-lim) and time to exhaustion (t(lim)) can be described by the equation: W-lim = a + CP.t(lim). Critical power (CP) is the slope of this line and is thought to represent a maximum rate of ATP synthesis without exhaustion, presumably an inherent characteristic of the aerobic energy system. The present investigation determined whether the choice of predictive tests would elicit significant differences in the estimated CP. Ten female physical education students completed, in random order and on consecutive days, five art-out predictive tests at preselected constant-power outputs. Predictive tests were performed on an electrically-braked cycle ergometer and power loadings were individually chosen so as to induce fatigue within approximately 1-10 mins. CP was derived by fitting the linear W-lim-t(lim) regression and calculated three ways: 1) using the first, third and fifth W-lim-t(lim) coordinates (I-135), 2) using coordinates from the three highest power outputs (I-123; mean t(lim) = 68-193 s) and 3) using coordinates from the lowest power outputs (I-345; mean t(lim) = 193-485 s). Repeated measures ANOVA revealed that CPI123 (201.0 +/- 37.9W) > CPI135 (176.1 +/- 27.6W) > CPI345 (164.0 +/- 22.8W) (P < 0.05). When the three sets of data were used to fit the hyperbolic Power-t(lim) regression, statistically significant differences between each CP were also found (P < 0.05). The shorter the predictive trials, the greater the slope of the W-lim-t(lim) regression; possibly because of the greater influence of 'aerobic inertia' on these trials. This may explain why CP has failed to represent a maximal, sustainable work rate. The present findings suggest that if CP is to represent the highest power output that an individual can maintain for a very long time without fatigue then CP should be calculated over a range of predictive tests in which the influence of aerobic inertia is minimised.

Bishadowing and hyperbolicity

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

Calorimetric demonstration of the potential of molecular crowding to emulate the effect of an allosteric activator on pyruvate kinase kinetics

A method based on isothermal calorimetry is described for the direct kinetic assay of pyruvate kinase. In agreement with earlier findings based on the standard coupled assay system for this enzyme in the presence of a fixed ADP concentration, the essentially rectangular hyperbolic dependence of initial velocity upon phosphoenolpyruvate concentration is rendered sigmoidal by the allosteric inhibitor phenylalanine. This effect of phenylalanine can be countered by including a high concentration of a space- filling osmolyte such as proline in the reaction mixtures. This investigation thus affords a dramatic example that illustrates the need to consider potential consequences of thermodynamic nonideality on the kinetics of enzyme reactions in crowded molecular environments such as the cell cytoplasm.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

The thickness of the transport layer in stratified geomorphic flows

River Flow 2010

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.