A Handheld low-mass, impact instrument to measure nondestructive firmness of fruit

A portable, handheld impact firmness sensor was designed for nondestructive measurement of fruit firmness while the fruit remain attached to the tree or for use in other remote locations where the use of a benchtop instrument would be impractical. The instrument design was based on the low-mass, constant velocity, impact-type measurement concept. Validation tests of the handheld sensor using `Bartlett' pears from orchards in California and Washington showed excellent agreement (r2 = 0.92 and 0.96, respectively) with both ASAE Standard method S368.2 for determining the apparent modulus of intact fruit and the impact firmness scores from a commercial benchtop impact firmness instrument

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

On conformal measures and harmonic functions for group extensions

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.Comment: To appear in Proceedings of "New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo

Equilibrium states and invariant measures for random dynamical systems

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a consistency conditions for such systems, which admit some proper Markov partitions of connected spaces, are introduced, and further sufficient conditions for them are provided. It is shown that every uniformly continuous Markov system associated with a continuous random dynamical system is consistent if it has a dominating Markov chain. A necessary and sufficient condition for the existence of an invariant Borel probability measure for such a non-degenerate system with a dominating Markov chain and a finite (16) is given. The condition is also sufficient if the non-degeneracy is weakened with the consistency condition. A further sufficient condition for the existence of an invariant measure for such a consistent system which involves only the properties of the dominating Markov chain is provided. In particular, it implies that every such a consistent system with a finite Markov partition and a finite (16) has an invariant Borel probability measure. A bijective map between these measures and equilibrium states associated with such a system is established in the non-degenerate case. Some properties of the map and the measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on page 4 (the complete removal of the paragraph became the condition for the publication in the DCDS-A after the reviewer ran out of the citation suggestions collected in the paragraph

Renormalisation-induced phase transitions for unimodal maps

The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential $-t \log|Df|$. Multiple and indeed infinitely many phase transitions at positive $t$ can occur for some quadratic maps. All unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum.Comment: 14 pages, 2 figures. Revised following comments of referees. First page is blan

Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Statistical stability of equilibrium states for interval maps

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto-t\log|Df(x)|$, for $t$ close to 1. We show that these equilibrium states vary continuously in the weak$^*$ topology within such families. Moreover, in the case $t=1$, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.Comment: More details given and the appendices now incorporated into the rest of the pape

Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

The Lyapunov spectrum is not always concave

We characterize one-dimensional compact repellers having nonconcave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra