Nekhoroshev theorem for the periodic Toda lattice

The periodic Toda lattice with $N$ sites is globally symplectomorphic to a two parameter family of $N-1$ coupled harmonic oscillators. The action variables fill out the whole positive quadrant of $\R^{N-1}$. We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space.Comment: 28 page

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Absolute instabilities of travelling wave solutions in a Keller-Segel model

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis

Physiological plant studies in South Africa Part I : wilting and osmotic phenomena of grasses and other plants under arid conditions

A description of the meteorological, tellurical, and edaphic features of a typical farm in the semi-arid region of Bechuanaland is given, and the osmotic behaviour of the local flora recorded. The differences between suction force of grasses and of plants other than grasses are recorded in relation to soil moisture, atmospheric humidity, rainfall, and insolation. The phenomenon of wilting is explained upon the basis of the osmotic gradient between root and leaf, withering commencing in most grasses, under the conditions of soil and climate investigated, when the difference exceeds 0.2 molar sucrose. The local grasses display no morphological mechanism for protection against drought and show enormous variations in osmotic values. The other plants which survive throughout the year display various protective devices of an anatomical and physiological nature, and are characterized by high suction force. Those for which the lifecycle is confined to the brief rainy season of summer show low values incapable of much variation. Quantitative protocols are compared with figures on European plants and with the very scanty data available for arid regions in other parts of the world.The articles have been scanned in colour with a HP Scanjet 5590; 300dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.ab202

The chlorophyll content of grasses in Bechuanaland

1. The chlorophyll-content of Bechuanaland grasses is not constant throughout the year, but varies from a very high initial value on young leaves, decreases according to the duration and intensity of drought periods, and increases again after rains. 2. Even during periods of twenty-four hours the chlorophyll-content varies greatly, decreasing from early morning to midday, and increasing again during the ensuing night. Decrease and increase depend upon meteorological factors ot the moment, so that on rainy days the variation lies within a few per cent., but on extremely dry and sunny days may extend to 30 per cent. 3. High nocturnal temperature favours a higher general chlorophyll-content throughout the day. Low nocturnal temperature is associated with low chlorophyll, even although the soil moisture is adequate. In both cases, however, chlorophyll destruction and chlorophyll synthesis are regarded as occurring concurrently, the actual content at any time representing the equilibrium between the two processes. 4. The values found in 1923-24 were higher than those found in 1924-25 owing to differences in nocturnal temperature in the two seasons. In the 1923 growing season the chlorophyll-content of the grasses of the Vryburg District was higher than that of European grasses; in the 1924 season about the same, or rather lower. Since the average chlorophyll-content is different in the two seasons, the data cannot be directly compared. What is termed a low value for 1923 would be high for 1924. Apart from nocturnal temperature, other factors, as yet uninvestigated, may play a role.Includes bibliographical referencesThe articles have been scanned in colour with a HP Scanjet 5590; 300dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.ab202

Mapping the phase diagram of strongly interacting matter

We employ a conformal mapping to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$. This method allows us to identify the singularity corresponding to the critical point of a second-order phase transition at finite $\mu$, given information only at $\mu=0$. The scheme is potentially useful for computing thermodynamic properties of strongly interacting hot and dense matter in lattice gauge theory. The technique is illustrated by an application to a chiral effective model.Comment: 5 pages, 3 figures; published versio

Global Birkhoff coordinates for the periodic Toda lattice

In this paper we prove that the periodic Toda lattice admits globally defined Birkhoff coordinates.Comment: 32 page

Spectral analysis and an area-preserving extension of a piecewise linear intermittent map

We investigate spectral properties of a 1-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius--Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius--Perron operator has two simple real eigenvalues 1 and $\lambda_d \in (-1,0)$, and a continuous spectrum on the real line $[0,1]$. From these spectral properties, we also found that this system exhibits power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.Comment: 12 pages, 3 figure

Phase transitions, double-scaling limit, and topological strings

Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q--deformed 2d Yang--Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2d gravity. We give strong evidence that there is a double--scaled theory at the critical point whose all genus free energy is governed by the Painlev\'e I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2d supergravity. We also give evidence for a new open/closed duality relating these Calabi--Yau backgrounds to open strings with framing.Comment: 49 pages, 3 eps figures; section added on non-perturbative proposal and 2d gravity; minor typos correcte