Stomatal patchiness of grapevine leaves .1. Estimation of non-uniform stomatal apertures by a new infiltration technique

Non-uniform stomatal behaviour of vine leaves is associated with a heterobaric leaf structure. A microscopical analysis of cross sections of glasshouse- and in vitro-grown Silvaner leaves indicates single airspaces which are pneumatically isolated by vessels, bundle sheath extensions and the abaxial and adaxial epidermes. A pressure-regulated infiltration technique is presented by which the infiltration process and the infiltration capacity (percentage of the surface area of infiltrated airspaces) can be estimated and photographed using a light microscope. The average surface area of airspaces ranged from 0.10 mm2 (Regent) to 0.14 mm2 (Silvaner), the number of stomata per airspace from 35 (Regent) to 42 (Silvaner). The infiltration capacity of turgid leaves is shown to be negatively correlated with the surface tension of the infiltrated liquid and positively with stomatal conductance and with infiltration pressure, except for very low stomatal conductances (e.g. 12 mmol H2O m-2 s-1). The latter relationship follows a saturation curve confirming heterogenous stomatal aperture over the leaf blade. The distribution of stomatal apertures does not appear to be bimodal but to follow a bell-shaped curve. There is some evidence for the stomata of an airspace to behave heterogenously as well

Stomatal patchiness of grapevine leaves. 2. Uncoordinated and coordinated stomatal movements

The dynamics of stomatal patchiness of grapevine leaves (var. Richter 110) were studied by in situ infiltration of water into the intercellular spaces (see: DÜRING and LOVEYS 1996). As infiltrations were shown not to affect stomatal conductance (g) a series of experiments was performed in which a leaf segment was infiltrated and photographed repeatedly. While stomata of some patches did not alter their apertures within a 90-minute experiment, others opened and closed their stomata more or less frequently leading to irregular fluctuations of patches with open, partly open and closed stomata. In contrast to this uncoordinated behavior coordinated, synchronous stomatal movements were recorded by gas exchange. Sinus wave-like stomatal oscillations with periods of 32-70 min and amplitudes of 38-95 mmol CO2 m-2 s-1 at constant ambient conditions were observed in a 12 h experiment. The stomatal oscillations were closely related to rhythmic alterations of the intercellular CO2 concentration (ci) and to the rate of CO2 assimilation (A). An increase of amplitudes of g was associated with a decrease of the carboxylation efficiency (A/ci) and the water use efficiency (A/g). It is concluded that uncoordinated, patchy fluctuations of stomatal apertures enable effective adaptation of single patches to changes of ambient stress factors

Low-dimensional chaos induced by frustration in a non-monotonic system

We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order-parameter equations. Then we analytically show that the chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that the chaos definitely does not occur without the frustration.Comment: 2 figure

Toward a microscopic description of flow near the jamming threshold

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that (i) the viscosity {\eta} diverges with the coordination z as {\eta} ~ (z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure

Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects

In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments

Generating functional analysis of CDMA detection dynamics

We investigate the detection dynamics of the parallel interference canceller (PIC) for code-division multiple-access (CDMA) multiuser detection, applied to a randomly spread, fully syncronous base-band uncoded CDMA channel model with additive white Gaussian noise (AWGN) under perfect power control in the large-system limit. It is known that the predictions of the density evolution (DE) can fairly explain the detection dynamics only in the case where the detection dynamics converge. At transients, though, the predictions of DE systematically deviate from computer simulation results. Furthermore, when the detection dynamics fail to convergence, the deviation of the predictions of DE from the results of numerical experiments becomes large. As an alternative, generating functional analysis (GFA) can take into account the effect of the Onsager reaction term exactly and does not need the Gaussian assumption of the local field. We present GFA to evaluate the detection dynamics of PIC for CDMA multiuser detection. The predictions of GFA exhibits good consistency with the computer simulation result for any condition, even if the dynamics fail to convergence.Comment: 14 pages, 3 figure

Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For over-damped flows, more observations are needed to decide if friction is a relevant perturbation or not. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.Comment: 13 pages + 3 pages S

Kinetic models for optimal control of wealth inequalities

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker-Planck based models and taxation-redistribution policies and the present approach are also discussed