Hydrodynamics from kinetic models of conservative economies

In this paper, we introduce and discuss the passage to hy- drodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The collision operator used here is the Fokker-Planck operator introduced by J.P. Bouchaud and M. Mezard in [4], which has been recently obtained in a suitable asymp- totic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [11]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.Wealth and income distributions, Boltzmann equation, hy- drodynamics, Euler equations

Structure and function of grapevine leaves (Vitis vinifera L.) as affected by the European red mite (Panonychus ulmi KOCH)

Strukturelle und funktionelle Veränderungen an den Blättern der Rebe ( Vitisvinifera L.) unter dem Einfluß der Obstbaumspinnmilbe (Panonychus ulmi KOCH)Die durch Panonychus ulmi verursachte Schädigung der Blätter von Vitis vinifera-Sorten wurde untersucht:In den befallenen Blättern wurden histologische Veränderungen an Zellen der unteren und oberen Epidermis und im Schwamm- und Palisadenparenchym festgestellt. Die Schädigung reichte vom Abbau der Zellorganenellen bis zur vollständigen Zerstörung von Zellen, so daß im Mesophyllgewebe nekrotische Hohlräume entstanden.Die Häufigkeit und Ausdehnung dieser Nekrosen nahm mit dem Grad der Blattverfärbung durch Spinnmilbenbefall ("Bronzierung") zu.Der Chlorophyllgehalt der befallenen Blätter verringerte sich mit fortschreitender Blattverfärbung.Befallene Blätter zeigten mit zunehmender Blattverfärbung sowohl unter natürlichen wie konstanten Umweltbedingungen einen Rückgang der stomatären Leitfähigkeit, Photosynthese und Transpiration.Signifikante negative Korrelationen zwischen dem Grad der Blattverfärbung und dem Chlorophyllgehalt sowie den oben genannten Parametern des Gaswechsels bestätigten die Brauchbarkeit eines auf visueller Bonitur beruhenden Klassifzierungssystems (RILLING 1989), das für die Selektion spinnmilbentoleranter Reben vorgeschlagen wurde

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

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

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

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

Einfluß der Photoperiode auf Wachstum und Abscisinsäuregehalt der Rebe

In Abhängigkeit von photoperiodischen Einflüssen (Kurztag, Störlicht, Langtag, Dauerlicht) wurde die Entwicklung des Längenwachstums und die der ABS-Gehalte in Blättern und Sproßachsen zweier Sorten (Müller-Thurgau, A-100-3) untersucht. Ein neunstündiger Kurztag ließ die Pflanzen beider Sorten bereits nach 10 Tagen in einen Zustand der Wachstumsruhe übergehen. Die ABS-Gehalte der Laubblätter unterschieden sich hierbei nicht nennenswert von denen der Langtagvariante, die nur geringfügig zunahmen, wohingegen die Werte der Sproßachsen nach Kurztagbehandlung bei Müller-Thurgau kontinuierlich, bei der Neuzucht A-100-3 progressiv zunahmen. Die vorliegenden Befunde lassen einen Transport der ABS aus den Blättern in die Sproßachsen vermuten, wo die ABS nach Erreichen einer bestimmten Konzentration an der Induktion der Dormanz beteiligt ist. Eine Störlichtbehandlung förderte das Wachstum ähnlich wie Dauerlicht. Auch Störlicht und Dauerlicht ließen in den Blättern keine signifikanten Abweichungen der ABS-Werte von denen der Langtagvariante erkennen, doch zeigten die Sproßachsen beider Varianten bedeutend geringere ABS-Zunahmen als die Langtagvariante. Aus den Ergebnissen geht hervor, daß eine Verkürzung (Langtag), Unterbrechung (Störlicht) oder Aufhebung (Dauerlicht) der Dunkelphase sich deutlich vermindernd auf den ABS-Gehalt der Sproßachsen auswirkt, wodurch die Auffassung, daß es sich um einen photosensiblen Hemmstoff handelt, bekräftigt wird. Influence of photoperiodism on growth and abscisic acid content in grape-vines Taking into account the photoperiodical influences of short day (SD), light interrupted SD, long day (LD) and permanent light (PL), the development of longitudinal growth and the ABA content of leaves and shoots of the two cultivars Milller-Thurgau and A-100-3 were investigated. After being subjected to a 9 hour SD over a period of 10 days both cultivars passed into a state of dormancy. The leaves of these plants showed no noticeable differences in ABA content compared to the LD plants, which had a negligeable increase. On the other hand, the ABA content of the shoots increased continually after an SD treatment in the Milller-Thurgau cv. and progressively in the newbreed A-100-3. It is suggested that ABA is transported from the leaves to the shoots, where, once the ABA achieves a certain concentration, it probably contributes to the induction of dormancy. A light interrupted SD-treatment stimulated growth in a similar manner as a PL treatment. After both treatments no significant differences were observed in the ABA content of the leaves compared to the LD-treated plants. However, in the shoots of light interrupted SD and LD treated plants, a significantly smaller ABA increase was observed when compared to the LD treated plants. It is seen from the results that a shortening (LD), an interruption (light interrupted SD), or a removal (PL) of the dark period has a distinctly decreasing effect on the ABA content of the shoots, which corroborates the opinion that ABA is a photosensitive inhibitor