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

Stomatal patchiness of field-grown sultana leaves: Diurnal changes and light effects

Unirrigated, field-grown Sultana vines were used to study diurnal changes of stomatal patchiness under the natural ambient conditions of South Australia. Non-homogenous aperture of stomata (patchiness) was determined by an infiltration technique and by counting infiltrated patches. Stomatal conductance was linearly related to the number of patches with open stomata (r2 = 0.622). Both parameters increased in the early morning (maxima at 8 a.m.) and decreased thereafter. In the afternoon stomatal conductance and the number of patches with open stomata remained at a low level. When dark adapted leaves were exposed to sun light (900 -1000 mu mol quanta . m-2 . s-1) the number of patches with open stomata increased from 23 to 143 cm-2 within 15 min, indicating that besides several stress factors light induces non-homogenous stomatal opening. It is assumed that stomatal action of single patches is autonomous, i.e. stomata of single patches will regulate water loss and CO2 uptake according to local changes of ambient and endogenous conditions

Diurnal changes in water relations and abscisic acid in field grown Vitis vinifera cvs. I. Leaf water potential components and leaf conductance under humid temperate and semiarid conditions

Diurnal changes of water potential (Ψw) and its components (Ψs, Ψp) and leaf conductance were analysed under the humid temperate climate of Germany (Geilweilerhof) and the semiarid climate of South Australia (Adelaide) comparing the two cultivars, Riesling and Silvaner, which appear to differ in their adaptation to drought.At Geilweilerhof predawn water potential was close to 0 and leaf conductance very low. Stomata opened during the morning as light intensity and temperature increased. At 3 p. m. stomata started to close, leaf conductance declining earlier in Silvaner than in Riesling. Ψw of Silvaner was slightly lower during the day than that of Riesling except during the late afternoon.Under the semiarid conditions of Adelaide predawn Ψw. was -6 bar (Riesling) and -7bar (Silvaner); it decreased rapidly to -14 bar (Riesling) and -16 bar (Silvaner) at 10 a. m.; leaf conductance at thattime had reached its maximum which in Riesling was distinctly higher than in Silvaner. lt rapidly declined thereafter in Riesling and more slowly in Silvaner. Ψw remained low until the late afternoon, Silvaner always having lower values than Riesling.While there were no distinct diurnal changes in the osmotic potential (Ψs), turgor potential (Ψp) decreased during the day, Ψp of Silvaner always being lower than that of Riesling. After 10 a. m. under semiarid conditions, Ψp of Silvaner was close to 0.4. The osmotic potential of leaves was generally lower under semiarid conditions indicating osmotic adjustment. In Riesling, the osmotic potential was generally lower and tissue elasticity higher than in Silvaner.Under semiarid conditions fruitload increased Ψs and lowered Ψp in the leaves of Silvaner but not in Riesling.Der Tagesgang des Wasserhaushaltes und der Abscisinsäure bei Vitis-vinifera-Sorten im FreilandI. Die Komponenten des Blattwasserpotentials und die stomatäre Leitfähigkeit unter gemäßigt humiden und semiariden BedingungenUnter den gemäßigt humiden Klimabedingungen Deutschlands (Geilweilerhof) und im semiariden Klima Südaustraliens (Adelaide) wurden der diurnale Verlauf des Wasserpotentials (Ψw) und seiner Komponenten, das osmotische Potiential (Ψs) und das Turgorpotential (Ψp), sowie die stomatäre Leitfähigkeit untersucht; hierzu wurden die Sorten Riesling und Silvaner miteinander verglichen, die sich offenbar hinsichtlich ihrer Anpassungsfähigkeit an Trockenheit unterscheiden.Auf dem Geilweilerhof lag das Ψwvor Sonnenaufgang nahe bei 0 bar, und die stomatäre Leitfähigkeit war sehr niedrig. Mit zunehmender Lichtintensität und Temperatur öffneten sich die Stomata am Vormittag. Um 15 Uhr begannen die Stomata sich zu schließen, wobei die stomatäre Leitfähigkeit bei Silvaner rascher abnahm als bei Riesling. Mit Ausnahme des späten Nachmittags lag das Ψw des Silvaners im Tagesverlauf geringfügig unter dem des Rieslings.Unter den semiariden Bedingungen Adelaides betrug das Ψw vor Sonnenaufgang -6 bar (Riesling) bzw. - 7 bar (Silvaner); es nahm um 10 Uhr rasch auf -14 bar (Riesling) bzw. -16 bar (Silvaner) ab; die stomatäre Leitfähigkeit hatte zu dieser Zeit Maximalwerte erreicht, die bei Riesling deutlich höher lagen als bei Silvaner. Danach nahm die stomatäre Leitfähigkeit bei Riesling rasch, bei Silvaner etwas langsamer ab. Die Ψw-Werte blieben bis zum späten Nachmittag niedrig, wobei Silvaner stets geringere Werte aufwies als Riesling.Während Ψs keine deutlichen Veränderungen im Tagesverlauf erkennen ließ, nahmen die ljlpWerte insgesamt ab; die Ψp-Werte des Silvaners lagen hierbei stets unter denen des Rieslings. Unter semiariden Bedingungen lag Ψp bereits ab 10 Uhr nahe bei 0 bar.Unter semiariden Bedingungen waren die Ψs-Werte der Blätter grundsätzlich vermindert, was auf eine osmotische Anpassung hindeutet. Bei Riesling war das osmotische Potential niedriger und die Gewebeelastizität höher als bei Silvaner.Unter semiariden Bedingungen löste der Traubenbehang einen Anstieg der Ψs-Werte und eine Abnahme der Ψp-Werte bei Silvaner, nicht jedoch bei Riesling aus

Efficient hedging in Bates model using high-order compact finite differences

We evaluate the hedging performance of the scheme developed in B. Düring, A. Pitkin, ”High-order compact finite difference scheme for option pricing in stochastic volatility jump models”, 2017. We compare the scheme’s hedging performance to standard finite difference methods in different examples. We observe that the new scheme achieves fourth-order convergence, outperforming a standard, second-order central finite difference approximation in all our experiments

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

Partial drying of the rootzone of grape. II. Changes in the pattern of root development

Split-root plants, where the root system was divided between two containers, were used to study the effect of partial drying of the root system on gas exchange and root growth of 110 Richter (Vitis berlandieri x Vitis rupestris). The initial decrease in gas exchange in response to half-drying coincided with the decrease in soil water content of the dried half of the root system. Recovery of gas exchange of half-dried grapevines occurred without any further change in soil water content of the dried half of the root system, and coincided with the point at which there was no further decrease in soil water content. For half-dried plants, there was a relative increase in root development in moist soil layers, both in the wet container as a whole or in the lower part of the dry container. Recovery of gas exchange of half-dried plants occurred at the time when there were no more roots dried in the dry container. We propose that, for half-dried plants, the part of the root system in dry soil can survive because water moves from wet roots to dry roots

Partial drying of the rootzone of grape. I. Transient changes in shoot growth and gas exchange

Split-root  plants, where  the  root  system was  divided between  two containers, were used  to  study  the effect  of  partial  drying  of  the  root  system  on  shoot growth and gas exchange of Shiraz  (syn. Syrah)  (Vitis vinifera), Kober 5 BB  (Vitis berlandieri x Vitis  riparia) and 110 Richter (Vitis berlandieri x Vitis rupestris). The initial decrease  in both shoot growth rate and gas exchange  in  response  to half-drying  coincided with  the decrease  in  soil water content of  the dried half of  the root  system. Recovery  of  shoot  function  of half-dried grapevines  occurred without  rewatering  of  the dried half  of  the  root  system,  and  commenced when  there was no  further decrease  in  soil water  content. There was no effect of half-drying on  leaf water potential at the  times  of  greatest  inhibition  of  shoot  growth  rate and stomatal conductance relative to control; this suggests  the  involvement of a non-hydraulic  signal originating  from  the  roots  in drying  soil. Changes  in  stomatal  conductance  in  response  to  half-drying were strongly  correlated with  shoot  growth  rate

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

Pre-oil globalization in a rural community: the Late Islamic village of Sahlat in the Suhar region

Archaeology of the Near Eas