Global well-posedness of the critical Burgers equation in critical Besov spaces

We make use of the method of modulus of continuity \cite{K-N-S} and Fourier localization technique \cite{A-H} to prove the global well-posedness of the critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in critical Besov spaces $\dot{B}^{\frac{1}{p}}_{p,1}(\mathbb{R})$ with $p\in[1,\infty)$, where $\Lambda=\sqrt{-\triangle}$.Comment: 21page

Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation

In this paper we consider the following modified quasi-geostrophic equation \partial_{t}\theta+u\cdot\nabla\theta+\nu |D|^{\alpha}\theta=0, \quad u=|D|^{\alpha-1}\mathcal{R}^{\bot}\theta,\quad x\in\mathbb{R}^2 with $\nu>0$ and $\alpha\in ]0,1[\,\cup \,]1,2[$. When $\alpha\in]0,1[$, the equation was firstly introduced by Constantin, Iyer and Wu in \cite{ref ConstanIW}. Here, by using the modulus of continuity method, we prove the global well-posedness of the system with the smooth initial data. As a byproduct, we also show that for every $\alpha\in ]0,2[$, the Lipschitz norm of the solution has a uniform exponential bound.Comment: In this version we extend the range of $\alpha$ from (0,1) to (0,2), we also show that for every $\alpha\in (0,2)$, the Lipschitz norm of the solution has a uniform exponential bound. 27page

Research on Suppressing Premixed Fuel-air Explosion by Ultra-fine Cold Aerosol

AbstractThe problem of prevention and suppression of gas-and air explosions is extremely important because such explosions represent serious threat to firemen life. It is significant that ultra-fine cold aerosol with typical characteristics of compressibility, flow ability and good dispersion attributed, can suppress the deflagration and detonation of leaking of flammable oil gases. In this paper, some series of the explosion suppression experiments were carried out in the laboratory 20-liter apparatus with three gas routes and two igniters of chemical and high-voltage pulse which provide a reliable, multiple-point ignition source. The main series were about the suppressing the developed explosion process of oil gas premixed air and ultra-fine cold aerosol, or 1301 fire extinguishing agent. The results are shown that in case of suppressing the developed explosion, the increase of the concentration of ultra-fine powder and 1301 both causes the decrease of the maximum explosion pressure and maximum rate of pressure rise of oil gases. Moreover, 1301 fire extinguishing agent has distinctly threshold nature and the induced time of oil explosion is delayed. Furthermore, it is shown that the explosion suppression effect is associated to inherent property and concentration of suppressing agent and ignition condition. And the rank of suppressing capability of ultra-fine aerosol or gas suppressing agent for oil gas atmosphere was proposed, and the maximum suppressed explosion pressure may be used as the criterion to estimate explosion-suppression efficiency of oil gas. This research helps optimize explosion suppression condition of oil gas, and have important reference values for further application on explosion suppression technology in large oil rank farm and other danger sites

Modeling the spatial distribution of grazing intensity in Kazakhstan

<div><p>With increasing affluence in many developing countries, the demand for livestock products is rising and the increasing feed requirement contributes to pressure on land resources for food and energy production. However, there is currently a knowledge gap in our ability to assess the extent and intensity of the utilization of land by livestock, which is the single largest land use in the world. We developed a spatial model that combines fine-scale livestock numbers with their associated energy requirements to distribute livestock grazing demand onto a map of energy supply, with the aim of estimating where and to what degree pasture is being utilized. We applied our model to Kazakhstan, which contains large grassland areas that historically have been used for extensive livestock production but for which the current extent, and thus the potential for increasing livestock production, is unknown. We measured the grazing demand of Kazakh livestock in 2015 at 286 Petajoules, which was 25% of the estimated maximum sustainable energy supply that is available to livestock for grazing. The model resulted in a grazed area of 1.22 million km², or 48% of the area theoretically available for grazing in Kazakhstan, with most utilized land grazed at low intensities (average off-take rate was 13% of total biomass energy production). Under a conservative scenario, our estimations showed a production potential of 0.13 million tons of beef additional to 2015 production (31% increase), and much more with utilization of distant pastures. This model is an important step forward in evaluating pasture use and available land resources, and can be adapted at any spatial scale for any region in the world.</p></div

Global well-posedness for the micropolar fluid system in the critical Besov spaces

We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation to the solutions and using the Fourier localization method, especially combined with a new $L^p$ estimate for the Green matrix to the linear system of the transformed equation. This result allows to construct global solutions for a class of highly oscillating initial data of Cannone's type. Meanwhile, we analyze the long behavior of the solutions and get some decay estimates.Comment: 23page

Viskosität metallischer Schmelzen und deren präzise Messung

Diese Arbeit berichtet über die Planung und den Aufbau eines neuen Viskosimeters und über Viskositätsuntersuchungen einiger metallischer Systeme. Diese letzteren Messungen wurden mit einem vorhandenen Viskosimeter gemacht, in dem kein besseres Vakuum als 10^(-3)mbar und keine höhere Temperatur als 1430K erreicht werden kann. Das beste Vakuum und die maximale erreichbare Temperatur in dem neuen Viskosimeter sind 10^(-6)mbar bzw. 1870K. Diese beiden Grundbedingungen ermöglichen die Viskositätsmessung metallischer Systeme, die aktive Elemente wie Al, Mg und P enthalten oder/und einen höheren Schmelzpunkt besitzen. Mit dem Drei-Zonen-Ofen erlaubt die neue Apparatur auch ein schnelleres Homogenisieren der zu untersuchenden Schmelze, besonders der monotektischen Systeme. Der Einfluß der Temperatur des Torsionsdrahtes und der Anfangsphase der Schwingung auf die Genauigkeit der Viskostätsmessung wurden analysiert und entsprechende Verbesserungen vorgeschlagen. Die untersuchten Systeme sind das Zn-Pb basierte ternäre System, die monotektischen Systeme Ag-Te und Li-Na, das Verbindungssystem Sb-Zn, die halbleitenden Cd-Te Legierungen und Schaummaterialien ZACT und ZACM.Viscosity of metallic melts and its precise measurement This thesis reports the design and the construction of a new oscillating cup viscometer and the viscosity investigation of several metallic systems. The measurements were carried out with an existing viscometer by which one could not get better vacuum than 10^(-3)mbar or higher temperature than 1430K. With the new apparatus the best vacuum of 10^(-6)mbar and the highest temperature of 1870K can be reached. These two basic conditions permit the measurement of systems which contain active elements such as Al, Mg and P and/or have very hight melting points. The construction of the three-zone furnace in the new viscometer allows the acceleration of the homogenising process, which is especially important for monotectic systems. The influences of the temperature of the torsion thread and the initial oscillating phase on the accuracy of viscosity measurement were analysed and the corresponding solutions were put forward. The investigated systems are the Zn-Pb based ternary system, the monotectic systems Ag-Te and Li-Na, the Sb-Zn system which contains compounds in the solid phases, the semiconducting Cd-Te alloys and the foaming materials ZACT and ZACM

FarmAgriPoliS – Ein agentenbasiertes Modell zur Untersuchung des Agrarstrukturwandels mittels Verhaltensexperimenten

Agrarpolitische Maßnahmen basieren in der Regel auf den Annahmen des Modells des homo oeconomicus. Erste empirische Befunde aus der Verhaltensökonomie deuten darauf hin, dass dieses Modell das reale Entscheidungsverhalten von Landwirten oft nur unzureichend beschreibt. Die experimentelle Wirtschaftsforschung kann einen wichtigen Beitrag zum besseren Verständnis des Verhaltens von Landwirten und somit auch zu einer verbesserten Agrarpolitik leisten. In diesem Beitrag stellen wir die am Leibniz-Institut für Agrarentwicklung in Transformationsökonomien entwickelte Software FarmAgriPoliS vor. In FarmAgriPoliS übernehmen Spielerinnen und Spieler die Rolle eines Betriebsleiters und entscheiden über die Pacht von Boden, Investitionen und Betriebsaufgabe. Anders als in einfachen ökonomischen Experimenten, wird eine Vielzahl von Entscheidungen getroffen, die möglichst realitätsnah ist. Räumliche Interaktionseffekte mit konkurrierenden Betrieben sind wesentlicher Bestandteil des Spiels und werden über den Bodenmarkt umgesetzt. Vor- und Nachteile der Komplexität des Spiels im Vergleich zu anderer Experimentalsoftware und zukünftige Einsatzmöglichkeiten in der agrarökonomischen Lehre werden diskutiert

FarmAgriPoliS: An agricultural business management game for behavioral experiments, teaching, and gaming

Business management games have been used for decades, primarily for educational purposes, training, and entertainment. More recently, the use of such games has expanded to an experimental platform. Usually business management games are directly designed and developed for one or more of these purposes; however, this paper discusses another possibility: the development of a business management game based on an existing agent-based model. We encourage this use and describe the extension of the agent-based model AgriPoliS, which has been widely used to analyze structural change in agriculture. We document the resulting software FarmAgriPoliS and provide a systematic classification of FarmAgriPoliS into the framework of business management games with agricultural background. Furthermore, we evaluate the suitability of FarmAgriPoliS for teaching, experimental use, and online gaming

Application of Deep Learning to Emulate an Agent-Based Model

In light of the dynamic challenges facing agricultural land markets, the conventional analytical frameworks fall short in capturing the intricate interplay of strategic decisions and evolving complexities. This necessitates the development of a novel method, integrating deep learning into Agent-based Modelling, to provide a more realistic and nuanced understanding of land market dynamics, enabling informed policy assessments and contributing to a comprehensive discourse on agricultural structural change. In this paper, different deep learning models are tested and evaluated, as emulators of AgriPoliS (Agricultural Policy Simulator). AgriPoliS is an agent-based model used to model the evolution of structural change in agriculture resultant on the change in the policy environment. This study is part of preliminary works towards integrating deep learning methods and predictions with AgriPoliS to capture strategic decision making and actions of agents in land markets. The paper tests the models on their suitability, computational requirements and run-time complexities. The output from AgriPoliS serves as the input features for the deep learning models. Models are evaluated using a combination of coefficient of determination (R2 score), mean absolute error, visual displays and runtime. The models were able to replicate the variable of interest with a high degree of accuracy with R2 score of more than 90%. The CNN was the most suited for replicating the data. Through this work, we learned the required complexities, computational and training efforts needed to integrate deep learning and AgriPoliS to capture strategic decision-making