This paper studies the heat flow on Finsler manifolds. A Finsler manifold is a smooth manifold M equipped with a Minkowski norm F(x, ·) : TxM → R+ on each tangent space. Mostly, we will require that this norm is strongly convex and smooth and that it depends smoothly on the base point x

Object oriented modeling of physical systems is an interesting paradigm, which has the potential to offer reusable models and model components. The aim of this study is to investigate how to build mean value models for automotive engines. MathModelica, a modeling tool for the object oriented modeling language Modelica, is used in this study. Several sub models have been developed for the different parts of the engine. The models cover the air filter, intercooler, throttle, base engine, exhaust system, compressor, turbine, turbine shaft, and volumes. It is shown how the components can be connected to form both turbo charged engines as well as a naturally aspirated engines, which shows that the paradigm is applicable for the modeling and confirms the modeling principle. One problem that has popped up at several occasions is the selection of initial conditions for the simulation. Especially when restrictions with low pressure drops are connected between two volumes, the simulation engine has problems finding initial conditions. The models have been compared to measured engine data collected at a test bench in Vehicular Systems laboratory at Linköping University. The agreement with measurement data is good and the models work as expected. Nomenclature

We prove that on compact Alexandrov spaces with curvature bounded below the gradient flow of the Dirichlet energy in the L²-space produces the same evolution as the gradient flow of the relative entropy in the L²-Wasserstein space. This means that the heat flow is well defined by either one

Heat is continually escaping across the earth’s surface because the interior is relatively warm, and heat flows by conduction from warm regions to cooler ones. This flux at the earth’s solid surface of heat conducted from the interior is referred to in geophysics as “heat flow. ” Other things being

The average of twenty-six new heat flow determinations in the North Central area of the United States is 1.36±0.34 HFUt the values range from 0.90 to 2.2 HFU. Except for two determinations in Indiana, all of the measurements were obtained from continuous temperature-depth curves that were recorded

New heat flow determinations have been made at 88 sites in Utah using information from oil and gas wells. These sites fill many gaps in the previous heat flow coverage and allow us to better delineate the thermal transition between the Colorado Plateau and the Basin and Range provinces in central

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The terrestrial heat flow is defined as the quantity of heat escaping per unit time from the Earth’s interior across each unit area of the Earth’s solid surface. The quantity varies from place to place over the surface of the Earth, as well as with time throughout Earth history. The total heat

Abstract. Dirac-geodesics are Dirac-harmonic maps from one dimensional domains. In this paper, we introduce the heat flow for Dirac-geodesics and establish its long-time existence and an asymptotic property of the global solution. We classify Dirac-geodesics on the standard 2-sphere S 2

Pollack, H.N. and Chapman, D.S., 1977. On the regional variation of heat flow, geo-therms, and lithospheric thickness. Tectonophysics, 38: 279-296. Geotherm families in which surface heat flow is the principal independent variable have been constructed for continental and oceanic lithospheres