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  • Verification of Arithmetic Properties using Gröbner Bases

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    No description available
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    Added by AlexanderDreyer on 2012-03-20 14:27


    Verification of Arithmetic Properties using Gröbner Bases
  • Viscous Flow in Highly Porous Media (Brinkman)

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    Viscous Flow in Highly Porous Media
    Tags: flowporous_mediaviscous_flow
    Added by Martin on 2011-07-12 16:24


    Viscous Flow in Highly Porous Media (Brinkman) Viscous Flow in Highly Porous Media
  • Upscaling Heat Equation in High-Contrast Fibrous Materials

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    Upscaling Heat Equation in High-Contrast Fibrous Materials
    Tags: fibrous_materialsheat_equation
    Added by Martin on 2011-07-12 16:21


    Upscaling Heat Equation in High-Contrast Fibrous Materials Upscaling Heat Equation in High-Contrast Fibrous Materials
  • Uniaxial Spinning of Viscous Fibers

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    In the considered spinning processes a viscous fiber is obtained by the continuous extrusion of a molten granular through a narrow nozzle in direction of gravity. Thereby, cross-section and mean inflow velocity at the nozzle are given. The temporal evolution of the fiber length as well as the cross-sections and velocities in the fiber domain are described by a simplified one-dimensional model that can be deduced f...
    Tags: fibersfree_boundary_value_problemspinning
    Added by Martin on 2011-07-12 16:11


    Uniaxial Spinning of Viscous Fibers In the considered spinning processes a viscous fiber is obtained by the continuous extrusion of a molten granular through a narrow nozzle in direction of gravity. Thereby, cross-section and mean inflow velocity at the nozzle are given. The temporal evolution of the fiber length as well as the cross-sections and velocities in the fiber domain are described by a simplified one-dimensional model that can be deduced from the three-dimensional Navier-Stokes equations for a Newtonian fluid via asymptotic analysis. Preparation and spinning of textile fibres Stokes and Navier-Stokes equations Navier-Stokes equations Free boundary problems for PDE
  • Stochastic Air Drag Model for Fibers in Turbulent Flows

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    No description available
    Tags: fibersturbulent_flows
    Added by Martin on 2011-07-12 16:02


    Stochastic Air Drag Model for Fibers in Turbulent Flows
  • Second Order Correction of Acoustic Helmholtz Equation

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    If a strong sinusoidal signal is sent to a vented bass loudspeaker we will hear not only the fundamental frequency, but also higher harmonics. This nonlinear distortion is partially due to the response of the electro-mechanical components and partially due to the transfer behavior of the enclosed air. Here, we deal with the latter effect. It is well known that the edges of reflex tubes have to be chamfered to avoi...
    Tags: acousticsasymptotic_analysishelmholtzhelmholtz_equationnon_linear_acoustics
    Added by Martin on 2011-07-12 15:52


    Second Order Correction of Acoustic Helmholtz Equation If a strong sinusoidal signal is sent to a vented bass loudspeaker we will hear not only the fundamental frequency, but also higher harmonics. This nonlinear distortion is partially due to the response of the electro-mechanical components and partially due to the transfer behavior of the enclosed air. Here, we deal with the latter effect. It is well known that the edges of reflex tubes have to be chamfered to avoid noise. The present model is designed to investigate this phenomenon with minimal numerical costs . Obviously, linear acoustics are insufficient. Solving the full Euler equations, however, requires an unreasonably high effort. Therefore, we propose a correction to the linear Helmholtz equation which consists just in a second inhomogeneous Helmholtz equation for the first harmonic and an algebraic equation for the radiation pressure. For medium displacements it allows to predict how the energy inserted into the loudspeaker at a given frequency is distributed between the keynote and the first harmonic.
  • Reynolds-averaged Navier-Stokes with k-epsilon Model

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    No description available
    Tags: fluid_dynamicsfluidsturbulence
    Added by Martin on 2011-07-12 15:46


    Reynolds-averaged Navier-Stokes with k-epsilon Model
  • Parker Model of the Solar Wind

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    In 1957 Chapman developed a hydrostatic model describing the Sun's atmosphere (see ). In 1958 Parker showed that the pressure resulting from Chapman's model was too low compared to the total pressure given by the galactic magnetic field, the interstellar gas, and the cosmic radiation. Additionally, this model can not explain the observation of the Ludwig Biermann, who studied the fact that the ...
    Tags: atmospherecoronasun
    Added by Martin on 2011-07-12 15:43


    Parker Model of the Solar Wind In 1957 Chapman developed a hydrostatic model describing the Sun's atmosphere (see ). In 1958 Parker showed that the pressure resulting from Chapman's model was too low compared to the total pressure given by the galactic magnetic field, the interstellar gas, and the cosmic radiation. Additionally, this model can not explain the observation of the Ludwig Biermann, who studied the fact that the tail of a comet always points away from the sun whether it is headed towards or away from the sun. Furthermore, Biermann found a correlation between the drift of the comet's tails and fluctuations in the Earth's magnetic field. Hence, Parker skipped Chapman's assumption of a hydrostatic solar atmosphere. His dynamic model of the Sun's atmosphere describes the continuous ejection of plasma from the Sun's surface into and through interplanetary space. Due to Parkers proposal this particle flow is called solar wind.
  • One dimensional heat exchanger

    Views: 149 Average Rating:
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    Heat exchangers are of interest in a multitude of technical applications, such as heaters and air conditioners. Here we consider two fluids passing through parallel tubes which are in contact and exchange sensible heat via the surrounding wall material. We assume that the tubes as well as the common wall are long in comparison to their cross-sectional areas. Thus, we may take averages of all quantities over the cr...
    Tags: advectionheat_conductionheat_exchangermodel_reduction
    Added by Martin on 2011-07-12 15:40


    One dimensional heat exchanger Heat exchangers are of interest in a multitude of technical applications, such as heaters and air conditioners. Here we consider two fluids passing through parallel tubes which are in contact and exchange sensible heat via the surrounding wall material. We assume that the tubes as well as the common wall are long in comparison to their cross-sectional areas. Thus, we may take averages of all quantities over the cross sections. The heat exchange of the two fluids and the common surrounding wall material is modelled as heat transfer within the cross sections. It is assumed to be proportional to the local temperature differencies between the fluids and the common wall and will take place in every cross section separately. The model describes the heat transfer in longitudinal direction as advection along the tubes arising from the fluid velocities and as conduction along the walls of the tubes. Heat conduction in the fluid itself is ignored, since it plays a minor role in most applications. Thus, the model consists of three idealized one dimensional objects transporting and exchanging heat. Two of them describe the heat advection by the fluids and the third describes the conduction in the surrounding rigid material.
  • Inextensible Elastic Strings in Turbulent Flows

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    The model at hand is an extension of the ”Dynamics of Inextensible Elastic Strings”. Here, two functions to model deterministic aerodynamic forces as well as stochastic ones due to turbulence have been incorporated. The stochastic term is a white noise and changes the type of the evolution equation from a PDE to a SPDE (stochastic partial diff...
    Tags: elastic_stringsfibersturbulent_flows
    Added by Martin on 2011-07-12 15:23


    Inextensible Elastic Strings in Turbulent Flows The model at hand is an extension of the {link:/AloeView/action/resourceDetailed?resourceId=n4qOwXC|”Dynamics of Inextensible Elastic Strings”}. Here, two functions to model deterministic aerodynamic forces as well as stochastic ones due to turbulence have been incorporated. The stochastic term is a white noise and changes the type of the evolution equation from a PDE to a SPDE (stochastic partial differential equation). In ”Stochastic Air Drag Model for Fibers in Turbulent Flows” both functions are specified in terms of an air drag model and a model for the so-called turbulence drag amplitude. In this way an one way coupling of the dynamics of fibers and of turbulent flows might be realized.
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