We found 28 mathematical models
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Added by AlexanderDreyer on 20120320 14:27
Verification of Arithmetic Properties using Gröbner Bases

Viscous Flow in Highly Porous Media (Brinkman)
Viscous Flow in Highly Porous Media

Upscaling Heat Equation in HighContrast Fibrous Materials
Upscaling Heat Equation in HighContrast Fibrous Materials

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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, crosssection and mean inflow velocity at the nozzle are given. The temporal evolution of the fiber length as well as the crosssections and velocities in the fiber domain are described by a simplified onedimensional model that can be deduced f...
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fibersfree_boundary_value_problemspinning
Added by Martin on 20110712 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, crosssection and mean inflow velocity at the nozzle are given. The temporal evolution of the fiber length as well as the crosssections and velocities in the fiber domain are described by a simplified onedimensional model that can be deduced from the threedimensional NavierStokes equations for a Newtonian fluid via asymptotic analysis.
Preparation and spinning of textile fibres
Stokes and NavierStokes equations
NavierStokes equations
Free boundary problems for PDE

Stochastic Air Drag Model for Fibers in Turbulent Flows

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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 electromechanical 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...
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acousticsasymptotic_analysishelmholtzhelmholtz_equationnon_linear_acoustics
Added by Martin on 20110712 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 electromechanical 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.

Reynoldsaveraged NavierStokes with kepsilon Model

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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 ...
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atmospherecoronasun
Added by Martin on 20110712 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.

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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 crosssectional areas. Thus, we may take averages of all quantities over the cr...
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advectionheat_conductionheat_exchangermodel_reduction
Added by Martin on 20110712 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 crosssectional 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.

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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...
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elastic_stringsfibersturbulent_flows
Added by Martin on 20110712 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 socalled turbulence drag amplitude. In this way an one way coupling of the dynamics of fibers and of turbulent flows might be realized.