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This model is an extension of the "Stochastic Model for Fiber Laydown in Nonwoven Production". The original model describes the image of a fiber on a conveyor belt by a system of stochastic differential equations for the fiber curve and the angle giving the tangent. Perturbing the angle with white noise a continuous curve is obtained. To improve the regularity to a differential curve the following model...
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fiberfiber_laydownmodelnonwovenstochasticstochastic_process
Added by Martin on 20100720 09:42
Improved Stochastic Model for Fiber Laydown in Nonwoven Production
This model is an extension of the "Stochastic Model for Fiber Laydown in Nonwoven Production". The original model describes the image of a fiber on a conveyor belt by a system of stochastic differential equations for the fiber curve and the angle giving the tangent. Perturbing the angle with white noise a continuous curve is obtained. To improve the regularity to a differential curve the following model relaxing to the deterministic behaviour of the original one perturbes the curvature.

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In the field of actuator and sensor application the electromechanical coupling is used to transfer an electrical excitation into a mechanical deformation and viceversa. This kind of coupling is normally realized on an atomistic level by materials like piezoelectric ceramics. In this type of materials the deformations are very limited because of their ceramic character. To achieve large deformations, the use of so...
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dielectric_elastomerfinite_elementstability
Added by Martin on 20110712 12:01
Dielectric Elastomer Actuators  Stability Analysis
In the field of actuator and sensor application the electromechanical coupling is used to transfer an electrical excitation into a mechanical deformation and viceversa. This kind of coupling is normally realized on an atomistic level by materials like piezoelectric ceramics. In this type of materials the deformations are very limited because of their ceramic character. To achieve large deformations, the use of so called soft dielectrics can be considered. Here the coupling is realized through the combination of soft elastomers and electrostatic forces.In the model presented here, the electromechanical coupling for soft dielectrics is implemented in the context of the nonlinear finite element method. The main focus here is not the implementation but the analysis of the stability for this coupling problem. This analysis is motivated by the fact, that the electrostatic force can exceed the mechanical forces at a certain deformation.

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In lightweight design saving of material has to be done in such a way that the material is not overloaded at any position of the construction. Otherwise a failure of the structure would be possible. Mathematical models are available for the simulation of the local stress in the material if the operating loads are applied. This simulation can also be used to detect regions of the structures, which are not necessary...
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descent_methodoptimal_designsensitivity_analysistopology_optimization
Added by Martin on 20100722 11:29
Topology Optimization
In lightweight design saving of material has to be done in such a way that the material is not overloaded at any position of the construction. Otherwise a failure of the structure would be possible. Mathematical models are available for the simulation of the local stress in the material if the operating loads are applied. This simulation can also be used to detect regions of the structures, which are not necessary for carrying the loads. The material can be removed from the detected regions, which have only small stresses, in the computer, i.e. the design of the structure can be improved automatically. The development of such algorithms and methods is a recent field of research. Software packages are already available for the automated optimal design of components, which have to carry static or dynamical mechanical loads and which have to fulfill also other functions. In the socalled shape optimization only the boundary of the structure is moved iteratively in such a way that e.g. notch stresses are reduced. On the other hand topology optimization algorithms are iterative methods, where the topology of the structure is changing during the iterations. E.g. new holes are created in unloaded regions of the components. Often the topology optimization is the first step and shape optimization the second step in the design of lightweight structures. Automatic structural optimization method are most efficient, if the are used at the beginning of design of a new product. Castings, which have a very flexible and filigree geometry, can be produced in foundries. Therefore structural optimization methods are often used for the design of castings. A standard problem is the minimization of the compliance of structures under given mechanical loads. This problem can be formulated as an optimization problem with constraints. In this case the constraints contain an elliptic boundary value problem for the equations of linear elasticity. For the solution of this problem many iterative algorithms are proposed in literature. In each iteration of these algorithms the structure is analyzed at first, then the sensitivity with respect to changes of the structures is computed, and finally the geometry of the structure is updated. The structural analysis is often performed by the finiteelement method (FEM) . Generalized derivatives (shape derivative, topological gradient) are used for the sensitivity analysis. The levelset method is a modern highly efficient mathematical tool for the representation of the boundary of the structure and also for the change of this boundary.

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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.

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The horizontal shot describes the ballistic trajectory of a masspoint (i.e. it moves without friction) on the planet earth. This model is one of the basic models of the mechanics theory founded by Isaac Newton.
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demomechanicsmodellphysicsschoolshot
Added by Martin on 20110712 12:52
Horizontal Shot
The horizontal shot describes the ballistic trajectory of a masspoint (i.e. it moves without friction) on the planet earth. This model is one of the basic models of the mechanics theory founded by Isaac Newton.

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The VogelFulcherTamman (VFT) equation is a model for the temperaturedependence of the dynamic viscosity of glass and other liquid materials like water, petroleum or molten metal. The inflection point of the logarithmic curves for almost all glass materials is found to be 10<sub>12</sup> Pa s. The corresponding temperature is called transformation temperature. If glass is cooled below the t...
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glassviscosity
Added by Martin on 20100722 15:59
VogelFulcherTammann Model
The VogelFulcherTamman (VFT) equation is a model for the temperaturedependence of the dynamic viscosity of glass and other liquid materials like water, petroleum or molten metal. The inflection point of the logarithmic curves for almost all glass materials is found to be 10<sub>12</sup> Pa s. The corresponding temperature is called transformation temperature. If glass is cooled below the transformation temperature then brittleness occurs.

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Nonwovens are technical textiles made of a web of fibers. They find their application in various branches of industry, e.g. in textile, hygiene, automobile and building industry. For the industrial production transversal, rotational and oscillating processes are of main relevance. Differing in details, they have in principal three things in common: spinning, entanglement and laydown. Thousands of fibers are obtai...
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fiber_laydownmodelnonwovenofficialstochastic_processtest
Added by Martin on 20100722 10:39
Stochastic Model for Fiber Laydown in Nonwoven Production
Nonwovens are technical textiles made of a web of fibers. They find their application in various branches of industry, e.g. in textile, hygiene, automobile and building industry. For the industrial production transversal, rotational and oscillating processes are of main relevance. Differing in details, they have in principal three things in common: spinning, entanglement and laydown. Thousands of fibers are obtained by a continuous extrusion of a molten granular through narrow nozzles. Then, they are stretched and entangled by acting turbulent air flows to form a web, while laying down on a moving conveyor belt.
The complete production process can in principle be described by a mathematical model that takes into account the entanglement and deposition of all fibers on the conveyor belt under the influence of turbulent air flows. Unfortunately, it turns out that the associated simulations are very timeconsuming, storage demanding and not suitable for the computation of huge nonwoven webs. But this high computational effort is not obligatory because huge bundles of fibers are realizations of the same stochastic process. Therefore, it makes sense to introduce a simplified surrogate stochastic process that describes the characteristic image of the fibers on the conveyor belt. This enables the easy and fast computation of a web of thousands of fibers.
The surrogate model is characterized by a deterministic reference curve Γ being the projection of the spinning position onto the moving conveyor belt. For example it is a straight line for transversal processes and a cycloid for rotational ones. Oscillating around the reference curve, the actual fiber curve and the angle that specifies its tangent are given by a system of stochastic differential equations. Containing typical parameters 1, 2 and A it can be calibrated by the dynamical full simulation of a single fiber.

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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