Fractal Theory Space: Spacetime of Noninteger Dimensionality

We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant ``compactification scale,'' M. The energy distribution of KK modes above M is controlled by an exponent in a scaling relation of the vacuum energy (Coleman-Weinberg potential), and corresponds to the dimensionality. For truncated-s-simplex lattices with coordination number s the spacetime dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space involve subtleties, owing to the 1+3 kinetic terms, yet the resulting dimensionalites are equivalent to thermal spin systems. Physical implications are discussed.Comment: 28 pages, 6 figures; Paper has been amplified with a more detailed discussion of a number of technical issue

Statistical Mechanics of Nonuniform Magnetization Reversal

The magnetization reversal rate via thermal creation of soliton pairs in quasi-1D ferromagnetic systems is calculated. Such a model describes e.g. the time dependent coercivity of elongated particles as used in magnetic recording media. The energy barrier that has to be overcome by thermal fluctuations corresponds to a soliton-antisoliton pair whose size depends on the external field. In contrast to other models of first order phase transitions such as the phi^4 model, an analytical expression for this energy barrier is found for all values of the external field. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of soliton-antisoliton pairs in the overdamped double sine-Gordon model. The present theory therefore includes the nucleation rate of soliton-antisoliton pairs in the double sine-Gordon chain as a special case. These results demonstrate that for elongated particles, the experimentally observed coercivity is significantly lower than the value predicted by the standard theories of N\'eel and Brown.Comment: 21 pages RevTex 3.0 (twocolumn), 6 figures available on request, to appear in Phys Rev B, Dec (1994

Quelques expériences sur la turbulence et la friction mutuelle dans l'hélium liquide

Pas de Résumé disponibl

Beyond classical design methods: Integrated design of an offshore wind turbine by simultaneous redesign of the support structure and controller parameters

In order for wind energy to become a well established source of alternative energy that is able to compete with the traditional forms of energy production, the costs of (offshore) wind energy should be lowered. This can be achieved by either increasing the energy output of a turbine or by reducing its production and maintenance costs. Current research on lowering the costs of energy of wind energy is conducted by multiple fields of engineering. In the field of structural engineering great effort is put into creating more accurate structural models of the turbine and the surrounding environment, such as the soil-structure interaction. Having more accurate models of the turbine potentially lowers the turbines costs by using a less conservative design when optimizing the system or by extending the lifetime by better understanding the applied loads to the system. In the field of control engineering there is a focus on control techniques which increase the energy output of the turbine or actively reduce the forces which act on the turbine. Integrating the controller and structural design into a single optimization routine is a heavily investigated area in other, less conservative, fields of engineering. Currently, little research focuses on applying this principle to wind turbine design. This research was partly conducted in collaboration with the SIEMENS wind power Centre of Competence in The Hague, to provide a framework for simultaneously redesigning the controller and structural parameters of their state of the art, multi-megawatt, offshore wind turbine and to define the key limitations of this framework. In order to meet this goal a framework has been presented that allows for simultaneously varying both structural and controller parameters of the wind turbine design. The framework allows one to find an combination of the controller and structural design parameters which optimize the overall performance of the turbine. This is achieved by evaluating the overall system performance in the frequency domain, while simultaneously optimizing over all tunable parameters. The capabilities of the method have been demonstrated on two design cases. In the first case a simple academic problem was optimized an the performance of the framework was analysed. The framework of simultaneously varying the structural and controller parameters is also applied to a commercial, state of the art, multi-megawatt, offshore wind turbine. The integrated design framework allows for varying physical properties of the structural model, in this case the wall thickness of the support structure. The derivatives of the mass and stiffness matrices of the turbine’s equations of motion are computed. Thereby obtaining a sensitivity description of the structural dynamics to the wall thickness. These derivatives are used to relate a change in wall thickness of tower elements to a change in the structural properties, and thereby the dynamical behaviour, of the entire wind turbine model. With the number of in- and output channels in the framework being linearly dependent to the number of states of the turbine model, the full turbine model description complicates the application of the integrated design framework. Therefore, the overall model of the wind turbine is reduced to capture only the relevant structural dynamics of the system. By using the reduced basis of the original system the derivative matrices are reduced, while keeping the dependency to the change in wall thickness parameters. This makes it possible to change the system dynamics, through wall thickness changes, while using a reduced number of in- and outputs in the framework. The integrated framework is used to design the rotor-speed controller parameters of the system, which is limited by the dynamics of the structural turbine model. The structural dynamics limited the overall performance of the system in two ways. First, a further increase in the frequency peak of the sensitivity function describing the closed loop system, is bounded by the designed performance weight. Second, due to the presence of right half plane zeros in the transfer function of the pitch angle to rotor-speed. A further increase of the system bandwidth is not possible due to controller limitations. Using the integrated design framework it is possible to minimize the net wall thickness of the tower elements in the turbine model and thereby changing the location of both the resonance frequency and the right half plane zeros. It can thus be concluded that the integrated wind turbine design, using the framework as shown in this work, allows one to optimize the structural and controller parameters simultaneously. Fundamental limitations in the controller design are analysed and used for redesigning the system for an increased overall performance.Mechanical, Maritime and Materials EngineeringDelft Center for Systems and Control (DCSC