The Stochastic Wave Equation with Multiplicative Fractional Noise: A Malliavin Calculus Approach

We consider the stochastic wave equation with multiplicative noise, which is fractional in time with index H > 1/2, and has a homogeneous spatial covariance structure given by the Riesz kernel of order α. The solution is interpreted using the Skorohod integral. We show that the sufficient condition for the existence of the solution is α > d − 2, which coincides with the condition obtained in Dalang (Electr J Probab 4(6):29, 1999), when the noise is white in time. Under this condition, we obtain estimates for the p-th moments of the solution, we deduce its H?lder continuity, and we show that the solution is Malliavin differentiable of any order. When d ≤ 2, we prove that the first-order Malliavin derivative of the solution satisfies a certain integral equation.     

Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

We consider the stochastic heat equation with multiplicative noise \(u_{t}=\frac{1}{2}\Delta u+u\dot{W}\) in ?₊×? ^d , whose solution is interpreted in the mild sense. The noise \(\dot{W}\) is fractional in time (with Hurst index H≥1/2), and colored in space (with spatial covariance kernel f). When H>1/2, the equation generalizes the Itô-sense equation for H=1/2. We prove that if f is the Riesz kernel of order α, or the Bessel kernel of order α<d, then the sufficient condition for the existence of the solution is d≤2+α (if H>1/2), respectively d<2+α (if H=1/2), whereas if f is the heat kernel or the Poisson kernel, then the equation has a solution for any d. We give a representation of the kth order moment of the solution in terms of an exponential moment of the “convoluted weighted” intersection local time of k independent d-dimensional Brownian motions.     

Fluctuation measurements with emissive probes in tokamaks

A new probe head, composed of two electro-emissive probes and two Langmuir probes has been designed to measure edge fluctuations in the CASTOR tokamak. In this contribution, only one Langmuir and one electron-emissive probe are used to measure the temperature and potential fluctuations and the phase angle between them.     

A novel approach to direct measurement of the plasma potential

A novel probe and approach to the direct measurements of the plasma potential in a strong magnetic field is suggested. The principle of this method is to reduce the electron saturation current to the same magnitude as that of the ion saturation current. In this case, the floating potential of the probe becomes indentical to the plasma potential. This goal is attained by a shield, which screens off an adjustable part of the electron current from the probe collector due to the much smaller gyro-radius of the electrons. First systematic measurements have been perfomred in the CASTOR tokamak.     

Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.     

Application of strain rate potentials with multiple linear transformations to the description of polycrystal plasticity

This paper reviews a class of anisotropic plastic strain-rate potentials, based on linear transformations of the plastic strain-rate tensor. A new formulation is proposed, which includes former models as particular cases and allows for an arbitrary number of linear transformations, involving an increasing number of anisotropy parameters. The formulation is convex and fully three-dimensional, thus being suitable for computer implementation in finite element codes. The parameter identification procedure uses a micromechanical model to generate evenly distributed reference points in the full space of possible loading modes. Material parameters are determined for several anisotropic, fcc and bcc sheet metals, and the gain in accuracy of the new models is demonstrated. For the considered materials, increasing the number of linear transformations leads to a systematic improvement of the accuracy, up to a number of five linear transformations. The proposed model fits very closely the predictions of the micromechanical model in the whole space of plastic strain-rate directions. The r-values, which are not directly used in the identification procedure, served for the validation of the models and to demonstrate their improved accuracy.     

A Model Predictive Control Algorithm Applied To Non-Linear Processes

Model predictive control (MPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. In most of nonlinear strategies, the controllers are based on linear models with fixed parameters so that the vast body of linear control theory can be applied. Other solutions include the use of a nonlinear analytical model, combinations of linear empirical models, etc. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

Investigation of energy losses in low-coercivity resin-bonded magnets in alternating magnetic fields

Energy losses during alternating remagnetization of low-coercitivity resin-bonded magnets and commercially produced electrical steels were studied experimentally. The studies were conducted on several samples of resin-bonded magnets with different manufacturing technologies and samples of electrical steel sheets of various thicknesses. The static and dynamic magnetic properties of the samples were measured on a vibration magnetometer and a specially designed apparatus, respectively. It was found that the studied samples of bonded magnets have a relatively high level of hysteresis losses associated with high coercivity, which reaches a value of 4–5 Oe. At the same time, the remagnetization losses due to the Foucault currents in the bonded magnets are considerably lower than in electrical steels. The measurement results show that bonded magnets at high frequencies of remagnetization, especially in high-rpm motors, can be competitive in comparison with electrical steels.