Stable linearization using multilayer neural networks

The main limitation of linearization theory that prevents its application in practical problems is the need for an exact knowledge of the plant. This requirement is eliminated and it is shown that a multilayer network can synthesise the state feedback coefficients that linearize a nonlinear control affine plant. The stability of the linearizing closed loop can be guaranteed if the autonomous plant is asymptotically stable and the state feedback is bounded.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

Three dimensional picture of the local structure of 1,4-Polybutadiene from a complete atomistic model and neutron scattering data

An efficient method of combining neutron diffraction data over an extended Q range with detailed atomistic models is presented. A quantitative and qualitative mapping of the organization of the chain conformation in both glass and liquid phase has been performed. The proposed structural refinement method is based on the exploitation of the intrachain features of the diffraction pattern by the use of internal coordinates for bond lengths, valence angles and torsion rotations. Models are built stochastically by assignment of these internal coordinates from probability distributions with limited variable parameters. Variation of these parameters is used in the construction of models that minimize the differences between the observed and calculated structure factors. A series of neutron scattering data of 1,4-polybutadiene at the region 20320 K is presented. Analysis of the experimental data yield bond lengths for C-C and C=C of 1.54 and 1.35 Å respectively. Valence angles of the backbone were found to be at 112 and 122.8 for the CCC and CC=C respectively. Three torsion angles corresponding to the double bond and the adjacent R and β bonds were found to occupy cis and trans, s(, trans and g( and trans states, respectively. We compare our results with theoretical predictions, computer simulations, RIS models, and previously reported experimental results.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.