A rational fraction polynomials model to study vertical dynamic wheel-rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.

Effect of Molecular Flexibility on the Nematic-to-Isotropic Phase Transition for Highly Biaxial Molecular Non-Symmetric Liquid Crystal Dimers

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

Two Glass Transitions Associated to Different Dynamic Disorders in the Nematic Glassy State of a Non-Symmetric Liquid Crystal Dimer Dopped with gamma-Alumina Nanoparticles

In the present work, the nematic glassy state of the non-symmetric LC dimer -(4-cyanobiphenyl-4-yloxy)--(1-pyrenimine-benzylidene-4-oxy) undecane is studied by means of calorimetric and dielectric measurements. The most striking result of the work is the presence of two different glass transition temperatures: one due to the freezing of the flip-flop motions of the bulkier unit of the dimer and the other, at a lower temperature, related to the freezing of the flip-flop and precessional motions of the cyanobiphenyl unit. This result shows the fact that glass transition is the consequence of the freezing of one or more coupled dynamic disorders and not of the disordered phase itself. In order to avoid crystallization when the bulk sample is cooled down, the LC dimer has been confined via the dispersion of -alumina nanoparticles, in several concentrations.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.