Structural Equations and Beyond

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the “(causal) laws” or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended causal models with their two modalities can be subsumed under so called “counterfactual models” which contain just one modality. These two constraints will be formally precise versions of Lewis’ (1979) familiar “system of weights or priorities” governing overall similarity between possible worlds

Large Angle Transient Dynamics (LATDYN) user's manual

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system

Supercooled liquids under shear: A mode-coupling theory approach

We generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the generalized fluctuating hydrodynamic equations with a convection term. The method is applied to a two dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and shear viscosity is analyzed. The results show a drastic reduction of the structural relaxation time due to shear and strong shear thinning behavior of the viscosity which are in qualitative agreement with recent simulations. The microscopic theory with minimal assumptions can explain the behavior far beyond the linear response regime.Comment: 4 pages, 2 figures, Proceedings to Slow Dynamics in Complex Systems November3-8, 2003 -- Sendai, Japa

Order-of-magnitude physics of neutron stars

We use basic physics and simple mathematics accessible to advanced undergraduate students to estimate the main properties of neutron stars. We set the stage and introduce relevant concepts by discussing the properties of "everyday" matter on Earth, degenerate Fermi gases, white dwarfs, and scaling relations of stellar properties with polytropic equations of state. Then, we discuss various physical ingredients relevant for neutron stars and how they can be combined in order to obtain a couple of different simple estimates of their maximum mass, beyond which they would collapse, turning into black holes. Finally, we use the basic structural parameters of neutron stars to briefly discuss their rotational and electromagnetic properties.Comment: 13 pages, 3 figures, accepted for publication in European Physical Journal

Finite-element analysis on cantilever beams coated with magnetostrictive material

The main focus of this paper is to highlight some of the key criteria in successful utilization of magnetostrictive materials within a cantilever based microelectromechanical system (MEMS). The behavior of coated cantilever beams is complex and many authors have offered solutions using analytical techniques. In this study, the FEMLAB finite-element multiphysics package was used to incorporate the full magnetostrictive strain tensor and couple it with partial differential equations from structural mechanics to solve simple cantilever systems. A wide range of geometries and material properties were solved to study the effects on cantilever deflection and the system resonance frequencies. The latter were found by the use of an eigen-frequency solver. The models have been tailored for comparison with other such data within the field and results also go beyond previous work

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries, and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed and a solution strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201

Zircon to monazite phase transition in CeVO4

X-ray diffraction and Raman-scattering measurements on cerium vanadate have been performed up to 12 and 16 GPa, respectively. Experiments reveal that at 5.3 GPa the onset of a pressure-induced irreversible phase transition from the zircon to the monazite structure. Beyond this pressure, diffraction peaks and Raman-active modes of the monazite phase are measured. The zircon to monazite transition in CeVO4 is distinctive among the other rare-earth orthovanadates. We also observed softening of external translational Eg and internal B2g bending modes. We attributed it to mechanical instabilities of zircon phase against the pressure-induced distortion. We additionally report lattice-dynamical and total-energy calculations which are in agreement with the experimental results. Finally, the effect of non-hydrostatic stresses on the structural sequence is studied and the equations of state of different phases are reported.Comment: 45 pages, 8 figures, 8 table

Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations

We present a study of hydrogen at pressures higher than molecular dissociation using the Coupled Electron-Ion Monte Carlo method. These calculations use the accurate Reptation Quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of phase space, we report the free energy obtained by thermodynamic integration. We find very good agreement with DFT calculations for pressures beyond 600 GPa and densities above $\rho=1.4 g/cm^3$. Both thermodynamic as well as structural properties are accurately reproduced by DFT calculations. This agreement gives a strong support to the different approximations employed in DFT, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests a reinvestigation of planetary models, previously constructed using the Saumon-Chabrier-Van Horn equations of state.Comment: 9 pages, 7 figure

Models and numerical methods for electrolyte flows

The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier--Stokes equations for fluid flow. This contribution discusses historical and recent model developments beyond the dilute solution assumption and focuses on the effects of finite ion sizes and solvation. A novel numerical solution approach is presented and verified here which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces