General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove's theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem.Comment: Short comment on possible generalization to wider classes of systems added; accepted for publication in Journal of Statistical Physic

Estimating a Signal In the Presence of an Unknown Background

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density estimator. The method returns parameter estimates as well as errors on those estimates. Simulation studies show that these estimates are unbiased and that the errors are correct

Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems

Distributional impacts of carbon taxation and revenue recycling: a behavioural microsimulation. ESRI WP626, June 2019

Carbon taxation is a regressive policy which contributes to public opposition towards same. We employ the Exact Affine Stone Index demand system to examine the extent to which carbon taxation in Ireland reduces emissions, as well as its distributional impacts. The Engel curves for various commodity groupings are found to be non-linear, which renders the particular demand system we have chosen more suitable than other methods found in the extant literature. We find that a carbon tax increase can decrease emissions, but is indeed regressive. Recycling the revenues to households mitigates these regressive effects. A targeted allocation that directs the revenues towards less affluent households is found to reduce inequality more than flat allocation that divides the revenues equally amongst all households; however both methods are capable of mitigating the regressive effects of the tax increase

Fatigue failure analysis of vibrating screen spring by means of finite element simulation: a case study

Vibrating screens are often used in the mining industry to separate mineral particles by size. In many designs, spring arrays are used to provide the system with the necessary stiffness for screens to vibrate in a controlled manner. Naturally, these springs are subjected to varying loading cycles, which can cause their premature fatigue failure. This behavior has been studied by means of finite element analysis and compared with data obtained from a real case scenario, in which a helical spring failed. The 3D computational model was developed using the geometric characteristics and material properties of a fractured spring, as well as the loading characteristics of a specific vibrating screen. The meshing and the simulation tasks were performed in the general purpose software ANSYS Mechanical. Given the nature of the helical springs and the high-cycle loading conditions, for the fatigue analysis it was determined that a stress-life approach with constant amplitude and non-proportional loading best fit the investigated phenomenon. In solving the nonproportional loading case, stress values of two static scenarios were required to determine the upper and lower limits. Then, to perform the fatigue calculations a solution combination was used. In addition, in order to correct the effect of mean stress and calculate the stresses component respectively the Goodman and Von Mises theories were employed. Simulation results showed that spring would present failure below the second turn of the coil when working with the full nominal load during nearly forty million cycles. These results strongly agreed with the data extracted from a vibrating screen where fractured spring had been working. Fatigue analysis also predicted that the nominal load should be reduced to 90% in order for the spring to meet the minimum life requirements before failure occur