From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Online prevention of disordered eating in at-risk young-adult women: A two-country pragmatic randomized controlled trial

This article has been published in a revised form in Psychological Medicine. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2017. This author accepted manuscript is made available following 6 month embargo from date of publication (Dec 2017) in accordance with the publisher’s copyright policyDisordered eating (DE) is a widespread, serious problem. Efficacious prevention programs that can be delivered at-scale are needed. A pragmatic randomized controlled trial of two online programs was conducted. Participants were young-adult women from Australia and New Zealand seeking to improve their body image. Media Smart-Targeted (MS-T) and Student Bodies (SB) were both 9-module interventions released weekly, whilst control participants received positive body image information. Primary [Eating Disorder Examination–Questionnaire (EDE-Q) Global], secondary (DE risk factors) and tertiary (DE) outcome measures were completed at baseline, post-program, 6- and 12-month follow-up. Baseline was completed by 608 women (M age = 20.71 years); 33 were excluded leaving 575 randomized to: MS-T (N = 191); SB (N = 190) or control (N = 194). Only 66% of those randomized to MS-T or SB accessed the intervention and were included in analyses with controls; 78% of this sample completed measures subsequent to baseline. Primary intent-to-treat (ITT) analyses revealed no differences between groups, while measure completer analyses found MS-T had significantly lower EDE-Q Global than controls at 12-month follow-up. Secondary ITT analyses found MS-T participants reported significantly higher quality of life–mental relative to both SB and controls (6-month follow-up), while MS-T and controls had lower clinical impairment relative to SB (post-program). Amongst measure completers, MS-T scored significantly lower than controls and SB on 5 variables. Of those with baseline DE, MS-T participants were significantly less likely than controls to have DE at 12-month follow-up. Given both programs were not therapist-moderated, MS-T has potential to achieve reductions in DE risk at low implementation costs

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Forecasting the expansion of the invasive golden mussel Limnoperna fortunei in Brazilian and North American rivers based on its occurrence in the Paraguay River and Pantanal wetland of Brazil.

The bivalve Limnoperna fortunei (Dunker, 1857), also called golden mussel, is native to Asia but becoming dispersed around the world. The golden mussel resembles the invasive dreissenid bivalves in many respects, and although much less studied it evidently has broader environmental tolerances. The golden mussel was introduced into the La Plata River estuary (South America) and quickly expanded upstream to the north, into the tropical Paraguay River reaching a large floodplain area in Brazil known as the Pantanal wetland. The golden mussel tolerates environmental conditions in the Pantanal that would be inhospitable for most bivalves, but mussel mortality has been observed during the most extreme oxygen depletion events. Based on knowledge about the limiting factors for the golden mussel in the Pantanal wetland, its potential distribution was predicted for the remainder of the Paraguay River basin where the species is not present, as well as in other river systems throughout Brazil. Forecasts of potential distribution in Brazilian river systems were based on physicochemical limitations for shell calcification, and specifically on lower thresholds of dissolved calcium concentrations and the calcium carbonate (calcite) index of saturation, which may be a better indicator of calcification potential in low-calcium waters than calcium concentration alone. In addition to examining spatial patterns in calcium and calcification potential, these and other limnological and climate variables were used in ecological niche modeling using GARP and Maxent algorithms. Forecasts of potential distributions in three major North American river systems (Mississippi, Colorado, and Rio Grande) were based mainly on water temperature because calcium availability and calcification evidently would not be limiting to golden mussel establishment in those waters. Due to the greater tolerance of the golden mussel to conditions known to limit other bivalves, as well as its greater ability for shell calcification in low-calcium water, the golden mussel could potentially become broadly distributed throughout Brazil. According to its thermal tolerance L. fortunei could become established in the Mississippi, Colorado and Rio Grande drainage systems, although the northern Mississippi River system including the Missouri River may be too cool in the winter to support the golden mussel.Proceedings of the 16th International Conference on Aquatic Invasive Species

Some anomalies of mesosphere/lower thermosphere parameters during the recent solar minimum

The recent solar minimum has been characterized by an anomalous strong decrease of thermospheric density since 2005. Here we analyze anomalies of mesosphere/lower thermosphere parameters possibly connected with this effect. In particular, nighttime mean LF reflection heights measured at Collm, Germany, show a very strong decrease after 2005, indicating a density decrease. This decrease is also visible in mean meteor heights measured with VHF meteor radar at Collm. This density decrease is accompanied by an increase of gravity wave (GW) amplitudes in the upper mesosphere and a decrease in the lower thermosphere. On the decadal scale, GWs are negatively correlated with the background zonal wind, but this correlation is modulated in the course of the solar cycle, indicating the combined effect of GW filtering and density decrease

Lorenz integrable system moves \`a la Poinsot

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.Comment: 14 pages, 6 figure

Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in the literature to further split up the kinetic part of the Hamiltonian, which lowers the accuracy. The goal of this note is to comment on the best combination of optimized splitting and gradient methods that avoids splitting the kinetic energy. These schemes are generally applicable, but the optimal scheme depends on the desired level of accuracy. For simulations of liquid water it is found that the velocity Verlet scheme is only optimal for crude simulations with accuracies larger than 1.5%, while surprisingly a modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for publication in the Journal of Chemical Physic

Lie point symmetries and first integrals: the Kowalevsky top

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page