Hamilton's principle: why is the integrated difference of kinetic and potential energy minimized?

I present an intuitive answer to an often asked question: why is the integrated difference K-U between the kinetic and potential energy the quantity to be minimized in Hamilton's principle? Using elementary arguments, I map the problem of finding the path of a moving particle connecting two points to that of finding the minimum potential energy of a static string. The mapping implies that the configuration of a non--stretchable string of variable tension corresponds to the spatial path dictated by the Principle of Least Action; that of a stretchable string in space-time is the one dictated by Hamilton's principle. This correspondence provides the answer to the question above: while a downward force curves the trajectory of a particle in the (x,t) plane downward, an upward force of the same magnitude stretches the string to the same configuration x(t).Comment: 7 pages, 4 figures. Submitted to the American Journal of Physic

Self-Control in Cyberspace: Applying Dual Systems Theory to a Review of Digital Self-Control Tools

Many people struggle to control their use of digital devices. However, our understanding of the design mechanisms that support user self-control remains limited. In this paper, we make two contributions to HCI research in this space: first, we analyse 367 apps and browser extensions from the Google Play, Chrome Web, and Apple App stores to identify common core design features and intervention strategies afforded by current tools for digital self-control. Second, we adapt and apply an integrative dual systems model of self-regulation as a framework for organising and evaluating the design features found. Our analysis aims to help the design of better tools in two ways: (i) by identifying how, through a well-established model of self-regulation, current tools overlap and differ in how they support self-control; and (ii) by using the model to reveal underexplored cognitive mechanisms that could aid the design of new tools.Comment: 11.5 pages (excl. references), 6 figures, 1 tabl

Anomalous Behavior of the Contact Process with Aging

The effect of power-law aging on a contact process is studied by simulation and using a mean-field approach. We find that the system may approach its stationary state in a nontrivial, nonmonotonous way. For the particular value of the aging exponent, $\alpha=1$, we observe a rich set of behaviors: depending on the process parameters, the relaxation to the stationary state proceeds as $1/\ln t$ or via a power law with a nonuniversal exponent. Simulation results suggest that for $0<\alpha<1$, the absorbing-state phase transition is in the universality class of directed percolation.Comment: 4 pages revtex (twocolumn, psfig), 3 figure

Latitudinal decline in stand biomass and productivity at the elevational treeline in the Ural mountains despite a common thermal growth limit

Aim: To quantify tree biomass and stand productivity of treeline ecotones and identify driving factors. Location: treeline ecotones of seven regions from the South to Polar Urals, spanning a latitudinal gradient of 1,500 km. Taxa: Picea obovata, Betula pubescens, Larix sibirica. Methods: Stand biomass and productivity were estimated across 18 elevational transects from the tree species line to the closed forest line based on allometric measurements of 326 trees (including roots for 53 trees), stand structure assessments and demographic patterns of 20,600 trees. Stand growth data were linked to (a) temperatures monitored in situ for five years in the South and Polar Urals, (b) climate variables extrapolated from nearby climate stations and (c) measures of nutrient availability in soils and tree foliage. Results: treeline position along the latitudinal gradient occurred at a similar mean growing season temperature. Despite the common cold limitation of tree distribution along the Ural mountain range, stand biomass and productivity within the treeline ecotone decreased by a factor of three and five from the South to the Polar Urals, mainly due to a declining stand density. Among climatic variables, growing season length decreased by 20% and winter temperatures declined by 4°C towards the Polar Urals, whereas growing degree days > 5°C remained similar, averaging 554 ± 9°C. Soil development was poorer in the Polar than in the South Urals, and plant-available N and P in the soil were 20 and 30 times lower, respectively, probably due to lower winter temperatures. Main conclusions: Our results suggest that once the thermal limitation for tree growth is relieved, soil fertility—restricted by permafrost and low soil temperatures during winter—plays a key and yet underexplored role for stand productivity in treeline ecotones. The observed latitudinal decline in stand productivity is important for above- and belowground diversity and functioning. © 2020 The Authors. Journal of Biogeography published by John Wiley & Sons Lt

Linear frictional forces cause orbits to neither circularize nor precess

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov[1]. In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coeComment: 16 pages. 1 figure, Rewrite for resubmissio

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Gain and Loss Learning Differentially Contribute to Life Financial Outcomes

Emerging findings imply that distinct neurobehavioral systems process gains and losses. This study investigated whether individual differences in gain learning and loss learning might contribute to different life financial outcomes (i.e., assets versus debt). In a community sample of healthy adults (n = 75), rapid learners had smaller debt-to-asset ratios overall. More specific analyses, however, revealed that those who learned rapidly about gains had more assets, while those who learned rapidly about losses had less debt. These distinct associations remained strong even after controlling for potential cognitive (e.g., intelligence, memory, and risk preferences) and socioeconomic (e.g., age, sex, ethnicity, income, education) confounds. Self-reported measures of assets and debt were additionally validated with credit report data in a subset of subjects. These findings support the notion that different gain and loss learning systems may exert a cumulative influence on distinct life financial outcomes

A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.publishedVersionFil: Bellomo, Nicola. Universidad de Granada. Departamento de Matemática Aplicada; España.Fil: Bingham, Richard. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Chaplain, Mark A. J. University of St Andrews. School of Mathematics and Statistics; Scotland.Fil: Dosi, Giovanni. Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia.Fil: Forni, Guido. Accademia Nazionale dei Lincei; Italia.Fil: Knopoff, Damian A. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Knopoff, Damian A. Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina. Centro de Investigacion y Estudios de Matematica; Argentina.Fil: Lowengrub, John. University California Irvine. Department of Mathematics; United States.Fil: Twarock, Reidun. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Virgillito, Maria Enrica.Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia

Accommodating stake effects under prospect theory

One of the stylized facts underlying prospect theory is a four-fold pattern of risk preferences. People have been shown to be risk seeking for small probability gains and large probability losses, while being risk averse for large probability gains and small probability losses. Another fourfold pattern of risk preferences over outcomes, postulated by Harry Markowitz in 1952, has received much less attention and is currently not integrated into prospect theory. In two experiments, we show that risk preferences may change over outcomes. While we find people to be risk seeking for small outcomes, this turns to risk neutrality and later risk aversion as stakes increase. We then show how a one-parameter logarithmic utility function fits such stake effects significantly better under prospect theory than the power or exponential functions mostly used when fitting prospect theory models. We further investigate the extent to which the use of ill-suited functional forms to represent utility may result in violations of prospect theory, and whether such violations disappear when using logarithmic utility