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

Dynamics & Predictions in the Co-Event Interpretation

Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events for a range of systems including single time 'Copenhagen measurements'. This 'co-event interpretation' presents us with a new ontology, in which a single 'co-event' is real. A new ontology necessitates a review of the dynamical & predictive mechanism of a theory, and in this paper we begin the process by exploring means of expressing the dynamical and predictive content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein

U and Th content in the Central Apennines continental crust: a contribution to the determination of the geo-neutrinos flux at LNGS

The regional contribution to the geo-neutrino signal at Gran Sasso National Laboratory (LNGS) was determined based on a detailed geological, geochemical and geophysical study of the region. U and Th abundances of more than 50 samples representative of the main lithotypes belonging to the Mesozoic and Cenozoic sedimentary cover were analyzed. Sedimentary rocks were grouped into four main "Reservoirs" based on similar paleogeographic conditions and mineralogy. Basement rocks do not outcrop in the area. Thus U and Th in the Upper and Lower Crust of Valsugana and Ivrea-Verbano areas were analyzed. Based on geological and geophysical properties, relative abundances of the various reservoirs were calculated and used to obtain the weighted U and Th abundances for each of the three geological layers (Sedimentary Cover, Upper and Lower Crust). Using the available seismic profile as well as the stratigraphic records from a number of exploration wells, a 3D modelling was developed over an area of 2^{\circ}x2^{\circ} down to the Moho depth, for a total volume of about 1.2x10^6 km^3. This model allowed us to determine the volume of the various geological layers and eventually integrate the Th and U contents of the whole crust beneath LNGS. On this base the local contribution to the geo-neutrino flux (S) was calculated and added to the contribution given by the rest of the world, yielding a Refined Reference Model prediction for the geo-neutrino signal in the Borexino detector at LNGS: S(U) = (28.7 \pm 3.9) TNU and S(Th) = (7.5 \pm 1.0) TNU. An excess over the total flux of about 4 TNU was previously obtained by Mantovani et al. (2004) who calculated, based on general worldwide assumptions, a signal of 40.5 TNU. The considerable thickness of the sedimentary rocks, almost predominantly represented by U- and Th- poor carbonatic rocks in the area near LNGS, is responsible for this difference.Comment: 45 pages, 5 figures, 12 tables; accepted for publication in GC

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

The Alpine-Carpathian-Dinaridic orogenic system: correlation and evolution of tectonic units

A correlation of tectonic units of the Alpine-Carpathian-Dinaridic system of orogens, including the substrate of the Pannonian and Transylvanian basins, is presented in the form of a map. Combined with a series of crustal-scale cross sections this correlation of tectonic units yields a clearer picture of the threedimensional architecture of this system of orogens that owes its considerable complexity to multiple overprinting of earlier by younger deformations. The synthesis advanced here indicates that none of the branches of the Alpine Tethys and Neotethys extended eastward into the Dobrogea Orogen. Instead, the main branch of the Alpine Tethys linked up with the Meliata- Maliac-Vardar branch of the Neotethys into the area of the present-day Inner Dinarides. More easterly and subsidiary branches of the Alpine Tethys separated Tisza completely, and Dacia partially, from the European continent. Remnants of the Triassic parts of Neotethys (Meliata-Maliac) are preserved only as ophiolitic mélanges present below obducted Jurassic Neotethyan (Vardar) ophiolites. The opening of the Alpine Tethys was largely contemporaneous with the Latest Jurassic to Early Cretaceous obduction of parts of the Jurassic Vardar ophiolites. Closure of the Meliata-Maliac Ocean in the Alps and West Carpathians led to Cretaceous-age orogeny associated with an eclogitic overprint of the adjacent continental margin. The Triassic Meliata- Maliac and Jurassic Western and Eastern Vardar ophiolites were derived from one single branch of Neotethys: the Meliata-Maliac-Vardar Ocean. Complex geometries resulting from out-of-sequence thrusting during Cretaceous and Cenozoic orogenic phases underlay a variety of multi-ocean hypotheses, that were advanced in the literature and that we regard as incompatible with the field evidence. The present-day configuration of tectonic units suggests that a former connection between ophiolitic units in West Carpathians and Dinarides was disrupted by substantial Miocene-age dislocations along the Mid-Hungarian Fault Zone, hiding a former lateral change in subduction polarity between West Carpathians and Dinarides. The SW-facing Dinaridic Orogen, mainly structured in Cretaceous and Palaeogene times, was juxtaposed with the Tisza and Dacia Mega-Units along a NW-dipping suture (Sava Zone) in latest Cretaceous to Palaeogene times. The Dacia Mega-Unit (East and South Carpathian Orogen, including the Carpatho-Balkan Orogen and the Biharia nappe system of the Apuseni Mountains), was essentially consolidated by E-facing nappe stacking during an Early Cretaceous orogeny, while the adjacent Tisza Mega-Unit formed by NW-directed thrusting (in present-day coordinates) in Late Cretaceous times. The polyphase and multi-directional Cretaceous to Neogene deformation history of the Dinarides was preceded by the obduction of Vardar ophiolites onto to the Adriatic margin (Western Vardar Ophiolitic Unit) and parts of the European margin (Eastern Vardar Ophiolitic Unit) during Late Jurassic to Early Cretaceous times

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

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio