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

Wigner Distribution Function Approach to Dissipative Problems in Quantum Mechanics with emphasis on Decoherence and Measurement Theory

We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced WDF but in the context of an exact master equation (b) use of a WDF for the complete system corresponding to entanglement at all times

Teleology and Realism in Leibniz's Philosophy of Science

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Voices of a Natural Prison: Tourism Development and Fisheries Management among the Political Ghosts of Pisagua, Chile

Caught between the sea and one of the world’s driest deserts, Pisagua’s coastal desert landscape is being transformed by the ways people utilize its natural isolation and rich protected waters. Periodically, these waters are altered by El Niño events. As distinct stakeholders -- fishermen, political activists, government planners, tourists and developers -- appropriate the site, their competing voices and identities alter the patterns of resource use. The most consistent resident group is a small number of fishermen, who have been willing to forego modern infrastructure to live in Pisagua’s harsh natural, political, and economic isolation. Because of this isolation, three separate national administrations have utilized the town as a political prison. The fishermen visualize political ghosts roaming the wooden ruins of this once thriving nitrate port. Developers today, however, aim to sanitize local political history in order to create a tourist “paradise”, and are being aided by a government plan to incorporate Pisagua into the core Chilean economy. Political activists, who use Pisagua as a pilgrimage site to indemnify the horrors of the past, protest this plan as one of political sacrilege. The plan also has concrete ramifications for the fishing families of Pisagua, who not only struggle with scarcity during major El Niño events, but now face encroaching tourism as globalization encompasses their space. The resident grassroots community leader has proffered additions to the plan that directly benefit the community. He is a former political activist with visions of a community-based “paradise” that would incorporate the marginal voices of the fishermen. We discuss his role as part of an approach which views identity and livelihood as practical and essential elements of any economically viable management plan. We examine shifting identity roles in light of the Pisagua plans, and frame our discussion within the context of three overlapping climate changes: economic, political, and environmental. This lays the foundation for a suggested adaptive management strategy that serves the economic needs of Pisagua through a recognition of the importance of stakeholder identity and livelihood. Key words: Pisagua, Chile, political ecology, ethnography, space and place, identity, livelihood, environment, El Niño, climate change, political activism, pilgrim, globalization, fisheries, migration, tourism, MPA, co-management

Global surveillance of cancer survival 1995-2009: analysis of individual data for 25,676,887 patients from 279 population-based registries in 67 countries (CONCORD-2)

BACKGROUND: Worldwide data for cancer survival are scarce. We aimed to initiate worldwide surveillance of cancer survival by central analysis of population-based registry data, as a metric of the effectiveness of health systems, and to inform global policy on cancer control. METHODS: Individual tumour records were submitted by 279 population-based cancer registries in 67 countries for 25·7 million adults (age 15-99 years) and 75,000 children (age 0-14 years) diagnosed with cancer during 1995-2009 and followed up to Dec 31, 2009, or later. We looked at cancers of the stomach, colon, rectum, liver, lung, breast (women), cervix, ovary, and prostate in adults, and adult and childhood leukaemia. Standardised quality control procedures were applied; errors were corrected by the registry concerned. We estimated 5-year net survival, adjusted for background mortality in every country or region by age (single year), sex, and calendar year, and by race or ethnic origin in some countries. Estimates were age-standardised with the International Cancer Survival Standard weights. FINDINGS: 5-year survival from colon, rectal, and breast cancers has increased steadily in most developed countries. For patients diagnosed during 2005-09, survival for colon and rectal cancer reached 60% or more in 22 countries around the world; for breast cancer, 5-year survival rose to 85% or higher in 17 countries worldwide. Liver and lung cancer remain lethal in all nations: for both cancers, 5-year survival is below 20% everywhere in Europe, in the range 15-19% in North America, and as low as 7-9% in Mongolia and Thailand. Striking rises in 5-year survival from prostate cancer have occurred in many countries: survival rose by 10-20% between 1995-99 and 2005-09 in 22 countries in South America, Asia, and Europe, but survival still varies widely around the world, from less than 60% in Bulgaria and Thailand to 95% or more in Brazil, Puerto Rico, and the USA. For cervical cancer, national estimates of 5-year survival range from less than 50% to more than 70%; regional variations are much wider, and improvements between 1995-99 and 2005-09 have generally been slight. For women diagnosed with ovarian cancer in 2005-09, 5-year survival was 40% or higher only in Ecuador, the USA, and 17 countries in Asia and Europe. 5-year survival for stomach cancer in 2005-09 was high (54-58%) in Japan and South Korea, compared with less than 40% in other countries. By contrast, 5-year survival from adult leukaemia in Japan and South Korea (18-23%) is lower than in most other countries. 5-year survival from childhood acute lymphoblastic leukaemia is less than 60% in several countries, but as high as 90% in Canada and four European countries, which suggests major deficiencies in the management of a largely curable disease. INTERPRETATION: International comparison of survival trends reveals very wide differences that are likely to be attributable to differences in access to early diagnosis and optimum treatment. Continuous worldwide surveillance of cancer survival should become an indispensable source of information for cancer patients and researchers and a stimulus for politicians to improve health policy and health-care systems