Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile

35 pages; main theorems gathered in section 2; examples and counterexamples gathered in section 3; examples 3.1 and 3.4 added; example 3.3 extended to the case of smooth momentum profiles; proof of Maslov's Theorem 1.1 (formerly Proposition 7.4) removed; some typos corrected.International audienceConsider in the phase space of classical mechanics a Radon measure that is a probability density carried by the graph of a Lipschitz continuous (or even less regular) vector field. We study the structure of the push-forward of such a measure by a Hamiltonian flow. In particular, we provide an estimate on the number of folds in the support of the transported measure that is the image of the initial graph by the flow. We also study in detail the type of singularities in the projection of the transported measure in configuration space (averaging out the momentum variable). We study the conditions under which this projected measure can have atoms, and give an example in which the projected measure is singular with respect to the Lebesgue measure and diffuse. We discuss applications of our results to the classical limit of the Schrödinger equation. Finally we present various examples and counterexamples showing that our results are sharp

On the Classical Limit of the Schr\"{o}dinger Equation

This paper provides an elementary proof of the classical limit of the Schr\"{o}dinger equation with WKB type initial data and over arbitrary long finite time intervals. We use only the stationary phase method and the Laptev-Sigal simple and elegant construction of a parametrix for Schr\"{o}dinger type equations [A. Laptev, I. Sigal, Review of Math. Phys. 12 (2000), 749-766]. We also explain in detail how the phase shifts across caustics obtained when using the Laptev-Sigal parametrix are related to the Maslov index.Comment: 21 page

Semiclassical Propagation of Coherent States for the Hartree equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by C \sqrt {\var}, \var being the Planck constant. Finally we present a full formal asymptotic expansion

China's soil and groundwater management challenges: Lessons from the UK's experience and opportunities for China

There are a number of specific opportunities for UK and China to work together on contaminated land management issues as China lacks comprehensive and systematic planning for sustainable risk based land management, encompassing both contaminated soil and groundwater and recycling and reuse of soil. It also lacks comprehensive risk assessment systems, structures to support risk management decision making, processes for verification of remediation outcome, systems for record keeping and preservation and integration of contamination issues into land use planning, along with procedures for ensuring effective health and safety considerations during remediation projects, and effective evaluation of costs versus benefits and overall sustainability. A consequence of the absence of these overarching frameworks has been that remediation takes place on an ad hoc basis. At a specific site management level, China lacks capabilities in site investigation and consequent risk assessment systems, in particular related to conceptual modelling and risk evaluation. There is also a lack of shared experience of practical deployment of remediation technologies in China, analogous to the situation before the establishment of the independent, non-profit organisation CL:AIRE (Contaminated Land: Applications In Real Environments) in 1999 in the UK. Many local technology developments are at lab-scale or pilot-scale stage without being widely put into use. Therefore, a shared endeavour is needed to promote the development of technically and scientifically sound land management as well as soil and human health protection to improve the sustainability of the rapid urbanisation in China

Land Contamination and Brownfield Management Policy Development in China: Learning from the UK Experience

Ming Liu (Department of Science, Technology & Innovation, British Consulate-General Guangzhou), Xia Yang (Administrative Centre for China’s Agenda21) and Paul Wills (UK Trade & Investment) helped discussion and revision of the report. Diogo Gomes (Cranfield University) also provided support for the graphical arts and assisted with the editing. The authors are grateful to all partners of the SPF project which include a wide team of collaborators and advisors across China and UK for their useful discussions and contribution during the two workshops organised during the project. Government, Academia, Industry and Public bodies have been collaborating together to drive structural changes far beyond the scope of a single organisation.Over the last 30 years, China’s fast urbanisation along with huge expansion of its manufacturing industry has led to the emergence of significant soil and water contamination problems across China. In the meantime, a number of policies and regulatory agencies for the protection of the environment have been implemented to stop deliberate pollution and more recently to address pollution prevention at source on a wider scale. Soil protection and management have been featured in policy discussions since the late 1950s in China. However, the topic has recently been of greatly expanded interest in the development of emerging policies, particularly with regards to the role of soil as a resource, independent of the functions that it carries out. Soil provides multiple important functions such as provision of food and raw materials, a platform for urban development and human wellbeing and a filtering and transforming media for water, nutrients, and carbon. However as pointed out by Yuan Si, Deputy Director of the Environmental Protection and Resources Conservation Committee of the National People Congress (China Daily, 11 March 2016), the move toward integrated management that has been driving policies for air and water has proven to be a challenge for soil management, mainly due to the multiple functions that soils provide. This is also true internationally and explained by several drivers for soil protection including among others soil contamination, construction, agriculture and amenity value.Foreign and Commonwealth Office’s Prosperity Fund programme - China Prosperity Strategic Programme Fund (SPF) 15SU3

Promoting Sino-UK Collaboration on Developing Low Carbon and Sustainable Methodologies for Brownfields and Marginal Land Re-use in China

The authors are grateful to all partners of the SPF project which include a wide team of collaborators and advisors across China and UK for their useful discussions and contribution during the project. Ming Liu and Chris He (Department of Science, Technology & Innovation, British Consulate-General Guangzhou), Rongxia Liu and Xia Yang (Administrative Centre for China’s Agenda21), Kate Canning (Arup) and David Middleton (Department for Environment and Rural Affairs, UK) helped discussion and revision of the report. We acknowledge the financial support from the Foreign Common Office’s Prosperity Fund programme. We also are grateful to the contribution of the University of Brighton and the Land Trust who supported the PSRP case study development project and shared its findings with this project. This report is one of the outputs of the China Prosperity Strategic Programme Fund (SPF) on “Promoting Sino-UK collaboration on developing low carbon and sustainable methodologies for Brownfields and marginal land re-use in China” (project 16AG15)Rapid urbanisation and changes in land use resulting from industrial change has left a legacy of vast polluted industrial and commercial areas (also called brownfields) and marginal land areas. Recent evidence from the UK, EU and USA indicate that these land areas may have considerable potential for renewables production, for example from solar, wind or biomass. In parallel there are opportunities for carbon storage in rehabilitated soil, as well as substitution by the production of renewables. The UK is also leading the understanding in the wider parallel benefits that can be achieved from ecosystem services and public health benefits from improved provision of green space. These multiple services can be provided together, in synergy, from soft re-uses of post-industrial sites, and in this way the post-industrial regeneration areas in China should be seen as a major opportunity for new enterprise, society and the wider environment. The improving bankability of renewable energy projects, and the possibility of creating a voluntary carbon offset business, means that revenue streams may be sufficient to pay for ongoing land management over time as a profit generating activity. In terms of fastest benefit to UK PLC and China, the likelihood is that combination of renewable energies with “dual use” for habitat will provide both more readily commercial brownfield re-use opportunities for cities in China in the short term, and also create better carbon management opportunities, as well as a variety of wider sustainability benefits. Thus this type of re-uses will create a platform for rapid commercial exchange and development between Chinese and UK companies. Considering that China is preparing an action plan for managing soil pollution and remediation across the country estimated to be RMB 7tn which is equivalent to one-third of the national exchange reserves, this report on developing low carbon and sustainable methodologies for brownfields and marginal land re-use in China provides timely information that will support the decision making for sustainable remediation opportunities in China. The report is intended to serve as a tool and resource guide to stakeholders involved in land remediation willing to engage in sustainable remediation implementation for renewable energy and carbon management applications. It is intended to inform remediation stakeholders unfamiliar with sustainable remediation about the concept, practices, and available resources. The report capitalises on UK leadership positions on the sustainable rehabilitation of brownfields land (SURF-UK), the soft re-use of brownfields (e.g. for energy or amenity rather than buildings); effective end-use directed risk management for contaminated land, and sustainable remediation.Foreign Common Office’s Prosperity Fund programme SPF project 16AG1

The antibiotic and heavy metal tolerances of soil bacteria and heavy metal pollution

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