The effective equation method

In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behaviour of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three-- and four--wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. In the case of the NLS equation we use next some heuristic approximation from the arsenal of wave turbulence to show that under the iterated limit "the volume goes to infinity", taken after the limit "the amplitude of oscillations goes to zero", the energy spectrum of solutions for the effective equation is described by a Zakharov-type kinetic equation. Evoking the Zakharov ansatz we show that stationary in time and homogeneous in space solutions for the latter equation have a power law form. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanology

International Nuclear Medicine Consensus on the Clinical Use of Amyloid Positron Emission Tomography in Alzheimer's Disease.

Alzheimer's disease (AD) is the main cause of dementia, with its diagnosis and management remaining challenging. Amyloid positron emission tomography (PET) has become increasingly important in medical practice for patients with AD. To integrate and update previous guidelines in the field, a task group of experts of several disciplines from multiple countries was assembled, and they revised and approved the content related to the application of amyloid PET in the medical settings of cognitively impaired individuals, focusing on clinical scenarios, patient preparation, administered activities, as well as image acquisition, processing, interpretation and reporting. In addition, expert opinions, practices, and protocols of prominent research institutions performing research on amyloid PET of dementia are integrated. With the increasing availability of amyloid PET imaging, a complete and standard pipeline for the entire examination process is essential for clinical practice. This international consensus and practice guideline will help to promote proper clinical use of amyloid PET imaging in patients with AD

ASEAN and the Dynamics of Resistance to Sovereignty Violation:The Case of the Third Indochina War (1978–1991)

This article investigates the history of ASEAN’s relationship to external intervention in regional affairs. It addresses a specific question: What was the basic cause of the success of ASEAN resistance to the Vietnamese challenge to ASEAN’s sovereignty from 1978-1991? ASEAN’s history is understood in terms of a realist theoretical logic, in terms of the relationship between an ASEAN state with the most compelling interests at stake in a given issue, which I call a ‘vanguard state,’ and selected external powers. Using the Third Indochina War (1978–1991) as a case study, this article contends that ASEAN’s ability to resist violations to the sovereignty of Thailand from a Soviet-backed Vietnam is a consequence of high interest convergence between Thailand, and a designated external power, China

Planet-compatible pathways for transitioning the chemical industry

Chemical products, such as plastics, solvents, and fertilizers, are essential for supporting modern lifestyles. Yet, producing, using, and disposing of chemicals creates adverse environmental impacts which threaten the industry’s license to operate. This study presents seven planet-compatible pathways toward 2050 employing demand-side and supply-side interventions with cumulative total investment costs of US$1.2–3.7 trillion. Resource efficiency and circularity interventions reduce global chemicals demand by 23 to 33% and are critical for mitigating risks associated with using fossil feedstocks and carbon capture and sequestration, and constraints on available biogenic and recyclate feedstocks. Replacing fossil feedstocks with biogenic/air-capture sources, shifting carbon destinations from the atmosphere to ground, and electrifying/decarbonizing energy supply for production technologies could enable net negative emissions of 0.5 GtCO2eq y−1 across non-ammonia chemicals, while still delivering essential chemical-based services to society

Theory of magnetically powered jets

The magnetic theory for the production of jets by accreting objects is reviewed with emphasis on outstanding problem areas. An effort is made to show the connections behind the occasionally diverging nomenclature in the literature, to contrast the different points of view about basic mechanisms, and to highlight concepts for interpreting the results of numerical simulations. The role of dissipation of magnetic energy in accelerating the flow is discussed, and its importance for explaining high Lorentz factors. The collimation of jets to the observed narrow angles is discussed, including a critical discussion of the role of `hoop stress'. The transition between disk and outflow is one of the least understood parts of the magnetic theory; its role in setting the mass flux in the wind, in possible modulations of the mass flux, and the uncertainties in treating it realistically are discussed. Current views on most of these problems are still strongly influenced by the restriction to 2 dimensions (axisymmetry) in previous analytical and numerical work; 3-D effects likely to be important are suggested. An interesting problem area is the nature and origin of the strong, preferably highly ordered magnetic fields known to work best for jet production. The observational evidence for such fields and their behavior in numerical simulations is discussed. I argue that the presence or absence of such fields may well be the `second parameter' governing not only the presence of jets but also the X-ray spectra and timing behavior of X-ray binaries.Comment: 29 pages. Publication delays offered the opportunity for further corrections, an expansion of sect 4.2, and one more Fig. To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions

Improving Genetic Prediction by Leveraging Genetic Correlations Among Human Diseases and Traits

Genomic prediction has the potential to contribute to precision medicine. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7 for height to 47 for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait. © 2018 The Author(s)