The Amazon rainforest is threatened by land-use change and increasing drought and fire frequency. Studies suggest an abrupt dieback of large parts of the rainforest after partial forest loss, but the critical threshold, underlying mechanisms, and possible impacts of forest degradation on the monsoon circulation remain uncertain. Here, we use a nonlinear dynamical model of the moisture transport ...

Let <i><b>R</b></i> be a real closed field. We consider basic semi-algebraic sets defined by <i>n</i>-variate equations/inequalities of s symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by 2<i>d</i> &#60; <i>n</i>. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point ...

Low-salinity meltwater from Arctic sea ice and its snow cover accumulates and creates under-ice meltwater layers below sea ice.These meltwater layers can result in the formation of new ice layers, or false bottoms, at the interface of this low-salinity meltwater and colder seawater. As part of the Multidisciplinary drifting Observatory for the Study of the Arctic Climate (MOSAiC), we used a ...

We introduce maps of Cauchy–Green strain tensor eigenvalues to barycentric coordinates to quantify and visualize the full geometry of three-dimensional deformation in stationary and non-stationary fluid flows. As a natural extension of Lagrangian coherent structure diagnostics, which provide separate scalar fields and a one-dimensional quantification of fluid deformation, our barycentric mapping ...

Sea ice drift and deformation, namely sea ice dynamics, play a significant role in atmosphere–ice–ocean coupling. Deformation patterns in sea ice can be observed over a wide range of spatial and temporal scales, though high-resolution objective quantification of these features remains difficult. In an effort to better understand local deformation of sea ice, we adapt the trajectory-stretching exponents ...

We show the global dynamics of spatial correlation of Pc2 wave activity can track the evolution of the 2015 St. Patrick's Day geomagnetic storm for an 8 hr time window around onset. The global spatially coherent response is tracked by forming a dynamical network from 1 s data using the full set of 100+ ground-based magnetometer stations collated by SuperMAG and Intermagnet. The pattern of spatial ...

On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for his theta function φ(q): φ(e^{−7π√7}) = 7^{−3/4}φ(e^{−π√7}){1 + ( )^{2/7} + ( )^{2/7} + ( )^{2/7}}. We give the three missing terms. In addition, we calculate the class invariant G_{343} and further special values of φ(e^{−nπ}), for n = 7, 21, 35, and 49.

The density ridge framework for estimating principal curves and surfaces has in a number of recent works been shown to capture manifold structure in data in an intuitive and effective manner. However, to date there exists no efficient way to traverse these manifolds as defined by density ridges. This is unfortunate, as manifold traversal is an important problem for example for shape estimation in ...

Students of physics in Norway typically spend a lot of time on mandatory problemsolving exercises that they must get a passing grade on to be allowed to take the exam. This is often a primarily summative assessment, which can limit the learning potential. <p> <p>In this contribution, we present an intervention in which traditional mandatory assignments are modified to put more emphasis on ...