Zonal flow generation and toroidal Alfvén eigenmode excitation due to tearing mode induced energetic particle redistribution

Generation of the n = 0 zonal flow and excitation of the n = 1 toroidal Alfvén eigenmode (TAE) due to the redistribution of energetic particles (EPs) by the m/n = 2/1 tearing mode (TM) are systematically studied with the hybrid drift-kinetic magnetohydrodynamic (MHD) simulations (m and n represent the poloidal and toroidal mode number, respectively). In the presence of the m/n = 2/1 TM, the amplitude of the n = 1 TAE shows a slower decay after its first saturation due to the wave-particle nonlinearity and the nonlinear generation of the n = 0 & higher-n (n ≥ 2) sidebands. Meanwhile, a strong n = 0 zonal flow component is nonlinearly generated when both TAE and TM grow to large amplitudes. The redistribution of EPs by the m/n = 2/1 magnetic island results in a continuous drive on the background plasma, and finally produces the zonal flow through the MHD nonlinearity. In addition, the large m/n = 2/1 magnetic island is found to be responsible for the formation of the strong spatial gradient of the EP distribution through the resonance between EPs and TM, which can lead to burst of unstable TAE and destabilization of originally stable TAE.

Comparison of methods for recharge estimation and prediction in karstic aquifers under Mediterranean Climate

<p>Karst aquifers provided 9.2 % of the world’s population with fresh water in 2016 (Stevanović, 2019), but due to their dual flow behavior they are highly vulnerable to anthropogenic impacts and shifts in climate. In the near future, 52 out of 356 Mediterranean aquifers will be exposed to more extreme climatic conditions, which will enhance their water stress if the water usage is not adapted to available water resources (Nußbaum, 2020). Therefore, accurate and high resolution numerical - and empirical models are essential to calculate the groundwater recharge and water availability in complex karst aquifers that cover ~ 14 % of the earth’s ice free land (Stevanovic, 2019).</p><p>During the last decades, several empirical equations have been developed to calculate the recharge for Israel´s most important source of freshwater, the Western Mountain Aquifer (WMA). These equations calculate annual groundwater recharge of the entire 1.812 km<sup>2</sup> recharge area based on annual or monthly precipitation data. We analyzed the applicability of several new methods, such as Soil & Water Assessment Tool (SWAT), HydroGeoSphere (HGS) and Hydro- / Pedo- Transfer Functions (HPTF) to estimate groundwater recharge with  a higher resolution as this is essential to calculate proper water fluxes though the vadose zone of karstic aquifers when precipitation is affected by a high variability in space and time.</p><p>The hydrologic balance models,  e.g. SWAT (Neitsch et al., 2009),  calculate the water balance on a daily basis for specified Hydrologic Response Units (HRUs), while generalized HPTFs (Wessolek et al., 2009) use soil-, land cover-  and climate data to calculate  annual percolation rates on a coarse grid, in our case 500 m grid size. The dual continuum model using the code HGS (Brunner et al., 2011) is able to simulated based on Richards’s flow equation down- and upward water fluxes in the unsaturated zone accounting for both, a rapid flow component though the high permeable conduit and a slow flow component through the rock matrix.</p><p>The comparison of these empirical and new methods for groundwater recharge estimation show significant differences for hydrological extreme years, while results are similar during years with precipitation rates near the average value. For example, the empirical equation of Guttman & Zukerman (1995) gives  highest recharge values of all approaches during wet years, while the equation of Abusaada (2011) and the SWAT-model calculates  highest recharge values of all approaches during  dry years. Overall, the mean recharge ranges from 120 to 177 mm/a which equals 25 – 37 % of the average precipitation between 1990 – 2018.</p><p>These recharge rates are calculated based on IMS climate data. However, for recharge values used in water resources management regional climate projections are needed. For Israel a high resolution CORDEX-MENA climate projection (Hochman et al., 2018) is available for RCP4.5, showing an increase in temperature and decrease of precipitation during the winter of 2.5 °C and 40 %, respectively. Based on these climate projections the  SWAT-model estimates, that the average groundwater recharge for 2050 – 2070 will be 16 % lower than the reference period between 1980 – 2000.</p>

The superposition of a rotating wake with the atmospheric Ekman spiral

<p align="justify"><span>Stably stratified atmospheric boundary layers are often characterized by a veering wind profile, in which the wind direction changes clockwise (counterclockwise) with height in the Northern Hemisphere (Southern Hemisphere). Wind-turbine wakes respond to this veer in the incoming wind by stretching from a circular shape into an ellipsoid. Englberger, Dörnbrack and Lundquist (2020) investigate the relationship between this stretching and the direction of the turbine rotation by means of large-eddy simulations </span><span>(LESs)</span>.</p><p align="justify"><span>The basic physics underlying the interaction process of a rotating </span><span>wake</span><span> with a veering inflow can be described with the superposition of a Rankine vortex as representation of the wind-turbine </span><span>wake</span><span> with the characteristic </span><span>hemispheric-dependent </span><span>nighttime Ekman spiral of the atmospheric wind. </span><span>In dependence of the rotational direction </span><span>an</span><span>d</span><span> the hemisphere, this</span><span> superposition results in an amplification of the spanwise flow component if a </span><span>counterclockwise</span><span> rotating </span><span>rotor interacts with a northern hemispheric Ekman spiral </span><span>(</span><span>a clockwise rotating rotor interacts with a southern hemispheric Ekman spiral</span><span>)</span><span>. In case of a clockwise rotating rotor interacting with a northern hemispheric Ekman spiral </span><span>(</span><span>a counterclockwise rotating </span> <span>rotor interacting with a southern hemispheric Ekman spiral</span><span>)</span><span>, the superposition leads to a weakening of the spanwise flow component. In case of no veering inflow, the magnitude of the spanwise flow component is independent of the rotational direction.</span></p><p align="justify"><span>Th</span><span>ese theoretical</span> <span>superposition </span><span>effect</span><span> of the Ekman layer with the wake vortex </span><span>occur in nighttime </span><span>LESs, </span><span>where t</span><span>he rotational direction dependent magintude of the spanwise flow component further impacts the streamwise flow component in the wake. In particular, </span><span>there is a rotational direction dependent difference in </span><span>the </span><span>wake strength, </span><span>the </span><span>extension </span><span>of the wake</span><span>, </span><span>the wake </span><span>width, and </span><span>the wake </span><span>deflection </span><span>angle. </span><span>In more detail, a </span><span>northern hemispheric </span><span>veering wind in combination with a counterclockwise rotating actuator results in a larger streamwise velocity output, a larger spanwise wake width, and a larger wake deflection angle at the same downwind distance in comparison to a clockwise rotating turbine.</span></p><p><span>Englberger, Dörnbrack and Lundquist, 2020, Does the rotational direction of a wind turbine impact the wake in a stably stratified atmospheric boundary layer? </span><span><em>Wind Energ. Sci. </em></span><span><strong>5</strong></span><span>, 1359-1374.</span></p>

An Analysis of the Sources of Value Loss Following Financial Restatements

We decompose the total value loss around firms’ announcements of financial restatements into components arising from investors’ revisions in cash flows and discount rates. First, relative to population benchmarks, restatements represent circumstances in which the cash flow component becomes more important in explaining valuations. While we find significant contributions from both sources, with the cash flow component explaining more than 33% of the variation in stock returns surrounding restatement announcements, this component explains only 13% to 22% in comparable non-restating firms. When restatements are caused by underlying financial fraud, the discount rate impact becomes more important, explaining about 88% of return variation. On the contrary, the cash flow impact is relatively larger for firms with higher earnings persistence or restatements associated with errors. Our decomposition of the value loss helps explain returns in the post-announcement period. Firms with a higher relative discount rate impact experience a significant downward stock price drift after the initial announcement-related price decline. For firms with a higher relative cash flow impact, the evidence suggests the initial impact of the restatement announcement is more complete with no subsequent drift pattern. Our findings close gaps in the evidence on financial restatements and extend the literature on the drivers of stock price movements.

Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators

The mechanism underlying the emergence of seizures is one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous of endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.Author summaryDespite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems.

Nitrogen concentrations in flow separated river water

<p>Nitrogen (N) loads and concentrations have been successfully reduced in most Danish streams during the last 30 years. Thereby also reducing the impact of the main driver of marine eutrophication in Danish coastal waters. However, the trend in N-loads and concentrations vary substantially among the monitored streams. The understanding of this variation are of great importance and interest for the evaluation of measures implemented to combat N eutrophication and for forecasting of effects of further measures.</p><p>River hydrographs can be split into base flow and quick flow components and the N concentrations in these two components can, thereafter, be calculated. The N concentration in the two components varies over time showing both longer term and seasonal variation. The quick flow component typically having a high variation reflecting present days leaching of N from fields and this strata has been significantly reduced during the last 3 decades due to a more sustainable farming practices.</p><p>During base flow conditions, stream water typically holds less nitrogen due to N removal in groundwater. Reductions in agricultural nitrogen leaching over the past three decades has reduced concentrations in the quick flow component and reduced the load to ground water aquifers. As groundwater aquifers are often large with a capacity of several years of recharge, the response in base flow N-concentrations is expected to be slow compared to the response in quick flow. The low response of the N-concentrations in base flow have implications on the rate of change of the river concentrations and consequently riverine N-loads to coastal waters. In some cases, the base flow N-concentration might still be influenced by the larger N-leaching of the past (1960-1990).</p><p>We have analyzed a national data set for developments in N-concentrations during base flow and quick flow. The data set covers the in country range in catchment size, land use and geology. The data set spans 29 years covering the period 1990 – 2018. In addition, measurements from a few streams monitored for a longer period have been included in the analyses</p>

Partitioning of preferential flows in fracture networks: Smoothed Particle Dynamics simulations and analytical modeling of infiltration dynamics

<p>Recharge estimation in fractured-porous aquifers is an essential tool for proper water management and assessment of vulnerability. As opposed to diffuse infiltration, often encountered in consolidated and unconsolidated porous media, the infiltration dynamics in the unsaturated zone of fractured-porous media and karst aquifers often exhibit a rapid, gravity-driven flow component along preferential flow paths such as fractures, fracture networks, faults and fault zones. The partitioning into two hydraulically contrasting domains commonly leads to a breakdown of classical volume-effective flow equations employed in many FD or FEM modeling approaches which only consider the capillarity of the medium. Even in the presence of a porous matrix, preferential pathways along fractures have been shown to sustain flow percolation under equilibrium and non-equilibrium conditions. In order to properly capture the flow physics, various components have to be considered such as static and dynamic contact angles, surface tension, free-surface (multi-phase) interface dynamics, dynamic switching of flow modes (between droplets, rivulets, films) and associated formation of singularities in the case of merging or snapping flow. Here we study the process of vertical infiltration and partitioning at a single fracture intersection into a horizontal and vertical flow component. Via parallelized Smoothed Particle Hydrodynamics simulations we demonstrate how flow is first channeled into the horizontal fracture and then transitions into a Washburn-type inflow when pressure conditions are met and a connection to the next vertical flow path is established. We further proceed to capture this process with an analytical approach and finally demonstrate how to obtain a process-based transfer function to upscale this process to arbitrary fracture geometries and fracture cascades.</p>

Formalization of Fractional Flow Component in Higher-Order Logic Theorem Proving

Fractional calculus is a powerful tool for dealing with complex systems, and fractional flow component can effectively reflect the nonlinear gradual change of rheology in vibration state. Besides, higher-order logic theorem proving is a formal method for specification and verification. This paper, accordingly, presents a higher-order logic formalization of fractional flow component based on fractional calculus Caputo definition. The relationship between fractional order differential and integer order differential is verified according to fractional calculus Caputo definition in higher-order logic theorem proving, where fluid mechanics fractional flow component is then formally analyzed.