Direct Numerical Simulations of turbulent flow in a driven cavity

Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large computing resources needed for DNS cost-effective and accurate numerical methods are to be selected. Here, various-order accurate spatial discretization methods for DNS have been evaluated by applying them to the 2D driven cavity at Re = 22,000. To analyze the results of the DNS of the 2D flow in a driven cavity at Re = 22,000 the proper orthogonal decomposition (POD) technique has been applied. POD is an unbiased method to determine coherent structures. The Galerkin projection of the Navier-Stokes equations on the space spanned by the POD-basis-functions yields a relatively low-dimensional set of ordinary differential equations that mimics the dynamics of the Navier-Stokes equations. 3D DNS with no-slip conditions at all walls of the cavity have been performed at both Re = 3,200 and Re = 10,000. The results reproduce the experimentally observed Taylor-Görtler-like vortices.

A framework for randomized time-splitting in linear-quadratic optimal control

Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal control. In our proposed framework, the linear dynamics of the original problem is replaced by a randomized dynamics. To obtain the randomized dynamics, the system matrix is split into simpler submatrices and the time interval of interest is split into subintervals. The randomized dynamics is then found by selecting randomly one or more submatrices in each subinterval. We show that the dynamics, the minimal values of the cost functional, and the optimal control obtained with the proposed randomized time-splitting method converge in expectation to their analogues in the original problem when the time grid is refined. The derived convergence rates are validated in several numerical experiments. Our numerical results also indicate that the proposed method can lead to a reduction in computational cost for the simulation and optimal control of large-scale linear dynamical systemsThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No: 694126- DyCon), the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No.765579-ConFlex and the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks”, project C08, of the German DFG, the grant PID2020-112617GB-C22, “Kinetic equations and learning control” of the Spanish MINECO, and the COST Action grant CA18232, “Mathematical models for interacting dynamics on networks” (MAT-DYN-NET

ADAPTIVE ESTIMATION OF BINOMIAL PROBABILITIES UNDER MISCLASSIFICATION

If misclassification occurs the standard binomial estimator is usually seriously biased. It is known that an improvement can be achieved by using more than one observer in classifying the sample elements. Here it will be investigated which number of observers is optimal given the total number of judgements that can be made. An adaptive estimator for the probability of interest is introduced which uses an estimator of this optimal number of observers, obtained without additional cost. Some simulation results are presented which suggest that the adaptive procedure performs quite well

Branching of the Falkner-Skan solutions for λ < 0

The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.

Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

The simulation of turbulent flows by means of computational fluid dynamics is highly challenging. The costs of an accurate direct numerical simulation (DNS) are usually too high, and engineers typically resort to cheaper coarse-grained models of the flow, such as large-eddy simulation (LES). To be suitable for the computation of turbulence, methods should not numerically dissipate the turbulent flow structures. Therefore, energy-conserving discretizations are investigated, which do not dissipate energy and are inherently stable because the discrete convective terms cannot spuriously generate kinetic energy. They have been known for incompressible flow, but the development of such methods for compressible flow is more recent. This paper will focus on the latter: LES and DNS for turbulent subsonic flow. A new theoretical framework for the analysis of energy conservation in compressible flow is proposed, in a mathematical notation of square-root variables, inner products, and differential operator symmetries. As a result, the discrete equations exactly conserve not only the primary variables (mass, momentum and energy), but also the convective terms preserve (secondary) discrete kinetic and internal energy. Numerical experiments confirm that simulations are stable without the addition of artificial dissipation. Next, minimum-dissipation eddy-viscosity models are reviewed, which try to minimize the dissipation needed for preventing sub-grid scales from polluting the numerical solution. A new model suitable for anisotropic grids is proposed: the anisotropic minimum-dissipation model. This model appropriately switches off for laminar and transitional flow, and is consistent with the exact sub-filter tensor on anisotropic grids. The methods and models are first assessed on several academic test cases: channel flow, homogeneous decaying turbulence and the temporal mixing layer. As a practical application, accurate simulations of the transitional flow over a delta wing have been performed

How climate, topography, soils, herbivores, and fire control forest–grassland coexistence in the Eurasian forest-steppe

Recent advances in ecology and biogeography demonstrate the importance of fire and large herbivores - and challenge the primacy of climate - to our understanding of the distribution, stability, and antiquity of forests and grasslands. Among grassland ecologists, particularly those working in savannas of the seasonally dry tropics, an emerging fire-herbivore paradigm is generally accepted to explain grass dominance in climates and on soils that would otherwise permit development of closed-canopy forests. By contrast, adherents of the climate-soil paradigm, particularly foresters working in the humid tropics or temperate latitudes, tend to view fire and herbivores as disturbances, often human-caused, which damage forests and reset succession. Towards integration of these two paradigms, we developed a series of conceptual models to explain the existence of an extensive temperate forest-grassland mosaic that occurs within a 4.7 million km(2) belt spanning from central Europe through eastern Asia. The Eurasian forest-steppe is reminiscent of many regions globally where forests and grasslands occur side-by-side with stark boundaries. Our conceptual models illustrate that if mean climate was the only factor, forests should dominate in humid continental regions and grasslands should prevail in semi-arid regions, but that extensive mosaics would not occur. By contrast, conceptual models that also integrate climate variability, soils, topography, herbivores, and fire depict how these factors collectively expand suitable conditions for forests and grasslands, such that grasslands may occur in more humid regions and forests in more arid regions than predicted by mean climate alone. Furthermore, boundaries between forests and grasslands are reinforced by vegetation-fire, vegetation-herbivore, and vegetation-microclimate feedbacks, which limit tree establishment in grasslands and promote tree survival in forests. Such feedbacks suggest that forests and grasslands of the Eurasian forest-steppe are governed by ecological dynamics that are similar to those hypothesised to maintain boundaries between tropical forests and savannas. Unfortunately, the grasslands of the Eurasian forest-steppe are sometimes misinterpreted as deforested or otherwise degraded vegetation. In fact, the grasslands of this region provide valuable ecosystem services, support a high diversity of plants and animals, and offer critical habitat for endangered large herbivores. We suggest that a better understanding of the fundamental ecological controls that permit forest-grassland coexistence could help us prioritise conservation and restoration of the Eurasian forest-steppe for biodiversity, climate adaptation, and pastoral livelihoods. Currently, these goals are being undermined by tree-planting campaigns that view the open grasslands as opportunities for afforestation. Improved understanding of the interactive roles of climate variability, soils, topography, fire, and herbivores will help scientists and policymakers recognise the antiquity of the grasslands of the Eurasian forest-steppe

Season of Prescribed Fire Determines Grassland Restoration Outcomes After Fire Exclusion and Overgrazing

Fire exclusion and mismanaged grazing are globally important drivers of environmental change in mesic C4 grasslands and savannas. Although interest is growing in prescribed fire for grassland restoration, we have little long-term experimental evidence of the influence of burn season on the recovery of herbaceous plant communities, encroachment by trees and shrubs, and invasion by exotic grasses. We conducted a prescribed fire experiment (seven burns between 2001 and 2019) in historically fire-excluded and overgrazed grasslands of central Texas. Sites were assigned to one of four experimental treatments: summer burns (warm season, lightning season), fall burns (early cool season), winter burns (late cool season), or unburned (fire exclusion). To assess restoration outcomes of the experiment, in 2019, we identified old-growth grasslands to serve as reference sites. Herbaceous-layer plant communities in all experimental sites were compositionally and functionally distinct from old-growth grasslands, with little recovery of perennial C4 grasses and long-lived forbs. Unburned sites were characterized by several species of tree, shrub, and vine; summer sites were characterized by certain C3 grasses and forbs; and fall and winter sites were intermediate in composition to the unburned and summer sites. Despite compositional differences, all treatments had comparable plot-level plant species richness (range 89–95 species/1000 m2). At the local-scale, summer sites (23 species/m2) and old-growth grasslands (20 species/m2) supported greater richness than unburned sites (15 species/m2), but did not differ significantly from fall or winter sites. Among fire treatments, summer and winter burns most consistently produced the vegetation structure of old-growth grasslands (e.g., mean woody canopy cover of 9%). But whereas winter burns promoted the invasive grass Bothriochloa ischaemum by maintaining areas with low canopy cover, summer burns simultaneously limited woody encroachment and controlled B. ischaemum invasion. Our results support a growing body of literature that shows that prescribed fire alone, without the introduction of plant propagules, cannot necessarily restore old-growth grassland community composition. Nonetheless, this long-term experiment demonstrates that prescribed burns implemented in the summer can benefit restoration by preventing woody encroachment while also controlling an invasive grass. We suggest that fire season deserves greater attention in grassland restoration planning and ecological research

Single crystallites in "planar polycrystalline" oligothiophene films:Determination of orientation and thickness by polarization microscopy

Thin films of evaporated oligothiophenes (alpha-nT, n = 4-8) show a "planar polycrystalline" structure: each of the individual crystallites has a random azimuthal orientation, the (a, b) face of its unit cell is aligned with the surface plane, We introduce a technique to determine the orientation and thickness of such aligned thiophene crystals by optical polarization microscopy. Due to the optical birefringence of the crystal, It appears with different colors in the microscope dependent on its orientation and thickness. To support the method proposed, we solve Maxwell's equations and obtain quantitative agreement with the observed colors. The organic crystal shows biaxial anisotropy. For unsubstituted quaterthiophene, alpha-4T, we find effective refractive indices n(b) = 1.84 +/- 0.1 and n(a) = 1.61 +/- 0.1 for waves under normal incidence. Our conclusions are fully confirmed by atomic force microscopy with molecular resolution. Our analyses result in a simple recipe to obtain the directions of the rr and b crystal axes from the optical experiment. (C) 1998 American Institute of Physics. [S0021-8979(98)02007-6]

Emerging Synergisms Between Drugs and Physiologically-Patterned Weak Magnetic Fields: Implications for Neuropharmacology and the Human Population in the Twenty-First Century

Synergisms between pharmacological agents and endogenous neurotransmitters are familiar and frequent. The present review describes the experimental evidence for interactions between neuropharmacological compounds and the classes of weak magnetic fields that might be encountered in our daily environments. Whereas drugs mediate their effects through specific spatial (molecular) structures, magnetic fields mediate their effects through specific temporal patterns. Very weak (microT range) physiologically-patterned magnetic fields synergistically interact with drugs to strongly potentiate effects that have classically involved opiate, cholinergic, dopaminergic, serotonergic, and nitric oxide pathways. The combinations of the appropriately patterned magnetic fields and specific drugs can evoke changes that are several times larger than those evoked by the drugs alone. These novel synergisms provide a challenge for a future within an electromagnetic, technological world. They may also reveal fundamental, common physical mechanisms by which magnetic fields and chemical reactions affect the organism from the level of fundamental particles to the entire living system