There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Cause, conseguenze e strategie di mitigazione Proponiamo il primo di una serie di articoli in cui affronteremo l’attuale problema dei mutamenti climatici. Presentiamo il documento redatto, votato e pubblicato dall’Ipcc - Comitato intergovernativo sui cambiamenti climatici - che illustra la sintesi delle ricerche svolte su questo tema rilevante.

/pdf/climate-change-2007-the-physical-science-basis-1x93ttz9jt.pdf

Climate Change 2007: The Physical Science Basis.

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Some bacteria have the remarkable capacity to fix atmospheric nitrogen to ammonia under ambient conditions, a reaction only mimicked on an industrial scale by a chemical process that requires high temperatures, elevated pressure and special catalysts. The ability of microorganisms to use nitrogen gas as the sole nitrogen source and engage in symbioses with host plants confers many ecological advantages, but also incurs physiological penalties because the process is oxygen sensitive and energy dependent. Consequently, biological nitrogen fixation is highly regulated at the transcriptional level by sophisticated regulatory networks that respond to multiple environmental cues.

Genetic regulation of biological nitrogen fixation

13. 벼잎선충의 약제처리 방법별 방제 효과

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Benard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Benard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

https://link.springer.com/content/pdf/10.1140%2Fepje%2Fi2012-12058-1.pdf

New perspectives in turbulent Rayleigh-Bénard convection.

Turbulent Rayleigh-Benard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

/pdf/turbulent-superstructures-in-rayleigh-benard-convection-1pk0cg88yk.pdf

Turbulent superstructures in Rayleigh-Bénard convection.

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 102 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.

https://www.pnas.org/content/pnas/111/30/10961.full.pdf

Small-scale universality in fluid turbulence

We present high-resolution direct numerical simulation studies of turbulent Rayleigh–Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We have also investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.

Resolving the fine-scale structure in turbulent Rayleigh–Bénard convection

Members of the protein family called ATPases associated with various cellular activities (AAA+) play a crucial role in transforming chemical energy into biological events. AAA+ proteins are complex molecular machines and typically form ring-shaped oligomeric complexes that are crucial for ATPase activity and mechanism of action. The Escherichia coli transcription activator phage shock protein F (PspF) is an AAA+ mechanochemical enzyme that functions to sense and relay the energy derived from nucleoside triphosphate hydrolysis to catalyze transcription by the σ54-RNA polymerase. Closed promoter complexes formed by the σ54-RNA polymerase are substrates for the action of PspF. By using a protein fragmentation approach, we identify here at least one σ54-binding surface in the PspF AAA+ domain. Results suggest that ATP hydrolysis by PspF is coupled to the exposure of at least one σ54-binding surface. This nucleotide hydrolysis-dependent presentation of a substrate binding surface can explain why complexes that form between σ54 and PspF are transient and could be part of a mechanism used generally by other AAA+ proteins to regulate activity.

https://www.pnas.org/content/pnas/100/5/2278.full.pdf

Jörg Schumacher

Papers

New perspectives in turbulent Rayleigh-Bénard convection.

Turbulent superstructures in Rayleigh-Bénard convection.

Small-scale universality in fluid turbulence

Resolving the fine-scale structure in turbulent Rayleigh–Bénard convection

The ATP hydrolyzing transcription activator phage shock protein F of Escherichia coli: Identifying a surface that binds σ54