Relaxation of the Boussinesq system and applications to the Rayleigh–Taylor instability

We consider the evolution of two incompressible fluids with homogeneous densities $$\rho _{-}<\rho _+$$ ρ - < ρ + subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential inclusion. The existence of a subsolution to the relaxation allows one to conclude the existence of turbulently mixing solutions to the original Boussinesq system. As a specific application we investigate subsolutions emanating from the classical Rayleigh-Taylor initial configuration where the two fluids are separated by a horizontal interface with the heavier fluid being on top of the lighter. It turns out that among all self-similar subsolutions the criterion of maximal initial energy dissipation selects a linear density profile and a quadratic growth of the mixing zone. The subsolution selected this way can be extended in an admissible way to exist for all times. We provide two possible extensions with different long-time limits. The first one corresponds to a total mixture of the two fluids, the second corresponds to a full separation with the lighter fluid on top of the heavier. There is no motion in either of the limit states.

Fibonacci Sequence-related Phenomenon During Chondrocyte Proliferation of the Gottingen Pig Knee Tibial Plateau

Background The aim of our study was to observe the quantitative changes in tibial plateau chondrocytes in the proliferation process from normal Gottingen pigs in vitro and compare them with the Fibonacci sequence.Methods Chondrocytes from normal Gottingen pig tibial plateau cartilage were isolated and cultured to the third generation, and the number of chondrocytes was measured to determine whether the chondrocyte growth was at the logarithmic growth phase. Chondrocytes were added to cell culture bottles at very a low density to allow full separation and allow each chondrocyte to grow as independently as possible. Thirty single chondrocytes were selected, and the number of chondrocyte colonies were observed and recorded every day. Results Among the 30 chondrocyte colonies, the changes in the numbers of 16 chondrocyte colonies were 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, and 987, which conformed to the numbers of the Fibonacci sequence.The number of other chondrocyte colonies was lower than corresponding numbers of the Fibonacci sequence at the same time point.Conclusion The numbers of normal Gottingen pig tibial plateau chondrocytes during the proliferation process were in line with the numbers of the Fibonacci sequence.Alignment to the Fibonacci sequence may be the fastest way for changes in the numbers of normal chondrocytes during the proliferation process in vitro.

Separation of variables in the WZW models

We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers-Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.

Relational communication

We study a communication game between an informed sender and an uninformed receiver with repeated interactions and voluntary transfers. Transfers motivate the receiver's decision‐making and signal the sender's information. Although full separation can always be supported in equilibrium, partial or complete pooling is optimal if the receiver's decision‐making is highly responsive to information. In this case, the receiver's decision‐making is disciplined by pooling states where she is most tempted to defect.

The Results of Field Tests of an Onion Set Harvesting Machine Equipped with a Shaker Arrangement Asymmetrical Bar Elevator

Introduction. Machines for harvesting roots and onions do not provide qualitative indices of root heap separation that leads to violation of technical requirements during harvesting. New solutions are needed to increase the quality of root separation, increase the quality of separation and reduce damage. Materials and Methods. The article presents the design of the onion set harvesting machine. The machine is equipped with a bar elevator with asymmetrical arrangement of shakers. The technique and results of field research to determine the quality of set onion separation at the experimental rod elevator are described. Results. The results of production research of the onion set harvesting machine showed qualitative performance of the technological process of separating onion heap at optimal values of parameters: center distance between elliptical shaker and supporting roller 0.36-0.4 m at full separation of 97.0-97.2% and onion damage 1.65-1.68%; forward speed of rod elevator with asymmetrical arrangement of elliptical shaker and supporting roller 1.6 m/s at full separation of 98.5% and bulb damage 1.3%. Discussion and Conclusion. The use of a bar elevator with an asymmetrical arrangement of the elliptical shaker and support roller allows, in comparison with the symmetrical arrangement of shakers, an increase in bulb separation by 2.0% and a decrease in onion damage by 1.1%.

Innovative Detection Strategies on Large Geometry SIMS open new challenging applications for light isotope ratio analyses

&lt;p&gt;Large Geometry Secondary Ion Mass Spectrometry (LG-SIMS), operating in multicollection mode, allows high precision light isotope ratio measurements at high lateral resolution (tens of &amp;#956;m down to sub-&amp;#956;m range). For some challenging applications involving fine scale analysis of low abundance isotopes (i.e. &lt;sup&gt;17&lt;/sup&gt;O or &lt;sup&gt;36&lt;/sup&gt;S) or low-concentration elements (i.e. nitrogen in diamonds) measurement of low signal intensities is required. Traditionally, count rates between the upper level of pulse counting systems ~10&lt;sup&gt;5&lt;/sup&gt; c/s and the lower level of Faraday Cup (FC) measurements ~10&lt;sup&gt;6&lt;/sup&gt; c/s are considered to be in a &amp;#8220;gap area&amp;#8221; where neither detection protocol can achieve performance better than the 1&amp;#8240; level.&lt;/p&gt;&lt;p&gt;Faraday Cup detectors (FC) offer high precision with no need for gain monitoring, however the uncertainty of FC measurements depends on the signal to noise ratio. One approach for measuring low signal intensities is to use FCs coupled to electrometers with high ohmic resistors. CAMECA LG-SIMS can now be equipped with low noise 10&lt;sup&gt;12&lt;/sup&gt; &amp;#937; resistor FC preamplifier boards for measuring signal intensities down to the ~ 3 x 10&lt;sup&gt;5&lt;/sup&gt; c/s range with precision better than the 0.5&amp;#8240; level (1SD).&lt;/p&gt;&lt;p&gt;For measurement of low-abundance isotopes, a complementary approach consists of using discrete-dynode pulse counting electron multiplier (EM) detectors, for which drift and aging effects are minimized using a fast automated EM high voltage adjustment routine.&lt;/p&gt;&lt;p&gt;During this PICO presentation, we will discuss the relevance of the detector choice (FC 10&lt;sup&gt;12&lt;/sup&gt; &amp;#937; vs EM) for few examples of innovative applications.&lt;/p&gt;&lt;p&gt;Example of mass independent fractionation:&lt;/p&gt;&lt;p&gt;In addition to classical isotopic ratio measurements (e.g. &amp;#948;&lt;sup&gt;13&lt;/sup&gt;C, &amp;#948;&lt;sup&gt;15&lt;/sup&gt;N, &amp;#948;&lt;sup&gt;18&lt;/sup&gt;O or &amp;#948;&lt;sup&gt;34&lt;/sup&gt;S), for which the instrumental mass fractionation (IMF) correction is mostly limited by the natural heterogeneity (chemical and isotopic) of the reference material, SIMS is particularly well suited for the measurement of mass independent fractionation (MIF, e.g. &amp;#8710;&lt;sup&gt;33&lt;/sup&gt;S, &amp;#8710;&lt;sup&gt;36&lt;/sup&gt;S and &amp;#8710;&lt;sup&gt;17&lt;/sup&gt;O). Along with classical geochemical processes, the degree of isotopic fractionation scales with the difference in mass of the isotopes involved (i.e. &amp;#948;&lt;sup&gt;33&lt;/sup&gt;S &amp;#8776; 0.515 * &amp;#948;&lt;sup&gt;34&lt;/sup&gt;S). MIF refers to non-conventional ratios that depart from these mass dependent rules. As instrumental mass fractionation has been shown to be strictly mass dependent, MIF measurements are not subject to IMF correction and are therefore measured directly. The use of SIMS in this specific case is particularly well suited and allows to fully explore the rich phenomenology of MIF source processes. We will discuss the advantages and disadvantages of using FC 10&lt;sup&gt;12&lt;/sup&gt; &amp;#937; for the minor Sulphur isotope (&lt;sup&gt;36&lt;/sup&gt;S) measurement.&lt;/p&gt;&lt;p&gt;Carbon and Nitrogen in diamond:&lt;/p&gt;&lt;p&gt;We will also show a recent analytical development aiming to measure &amp;#948;&lt;sup&gt;13&lt;/sup&gt;C in diamonds at mass resolution of ~5000 (allowing the full separation of &lt;sup&gt;13&lt;/sup&gt;C- and &lt;sup&gt;12&lt;/sup&gt;CH-) as well as N-content and N-isotopes in diamonds at a mass resolution of ~9000 (full separation of &lt;sup&gt;12&lt;/sup&gt;C&lt;sup&gt;14&lt;/sup&gt;N- and &lt;sup&gt;13&lt;/sup&gt;C&lt;sup&gt;13&lt;/sup&gt;C-). &amp;#160;For this purpose, the use of FC 10&lt;sup&gt;12&lt;/sup&gt; &amp;#937; greatly improves the data quality and allows the simultaneous measurement of N-content and &amp;#948;&lt;sup&gt;15&lt;/sup&gt;N.&lt;/p&gt;

Full Separation or Full Integration? An Investigation of the Optimal Renewables Policy Employing Tradable Green Certificate Systems in Two Countries’ Electricity Markets

Tradable green certificate (TGC) systems are increasingly used to promote renewable energy generation and mitigate greenhouse gas emissions. In this paper, we investigate the performance of the optimal renewables policy under full separation and full integration scenarios for two countries with TGCs. Our analysis suggests that under full separation, one country’s optimal renewable quota, which maximizes its own welfare, is strategically substitutional for the other country’s in a Cournot Nash equilibrium of the monopolistic market, when cross-border pollution exists. A country tends to become the “leader” in the market by using an information advantage to gain higher welfare. Using geometric illustrations we demonstrate the possibility that a potentially fully integrated electricity market under a TGC system can improve welfare for each country, when compensation between the countries is possible. From a policy point of view, this is significant in support of the demand for a convergence of national renewable policy schemes, where countries cooperate on solving cross-border environmental problems.

Ultra-thin fluorocarbon foils optimise multiscale imaging of three-dimensional native and optically cleared specimens

In three-dimensional light microscopy, the heterogeneity of the optical density in a specimen ultimately limits the achievable penetration depth and hence the three-dimensional resolution. The most direct approach to reduce aberrations, improve the contrast and achieve an optimal resolution is to minimise the impact of changes of the refractive index along an optical path. Many implementations of light sheet fluorescence microscopy operate with a large chamber filled with an aqueous immersion medium and a further inner container with the specimen embedded in a possibly entirely different non-aqueous medium. In order to minimise the impact of the latter on the optical quality of the images, we use multi-facetted cuvettes fabricated from vacuum-formed ultra-thin fluorocarbon (FEP) foils. The ultra-thin FEP-foil cuvettes have a wall thickness of about 10–12 µm. They are impermeable to liquids, but not to gases, inert, durable, mechanically stable and flexible. Importantly, the usually fragile specimen can remain in the same cuvette from seeding to fixation, clearing and observation, without the need to remove or remount it during any of these steps. We confirm the improved imaging performance of ultra-thin FEP-foil cuvettes with excellent quality images of whole organs such us mouse oocytes, of thick tissue sections from mouse brain and kidney as well as of dense pancreas and liver organoid clusters. Our ultra-thin FEP-foil cuvettes outperform many other sample-mounting techniques in terms of a full separation of the specimen from the immersion medium, compatibility with aqueous and organic clearing media, quick specimen mounting without hydrogel embedding and their applicability for multiple-view imaging and automated image segmentation. Additionally, we show that ultra-thin FEP foil cuvettes are suitable for seeding and growing organoids over a time period of at least ten days. The new cuvettes allow the fixation and staining of specimens inside the holder, preserving the delicate morphology of e.g. fragile, mono-layered three-dimensional organoids.