Limiting Current on Periodic Electron Sheets in a Planar Diode

We consider the steady state limiting current that can be carried by an infinite periodic array of thin electron sheets spaced by period p in a planar diode of gap voltage V and gap separation d. Our primary assumptions are (1) electron motion is restricted by an infinite magnetic field to the direction normal to the electrode surfaces, (2) all electrons are emitted from the cathode with initial kinetic energy Ein, and (3) electron motion is non-relativistic. The limiting current density, averaged over a period and normalized to the classical 1D Child-Langmuir (CL) current density (including a factor that accounts for non-zero Ein), is found to depend only on the two dimensionless parameters p/d and Ein/eV. This average limiting current density is computed from the maximum current density for which the iterative solution of a non-linear integral equation converges. Numerical results and empirical curve fits for the limiting current are presented, together with an analysis as p/d and Ein/eV approach zero or infinity, in which cases previously published results are recovered. Our main finding is that, while the local anode current density within each electron sheet is infinite in our model (that is, it exceeds the classical 1D CL value by an 'infinite' factor), the period average anode current density is in fact still bounded by the classical 1D CL value. This study therefore provides further evidence that the classical 1D Child-Langmuir current density is truly a fundamental limit that cannot be circumvented.Comment: This material has been submitted to Physics of Plasmas. After it is published, it will be found at https://pubs.aip.org/aip/po

On the Child-Langmuir Law in One, Two, and Three Dimensions

We consider the limiting current from an emitting patch whose size is much smaller than the anode-cathode spacing. The limiting current is formulated in terms of an integral equation. It is solved iteratively, first to numerically recover the classical one-dimensional Child-Langmuir law, including Jaffe's extension to a constant, nonzero electron emission velocity. We extend to 2-dimensions in which electron emission is restricted to an infinitely long stripe with infinitesimally narrow stripe width, so that the emitted electrons form an electron sheet. We next extend to 3-dimensions in which electron emission is restricted to a square tile (or a circular patch) with an infinitesimally small tile size (or patch radius), so that the emitted electrons form a needle-like line charge. Surprisingly, for the electron needle problem, we only find the null solution for the total line charge current, regardless of the assumed initial electron velocity. For the electron sheet problem, we also find only the null solution for the total sheet current if the electron emission velocity is assumed to be zero, and the total maximum sheet current becomes a finite, nonzero value if the electron emission velocity is assumed to be nonzero. These seemingly paradoxical results are shown to be consistent with the earlier works of the Child-Langmuir law of higher dimensions. They are also consistent with, or perhaps even anticipated by, the more recent theories and simulations on thermionic cathodes that used realistic work function distributions to account for patchy, nonuniform electron emission. The mathematical subtleties are discussed.Comment: This material has been submitted to Physics of Plasmas. After it is published, it will be found at https://pubs.aip.org/aip/po

A Rapid and Simple Bioassay Method for Herbicide Detection

Chlamydomonas reinhardtii, a unicellular green alga, has been used in bioassay detection of a variety of toxic compounds such as pesticides and toxic metals, but mainly using liquid culture systems. In this study, an algal lawn—agar system for semi-quantitative bioassay of herbicidal activities has been developed. Sixteen different herbicides belonging to 11 different categories were applied to paper disks and placed on green alga lawns in Petri dishes. Presence of herbicide activities was indicated by clearing zones around the paper disks on the lawn 2–3 days after application. The different groups of herbicides induced clearing zones of variable size that depended on the amount, mode of action, and chemical properties of the herbicides applied to the paper disks. This simple, paper-disk-algal system may be used to detect the presence of herbicides in water samples and act as a quick and inexpensive semi-quantitative screening for assessing herbicide contamination

Numerical Study of Magnetic Island Coalescence Using Magnetohydrodynamics With Adaptively Embedded Particle-In-Cell Model

Collisionless magnetic reconnection typically requires kinetic treatments that are, in general, computationally expensive compared to fluid-based models. In this study, we use the magnetohydrodynamics with adaptively embedded particle-in-cell (MHD-AEPIC) model to study the interaction of two magnetic flux ropes. This innovative model embeds one or more adaptive PIC regions into a global MHD simulation domain such that the kinetic treatment is only applied in regions where kinetic physics is prominent. We compare the simulation results among three cases: 1) MHD with adaptively embedded PIC regions, 2) MHD with statically (or fixed) embedded PIC regions, and 3) a full PIC simulation. The comparison yields good agreement when analyzing their reconnection rates and magnetic island separations, as well as the ion pressure tensor elements and ion agyrotropy. In order to reach a good agreement among the three cases, large adaptive PIC regions are needed within the MHD domain, which indicates that the magnetic island coalescence problem is highly kinetic in nature where the coupling between the macro-scale MHD and micro-scale kinetic physics is important.Comment: 9 pages, 10 figure

RbCa2Nb3O10 from X-ray powder data

Rubidium dicalcium triniobate(V), RbCa2Nb3O10, has been synthesized by solid-state reaction and its crystal structure refined from X-ray powder diffraction data using Rietveld analysis. The compound is a three-layer perovskite Dion–Jacobson phase with the perovskite-like slabs derived by termination of the three-dimensional CaNbO3 perovskite structure along the ab plane. The rubidium ions (4/mmm symmetry) are located in the inter­stitial space

Nucleosome-mediated cooperativity between transcription factors

Cooperative binding of transcription factors (TFs) to cis-regulatory regions (CRRs) is essential for precision of gene expression in development and other processes. The classical model of cooperativity requires direct interactions between TFs, thus constraining the arrangement of TFs sites in a CRR. On the contrary, genomic and functional studies demonstrate a great deal of flexibility in such arrangements with variable distances, numbers of sites, and identities of the involved TFs. Such flexibility is inconsistent with the cooperativity by direct interactions between TFs. Here we demonstrate that strong cooperativity among non-interacting TFs can be achieved by their competition with nucleosomes. We find that the mechanism of nucleosome-mediated cooperativity is mathematically identical to the Monod-Wyman-Changeux (MWC) model of cooperativity in hemoglobin. This surprising parallel provides deep insights, with parallels between heterotropic regulation of hemoglobin (e.g. Bohr effect) and roles of nucleosome-positioning sequences and chromatin modifications in gene regulation. Characterized mechanism is consistent with numerous experimental results, allows substantial flexibility in and modularity of CRRs, and provides a rationale for a broad range of genomic and evolutionary observations. Striking parallels between cooperativity in hemoglobin and in transcription regulation point at a new design principle that may be used in range of biological systems

Prediction of Low-Voltage Tetrafluoromethane Emissions Based on the Operating Conditions of an Aluminium Electrolysis Cell

Greenhouse gas (GHG) generation is inherent in the production of aluminium by a technology that uses carbon anodes. Most of those GHG are composed of CO2 produced by redox reaction that occurs in the cell. However, a significant fraction of the annual GHG production is composed of perfluorocarbons (PFC) resulting from anode effects (AE). Multiple investigations have shown that tetrafluoromethane (CF4) can be generated under low-voltage conditions in the electrolysis cells, without global anode effect. The aim of this paper is to find a quantitative relationship between monitored cell parameters and the emissions of CF4. To achieve this goal, a predictive algorithm has been developed using seven cell indicators. These indicators are based on the cell voltage, the noise level and other parameters calculated from individual anode current monitoring. The predictive algorithm is structured into three different steps. The first two steps give qualitative information while the third one quantitatively describes the expected CF4 concentration at the duct end of the electrolysis cells. Validations after each step are presented and discussed. Finally, a sensitivity analysis was performed to understand the effect of each indicator on the onset of low-voltage PFC emissions. The standard deviation of individual anode currents was found to be the dominant variable. Cell voltage, noise level, and maximum individual anode current also showed a significant correlation with the presence of CF4 in the output gas of an electrolysis cell