1D periodic potentials with gaps vanishing at k=0

Appearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterize them through a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occur of linearly independent solutions of the corresponding Schroedinger equation (Hill's equation). This result is placed in perspective of the previous related results available in the literature.Comment: 29 pages, 4 figures, version accepted for publication in Memoirs on Differential Equations and Mathematical Physic

Effective non-linear dynamics of binary condensates and open problems

We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Sch\"odinger equations. After reviewing and commenting our proof in the mean field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.Comment: Corrected typos, updated reference

Heat transfer simulation of evacuated tube collectors (ETC): An application to a prototype

Since fossil fuels shortages are predicted for the forthcoming generations, the use of renewable energy sources is playing a key role and is strongly recommended worldwide by national and international regulations. In this scenario, solar collectors for hot water preparation, space heating and cooling are becoming an increasingly interesting alternative, especially in the building sector because of population growth. Thus, the present paper is addressed to numerically investigate the thermal behaviour of a prototypal evacuated tube by solving the heat transfer differential equations using the Finite Element Method. This is to reproduce the heat transfer process occurring within the real system, helping the industry improve the prototype

Nonstationary probabilistic downscaling of extreme precipitation

n/

Regucalcin ameliorates doxorubicin-induced cytotoxicity in Cos-7 kidney cells and translocates from the nucleus to the mitochondria.

From Europe PMC via Jisc Publications RouterHistory: ppub 2022-01-01Publication status: PublishedDoxorubicin (DOX) is a potent anticancer drug, which can have unwanted side-effects such as cardiac and kidney toxicity. A detailed investigation was undertaken of the acute cytotoxic mechanisms of DOX on kidney cells, using Cos-7 cells as kidney cell model. Cos-7 cells were exposed to DOX for a period of 24 h over a range of concentrations, and the LC50 was determined to be 7 µM. Further investigations showed that cell death was mainly via apoptosis involving Ca2+ and caspase 9, in addition to autophagy. Regucalcin (RGN), a cytoprotective protein found mainly in liver and kidney tissues, was overexpressed in Cos-7 cells and shown to protect against DOX-induced cell death. Subcellular localization studies in Cos-7 cells showed RGN to be strongly correlated with the nucleus. However, upon treatment with DOX for 4 h, which induced membrane blebbing in some cells, the localization appeared to be correlated more with the mitochondria in these cells. It is yet to be determined whether this translocation is part of the cytoprotective mechanism or a consequence of chemically induced cell stress

On Singularity formation for the L^2-critical Boson star equation

We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption that the solution blows up in $H^{1/2}$ at finite time, we show that $u(t)$ has a unique weak limit in $L^2$ and that $|u(t)|^2$ has a unique weak limit in the sense of measures. Moreover, we prove that the limiting measure exhibits minimal mass concentration. A central ingredient used in the proof is a "finite speed of propagation" property, which puts a strong rigidity on the blowup behavior of $u$. As the second main result, we prove that any radial finite-time blowup solution $u$ converges strongly in $L^2$ away from the origin. For radial solutions, this result establishes a large data blowup conjecture for the $L^2$-critical boson star equation, similar to a conjecture which was originally formulated by F. Merle and P. Raphael for the $L^2$-critical nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704]. We also discuss some extensions of our results to other $L^2$-critical theories of gravitational collapse, in particular to critical Hartree-type equations.Comment: 24 pages. Accepted in Nonlinearit

Dynamical Collapse of Boson Stars

We study the time evolution in system of $N$ bosons with a relativistic dispersion law interacting through an attractive Coulomb potential with coupling constant $G$. We consider the mean field scaling where $N$ tends to infinity, $G$ tends to zero and $\lambda = G N$ remains fixed. We investigate the relation between the many body quantum dynamics governed by the Schr\"odinger equation and the effective evolution described by a (semi-relativistic) Hartree equation. In particular, we are interested in the super-critical regime of large $\lambda$ (the sub-critical case has been studied in \cite{ES,KP}), where the nonlinear Hartree equation is known to have solutions which blow up in finite time. To inspect this regime, we need to regularize the Coulomb interaction in the many body Hamiltonian with an $N$ dependent cutoff that vanishes in the limit $N\to \infty$. We show, first, that if the solution of the nonlinear equation does not blow up in the time interval $[-T,T]$, then the many body Schr\"odinger dynamics (on the level of the reduced density matrices) can be approximated by the nonlinear Hartree dynamics, just as in the sub-critical regime. Moreover, we prove that if the solution of the nonlinear Hartree equation blows up at time $T$ (in the sense that the $H^{1/2}$ norm of the solution diverges as time approaches $T$), then also the solution of the linear Schr\"odinger equation collapses (in the sense that the kinetic energy per particle diverges) if $t \to T$ and, simultaneously, $N \to \infty$ sufficiently fast. This gives the first dynamical description of the phenomenon of gravitational collapse as observed directly on the many body level.Comment: 40 page

Sowing density effect on common bean leaf area development

Sowing density is a major management factor that affects growth and development of grain crops by modifying the canopy light environment and interplant competition for water and nutrients. While the effects of sowing density and plant architecture on static vegetative and reproductive growth traits have been explored previously in the common bean, few studies have focused on the impacts of sowing density on the dynamics of node addition and leaf area development. We present the results from two sites of field experiments where the effects of sowing densities (5, 10, 15, 20, 25 and 35 plants m-2) and genotypes with contrasting plant architectures (two each from growth habits I through III) on the dynamics of node addition and leaf area were assessed. Analysis of the phyllochron (°C node-1) indicated genotype and density effects (but no interaction) on the rate of node addition. While significant, these differences amounted to less than two days of growth at either site. In terms of leaf area development, analysis using a power function reflected large differences in the dynamics and final size of individual plant leaf area between the lower density (20 plants m-2) at the growth habit, but not genotype level. These differences in node addition and leaf development dynamics translated to marked differences between growth habits and sowing densities in estimated leaf area indices, and consequently, in the estimated fraction of intercepted light at lower densities

Resistance of rumen bacteria murein to bovine gastric lysozyme

BACKGROUND: Lysozymes, enzymes mostly associated with defence against bacterial infections, are mureinolytic. Ruminants have evolved a gastric c type lysozyme as a digestive enzyme, and profit from digestion of foregut bacteria, after most dietary components, including protein, have been fermented in the rumen. In this work we characterized the biological activities of bovine gastric secretions against membranes, purified murein and bacteria. RESULTS: Bovine gastric extract (BGE) was active against both G+ and G- bacteria, but the effect against Gram- bacteria was not due to the lysozyme, since purified BGL had only activity against Gram+ bacteria. We were unable to find small pore forming peptides in the BGE, and found that the inhibition of Gram negative bacteria by BGE was due to an artefact caused by acetate. We report for first time the activity of bovine gastric lysozyme (BG lysozyme) against pure bacterial cultures, and the specific resistance of some rumen Gram positive strains to BGL. CONCLUSIONS: Some Gram+ rumen bacteria showed resistance to abomasum lysozyme. We discuss the implications of this finding in the light of possible practical applications of such a stable antimicrobial peptide

Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N \to \infty$ and $G \to 0$ while $GN = \lambda$ fixed. In the super-critical regime of large $\lambda$, we introduce the regularized interaction where the cutoff vanishes as $N \to \infty$. We show that the difference between the many-body semi-relativistic Schr\"{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $\lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal.Comment: 29 page