Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review

Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues

We study the transition in conductance properties of chaotic mesoscopic cavities as time-reversal symmetry is broken. We consider the Brownian motion model for transmission eigenvalues for both types of transitions, viz., orthogonal-unitary and symplectic-unitary crossovers depending on the presence or absence of spin-rotation symmetry of the electron. In both cases the crossover is governed by a Brownian motion parameter {\tau}, which measures the extent of time-reversal symmetry breaking. It is shown that the results obtained correspond to the Jacobi crossover ensembles of random matrices. We derive the level density and the correlation functions of higher orders for the transmission eigenvalues. We also obtain the exact expressions for the average conductance, average shot-noise power and variance of conductance, as functions of {\tau}, for arbitrary number of modes (channels) in the two leads connected to the cavity. Moreover, we give the asymptotic result for the variance of shot-noise power for both the crossovers, the exact results being too long. In the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the weak time-reversal symmetry breaking regime our results are shown to be in agreement with the semiclassical predictions.Comment: 24 pages, 5 figure

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

An analysis of the efficacy of uterine artery embolization in obstetrical hemorrhage

Background: Obstetrical hemorrhage is the single most important cause of maternal morbidity and mortality. The study is conducted at a tertiary-care hospital to assess the efficacy of uterine artery embolization as a treatment for obstetrical uterine hemorrhage. It examines various aspects such as the outcome of the procedure, need of blood and blood products, need of secondary procedures post intervention and the possibility of future pregnancies. Methods: It was a retrospective observational study conducted with sample size of 20 patients with obstetrical hemorrhage at the Department of Obstetrics and Gynecology of Bhagwan Mahaveer Jain Hospital, Bengaluru in India between January 2011 to July 2019. Results: Records of 20 patients with obstetrical hemorrhage were assessed. The study indicates that 11 patients experienced postpartum hemorrhage (PPH), 5 postabortal bleeding & 4 bleeding due to scar ectopic. Out of 20 patients, hemodynamic stability was achieved in 17 cases (85%), hysterectomy was needed in 2 cases (10%) and 1 (5%) patient died after the procedure. Of total 20 cases, 18 (90%) required secondary procedures post-intervention like dilatation and evacuation 6 cases (33.3% of total cases), vaginal suturing and packing 10 cases (55.5% of total cases) and supportive measures like PPH and Disseminated intravascular coagulation (DIC) management in 2 cases (11.1% of total cases). Blood transfusion was given in 15 cases (75%) after the procedure. Future pregnancy was attained in 8 cases (47%) after considering the history of the patients, loss of follow-up, possibility of complications, family planning and hysterectomy performed. Conclusions: Uterine artery embolization is a very effective method to control obstetric hemorrhage with high success and low complication rate and hysterectomy can be avoided to preserve fertility

Effect of Ethephon (2-chloroethyl phosphonic acid) on quality and ripening of Beauty Seedless grape

Ethephon (2-chloroethyl phosphonic acid) at 0, 125, 250 and 500 ppm was applied as spray to Beauty Seedless grapes on dormant vines after pruning, after berry set and at veraison. Ethephon (500 ppm) application at veraison improved the quality by increasing total soluble solids to acid ratio and colour development and by reducing the acidity. This treatment also enhanced ripening and reduced the duration of harvest.Der Einfluß von Ethephon (2-Chloräthylphosphonsäure) auf die Qualität und Reife der Rebensorte Beauty SeedlessEthephon (2-Chloräthylphosphonsäure) wurde, neben einer Kontrollbehandlung, in den Konzentrationen 125, 250 und 500 ppm auf Reben der Sorte Beauty Seedless gesprüht; die Behandlung erfolgte nach dem Schnitt noch während der Dormanz, nach dem Beerenansatz und beim Weichwerden der Beeren. Anwendung von 500 ppm Ethephon während des Weichwerdens verbesserte die Traubenqualität durch Erhöhung des Zucker/Säure-Verhältnisses, durch Steigerung der Farbstoffausbeute und durch Abbau der Säure. Diese Behandlung beschleunigte auch die Reife und verkürzte die Dauer der Ernte

Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot

The autocorrelation function C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)= \langle \delta g(\varphi,\,\eps)\, \delta g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle ($\varphi$ and \eps are rescaled magnetic flux and energy) for the magnetoconductance of a ballistic chaotic quantum dot is calculated in the framework of the supersymmetric non-linear $\sigma$-model. The Hamiltonian of the quantum dot is modelled by a Gaussian random matrix. The particular form of the symmetry breaking matrix is found to be relevant for the autocorrelation function but not for the average conductance. Our results are valid for the complete crossover from orthogonal to unitary symmetry and their relation with semiclassical theory and an $S$-matrix Brownian motion ensemble is discussed.Comment: 7 pages, no figures, accepted for publication in Europhysics Letter

Polynuclear growth model, GOE2^2 and random matrix with deterministic source

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.Comment: 27pages, 4 figure

Nanoscale Defect Formation on InP(111) Surfaces after MeV Sb Implantation

We have studied the surface modifications as well as the surface roughness of the InP(111) surfaces after 1.5 MeV Sb ion implantations. Scanning Probe Microscope (SPM) has been utilized to investigate the ion implanted InP(111) surfaces. We observe the formation of nanoscale defect structures on the InP surface. The density, height and size of the nanostructures have been investigated here as a function of ion fluence. The rms surface roughness, of the ion implanted InP surfaces, demonstrates two varied behaviors as a function of Sb ion fluence. Initially, the roughness increases with increasing fluence. However, after a critical fluence the roughness decreases with increasing fluence. We have further applied the technique of Raman scattering to investigate the implantation induced modifications and disorder in InP. Raman Scattering results demonstrate that at the critical fluence, where the decrease in surface roughness occurs, InP lattice becomes amorphous.Comment: 18 pages, 9 figure