Persistence of Randomly Coupled Fluctuating Interfaces

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2, however, is coupled to h_1 via a quenched random velocity field. In the limit d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t_0\to \infty, the stochastic process h_2, at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H_2=1-\beta_1/2, where \beta_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be \theta_s^2=1-H_2=\beta_1/2. These analytical results are verified by numerical simulations.Comment: 15 pages, 3 .eps figures include

Persistence in nonequilibrium surface growth

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be $\theta^S_{+} = 0.66 \pm 0.02$ and $\theta^S_{-} = 0.78 \pm 0.02$, respectively, in (1+1) dimensions, and $\theta^S_{+} = 0.76 \pm 0.02$ and $\theta^S_{-} =0.85 \pm 0.02$, respectively, in (2+1) dimensions. The noise reduction technique is applied on some of the (1+1)-dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.Comment: 28 pages, 16 figure

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let

Cemented hemi-arthroplasty for unstable intertrochanteric fractures in the elderly: a retrospective study

Background: Unstable intertrochanteric fractures belonging to 31A2 and A3 varieties are difficult challenges for orthopaedic surgeons, particularly in the elderly patients. Osteosynthesis by dynamic hip screw or proximal femoral nail are often plagued by complications like screw cut-out, excessive collapse and fixation failures due to osteoporotic bones. Because of these complications, patients are often kept confined to the bed which may increase the risks of pressure sores, venous thrombosis and pulmonary infections. So, it is desirable to mobilize these elderly patients as quickly as possible following surgery. In recent decades, primary hemi-arthroplasty has emerged as a valuable treatment option for mobilizing these patients early.Methods: We present our retrospective study on 27 patients above 60 years of age, who were managed with cemented bipolar hemi-arthroplasty after sustaining unstable intertrochanteric fractures. All the patients were operated through modified Hardinge approach. The fractured fragments were secured by stainless steel wiring, particularly the greater trochanter, wherever necessary.Results: Twenty-three patients (85%) were able to stand up with walkers by third post-operative day and were able to walk by fifth post-operative day. There was one case of hip dislocation; it was reduced under anaesthesia. No other complications were encountered at an average follow-up of 3.1 years. The Harris hip score was ‘good’ or ‘excellent’ in more than 60% patients.Conclusions: Cemented hemi-arthroplasty appears to be a reliable treatment method for unstable intertrochanteric fractures in the elderly and it allows early weight-bearing and rehabilitation in most patients following surgery.

Spatial Persistence of Fluctuating Interfaces

We show that the probability, P_0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P_0(l) \sim l^(-\theta). Here \theta is a `spatial' persistence exponent, and takes different values, \theta_s or \theta_0, depending on how the point from which l is measured is specified. While \theta_s is related to fractional Brownian motion, and can be determined exactly, \theta_0 is non-trivial even for Gaussian interfaces.Comment: 5 pages, new material adde

Survival in equilibrium step fluctuations

We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. $S(t)$ is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111) surfaces.Comment: RevTeX, 4 pages, 3 figure

Biofabrication of Anisotropic Gold Nanotriangles Using Extract of Endophytic Aspergillus clavatus as a Dual Functional Reductant and Stabilizer

Biosynthesis of metal and semiconductor nanoparticles using microorganisms has emerged as a more eco-friendly, simpler and reproducible alternative to the chemical synthesis, allowing the generation of rare forms such as nanotriangles and prisms. Here, we report the endophytic fungus Aspergillus clavatus, isolated from surface sterilized stem tissues of Azadirachta indica A. Juss., when incubated with an aqueous solution of chloroaurate ions produces a diverse mixture of intracellular gold nanoparticles (AuNPs), especially nanotriangles (GNT) in the size range from 20 to 35 nm. These structures (GNT) are of special interest since they possess distinct plasmonic features in the visible and IR regions, which equipped them with unique physical and optical properties exploitable in vital applications such as optics, electronics, catalysis and biomedicine. The reaction process was simple and convenient to handle and was monitored using ultraviolet–visible spectroscopy (UV–vis). The morphology and crystalline nature of the GNTs were determined from transmission electron microscopy (TEM), atomic force spectroscopy (AFM) and X-ray diffraction (XRD) spectroscopy. This proposed mechanistic principal might serve as a set of design rule for the synthesis of anisotropic nanostructures with desired architecture and can be amenable for the large scale commercial production and technical applications

Genotype-Phenotype Study of the Middle Gangetic Plain in India Shows Association of rs2470102 with Skin Pigmentation

Our understanding of the genetics of skin pigmentation has been largely skewed towards populations of European ancestry, imparting less attention to South Asian populations, who behold huge pigmentation diversity. Here, we investigate skin pigmentation variation in a cohort of 1,167 individuals in the Middle Gangetic Plain of the Indian subcontinent. Our data confirm the association of rs1426654 with skin pigmentation among South Asians, consistent with previous studies, and also show association for rs2470102 single nucleotide polymorphism. Our haplotype analyses further help us delineate the haplotype distribution across social categories and skin color. Taken together, our findings suggest that the social structure defined by the caste system in India has a profound influence on the skin pigmentation patterns of the subcontinent. In particular, social category and associated single nucleotide polymorphisms explain about 32% and 6.4%, respectively, of the total phenotypic variance. Phylogeography of the associated single nucleotide polymorphisms studied across 52 diverse populations of the Indian subcontinent shows wide presence of the derived alleles, although their frequencies vary across populations. Our results show that both polymorphisms (rs1426654 and rs2470102) play an important role in the skin pigmentation diversity of South Asians

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data