A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations

We consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\phi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\rm 94}$, $61-66 ({\rm 1984})$]. By taking an $L^{\infty}$ norm of the energy of the full binary system, designated as $E_{\infty}$, we have shown that $\int_{0}^{t}E_{\infty}(\tau)\,d\tau$ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs), of the 3D CHNS equations, for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with $128^3$ to $512^3$ collocation points and over the duration of our DNSs, confirm that $E_{\infty}$ remains bounded as far as our computations allow.Comment: 11 pages, 3 figure

The role of BKM-type theorems in 3D3D Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis

The Beale-Kato-Majda theorem contains a single criterion that controls the behaviour of solutions of the $3D$ incompressible Euler equations. Versions of this theorem are discussed in terms of the regularity issues surrounding the $3D$ incompressible Euler and Navier-Stokes equations together with a phase-field model for the statistical mechanics of binary mixtures called the $3D$ Cahn-Hilliard-Navier-Stokes (CHNS) equations. A theorem of BKM-type is established for the CHNS equations for the full parameter range. Moreover, for this latter set, it is shown that there exists a Reynolds number and a bound on the energy-dissipation rate that, remarkably, reproduces the $Re^{3/4}$ upper bound on the inverse Kolmogorov length normally associated with the Navier-Stokes equations alone. An alternative length-scale is introduced and discussed, together with a set of pseudo-spectral computations on a $128^{3}$ grid.Comment: 3 figures and 3 table

Effect of shape anisotropy on transport in a 2-dimensional computational model: Numerical simulations showing experimental features observed in biomembranes

We propose a 2-d computational model-system comprising a mixture of spheres and the objects of some other shapes, interacting via the Lennard-Jones potential. We propose a reliable and efficient numerical algorithm to obtain void statistics. The void distribution, in turn, determines the selective permeability across the system and bears a remarkable similarity with features reported in certain biological experiments.Comment: 1 tex file, 2 sty files and 5 figures. To appear in Proc. of StatPhys conference held in Calcutta, Physica A 199

Spreading and shortest paths in systems with sparse long-range connections

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered by the spreading quantity on an infinite system is exactly calculated in all dimensions. We find that V(t) grows initially as t^d/d for t>t^*$, generalizing a previous result in one dimension. Using the properties of V(t), the average shortest-path distance \ell(r) can be calculated as a function of Euclidean distance r. It is found that \ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and \ell(r) = r_c for r>r_c. The characteristic length r_c, which governs the behavior of shortest-path lengths, diverges with system size for all p>0. Therefore the mean separation s \sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for shortest-path lengths. We notice however that the globally averaged shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi

Obstetrics critical care: a 2 years retrospective study in a medical college hospital of western India

Background: This study highlights the possibilities of new contribution to the management of high risk pregnancies and those pregnancies with unpredictable outcomes. The objective was to study the incidence and the clinical profile of antenatal and postpartum women requiring admission to the ICU, the interventions required in these women and final outcome.Methods: A retrospective cohort study of all obstetric critical care admissions during 2-year period from January 2016 to December 2017 was done at 1296 bedded tertiary care hospital. During the study total 349 obstetric patients were admitted to the ICU. The data were analysed by using percentage.Results: Primigravida (54.73%) were more as compared to multigravida (45.27%). Only 15.76% patients were in antepartum period while majority of patients (84.24%) were admitted during postpartum period. The main obstetric indications for ICU admission were pregnancy-induced hypertension (14.32%) followed by obstetric hemorrhage (9.16%) and community acquired pneumonia (7.44%). Other indications were valvular heart disease (5.44%), ANC with severe anemia (1.72%), monitoring (6.30%). In the present study maternal mortality among the women admitted to ICU was 18.05%. The leading cause of maternal death was obstetric hemorrhage (28.57%) followed by pregnancy induced hypertension (25.40%). An ICU intervention during the stay of the patients in terms of mechanical ventilation was used in 250 (71.63%) cases.Conclusions: A high quality multidisciplinary care is required in complicated pregnancies for safe motherhood. So, there is a need for dedicated ICU for obstetric patients

Assessment of antimicrobial prescribing and rationality of drug usage in general practitioners in Pune city, India

Background: Most of the common ailments are managed by general practitioners (GPs). GPs prescribe major bulk of the drugs sold in the market. Naturally, irrational use of drugs at this level could lead to disastrous consequences. So this study was undertaken to determine prescribing pattern of Antimicrobials (AMA) and the rationality of drug usage by GPs in Pune city.Methods: It was a cross-sectional study. Pune city was divided into 5 zones. MBBS, BAMS and BHMS GPs doing Allopathic practice were selected randomly. 2 GPs of each specialty per zone were selected; this gave us 10 GPs of each degree – so total 30 GPs.30 Prescriptions at each GP were collected – total 900 prescriptions. The following parameters were studied- Diagnosis of patient, Average no. of drugs/prescription Percentage of AMAs prescribed, Rationality of AMA, Selection of AMAs diagnosis wise, Rationality of Prescription.Results: More than 75% patients coming to GPs were suffering from communicable diseases. Average no. of drugs / prescription and percentage of prescription with AMAs was high in all GPs. Macrolides was the most common group of AMA used by MBBS whereas Cephalosporins was used by BAMS and BHMS. Irrational use of AMAs was high in BHMS GPs. Use of irrational FDCs, banned drugs, steroids was high in BAMS GPs.Conclusions: There are deficiencies in prescription practices among all GPs. Not only are GPs prescribing the highest number of  AMAs  per prescription anywhere, their prescription practices for common health problems are highly inappropriate. High level of irrational use of drugs by BAMS and BHMS GPs are cause of concern

Biometric Personal Identification based on Iris Patterns

This paper discusses an analysis of human iris patterns for recognition of biometric system which consists of a segmentation system that is based on the Hough transform, and is able to localize the circular iris and pupil region, occluding eyelids and eyelashes, and reflections. The extracted iris region is then normalized into a rectangular block with constant dimensions to account for imaging inconsistencies. To encode the unique pattern of the iris into a bit-wise biometric template, 1D Log-Gabor filter is used.Finally to match two iris templates hamming distance is used as matching metric. The system performance is analyzed on 312 iris images taken from standard CASIA Iris Interval database version 4. To establish the verification accuracy of iris representation and matching approach, each iris image in the database is matched with all the other iris images in the database and genuine and imposter distribution is found .The performance of the system is implemented by evaluating the Decidability Index (DI), False match rate (FMR), False Non-match rate (FNMR), Genuine Accept Rate (GAR) and Equal error rate (EER)