Linear and nonlinear stability of plane poiseuille-couette flow

The problem of the response of a viscous fluid in a channel to the dual effects of wall sliding and constant streamwise pressure gradient has received considerable attention from researchers over the years, due to its relevance to applications such as micro-electro-mechanical systems, aerodynamics heating, electrostatic precipitation and also of course the fact that the basic undisturbed profile, plane Poiseuille-Couette flow (PPCF), is an exact Navier-Stokes solution. The purpose of the thesis is to investigate the linear and nonlinear stability of this flow at asymptotically large Reynolds numbers and numerically at finite Reynolds numbers. The advantage of using an asymptotic approach is that it provides useful physical insight, theoretical understanding of underlying physical mechanisms, gives an easier access to the non-linear regime and forms the basis for carrying out numerical work at finite Reynolds numbers for the flow. The linear and nonlinear stability of PPCF to three-dimensional disturbances is investigated asymptotically at large values of the Reynolds numbers R based on channel half-width and the maximum velocity of the Poiseuille component. One of the main achievements of the thesis is demonstrating that three-dimensional nonlinear neutral modes exist in PPCF for disturbances with the magnitude of O(R^-4/9) when R >>1. The asymptotic theory, aimed at a detailed understanding of the physical mechanisms governing the amplitude-dependent stability properties of the flow, shows that the phase shifts induced across the critical layer and a near-wall shear layer are comparable when the disturbance size Δ = O(R^-4/9). In addition, it emerges that at this crucial size both streamwise and spanwise wavelengths of the travelling wave disturbance are comparable with the channel width, with an associated phase speed of O(1). Neutral solutions are found to exist in the range 0 < V < 2 with c0 = V to leading order, where c0 and V are non-dimensional quantities representing the dominant phasespeed of the nonlinear travelling waves and the wall sliding speed respectively. Moreover, these instability modes exist at sliding speeds well in excess of the linear instability cut-off V = 0.34. The amplitude equation governing these modes is derived analytically and we further find that this asymptotic structure breaks down in the limit V→ 2 when the disturbance streamwise wavelength decreases to O(R^-1/3) and the maximum of the basic flow becomes located at the upper wall. The numerical results from this interaction are found to compare well with full solutions of the Navier-Stokes equations. The second achievement of the thesis is that we demonstrate that three-dimensional nonlinear neutral modes exist in PPCF for disturbances with the magnitude of O(R^-1/3) when R >> 1. By analysing the nature of the instability for increasing disturbance size Δ, the scaling Δ = O(R^-1/3) is identified for which a strongly nonlinear neutral wave structure emerges, involving the interaction of two inviscid critical layers. The striking feature of this structure is that the travelling wave disturbances have both streamwise and spanwise wavelengths comparable to the channel width, with an associated phase speed of O(1). A method involving the classical balancing of the phase shifts enables the amplitude-dependence of the neutral modes to be determined in terms of the wavenumbers and the properties of the basic flow. Numerical computation of the Rayleigh equation which governs the flow outside of the critical layers shows that neutral solutions exist for non-dimensional wall sliding speeds in the range 0 =< V < 2. It transpires that the critical layers merge and the asymptotic structure referred to above breaks down both in the large-amplitude limit and the limit V→2 when the maximum of the basic flow becomes located at the upper wall. The validity of these asymptotic structures is confirmed by comparison with numerical solutions obtained at finite Reynolds numbers.Open Acces

Precision targeting of preventative therapy for tuberculosis

Background: Scale-up of preventative treatment for tuberculosis (TB) represents a cornerstone of global control efforts. I examined a range of approaches to enable more precise targeting of preventative treatment to people at highest risk. Methods: I evaluated whether prognostic tests for TB (tuberculin skin test (TST), QuantiFERON Gold-in-tube (QFT-GIT) and T-SPOT.TB) may be optimised by implementing higher thresholds, or by a newer generation assay (QuantiFERON-TB Gold Plus; QFT-Plus). Next, I conducted a systematic review and individual participant data meta-analysis (IPD-MA) to examine TB risk among people tested for latent infection (LTBI) in settings with low TB transmission and to develop a multivariable prognostic model for incident TB. Finally, I performed a systematic review and IPD-MA of whole-blood RNA sequencing data to evaluate blood transcriptomic signatures as next-generation biomarkers. Results: In a UK cohort of 9,610 adults, higher TST, QFT-GIT and T-SPOT.TB results were associated with increased incident TB risk. Implementing higher cut-offs led to a marginal improvement in positive predictive value, but at the cost of a marked loss in sensitivity. The newer generation QFT-Plus had similar predictive ability. In a pooled dataset of >80,000 participants from 18 cohort studies, TB risk was heterogeneous among people with LTBI, even after stratification by indication for testing. I developed and validated a multivariable prognostic model, which incorporates quantitative LTBI test results and clinical covariates, and demonstrated strong potential for clinical utility to inform provision of preventative treatment. Among 1,126 whole-blood RNA sequencing samples, eight transcriptomic signatures (comprising 1-25 transcripts) performed similarly for predicting incident TB, but only met global accuracy benchmarks over a 3-6 month time-horizon. Conclusions: Personalised risk estimates integrating quantitative LTBI test results and clinical covariates may facilitate more precise targeting of preventative treatment. Blood transcriptomic biomarkers show promise, but only represent short-term TB risk. Future research priorities are highlighted

Elective Subject Selection Recommender System

Performance of student is dependent on their subject select and faculty’s expertise who teach the subject. Sometimes subject selection done by the student. Few students’ select subject wisely, few of them select because of friend influence, faculty influence, without thinking on it. To reduce the cost and related overhead department tries to reduce the variety of elective. Wisely selected and offered subject will increase the performance of student and throughput of the faculty. In this paper a recommender system is proposed which find the score of knowledge level for student and score of faculty score. These scores will be used to recommend the right subject to adept faculty of that subject

A semi–analytical study of diffusion type multi–term time fractional partial differential equation

This work suggested algorithm for the solution of multi–term time fractional partial differential equation by the application of homotopy analysis fractional Sumudu transform method based on iterative process. The method is cumulation of Sumudu transform and homotopy analysis method. Also, the multi-term time fractional partial differential equation represented in the form of system of fractional partial differential equations as per certain conditions of fractional derivatives. The Caputo fractional order derivatives are taken for the multi–term time fractional partial differential equations. Numerical examples are discussed for the support of theory and the approximate solution compared with exact solutions at the integer value of derivatives.Emerging Sources Citation Index (ESCI)MathScinetScopu

Business Judgment Rule: Defense for the Directors in Cases of Alleged Breach of Duties

In this article researchers will explain about Business Judgment Rule and how it can be used as a defence by the directors’ of the corporation. In simple language it can be said that the “Business judgment rule” is nothing but a judicially evolved doctrine derived out of case laws in the field of corporate laws. This doctrine has its origin in USA followed by U.K. The rule is in use in some form or the other in the common law countries e.g. whales, Australia, Canada, India &amp;c. Australia has codified this rule under sec.1180(2) Corporations Act 2001, in South Africa Companies Act 71 of 200 section 76(4) provides for director’s duty to work towards best interest of the business with due care, skill and diligence, in India section 166(2) of Companies Act, 2013 requires that for the benefit of different constituencies of a company a director must act bona fide to promote the object of the company. The Business Judgment Rule tries to protect the directors of the company by creating a safe harbour for those who works for the betterment and interest of the corporations in an honest manner and in good faith. The scope of the paper is restricted to mainly US decisions, which has seen the greatest development in interpreting cases, though certain important landmarks in the Indian and UK context have also been referred to. The paper is limited by secondary sources such as books, articles and reports available on the subject

Thermo-Chromic Response of Polymer Stabilized Cholesteric Liquid Crystal for Thermal Imaging

Cholesteric liquid crystal (Ch-LC) exhibits many remarkable optical properties due to formation of a macroscopic helical structure. A low amount of monomer (5wt.%) is dispersed into cholesteric liquid crystal and get polymerized under UV radiations to form polymer stabilized cholesteric texture (PSCT). The thermo-chromic response made this device suitable for the developing applications in thermal imaging. Temperature based measurements of PSCT exploits the key property of some polymer stabilized cholesteric liquid crystals (PSCLC) to reflect definite colors at specific temperatures. The selective color of PSCT texture shifts with raise in temperature from 30oC to 85oC, which can be utilized in thermal imaging applications