Shock Dynamics in Particle-Laden Thin Films

PRL 94(11) March 25, 2005 117803We present theory and experiments for thin film particle-laden flow on an incline. At higher particle concentration and inclination angle, a new phenomenon is observed in which a large particle-rich ridge forms at the contact line. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels recent findings of double shocks in thermal-gravity driven flow [A. L. Bertozzi et. al., PRL, 81, 5169 (1998), J. Sur et. al., PRL 90, 126105 (2003), A. M¨unch, PRL 91, 016105 (2003)]. However, here the emergence of the shocks arises from a new mechanism involving the settling rates of the species.NS

Effect of inertial lift on a spherical particle suspended in flow through a curved duct

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrates. The Navier-Stokes equations determine the hydrodynamic forces acting on a particle. A leading order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales, specifically the particle radius, duct height, and duct bend radius. Additionally, a trapezoidal shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.Brendan Harding, Yvonne M. Stokes and Andrea L. Bertozz

Spectral theory for the failure of linear control in a nonlinear stochastic system

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems the nonnormality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the nonnormality and the type of nonlinearity are all crucially important to understanding and describing the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong nonnormality is due to the presence of mean flow rather than the action of control.Comment: Submitted to Physical Review

Absence of squirt singularities for the multi-phase Muskat problem

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.Comment: 16 page

The McKean-Vlasov Equation in Finite Volume

We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, $\theta^{\sharp}$ of the interaction parameter. We show that the uniform density (which may be interpreted as the liquid phase) is dynamically stable for $\theta < \theta^{\sharp}$ and prove, abstractly, that a {\it critical} transition must occur at $\theta = \theta^{\sharp}$. However for this system we show that under generic conditions -- $L$ large, $d \geq 2$ and isotropic interactions -- the phase transition is in fact discontinuous and occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded interactions with discontinuous transitions we show that, with suitable scaling, the \theta\t(L) tend to a definitive non--trivial limit as $L\to\infty$

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Global and national burden of diseases and injuries among children and adolescents between 1990 and 2013 findings from the global burden of disease 2013 study

IMPORTANCE: The literature focuses on mortality among children younger than 5 years. Comparable information on nonfatal health outcomes among these children and the fatal and nonfatal burden of diseases and injuries among older children and adolescents is scarce. OBJECTIVE: To determine levels and trends in the fatal and nonfatal burden of diseases and injuries among younger children (aged < 5 years), older children (aged 5-9 years), and adolescents (aged 10-19 years) between 1990 and 2013 in 188 countries from the Global Burden of Disease (GBD) 2013 study. EVIDENCE REVIEW: Data from vital registration, verbal autopsy studies, maternal and child death surveillance, and other sources covering 14 244 site-years (ie, years of cause of death data by geography) from 1980 through 2013 were used to estimate cause-specific mortality. Data from 35 620 epidemiological sources were used to estimate the prevalence of the diseases and sequelae in the GBD 2013 study. Cause-specific mortality for most causes was estimated using the Cause of Death Ensemble Model strategy. For some infectious diseases (eg, HIVinfection/AIDS, measles, hepatitis B) where the disease process is complex or the cause of death data were insufficient or unavailable, we used natural history models. For most nonfatal health outcomes, DisMod-MR2.0, a Bayesian metaregression tool, was used to meta-analyze the epidemiological data to generate prevalence estimates. FINDINGS: Of the 7.7 (95 uncertainty interval UI, 7.4-8.1) million deaths among children and adolescents globally in 2013,6.28 million occurred amongyounger children, 0.48 million among older children, and 0.97 million among adolescents. In 2013, the leading causes of death were lower respiratory tract infections amongyounger children (905 059 deaths; 95% UI, 810 304-998125), diarrheal diseases among older children (38 325 deaths; 95% UI, 30 365-47 678), and road injuries among adolescents (115186 deaths; 95% UI, 105185-124 870). Iron deficiency anemia was the leading cause of years lived with disability among children and adolescents, affecting 619 (95% UI, 618-621) million in 2013. Large between-country variations exist in mortality from leading causes among children and adolescents. Countries with rapid declines in all-cause mortality between 1990 and 2013 also experienced large declines in most leading causes of death, whereas countries with the slowest declines had stagnant or increasing trends in the leading causes of death. In 2013, Nigeria had a 12% global share of deaths from lower respiratory tract infections and a 38% global share of deaths from malaria. India had 33% of the world's deaths from neonatal encephalopathy. Half of the world's diarrheal deaths among children and adolescents occurred injust 5 countries: India, Democratic Republic of the Congo, Pakistan, Nigeria, and Ethiopia. CONCLUSIONS AND RELEVANCE: Understanding the levels and trends of the leading causes of death and disability among children and adolescents is critical to guide investment and inform policies. Monitoring these trends over time is also key to understanding where interventions are having an impact. Proven interventions exist to prevent or treat the leading causes of unnecessary death and disability among children and adolescents. The findings presented here show that these are underused and give guidance to policy makers in countries where more attention is needed. Copyright 2016 American Medical Association. All rights reserved