Shaping liquid drops by vibration

We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragmentat into smaller drops

Morphology changes in the evolution of liquid two-layer films

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions or the Marangoni effect. Using a long wave approximation we derive coupled evolution equations for the interafce profiles for a general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses are performed for isothermal ultrathin layers below 100 nm thickness under the influence of destabilizing long-range and stabilizing short-range interactions. Flat films may be unstable to varicose, zigzag or mixed modes. During the long-time evolution the nonlinear mode type can change via switching between two different branches of stable stationary solutions or via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil

Pattern formation in intracortical neuronal fields

The present article introduces a neuronal field model for both excitatory and inhibitory connections. A single integro-differential equation with delay is derived and studied at a critical point by stability analysis, which yields conditions for static periodic patterns and wave instabilities. It turns out that waves only occur below a certain threshold of the activity propagation velocity. An additional brief study exhibits increasing phase velocities of waves with decreasing slope subject to increasing activity propagation velocities, which are in accordance to experimental results. Numerical studies near and far from instability onset supplement the work

Patterns and predictors of statin prescription in patients with type 2 diabetes

<p>Abstract</p> <p>Background</p> <p>The benefit of statins for prevention of cardiovascular events in type 2 diabetes is established, but a gap exists between guideline recommendations and clinical practice. The aim of the study was to identify patient-related factors predicting statin prescription.</p> <p>Methods</p> <p>We assessed the quality of care in 51,640 patients with type 2 diabetes in a German diabetes registry. Patients were stratified according to primary and secondary prevention. Five-year risk for cardiovascular events was calculated in primary prevention patients. A multivariate adjusted logistic regression model was constructed to determine which parameters influenced statin prescription.</p> <p>Results</p> <p>34% had established atherosclerotic disease and 25.5% received a statin. Prescription was significantly higher in the secondary compared to the primary prevention group (38.1% [95% CI 37.4–38.9%] vs. 18.5% [95% CI 18.0–19.0%], respectively). In primary prevention the odds for statin prescription increased with estimated cardiovascular risk (OR 1.17 per 5% increase in 5-year risk, 95% CI 1.11–1.22). Positive predictors for statin prescription were secondary prevention, hypertension, former smoking, baseline LDL-cholesterol, and microalbuminuria. The odds of receiving a statin had an inverted U-shaped relation with age (nadir, 66 years), age at first diagnosis of diabetes (nadir, 56 years), and body mass index (nadir, 32 kg/m²). The model predicted prescription in 70% of the patients correctly.</p> <p>Conclusion</p> <p>The majority of patients with type 2 diabetes are not receiving statins. The predominant factors determining statin prescription are the patient's prevention status and, in primary prevention, estimated cardiovascular risk. The results suggest that although physicians are aware of the general concept of cardiovascular risk, they fail to consistently implement guidelines.</p

A four compartment epidemic model with retarded transition rates

We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet not infectious (C), infected and infectious (I), and recovered - immune (R). An infection is 'visible' only when an individual is in state I. Upon infection, an individual performs the transition pathway S to C to I to R to S remaining in each compartments C, I, and R for certain random waiting times, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We obtain formulae for the endemic equilibrium and a condition of its existence for cases when the waiting time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. We implement a simple multiple random walker's approach (microscopic model of Brownian motion of Z independent walkers) with random SCIRS waiting times into computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random walker's approach offers an appropriate microscopic description for the macroscopic model.Comment: 26 pages, 11 figure

Alternative pathways of dewetting for a thin two-layer film of soft matter

We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show that depending on the long-range van-der-Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate

Defect Motion in Rotating Fluids

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