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These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Partial differential equations --- Interfaces (Physical sciences) --- Turbulence --- Burgers equation --- Differential equations, Parabolic --- Mathematical models --- Mathematical Theory --- Atomic Physics --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Differentiaalvergelijkingen [Parabolische ] --- Differential equations [Parabolic] --- Diffusion equation [Nonlinear ] --- Equations differentielles paraboliques --- Heat flow equation [Nonlinear ] --- Interface (Physical sciences) --- Partial differential equations. --- Probabilities. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Burgers equation. --- Mathematical models. --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Heat equation --- Navier-Stokes equations --- Interfaces (Physical sciences) - Mathematical models --- Turbulence - Mathematical models

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Asymptotic expansions. --- Burgers equation. --- Turbulence --- Mathematical models. --- Burgers equation --- Asymptotic expansions --- Burgers, Equation de --- Développements asymptotiques --- 532.517 --- -Flow, Turbulent --- Turbulent flow --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Heat equation --- Asymptotes --- Convergence --- Divergent series --- Liquid motion according to type of flow --- -Liquid motion according to type of flow --- 532.517 Liquid motion according to type of flow --- -Diffusion equation, Nonlinear --- Flow, Turbulent --- Développements asymptotiques --- Navier-Stokes equations --- Asymptotic developments --- Difference equations --- Functions --- Numerical analysis --- Mathematical models --- Mathematical physics --- Fluid mechanics --- Modèles mathématiques --- Turbulence - Mathematical models

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Rheology, defined as the science of deformation and flow of matter, is a multidisciplinary scientific field, covering both fundamental and applied approaches. The study of rheology includes both experimental and computational methods, which are not mutually exclusive. Its practical importance embraces many processes, from daily life, like preparing mayonnaise or spread an ointment or shampooing, to industrial processes like polymer processing and oil extraction, among several others. Practical applications include also formulations and product development. This Special Issue aims to present the latest advances in the fields of experimental and computational rheology applied to the most diverse classes of materials (foods, cosmetics, pharmaceuticals, polymers and biopolymers, multiphasic systems and composites) and processes. This Special Issue will comprise, not only original research papers, but also review articles.

n/a --- microstructure --- microfluidization --- yield stress --- nonlinear diffusion equation --- particle suspensions --- colloids --- viscous gravity spreading --- nanocomposites --- BMP model --- LCB polypropylene --- diutan gum --- thixotropy --- complex fluids --- traction test --- viscoelasticity --- biopolymer --- normal stresses --- start-up shear --- OpenFOAM --- flow properties --- rheometry --- oscillatory flows --- linear viscoelasticity --- continuum model --- steady-state and transient flow --- interfacial shear rheology --- shear-banding flow --- pressure transducers --- jetting --- natural hydraulic lime --- generalized Boussinesq equation --- prototyping --- piezoelectric --- masonry --- polymer processing --- eco-friendly surfactant --- emulsion stability --- rhamsan gum --- lubricating grease --- computational rheology --- Saffman–Taylor instability --- extrusion --- volume of fluid method --- polymers --- weak gel --- cement pastes --- Carbopol --- thyme oil --- elongational flow --- rheology --- grout --- epoxy --- polystyrene --- shear thickening --- bulk rheology --- porous medium equation --- consolidation --- Dupuit-Forchheimer assumption --- yield stress fluid --- drop formation --- dilatational rheology --- droplet size distribution (DSD) --- Navier-Stokes equations --- Saffman-Taylor instability