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A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed,…
We consider nonnegative solutions of the porous medium equation (PME) on a Cartan-Hadamard manifold whose negative curvature can be unbounded. We take compactly supported initial data because we are also interested in free boundaries. We…
The established microalgae growth models are semi-empirical or considerable fitting coefficients exist currently. Therefore, the ability of the model prediction is reduced by the numerous fitting coefficients. Furthermore, the predicted…
The lattice Boltzmann (LB) method is used to study the kinetics of domain growth of a binary fluid in a number of geometries modeling porous media. Unlike the traditional methods which solve the Cahn-Hilliard equation, the LB method…
The growth of laminar-turbulent band patterns in plane Couette flow is studied in the vicinity of the global stability threshold R_g below which laminar flow ultimately prevails. Appropriately tailored direct numerical simulations are…
We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched…
Solar polar plumes are bright radial rays rooted at the sun's polar areas. They are widely believed to have the structure of expanding tube. A four degree polynomial function was assumed to represent the change of cross section diameter as…
We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of non-overlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws…
In this stub article, we show that laminar quasi-periodically developed flow is characterized by velocity and pressure modes which decay exponentially along the main flow direction. As the amplitudes of these modes exhibit streamwise…
We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the kernel concentrates around the origin, the nonlocal equation…
We study pore nucleation in a model membrane system, a freestanding polymer film. Nucleated pores smaller than a critical size close, while pores larger than the critical size grow. Holes of varying size were purposefully prepared in liquid…
Bubble solutions are of growing interest because of various technological applications in surface cleaning, water treatment, and agriculture. However, their physicochemical properties such as the stability and interfacial charge of bubbles…
We study non-equilibrium bacterial colony growth using a geometry-first, time-resolved analysis of morphology. From time-lapse microscopy data, we track the coupled evolution of area, perimeter, and boundary-sensitive shape descriptors…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
The inward drift of mm-cm sized pebbles in protoplanetary disks has become an important part of our current theories of planet formation and, more recently, planet composition as well. The gas-to-dust size ratio of protoplanetary disks can…
We use laboratory experiments to investigate the entrainment of ambient fluid into an axisymmetric turbulent plume that contains dense particles with a settling velocity that is considerably smaller than the plume velocity. We consider the…
The growth of a rough and porous thin surface by deposition of randomly shaped clusters with different sizes over an initially flat linear substrate is simulated, using Monte Carlo technique. Unlike the ordinary Random Deposition, our…
Context. Several physical properties of solar polar plumes have been identified by different published studies, however such studies are rare and sometimes in disagreement. Aims. The purpose of the present work is to analyze a set of…
We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biot's model in an infinite bilayered medium, with a plane interface. We adopt the Cagniard-De Hoop's technique. This report is devoted to…
The presence of stratified layer in atmosphere and ocean leads to buoyant vertical motions, commonly referred to as plumes. It is important to study the mixing dynamics of a plume at a local scale in order to model their evolution and…