A stronger topology for the Brownian web

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the diffusively rescaled weight distribution in a silo model (as well as the equivalent output distribution in a river basin model), interpreted in terms of (dual) diffusively rescaled coalescing random walks, to corresponding objects defined in terms of the Brownian web.Comment: 22 page

Imbibition in Disordered Media

The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.Comment: Review article, to appear in Advances in Physics, 53 pages LaTe

Study on the sound absorption behavior of multi-component polyester nonwovens: experimental and numerical methods

This study presents an investigation of the acoustical properties of multi-component polyester nonwovens with experimental and numerical methods. Fifteen types of nonwoven samples made with staple, hollow and bi-component polyester fibers were chosen to carry out this study. The AFD300 AcoustiFlow device was employed to measure airflow resistivity. Several models were grouped in theoretical and empirical model categories and used to predict the airflow resistivity. A simple empirical model based on fiber diameter and fabric bulk density was obtained through the power-fitting method. The difference between measured and predicted airflow resistivity was analyzed. The surface impedance and sound absorption coefficient were determined by using a 45 mm Materiacustica impedance tube. Some widely used impedance models were used to predict the acoustical properties. A comparison between measured and predicted values was carried out to determine the most accurate model for multi-component polyester nonwovens. The results show that one of the Tarnow model provides the closest prediction to the measured value, with an error of 12%. The proposed power-fitted empirical model exhibits a very small error of 6.8%. It is shown that the Delany–Bazley and Miki models can accurately predict surface impedance of multi-component polyester nonwovens, but the Komatsu model is less accurate, especially at the low-frequency range. The results indicate that the Miki model is the most accurate method to predict the sound absorption coefficient, with a mean error of 8.39%

Complex Fluids and Hydraulic Fracturing

Nearly 70 years old, hydraulic fracturing is a core technique for stimulating hydrocarbon production in a majority of oil and gas reservoirs. Complex fluids are implemented in nearly every step of the fracturing process, most significantly to generate and sustain fractures and transport and distribute proppant particles during and following fluid injection. An extremely wide range of complex fluids are used: naturally occurring polysaccharide and synthetic polymer solutions, aqueous physical and chemical gels, organic gels, micellar surfactant solutions, emulsions, and foams. These fluids are loaded over a wide range of concentrations with particles of varying sizes and aspect ratios and are subjected to extreme mechanical and environmental conditions. We describe the settings of hydraulic fracturing (framed by geology), fracturing mechanics and physics, and the critical role that non-Newtonian fluid dynamics and complex fluids play in the hydraulic fracturing process

Numerical Modeling of Fluid Flow in Solid Tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges

Water relations of evergreen and drought-deciduous trees along a seasonally dry tropical forest chronosequence

Seasonally dry tropical forests (SDTF) are characterized by pronounced seasonality in rainfall, and as a result trees in these forests must endure seasonal variation in soil water availability. Furthermore, SDTF on the northern Yucatan Peninsula, Mexico, have a legacy of disturbances, thereby creating a patchy mosaic of different seral stages undergoing secondary succession. We examined the water status of six canopy tree species, representing contrasting leaf phenology (evergreen vs. drought-deciduous) at three seral stages along a fire chronosequence in order to better understand strategies that trees use to overcome seasonal water limitations. The early-seral forest was characterized by high soil water evaporation and low soil moisture, and consequently early-seral trees exhibited lower midday bulk leaf water potentials (ΨL) relative to late-seral trees (−1.01 ± 0.14 and −0.54 ± 0.07 MPa, respectively). Although ΨL did not differ between evergreen and drought-deciduous trees, results from stable isotope analyses indicated different strategies to overcome seasonal water limitations. Differences were especially pronounced in the early-seral stage where evergreen trees had significantly lower xylem water δ18O values relative to drought-deciduous trees (−2.6 ± 0.5 and 0.3 ± 0.6‰, respectively), indicating evergreen species used deeper sources of water. In contrast, drought-deciduous trees showed greater enrichment of foliar 18O (∆18Ol) and 13C, suggesting lower stomatal conductance and greater water-use efficiency. Thus, the rapid development of deep roots appears to be an important strategy enabling evergreen species to overcome seasonal water limitation, whereas, in addition to losing a portion of their leaves, drought-deciduous trees minimize water loss from remaining leaves during the dry season

Upscaling Flow and Transport Processes

Peer reviewe

Traveling Wave Solutions in a Generalized Theory for Macroscopic Capillarity

One-dimensional traveling wave solutions for imbibition processes into a homogeneous porous medium are found within a recent generalized theory of macroscopic capillarity. The generalized theory is based on the hydrodynamic differences between percolating and nonpercolating fluid parts. The traveling wave solutions are obtained using a dynamical systems approach. An exhaustive study of all smooth traveling wave solutions for primary and secondary imbibition processes is reported here. It is made possible by introducing two novel methods of reduced graphical representation. In the first method the integration constant of the dynamical system is related graphically to the boundary data and the wave velocity. In the second representation the wave velocity is plotted as a function of the boundary data. Each of these two graphical representations provides an exhaustive overview over all one-dimensional and smooth solutions of traveling wave type, that can arise in primary and secondary imbibition. Analogous representations are possible for other systems, solution classes, and processes.</p