Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Experimental investigation of transient natural convection cooling of high prandtl number fluid with variable viscosity

Report for the scientific sojourn at the James Cook University, Australia, between June to December 2007. Free convection in enclosed spaces is found widely in natural and industrial systems. It is a topic of primary interest because in many systems it provides the largest resistance to the heat transfer in comparison with other heat transfer modes. In such systems the convection is driven by a density gradient within the fluid, which, usually, is produced by a temperature difference between the fluid and surrounding walls. In the oil industry, the oil, which has High Prandtl, usually is stored and transported in large tanks at temperatures high enough to keep its viscosity and, thus the pumping requirements, to a reasonable level. A temperature difference between the fluid and the walls of the container may give rise to the unsteady buoyancy force and hence the unsteady natural convection. In the initial period of cooling the natural convection regime dominates over the conduction contribution. As the oil cools down it typically becomes more viscous and this increase of viscosity inhibits the convection. At this point the oil viscosity becomes very large and unloading of the tank becomes very difficult. For this reason it is of primary interest to be able to predict the cooling rate of the oil. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of high Prandtl fluid considering the variable viscosity effects.

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Computational calculations of magnetic relaxation and viscosity in small magnetic grains

In this article we present a phenomenological model which simulates very well the mag¿ netic relaxation behavior experimentally observed in small magnetic grains and single domain particles. In this model, the occurrence of quantum tunneling of magnetization below a certain temperature is taken into account. Experimental results for different materials are presented to illustrate the most important behavior deduced from our model

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Fabricació i anàlisi del biodièsel

La producció de biodièsel a partir d'olis de cuina utilitzats, amb l'objectiu de transformar un residu en un producte amb valor comercial i ambiental, és més net que els combustibles fòssils i contribueix a disminuir el gran consum de petroli que estem fent. En una primera part teòrica s’ha realitzat un treball de recerca d' informació del biodièsel per saber si és un bon combustible i si podria ser un possible substitut dels combustibles fòssils. En quant a la part pràctica l'objectiu principal ha estat fabricar el biodièsel . Les matèries primeres són oli de gira-sol i oli de cuina utilitzat, per tal de comparar les seves qualitats. S’ha arribat a la conclusió que presenten característiques molt semblants. Després de fer les anàlisis físico-químics de qualitat vam fer una mescla dels dos biodièsels fabricats, i el vam provar en un motor Dièsel per comprovar si funciona correctament i fer una comparació dels gasos emesos pel nostre combustible amb els emesos pel gasoil comercial. El resultat va ser molt positiu ja que el motor va funcionar correctament, i la comparació de gasos va sortir tal i com esperàvem ja que les quantitats de diòxid i monòxid de carboni emeses eren menors que en el gasoil.

Why are slip lengths so large in carbon nanotubes?

The enhanced flow in carbon nanotubes is explained using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why `slip-lengths' may be greater than the tube radius.

Management of corn stalk waste as reinforcement for polypropylene injection moulded composites

The main objective of this study was the management of corn stalk waste as reinforcement for polypropylene (PP) injection moulded composites as an alternative to wood flour and fibers. In the first step, corn stalk waste was subjected to various treatments, and four different corn stalk derivatives (flour and fibers) able to be used as reinforcement of composite materials were prepared and characterized. These derivatives are corn stalk flour, thermo-mechanical, semi-chemical, and chemical fibers. They were characterized in terms of their yield, lignin content, Kappa number, fiber length/diameter ratio, fines, coarseness, viscosity, and the length at the break of a standard sheet of paper. Results showed that the corn stalk derivatives have different physico-chemical properties. In the second step, the prepared flour and fibers were explored as a reinforcing element for PP composites. Coupled and non-coupled PP composites were prepared and tested for tensile properties. For overall trend, with the addition of a coupling agent, tensile properties of composites significantly improved, as compared with non-coupled samples. In addition, a morphological study revealed the positive effect of the coupling agent on the interfacial bonding. The composites prepared with semichemical fiber gave better results in comparison with the rest of the corn stalk derivatives due to its chemical characteristics

Estimation of the viscoelastic properties of vessel walls using a computational model and Doppler ultrasound

Human arteries affected by atherosclerosis are characterized by altered wall viscoelastic properties. The possibility of noninvasively assessing arterial viscoelasticity in vivo would significantly contribute to the early diagnosis and prevention of this disease. This paper presents a noniterative technique to estimate the viscoelastic parameters of a vascular wall Zener model. The approach requires the simultaneous measurement of flow variations and wall displacements, which can be provided by suitable ultrasound Doppler instruments. Viscoelastic parameters are estimated by fitting the theoretical constitutive equations to the experimental measurements using an ARMA parameter approach. The accuracy and sensitivity of the proposed method are tested using reference data generated by numerical simulations of arterial pulsation in which the physiological conditions and the viscoelastic parameters of the model can be suitably varied. The estimated values quantitatively agree with the reference values, showing that the only parameter affected by changing the physiological conditions is viscosity, whose relative error was about 27% even when a poor signal-to-noise ratio is simulated. Finally, the feasibility of the method is illustrated through three measurements made at different flow regimes on a cylindrical vessel phantom, yielding a parameter mean estimation error of 25%.