Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media
Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi
2016-09-01
We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.
Superfast non-linear diffusion: Capillary transport in particulate porous media
Lukyanov, A V; Baines, M J; Theofanous, T G
2013-01-01
The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving bounda...
Smoothing and Decay Estimates for Nonlinear Diffusion Equations Equations of Porous Medium Type
Vázquez, Juan Luis
2006-01-01
This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porou
Directory of Open Access Journals (Sweden)
Eloise C. Tredenick
2017-05-01
Full Text Available The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.
Nonlinear Diffusion and Transient Osmosis
Akira, Igarashi; Lamberto, Rondoni; Antonio, Botrugno; Marco, Pizzi
2011-08-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call “transient osmosis". We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.
Nonlinear Diffusion and Transient Osmosis
Institute of Scientific and Technical Information of China (English)
Akira Igarashi; Lamberto Rondon; Antonio Botrugno; Marco Pizzi
2011-01-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call ＂transient osmosis＂. We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.
Diffusion in porous crystalline materials
Krishna, R.
2012-01-01
The design and development of many separation and catalytic process technologies require a proper quantitative description of diffusion of mixtures of guest molecules within porous crystalline materials. This tutorial review presents a unified, phenomenological description of diffusion inside meso-
Diffusion in porous crystalline materials.
Krishna, Rajamani
2012-04-21
The design and development of many separation and catalytic process technologies require a proper quantitative description of diffusion of mixtures of guest molecules within porous crystalline materials. This tutorial review presents a unified, phenomenological description of diffusion inside meso- and micro-porous structures. In meso-porous materials, with pore sizes 2 nm < d(p) < 50 nm, there is a central core region where the influence of interactions of the molecules with the pore wall is either small or negligible; meso-pore diffusion is governed by a combination of molecule-molecule and molecule-pore wall interactions. Within micro-pores, with d(p) < 2 nm, the guest molecules are always under the influence of the force field exerted with the wall and we have to reckon with the motion of adsorbed molecules, and there is no "bulk" fluid region. The characteristics and physical significance of the self-, Maxwell-Stefan, and Fick diffusivities are explained with the aid of data obtained either from experiments or molecular dynamics simulations, for a wide variety of structures with different pore sizes and topology. The influence of adsorption thermodynamics, molecular clustering, and segregation on both magnitudes and concentration dependences of the diffusivities is highlighted. In mixture diffusion, correlations in molecular hops have the effect of slowing-down the more mobile species. The need for proper modeling of correlation effects using the Maxwell-Stefan formulation is stressed with the aid of examples of membrane separations and catalytic reactors.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Effects of Porous Throat on Transonic Diffuser
屋我, 実; 永井, 實; 富田, 教夫; 芳賀, 剛; 宮良, 透; Yaga, Minoru; Nagai, Minoru; Tomita, Norio; Haga, Tsuyoshi; Miyara, Tooru
1995-01-01
The effects of the porous throat on a transonic diffuser were investigated experimentally by wall static pressure measurements and by schlieren optical observations. The porous throat consists of a wall with 126 holes and a cavity underneath it so that the flow around the shock wave can circulate through the porous wall. The results show that no shock wave was observed at 80% of the porous region from the throat and that the pressure fluctuations in the transonic diffuser were greatly reduced...
Logarithmic diffusion and porous media equations: a unified description.
Pedron, I T; Mendes, R S; Buratta, T J; Malacarne, L C; Lenzi, E K
2005-09-01
In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a Lorentzian form, consequently this equation characterizes a superdiffusion like a Lévy kind. In addition an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension, is obtained. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.
Mathematical models of a diffusion-convection in porous media
Directory of Open Access Journals (Sweden)
Anvarbek M. Meirmanov
2012-06-01
Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Diffusion of copper in porous silicon
Energy Technology Data Exchange (ETDEWEB)
Andsager, D.; Hetrick, J.M.; Hilliard, J.; Nayfeh, M.H. [Department of Physics, 1110 West Green Street, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)
1995-05-01
We present a study on the nature of diffusion of copper in {ital p}-type porous silicon. The diffusion of evaporated copper in porous silicon and deposition of metal ions in aqueous solution through the porous network was measured by monitoring the metal concentration depth profile as a function of time using Auger electron spectroscopy. We observed that increasing metal penetration from copper evaporated samples correlates with quenching of photoluminescence, in agreement with previous ion quenching results. We extracted a diffusion coefficient from Auger concentration depth profiles which was seven orders of magnitude lower than that expected for diffusion of copper in bulk crystalline Si at room temperature. Deposition of ionic species cannot be characterized as a simple diffusion process. The observed deposition rates were strongly dependent on the solution concentration.
Pressure diffusion waves in porous media
Energy Technology Data Exchange (ETDEWEB)
Silin, Dmitry; Korneev, Valeri; Goloshubin, Gennady
2003-04-08
Pressure diffusion wave in porous rocks are under consideration. The pressure diffusion mechanism can provide an explanation of the high attenuation of low-frequency signals in fluid-saturated rocks. Both single and dual porosity models are considered. In either case, the attenuation coefficient is a function of the frequency.
MACROSCOPIC STRAIN POTENTIALS IN NONLINEAR POROUS MATERIALS
Institute of Scientific and Technical Information of China (English)
刘熠; 黄筑平
2003-01-01
By taking a hollow sphere as a representative volume element (RVE), the macroscopic strain potentials of porous materials with power-law incompressible matrix are studied in this paper.According to the principles of the minimum potential energy in nonlinear elasticity and the variational procedure, static admissible stress fields and kinematic admissible displacement fields are constructed,and hence the upper and the lower bounds of the macroscopic strain potential are obtained. The bounds given in the present paper differ so slightly that they both provide perfect approximations of the exact strain potential of the studied porous materials. It is also found that the upper bound proposed by previous authors is much higher than the present one, and the lower bounds given by Cocks is much lower. Moreover, the present calculation is also compared with the variational lower bound of Ponte Castafneda for statistically isotropic porous materials. Finally, the validity of the hollow spherical RVE for the studied nonlinear porous material is discussed by the difference between the present numerical results and the Cocks bound.
Nonlinear Behavior Of Saturated Porous Media Under External Impact
Perepechko, Y.
2005-12-01
This paper deals with nonlinear behavior of liquid saturated porous media in gravity filed under external impact. The continuum is assumed to be a two-velocity medium; it consists of a deformable porous matrix (with Maxwell's reology) and a Newtonian liquid that saturates this matrix. The energy dissipation in this model takes place due the interface friction between the solid matrix and saturating liquid, and also through relaxation of inelastic shear stress in the porous matrix. The elaborated nonisothermal mathematical model for this kind of medium is a thermodynamically consistent and closed model. Godunov's explicit difference scheme was used for computer simulation; the method implies numerical simulation for discontinuity decay in flux calculations. As an illustrative example, we consider the formation of dissipation structures in a plain layer of that medium after pulse or periodic impact on the background of liquid filtration through the porous matrix. At the process beginning, one can observe elastic behavior of the porous matrix. Deformation spreading through the saturated porous matrix occurs almost without distortions and produces a channel-shaped zone of stretching with a high porosity. Later on, dissipation processes and reology properties of porous medium causes the diffusion of this channel. We also observe a correlation between the liquid distribution (porosity for the solid matrix) and dilatancy fields; this allows us to restore the dilatancy field from the measured fluid saturation of the medium. This work was supported by the RFBR (Grant No. 04-05-64107), the Presidium of SB RAS (Grant 106), the President's Grants (NSh-2118.2003.5, NSh-1573.2003.5).
Diffusion of oriented particles in porous media
Energy Technology Data Exchange (ETDEWEB)
Haber, René [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Prehl, Janett [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Herrmann, Heiko [Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Hoffmann, Karl Heinz, E-mail: hoffmann@physik.tu-chemnitz.de [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany)
2013-11-29
Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.
Nonlinear Taylor dispersion in gravity currents in porous media
Szulczewski, Michael; Juanes, Ruben
2012-11-01
Taylor dispersion describes how a non-uniform flow can accelerate diffusive mixing between fluids by elongating the fluid-fluid interface over which diffusion acts. While Taylor dispersion has been extensively studied in simple systems such as Poiseuille and Couette flows, it is poorly understood in more complex systems such as porous-media flows. Here, we study Taylor dispersion in porous media during a gravity-driven flow using theory and simulations. We consider a simple geometry for physical insight: a horizontal, confined layer of permeable rock in which two fluids of different densities are initially separated by a vertical interface. We show that the flow exhibits a non-uniform velocity field that leads to Taylor dispersion at the aquifer scale. Unlike the classical model of Taylor dispersion, however, the diffusive mixing is coupled to the flow velocity because it reduces the lateral density gradient that drives the flow. This coupling causes the flow to continually decelerate and eventually stop completely. To model the flow, we develop a non-linear diffusion equation for the concentration of the more dense fluid, which admits an analytical similarity solution. We discuss applications of the model to CO2 sequestration.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Multicomponent Gas Diffusion in Porous Electrodes
Fu, Yeqing; Dutta, Abhijit; Mohanram, Aravind; Pietras, John D; Bazant, Martin Z
2014-01-01
Multicomponent gas transport is investigated with unprecedented precision by AC impedance analysis of porous YSZ anode-supported solid oxide fuel cells. A fuel gas mixture of H2-H2O-N2 is fed to the anode, and impedance data are measured across the range of hydrogen partial pressure (10-100%) for open circuit conditions at three temperatures (800C, 850C and 900C) and for 300mA applied current at 800C. For the first time, analytical formulae for the diffusion resistance (Rb) of three standard models of multicomponent gas transport (Fick, Stefan-Maxwell, and Dusty Gas) are derived and tested against the impedance data. The tortuosity is the only fitting parameter since all the diffusion coefficients are known. Only the Dusty Gas model leads to a remarkable data collapse for over twenty experimental conditions, using a constant tortuosity consistent with permeability measurements and the Bruggeman relation. These results establish the accuracy of the Dusty Gas model for multicomponent gas diffusion in porous med...
Highly nonlinear photoluminescence threshold in porous silicon
Energy Technology Data Exchange (ETDEWEB)
Nayfeh, M. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Akcakir, O. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Therrien, J. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Yamani, Z. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Barry, N. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Yu, W. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Gratton, E. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)
1999-12-27
Porous silicon is excited using near-infrared femtosecond pulsed and continuous wave radiation at an average intensity of {approx}10{sup 6} W/cm{sup 2} (8x10{sup 10} W/cm{sup 2} peak intensity in pulsed mode). Our results demonstrate the presence of micron-size regions for which the intensity of the photoluminescence has a highly nonlinear threshold, rising by several orders of magnitude near this incident intensity for both the pulsed and continuous wave cases. These results are discussed in terms of stimulated emission from quantum confinement engineered intrinsic Si-Si radiative traps in ultrasmall nanocrystallites, populated following two-photon absorption. (c) 1999 American Institute of Physics.
National Research Council Canada - National Science Library
Sunil; Mahajan, Amit
2009-01-01
A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD...
Analysis of Erbium and Vanadium Diffusion in Porous Silicon Carbide
Directory of Open Access Journals (Sweden)
Marina G. Mynbaeva
2012-01-01
Full Text Available Experimental data on diffusion of erbium and vanadium in porous and nonporous silicon carbide at 1700 and 2200°C have been used for modelling diffusion in porous SiC. It is shown that the consideration of pore structure modification under annealing via vacancy redistribution allows for satisfactory description of dopant diffusion. As expected, important contribution to the diffusion in the porous medium is found to be made by the walls of the pores: in SiC, the vacancy surface diffusion coefficient on the walls appears to exceed that in the bulk of the material by an order of magnitude. When thermal treatment transforms pore channels into closed voids, pathways for accelerated diffusion cease to exist and diffusion rates in porous and nonporous SiC become similar.
Image denoising using modified nonlinear diffusion approach
Upadhyay, Akhilesh R.; Talbar, Sanjay N.; Sontakke, Trimbak R.
2006-01-01
Partial Differential Equation (PDE) based, non-linear diffusion approaches are an effective way to denoise the images. In this paper, the work is extended to include anisotropic diffusion, where the diffusivity is a tensor valued function, which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. The diffusion tensor is a function of differential structure of the evolving image itself. Such a feedback leads to nonlinear diffusion filters. It shows improved performance in the presence of noise. The original anisotropic diffusion algorithm updates each point based on four nearest-neighbor differences, the progress of diffusion results in improved edges. In the proposed method the edges are better preserved because diffusion is controlled by the gray level differences of diagonal neighbors in addition to 4 nearest neighbors using coupled PDF formulation. The proposed algorithm gives excellent results for MRI images, Biomedical images and Fingerprint images with noise.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Non-linear model of impurity diffusion in nanoporous materials upon ultrasonic treatment
Directory of Open Access Journals (Sweden)
R.M. Peleshchak
2014-06-01
Full Text Available Non-linear theory of diffusion of impurities in porous materials upon ultrasonic treatment is described. It is shown that at a defined value of deformation amplitude, an average concentration of vacancies and temperature as a result of the effect of ultrasound possibly leads to the formation of nanoclusters of vacancies and to their periodic educations in porous materials. It is shown that at a temperature smaller than some critical value, a significant growth of a diffusion coefficient is observed in porous materials.
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Numerical discretization for nonlinear diffusion filter
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
The Nonlinear Convection—Reaction—Diffusion Equation
Institute of Scientific and Technical Information of China (English)
ShiminTANG; MaochangCUI; 等
1996-01-01
A nonlinear convection-reaction-diffusion equation is used as a model equation of the El Nino events.In this model,the effects of convection,turbulent diffusion,linear feed-back and nolinear radiation on the anomaly of Sea Surface Temperature(SST) are considered.In the case of constant convection,this equation has exact kink-like travelling wave solutions,which can be used to explain the history of an El Nino event.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Linearization of Systems of Nonlinear Diffusion Equations
Institute of Scientific and Technical Information of China (English)
KANG Jing; QU Chang-Zheng
2007-01-01
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
Approximating parameters in nonlinear reaction diffusion equations
Directory of Open Access Journals (Sweden)
Robert R. Ferdinand
2001-07-01
Full Text Available We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computationally generated data.
Caserta, A; Salusti, E
2016-01-01
In this paper we reconsider the classical nonlinear diffusivity equation of real gas in an heterogenous porous medium in light of the recent studies about the generalized fractional equation of conservation of mass. We first recall the physical meaning of the fractional conservation of mass recently studied by Wheatcraft and Meerschaert (2008) and then consider the implications in the classical model of diffusion of a real gas in a porous medium. Then we show that the obtained equation can be simply linearized into a classical space-fractional diffusion equation, widely studied in the literature. We also consider the case of a power-law pressure-dependence of the permeability coefficient. In this case we provide some useful exact analytical results. In particular, we are able to find a Barenblatt-type solution for a space-fractional Boussinesq equation, arising in this context.
Nonlinear Cross-Diffusion with Size Exclusion
Burger, Martin
2010-01-01
The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.
Brem, G.; Brouwers, J.J.H.
1990-01-01
Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with
Simulation of the diffusion process in composite porous media by random walks
Institute of Scientific and Technical Information of China (English)
ZHANG Yong
2005-01-01
A new random-walk interpolation scheme was developed to simulate solute transport through composite porous media with different porosities as well as different diffusivities. The significant influences of the abrupt variations of porosity and diffusivity on solute transport were simulated by tracking random walkers through a linear interpolation domain across the heterogeneity interface. The displacements of the random walkers within the interpolation region were obtained explicitly by establishing the equivalence between the Fokker-Planck equation and the advection-dispersion equation. Applications indicate that the random-walk interpolation method can simulate one- and two-dimensional, 2nd-order diffusion processes in composite media without local mass conservation errors. In addition, both the theoretical derivations and the numerical simulations show that the drift and dispersion of particles depend on the type of Markov process selected to reflect the dynamics of random walkers. If the nonlinear Langevin equation is used, the gradient of porosity and the gradient of diffusivity strongly affect the drift displacement of particles. Therefore, random-walking particles driven by the gradient of porosity,the gradient of diffusivity, and the random diffusion, can imitate the transport of solute under only pure diffusion in composite porous media containing abrupt variations of porosity and diffusivity.
DIFFUSIVITY OF ARRE EARTH ION IN POROUS ION EXCHANGE RESINS
Institute of Scientific and Technical Information of China (English)
LingDaren; LiuYucheng; 等
1997-01-01
The self-diffusion of Eu3+ ion in porous resins D72 and D751 was studied by isotope exchange reaction.Applying Kataoka's bidisperse pore model,the intraparticle effective diffusivity De were resolved into a solid diffusivity Dg and a macropore diffusivity Dp.The experiments show that De.Dp and Dg all increase with the increase of reaction temperature;the response Dp and Dg of D751 resin is smaller than that of D72 resin;the diffusivity of Eu3+ ion in solution is larger than Dp,which leads to the conclusion that the diffusion of ion in the pore of resin can not completely be equal to that in solution.
Modified nonlinear complex diffusion filter (MNCDF).
Saini, Kalpana; Dewal, M L; Rohit, Manojkumar
2012-06-01
Speckle noise removal is the most important step in the processing of echocardiographic images. A speckle-free image produces useful information to diagnose heart-related diseases. Images which contain low noise and sharp edges are more easily analyzed by the clinicians. This noise removal stage is also a preprocessing stage in segmentation techniques. A new formulation has been proposed for a well-known nonlinear complex diffusion filter (NCDF). Its diffusion coefficient and the time step size are modified to give fast processing and better results. An investigation has been performed among nine patients suffering from mitral regurgitation. Images have been taken with 2D echo in apical and parasternal views. The peak signal-to-noise ratio (PSNR), universal quality index (Qi), mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) have been calculated, and the results show that the proposed method is much better than the previous filters for echocardiographic images. The proposed method, modified nonlinear complex diffusion filter (MNCDF), smooths the homogeneous area and enhances the fine details.
Gopalakrishnan, S. S.; Carballido-Landeira, J.; De Wit, A.; Knaepen, B.
2017-01-01
The relative role of convection and diffusion is characterized both numerically and experimentally for porous media flows due to a Rayleigh-Taylor instability of a horizontal interface between two miscible solutions in the gravity field. We show that, though globally convection dominates over diffusion during the nonlinear regime, diffusion can locally be as important as convection and even dominates over lateral convection far away from the fingertips. Our experimental and numerical computations of the temporal evolution of the mixing length, the width of the fingers, and their wavelength are in good agreement and show that the lateral evolution of fingers is governed by diffusion.
INTRAPARTICLE DIFFUSION OF RARE EARTHS IN POROUS CATION EXCHANGERS
Institute of Scientific and Technical Information of China (English)
LINGDaren; ZHENGZuying; 等
1993-01-01
Experiments for determining cerium isotope ion exchange rates with macroporous resins Amberlyst 15,D001 and XN1010 are discribed.The kinetics of the isotope ion exchange reaction has been examined by a simple theoretical equation of intraparticle effective diffustivity De in a porous ion exchanger.The ion exchange proceedes by diffusion within the macropores and the solid phase of the resin,De of cerium was affected by the concentration of the bulk solution C and was separated into a macropore diffusivity D-p and a solid phase diffusivity D-g by the equation.The diffusion coefficients of the exchanging ion are shown to have the values in the macropores comparable with those in the bulk solution and to have the values in the solid phase comparable with those in gel resin with the same crosslinkage as the resins used for the experiments.
The Lie algebra of infinitesimal symmetries of nonlinear diffusion equations
Kersten, Paul H.M.; Gragert, Peter K.H.
1983-01-01
By using developed software for solving overdetermined systems of partial differential equations, the authors establish the complete Lie algebra of infinitesimal symmetries of nonlinear diffusion equations.
Double diffusive convection in a porous medium layer saturated with an Oldroyd nanofluid
Umavathi, J. C.; Sasso, Maurizio
2017-01-01
The onset of double diffusive convection in a horizontal layer of a porous medium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy-Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values.
Diffusion of colloidal fluids in random porous media.
Chávez-Rojo, M A; Juárez-Maldonado, R; Medina-Noyola, M
2008-04-01
The diffusive relaxation of a colloidal fluid adsorbed in a porous medium depends on many factors, including the concentration and composition of the adsorbed colloidal fluid, the average structure of the porous matrix, and the nature of the colloid-colloid and colloid-substrate interactions. A simple manner to describe these effects is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural properties. Within this model one may describe the relaxation of concentration fluctuations of the adsorbed fluid by simply setting to zero the short-time mobility of one species (the porous matrix) in a theory of the dynamics of equilibrium colloidal mixtures, or by extending such dynamic theory to explicitly consider the porous matrix as a random external field, as recently done in the framework of mode coupling theory [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)]. Here we consider the first approach and employ the self-consistent generalized Langevin equation (SCGLE) theory of the dynamics of equilibrium colloidal mixtures, to describe the dynamics of the mobile component. We focus on the short- and intermediate-time regimes, which we compare with Brownian dynamics simulations involving a binary mixture with screened Coulomb interactions for two models of the average static structure of the matrix: a porous matrix constructed by quenching configurations of an equilibrium mixture in which both species were first equilibrated together, and a preexisting matrix with prescribed average structure, in which we later add the mobile species. We conclude that in both cases, if the correct static structure factors are provided as input, the SCGLE theory correctly predicts the main features of the dynamics of the permeating fluid.
Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative
Płociniczak, Łukasz; Okrasińska, Hanna
2013-10-01
In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.
Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes
Biesheuvel, P M
2009-01-01
The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes wi...
Budd, Christopher J
2015-01-01
We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \\theta_t = (D(\\theta)\\theta_x)_x, where the diffusivity is an exponential function D({\\theta}) = D_o exp(\\beta\\theta). This problem arises in the study of unsaturated flow in porous media where {\\theta} represents the liquid saturation. For the physical parameters corresponding to actual porous media, the diffusivity at the residual saturation is D(0) = D_o << 1 so that the diffusion problem is nearly degenerate. Such problems are characterised by wetting fronts that sharply delineate regions of saturated and unsaturated flow, and that propagate with a well-defined speed. Using matched asymptotic expansions in the limit of large {\\beta}, we derive an analytical description of the solution that is uniformly valid throughout the wetting front. This is in contrast with most other related analyses that instead truncate the solution at some specific wetting front location, which is then calculated as part...
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
Suitability of various materials for porous filters in diffusion experiments
Energy Technology Data Exchange (ETDEWEB)
Aldaba, David; Vidal, Miquel; Rigol, Anna [Univ. de Barcelona (Spain). Dept. de Quimica Analitica; Glaus, Martin; Van Loon, Luc [Paul Scherrer Institut, Villigen PSI (Switzerland). Lab. for Waste Management; Leupin, Olivier [Nagra, Wettingen (Switzerland)
2014-10-01
The suitability of different porous materials (stainless steel, VYCOR {sup registered} glass, Al{sub 2}O{sub 3} and PEEK) for use as confining filters in diffusion experiments was evaluated by measuring the effective diffusion coefficients (D{sub e}) of neutral (HTO) and ionic solutes (Na{sup +}, Cs{sup +}, Sr{sup 2+}, Cl{sup -}, SeO{sub 4}{sup 2-}) in the materials in through-diffusion experiments. For stainless steel filters, the D{sub e} values of the target solutes correlated satisfactorily with their bulk diffusion coefficient in water (D{sub w}); thus, the diffusion process in the stainless steel filters was primarily controlled by the diffusivity of the solvated ions. For the remaining materials, the D{sub e} and D{sub w} values were also correlated for the target solutes, and the geometric factors were in the sequence: VYCOR {sup registered} glass < Al{sub 2}O{sub 3} < PEEK. Stainless steel and VYCOR {sup registered} glass were the most appropriate materials because of their high D{sub e} values, but a specific interaction of caesium with VYCOR {sup registered} glass was hypothesised because the D{sub e} values obtained for this solute were slightly higher than expected.
Describing diffusion, reaction and convection on porous medium
D'Ajello, P C T; Nunes, G L
2013-01-01
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic medium diffuses until they react to the electrode surface and become part thereof. Our model consists in formulating convenient boundary conditions for the transport equation, that somewhat resembles the real system but is nevertheless simple enough to be solved, and then solve it. Similar approach was taken by Nicholson [1, 2], except that, to avoid the difficulties regarding the boundary conditions, he considered none whatsoever, and proposed a modified diffusion coefficient for the porous medium instead. Apropos, our model, with moving boundary condition pertain to the class of problems know as The Stefan problem [3].
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Brem, G.; Brouwers, J.J.H.
1990-01-01
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Malacarne, L C; Mendes, R S; Pedron, I T; Lenzi, E K
2001-03-01
The nonlinear diffusion equation partial delta rho/delta t=D Delta rho(nu) is analyzed here, where Delta[triple bond](1/r(d-1))(delta/delta r)r(d-1-theta) delta/delta r, and d, theta, and nu are real parameters. This equation unifies the anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact point-source solution is obtained, enabling us to describe a large class of subdiffusion [ theta>(1-nu)d], "normal" diffusion [theta=(1-nu)d] and superdiffusion [theta<(1-nu)d]. Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.
Diffusion of organic pollutants within a biofilm in porous media
Fan, Chihhao; Kao, Chen-Fei; Liu, You-Hsi
2017-04-01
The occurrence of aquatic pollution is an inevitable environmental impact resulting from human civilization and societal advancement. Either from the natural or anthropogenic sources, the aqueous contaminants enter the natural environment and aggravate its quality. To assure the aquatic environment quality, the attached-growth biological degradation is often applied to removing organic contaminants by introducing contaminated water into a porous media which is covered by microorganism. Additionally, many natural aquatic systems also form such similar mechanism to increase their self-purification capability. To better understand this transport phenomenon and degradation mechanism in the biofilm for future application, the mathematic characterization of organic contaminant diffusion within the biofilm requires further exploration. The present study aimed to formulate a mathematic representation to quantify the diffusion of the organic contaminant in the biofilm. The BOD was selected as the target contaminant. A series of experiments were conducted to quantify the BOD diffusion in the biofilm under the conditions of influent BOD variation from 50 to 300 mg/L, COD:N:P ratios of 100:5:1 and 100:15:3, with or without auxiliary aeration. For diffusion coefficient calculation, the boundary condition of zero diffusion at the interface between microbial phase and contact media was assumed. With the principle of conservation of mass, the removed contaminants equal those that diffuse into the biofilm, and eq 1 results, and the diffusion coefficient (i.e., eq 2) can be solved through calculus with equations from table of integral. ∂2Sf- Df ∂z2 = Rf (1) --(QSin--QSout)2Y--- Df = 2μmaxxf(Sb + Ks ln-Ks-) Sb+Ks (2) Using the obtained experimental data, the diffusion coefficient was calculated to be 2.02*10-6 m2/d with influent COD of 50 mg/L at COD:N:P ratio of 100:5:1 with aeration, and this coefficient increased to 6.02*10-6 m2/d as the influent concentration increased to
Effects of porous throuat on transonic diffuser; Tako shroat ga sen`onsoku diffuser ni oyobosu eikyo
Energy Technology Data Exchange (ETDEWEB)
Yaga, M.; Nagai, M.; Haga, T.; Miyara, T. [Univ. of the Ryukyus, Okinawa (Japan). College of Engineering; Tomita, N. [Hitachi, Ltd., Tokyo (Japan)
1995-09-30
The effects of the porous throat on a transonic diffuser were investigated experimentally by wall static pressure measurements and by schlieren optical observations. The porous throat consists of a wall with 126 holes and a cavity underneath it so that the flow around the shock wave can circulate through the porous wall. The results show that no shock wave was observed at 8096 of the porous region from the throat and that the pressure fluctuations in the transonic diffuser were greatly reduced by the porous throat. According to the frequency analysts, the frequency range attenuated by the porous region is between about 700 Hz and 1k Hz and the frequencies lower than 700 Hz have still remained. 9 refs., 8 figs.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
Entropic and gradient flow formulations for nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Dirr, Nicolas, E-mail: DirrNP@cardiff.ac.uk [School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG (United Kingdom); Stamatakis, Marios, E-mail: M.G.Stamatakis@bath.ac.uk; Zimmer, Johannes, E-mail: zimmer@maths.bath.ac.uk [Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom)
2016-08-15
Nonlinear diffusion ∂{sub t}ρ = Δ(Φ(ρ)) is considered for a class of nonlinearities Φ. It is shown that for suitable choices of Φ, an associated Lyapunov functional can be interpreted as thermodynamic entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role.
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
Existence of solutions of a nonlinear system modelling fluid flow in porous media
Directory of Open Access Journals (Sweden)
dam Besenyei
2006-12-01
Full Text Available We investigate the existence of weak solutions for nonlinear differential equations that describe fluid flow through a porous medium. Existence is proved using the theory of monotone operators, and some examples are given.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio J; Qian, Hong; Lin, Guang
2014-01-01
The currently existing theory of fluorescence correlation spectroscopy(FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems here are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Our results show that current linear FCS theory could be adequate ...
National Research Council Canada - National Science Library
Katherine McCulloh; John S. Sperry; Barbara Lachenbruch; Frederick C. Meinzer; Peter B. Reich; Steven Voelker
2010-01-01
Coniferous, diffuse-porous and ring-porous trees vary in their xylem anatomy, but the functional consequences of these differences are not well understood from the scale of the conduit to the individual...
Linear vs. Nonlinear Diffusion and Martingale Option Pricing
McCauley, J L; Bassler, K E
2006-01-01
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback. But the Tsallis model is only one of a very large class of linear diffusion with a student-t like density. Second, we show by stochastic calculus that our generalization of the Black-Scholes partial differential equation (pde) for variable diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the restricted case of Gaussian logarithmic returns by Harrison and Kreps, but we prove it here for large classes of empirically useful and theoretically interesting returns models where the diffusion coefficient D(x,t) depends on both logarithmic returns x and time t. Finally, we prove that option prices blow up if fat tails in returns x are included in the market distribution.
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
Indian Academy of Sciences (India)
R S Kaushal; Ranjit Kumar; Awadhesh Prasad
2006-08-01
Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.
Nonlinear Magnetic Diffusion and Magnetic Helicity Transport in Galactic Dynamos
Kleeorin, N; Rogachevskii, I; Sokoloff, D D
2003-01-01
We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the combined effect of algebraic and dynamic nonlinearities can limit the growth of the mean magnetic field. However, in contrast to our earlier work without quenching of the turbulent diffusivity, we cannot now find satisfactory solutions in the no-z approximation to the axisymmetric galactic dynamo problem.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Groundwater transport modeling with nonlinear sorption and intraparticle diffusion
Singh, Anshuman; Allen-King, Richelle M.; Rabideau, Alan J.
2014-08-01
Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of "dual mode" sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including "dual mode" and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.
Exact solutions of certain nonlinear chemotaxis diffusion reaction equations
Indian Academy of Sciences (India)
MISHRA AJAY; KAUSHAL R S; PRASAD AWADHESH
2016-05-01
Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Energy Technology Data Exchange (ETDEWEB)
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
2014-05-30
The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.
Institute of Scientific and Technical Information of China (English)
吴秀兰; 高文杰
2013-01-01
The authors investigated the extinction for a class of fast diffusion equations in finite time, giving the sufficient conditions about the extinction and the decay estimates of solutions with the help of Lp estimate methods and interpolation inequalities.%考虑快扩散方程解在有限时刻的熄灭性质,利用Lp估计和内插不等式给出了解在有限时刻熄灭的充分条件及衰退估计.
Quantum Arnol'd Diffusion in a Simple Nonlinear System
Demikhovskii, V Y; Malyshev, A I
2002-01-01
We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower that the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.
A New Contraction Family for Porous Medium and Fast Diffusion Equations
Chmaycem, G.; Jazar, M.; Monneau, R.
2016-08-01
In this paper, we present a surprising two-dimensional contraction family for porous medium and fast diffusion equations. This approach provides new a priori estimates on the solutions, even for the standard heat equation.
Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
Bazeia, D; Raposo, and E.P.
1998-01-01
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Wu, Hao; Noé, Frank
2011-03-01
Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
Murthy, P.V.S.N.
2011-12-26
Thermo-diffusion effect on free convection heat and mass transfer from a vertical surface embedded in a liquid saturated thermally stratified non - Darcy porous medium has been analyzed using a local non-similar procedure. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to the thermal conditions. The fluid flow, temperature and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N, thermo-diffusion parameter Sr and stratification parameter ?. Non-linear interactions of all these parameters on the convective transport has been analyzed and variation of heat and mass transfer coefficients with thermo-diffusion parameter in the thermally stratified non-Darcy porous media is presented through computer generated plots.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
Fractal scaling of effective diffusion coefficient of solute in porous media
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Fractal approach is used to derive a power law relation betweeneffective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media. The results are consistent with the empirical equations analogous to Archie'slaw and are expected to be applied to prediction of effective diffusion coefficient.
Thermal diffusion in nanostructured porous InP
Indian Academy of Sciences (India)
R Srinivasan; K Ramachandran
2008-11-01
Nanostructured porous InP samples were prepared by electrochemical anodic dissolution of InP for various current densities and etching periods. The samples were characterized by SEM and photoluminescence (PL) where a blue shift was observed in PL. Thermal properties studied by photoacoustic (PA) spectroscopy revealed one order decrease in thermal conductivity of porous InP compared to the bulk. Further it is shown that the thermal conductivity of porous InP decreases with decrease in size of the particles.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources
Institute of Scientific and Technical Information of China (English)
WANG LU-SHENG; WANG ZE-JIA
2011-01-01
In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q0 and the critical Fujita exponent qc for the problem considered, and show that q0 ＝ qc for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that q0 ＜ qc for the onedimensional case; moreover, the value is different from the slow case.
Nonlinear saturation of trapped electron modes via perpendicular particle diffusion.
Merz, F; Jenko, F
2008-01-25
In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at
Directory of Open Access Journals (Sweden)
Swati Mukhopadhyay
2013-12-01
Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.
Symmetries and Similarity Reductions of Nonlinear Diffusion Equation
Institute of Scientific and Technical Information of China (English)
LI Hui-Jun; RUAN Hang-Yu
2004-01-01
The inverse recursion operator, three new sets of symmetries, and infinite-dimensional Lie algebras for the nonlinear diffusion equation are given. Some nonlocal symmetries related to eigenvectors of the recursion operator Ф with the eigenvalue λi are also obtained with the help of the recursion operator Фi = Ф - λi. Using a part of these symmetries we get twelve types of nontrivial new similarity reduction.
Symmetries and Similarity Reductions of Nonlinear Diffusion Equation
Institute of Scientific and Technical Information of China (English)
LIHui-Jun; RUANHang-Yu
2004-01-01
The inverse recursion operator, three new sets of symmetries, and infinite-dimensional Lie algebras for the nonlinear diffusion equation are given. Some nonlocal symmetries related to eigenvectors of the recursion operator with the eigenvalue λi are also obtained with the help of the recursion operator φi=φ-λi. Using a part of these symmetries we get twelve types of nontrivial new similarity reduction.
Solutions to a nonlinear drift-diffusion model for semiconductors
Directory of Open Access Journals (Sweden)
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Nonlinear dynamics of capacitive charging and desalination by porous electrodes
Biesheuvel, P.M.; Bazant, M.Z.
2010-01-01
The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salin
Multi-diffusive nonlinear Fokker-Planck equation
Ribeiro, Mauricio S.; Casas, Gabriela A.; Nobre, Fernando D.
2017-02-01
Nonlinear Fokker-Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker-Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker-Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker-Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution.
Theoretical analysis of a diffusion flame established in an inert porous medium
Max Akira Endo Kokubun
2014-01-01
In this work we analyze a steady, planar diffusion flame established in an inert porous matrix. Thc geomotry under consideration is a stagnation-point flow against a condensed (liquid) phase, with all the system (gas and liquid) immersed in an inert porous matrix. In order to better understand the coupled physical processes that occur in this confined problem, we divide the present work in three distinct, but closely related, parts. In the first part we analyze the frozen impinging flow again...
The effect of Coriolis force on nonlinear convection in a porous medium
Directory of Open Access Journals (Sweden)
D. H. Riahi
1994-01-01
Full Text Available Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.
Particle production and nonlinear diffusion in relativistic systems
Wolschin, Georg
2008-01-01
The short parton production phase in high-energy heavy-ion collisions is treated analytically as a nonlinear diffusion process. The initial buildup of the rapidity density distributions of produced charged hadrons within tau_p = 0.25 fm/c occurs in three sources during the colored partonic phase. In a two-step approach, the subsequent diffusion in pseudorapidity space during the interaction time of tau_int = 7-10 fm/c (mean duration of the collision) is essentially linear as expressed in the Relativistic Diffusion Model (RDM) which yields excellent agreement with the data at RHIC energies, and allows for predictions at LHC energies. Results for d+Au are discussed in detail.
Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential
Gizzi, A.; Loppini, A.; Ruiz-Baier, R.; Ippolito, A.; Camassa, A.; La Camera, A.; Emmi, E.; Di Perna, L.; Garofalo, V.; Cherubini, C.; Filippi, S.
2017-09-01
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
Oxygen Diffusion Measurements in Unsaturated Porous Media on the International Space Station
Heinse, R.; Jones, S. B.; Or, D.; Topham, T. S.; Podolskiy, I. G.; Bingham, G. E.
2007-12-01
Oxygen supply to plant roots in unsaturated porous media is regulated by the amount of water and its distribution pattern. The design of optimal plant growth media must strike a balance between the retention of sufficient amounts of water in pore spaces by capillarity and maintenance of sufficient air-filled pore connectivity for gaseous diffusion. The challenges presented by microgravity conditions aboard spacecraft require novel management approaches to ensure optimal conditions for plant roots. We developed and tested a system for measurement of oxygen diffusion in partially saturated porous media under microgravity conditions. A sealed dual-chamber diffusion cell was constructed and controlled by an automated measurement system capable of controlling porous media water content using a metered pumping system through a porous membrane, and tensiometers to measure matric potentials concurrently. Continuous measurements of oxygen concentrations in the cells were conducted with Galvanic-based sensors providing transient response data for estimating water content-dependent diffusion coefficients. Gas diffusion was modeled as a function of air-filled porosity in mm- sized aggregated particles. Data were collected on the International Space Station between July and September 2007 as part of the ORZS-MIS experimental flight package (http://www.sdl.usu.edu/programs/orzs). Oxygen diffusion measurements in microgravity were compared with earth-based data using triplicate cell measurements in three different porous media. Preliminary results point to enhanced hysteresis in oxygen diffusion dependency on air-filled porosity in microgravity, indicating altered water distribution patterns relative to earth-based measurements. Considering air invasion during drainage, we hypothesize that a critical air-filled pathway forms at lower saturation in microgravity due to the absence of hydrostatic water distribution. A shift in the critical air-filled in microgravity would require
Katherine McCulloh; John S. Sperry; Barbara Lachenbruch; Frederick D. Meinzer; Peter B. Reich; Steven Voelker
2010-01-01
Coniferous, diffuse-porous and ring-porous trees vary in their xylem anatomy, but the functional consequences of these differences are not well understood from the scale of the conduit to the individual. Hydraulic and anatomical measurements were made on branches and trunks from 16 species from temperate and tropical areas, representing all three wood types. Scaling of...
Ion Diffusion Within Water Films in Unsaturated Porous Media.
Tokunaga, Tetsu K; Finsterle, Stefan; Kim, Yongman; Wan, Jiamin; Lanzirotti, Antonio; Newville, Matthew
2017-04-05
Diffusion is important in controlling local solute transport and reactions in unsaturated soils and geologic formations. Although it is commonly assumed that thinning of water films controls solute diffusion at low water contents, transport under these conditions is not well understood. We conducted experiments in quartz sands at low volumetric water contents (θ) to quantify ion diffusion within adsorbed films. At the lowest water contents, we employed fixed relative humidities to control water films at nm thicknesses. Diffusion profiles for Rb(+) and Br(-) in unsaturated sand packs were measured with a synchrotron X-ray microprobe, and inverse modeling was used to determine effective diffusion coefficients, De, as low as ∼9 × 10(-15) m(2) s(-1) at θ = 1.0 × 10(-4) m(3) m(-3), where the film thickness = 0.9 nm. Given that the diffusion coefficients (Do) of Rb(+) and Br(-) in bulk water (30 °C) are both ∼2.4 × 10(-9) m(2) s(-1), we found the impedance factor f = De/(θDo) is equal to 0.03 ± 0.02 at this very low saturation, in agreement with the predicted influence of interface tortuosity (τa) for diffusion along grain surfaces. Thus, reduced cross-sectional area (θ) and tortuosity largely accounted for the more than 5 orders of magnitude decrease in De relative to Do as desaturation progressed down to nanoscale films.
Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media
Yu Bai; Ali Harajli; Yunping Xi
2015-01-01
Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation,...
Directory of Open Access Journals (Sweden)
R. Garra
2015-01-01
Full Text Available The evolution of strong transients of temperature and pressure in two adjacent fluid-saturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti (1996. We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quantities but also “time averaged” quantities. These boundary effects are here analyzed by using a “memory formalism”; that is, we replace the ordinary punctual time-derivatives with Caputo fractional time-derivatives. We therefore obtain a nonlinear fractional model, whose explicit solution is shown, and finally discuss its geological importance.
Diffuse-Interface Modelling of Flow in Porous Media
Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim
2016-11-01
Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.
DEFF Research Database (Denmark)
Johannesson, Björn
2009-01-01
Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...... for the non-linear global matrix formulation. The developed model and its numerical solution procedure are checked by running test examples which results demonstrates robustness of the proposed approach....
Nonlinear behavior of saturated porous crust under the influence of internal fluid source
Suetnova, Elena; Cherniavski, Vladimir
2010-05-01
We consider the effective stress evolution inside high porosity fault zone as a result of local dehydration due to heating. The rock is assumed to be a two-velocity medium; it consists of a deformable porous matrix (with Maxwell's rheology) and a Newtonian liquid that saturates this matrix. Nonlinear behavior of liquid saturated porous media in gravity filed under the influence of internal fluid source is modeled. The elaborated non-isothermal mathematical model is a thermodynamically consistent and closed model. The original scheme was used for computer simulation; the method implies numerical simulation for effective stress, deformation and flux time- space evolution. Deformation spreading through the saturated porous matrix occurs with pressure distortions. Calculations show that the peculiarity of effective stress evolution is dependent not only upon the volume of supplementary fluids, but upon the viscosity and elastic modules of matrix.
DEFF Research Database (Denmark)
Paradelo Pérez, Marcos; Soto-Gómez, Diego; Pérez-Rodrígez, Paula
2014-01-01
The release and transport of active ingredients (AIs) from controlled-release formulations (CRFs) have potential to reduce groundwater pesticide pollution. These formulations have a major effect on the release rate and subsequent transport to groundwater. Therefore the influence of CRFs should...... be included in modeling non-point source pollution by pesticides. We propose a simplified approach that uses a phase transition equation coupled to the diffusion equation that describes the release rate of AIs from commercial CRFs in porous media; the parameters are as follows: a release coefficient......, the solubility of the AI, and diffusion transport with decay. The model gives acceptable predictions of the pesticides release from commercial CRFs in diffusion cells filled with quartz sand. This approach can be used to study the dynamics of the CRF-porous media interaction. It also could be implemented in fate...
Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity mod
Directory of Open Access Journals (Sweden)
Palle Kiran
2016-06-01
Full Text Available This paper carried out a nonlinear thermal convection in a porous medium saturated with viscoelastic nanofluid under vibrations. The Darcy model has been used for the porous medium, while the nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The non-uniform vertical vibrations of the system, which can be realized by oscillating the system vertically, is considered to vary sinusoidally with time. In order to find the heat and mass transports for unsteady state, a nonlinear analysis, using a minimal representation of the truncated Fourier series of two terms, has been performed. Effect of various parameters has been investigated on heat and mass transport and then presented graphically. It is found that gravity modulation can be used effectively to regulate either heat or mass transports in the system.
Stability and nonlinear regimes of flow over a saturated porous medium
Directory of Open Access Journals (Sweden)
T. P. Lyubimova
2013-07-01
Full Text Available The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.
Moderately nonlinear diffuse-charge dynamics under an ac voltage
Stout, Robert F.; Khair, Aditya S.
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
Thermal diffusivity measurements on porous carbon fiber reinforced polymer tubes
Gruber, Jürgen; Gresslehner, Karl Heinz; Mayr, Günther; Hendorfer, Günther
2017-02-01
This work presents the application of methods for the determination of the thermal diffusivity well suited for flat bodies adapted to cylindrical bodies. Green's functions were used to get the temperature time history for small and large times, for the approach of intersecting these two straight lines. To verify the theoretical considerations noise free data are generated by finite element simulations. Furthermore effects of inhomogeneous excitation and the anisotropic heat conduction of carbon fiber reinforced polymers were taken into account in these numerical simulations. It could be shown that the intersection of the two straight lines is suitable for the determination of the thermal diffusivity, although the results have to be corrected depending on the ratio of the cylinders inner and outer radii. Inhomogeneous excitation affects the results of this approach as it lead to multidimensional heat flux. However, based on the numerical simulations a range of the azimuthal angle exists, where the thermal diffusivity is nearly independent of the angle. The method to determine the thermal diffusivity for curved geometries by the well suited Thermographic Signal Reconstruction method and taking into account deviations from the slab by a single correction factor has great advantages from an industrial point of view, just like an easy implementation into evaluation software and the Thermographic Signal Reconstruction methods rather short processing time.
Cumulative signal transmission in nonlinear reaction-diffusion networks.
Directory of Open Access Journals (Sweden)
Diego A Oyarzún
Full Text Available Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network's ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.
2D relaxation/diffusion correlations in porous media.
Godefroy, S; Callaghan, P T
2003-01-01
2D correlations between NMR relaxation and/or diffusion have been used to investigate water and oil dynamics in food and micro-emulsion systems. In the case of Mozzarella and Gouda cheese samples, a significant change in D/T2 correlation is appearing with cheese aging. In the case of a water/toluene micro-emulsion, some evidence for coalescence effects is suggested by D/D exchange spectra.
About diffusion in porous medium: the role of the correlation length
DÁjello, P C T; Piacentini, J J; Lauck, L
2012-01-01
In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The physical situation we try to model consists of systems of reduced dimensions (~0.001-1.0 cm^3) with pores of sub micrometric dimension. This is particularly suitable to represent organic structures or special cells in electrochemical devices. We try to explore two basic contributions as an answer for diffusion fading in porous medium, namely, the effect of the void geometry and a dissipative process as well. This dissipative process is in the kernel of our analysis and it is related to the heterogeneous fluctuations of the flux lines occurring at the border among pores. To mimic biophysical and electrochemical conditions we also include in our model a reactive process, such migration of species do not need, necessarily, a pressure gradient because of the reaction diffusion...
Diffusion and saponification inside porous cellulose triacetate fibers.
Braun, Jennifer L; Kadla, John F
2005-01-01
Cellulose triacetate (CTA) fibers were partially hydrolyzed in 0.054 N solutions of NaOH/H(2)O and NaOMe/MeOH. The surface concentration of acetyl groups was determined using ATR-FTIR. Total acetyl content was determined by the alkaline hydrolysis method. Fiber cross-sections were stained with Congo red in order to examine the interface between reacted and unreacted material; these data were used to estimate the rate constant k and effective diffusivity D(B) for each reagent during the early stages of reaction by means of a volume-based unreacted core model. For NaOH/H(2)O, k = 0.37 L mol(-1) min(-1) and D(B) = 6.2 x 10(-7) cm(2)/sec; for NaOMe/MeOH, k = 4.0 L mol(-1) min(-1) and D(B) = 5.7 x 10(-6) cm(2)/sec. The NaOMe/MeOH reaction has a larger rate constant due to solvent effects and the greater nucleophilicity of MeO(-) as compared to OH(-); the reaction has a larger effective diffusivity because CTA swells more in MeOH than it does in water. Similarities between calculated concentration profiles for each case indicate that the relatively diffuse interface seen in fibers from the NaOMe/MeOH reaction results from factors not considered in the model; shrinkage of stained fiber cross-sections suggests that increased disruption of intermolecular forces may be the cause.
Directory of Open Access Journals (Sweden)
R Mehdaoui
2016-09-01
Full Text Available Two-dimensional, double diffusion, natural convection in a partially porous cavity satured with a binary fluid is investigated numerically. Multiple motions are driven by the external temperature and concentration differences imposed across vertical walls. The wavy interface between fluid and porous layer is horizontal. The equations which describe the fluid flow and heat and mass transfer are described by the Navier-Stokes equations (fluid region, Darcy-Brinkman equation (porous region and energy and mass equations. The finite element method was applied to solve the governing equations. The fluid flow and heat and mass transfer has been investigated for different values of the amplitude and the wave number of the interface and the buoyancy ratio. The results obtained in the form of isotherms, stream lines, isoconcentrations and the Nusselt and Sherwood numbers; show that the wavy interface has a significant effect on the flow and heat and mass transfer.
Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; ZHONG Yi-Jun; HUANG Guo-Xiang
2004-01-01
Based on the lattice Boltzmann method and general theory of fluids flowing in porous media, a numerical model is presented for the diffusion-reaction-transport (DRT) processes in porous media. As a test, we simulate a DRT process in a two-dimensional horizontal heterogeneous porous medium. The influence of gravitation in this case can be neglected, and the DRT process can be described by a strongly heterogeneous diagnostic test strip or a thin confined piece of soil with stochastically distributing property in horizontal directions. The results obtained for the relations between reduced fluid saturation S, concentration c1, and concentration c2 are shown by using the visualization computing technique. The computational efficiency and stability of the model are satisfactory.
Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping
Institute of Scientific and Technical Information of China (English)
ZHU Changjiang; JIANG Mina
2006-01-01
In this paper, we study the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (-v(x, t), -u(x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (w0(x), z0(x))lies in (H3 × H2) (R) and |v+ - v-| + ‖w0‖3 + ‖z0‖2 is sufficiently small.Furthermore, the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions are also obtained.
Global-local nonlinear model reduction for flows in heterogeneous porous media
AlOtaibi, Manal
2015-08-01
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
New variable separation solutions for the generalized nonlinear diffusion equations
Fei-Yu, Ji; Shun-Li, Zhang
2016-03-01
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u,ux)uxx + B(u,ux) is studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie-Bäcklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. Project supported by the National Natural Science Foundation of China (Grant Nos. 11371293, 11401458, and 11501438), the National Natural Science Foundation of China, Tian Yuan Special Foundation (Grant No. 11426169), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JQ1014).
Nonlinear diffusion methods based on robust statistics for noise removal
Institute of Scientific and Technical Information of China (English)
JIA Di-ye; HUANG Feng-gang; SU Han
2007-01-01
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M[1] model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering,which is more effective than normal bilateral filter.
Markowich, Peter
2010-06-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty with respect to previous papers in the literature lies in the presence of nonlinear porous-medium-like diffusion in the equation for the density n of the bacteria, motivated by a finite size effect. We prove that, under the constraint m ε (3/2, 2] for the adiabatic exponent, such system features global in time solutions in two space dimensions for large data. Moreover, in the case m = 2 we prove that solutions converge to constant states in the large-time limit. The proofs rely on standard energy methods and on a basic entropy estimate which cannot be achieved in the case m = 1. The case m = 2 is very special as we can provide a Lyapounov functional. We generalize our results to the three-dimensional case and obtain a smaller range of exponents m ε (m*, 2] with m* > 3/2, due to the use of classical Sobolev inequalities.
Martelloni, Gianluca; Bagnoli, Franco
2016-04-01
Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an intense or long rain
Topgaard, Daniel; Söderman, Olle
2002-12-01
Water is an integral part of the structure in biological porous materials such as wood and starch. A problem often encountered in the preparation of samples for, e.g., electron microscopy is that removal of water leads to a decreasing distance between supermolecular structural elements and a distortion of the structure. It is, therefore, of interest to find methods to investigate these materials in the native water-swollen state. We present a method to study water-swollen biological porous structures using NMR to determine the amount and self-diffusion of water within the porous objects. The contribution of bulk water to the NMR signal is eliminated by performing experiments below the bulk freezing temperature. Further decrease of the temperature leads to a gradual freezing of water within the porous objects. The contribution of the freezing water fraction to the migration of water through the porous network is, thus, estimated. The results are rationalized in terms of the ultrastructure of the samples studied, namely, wood pulp fibers and potato starch granules.
Determination of Diffusion and Dispersion Parameters for Flow in Porous Media
Kohno, Iichiro; Nishigaki, Makoto
1982-01-01
The purposes of this research is an investigation of the intrusion of sea water into coastal aquifers. For this subject, this paper deals with proposing rational methods of getting diffusion coefficient and dispersion parameter for flow in porous media in a laboratory. These parameters of soil are indispensable in order to apply an analytical approach or a numerical approach to actual salt water intrusion problems. Experimental apparatuses were constructed and test procedures were also develo...
Effective diffusion coefficient of biological liquids in porous calcium phosphate coatings
Nazarenko, N. N.; Knyazeva, A. G.
2016-11-01
The study offers a method to estimate effective diffusion coefficients for transfer of biological liquids in porous materials. The method is based on the analysis of areas occupied by pores and solid materials on slice images. The possibility is shown for ascertaining a correlation between the effective coefficient and technological conditions because different structure and porosity are observed experimentally. The correlations of effective diffusion coefficients with the production voltage for different coating-base compositions, on which the coating was grown, have been built.
Density of capillaries and the oxygen diffusion model in the porous silk fibroin film
Institute of Scientific and Technical Information of China (English)
BAI Lun; XU Jianmei; SUN Qilong; DI Chuanxia; ZUO Baoqi; GUAN Guoping; WU Zhenyu
2007-01-01
In order to obtain porous silk fibroin films(PSFFs)fit for the repair of different tissues and organs and design the configuration of the PSFFs more rationally,a model of the oxygen diffusing system of the capillary was built,and also the equations of the model were solved.Moreover,the relationships between the distribution of the oxygen concentration and each affecting factors were discussed,a method was developed to estimate the density of the capillaries in the tissue,and hereby discussed the characteristics of the oxygen diffusion in the tissues around the open capillaries.
Nonlinear diffusion of a strong magnetic field in a conducting medium
Energy Technology Data Exchange (ETDEWEB)
Fedorov, V.F.
1985-09-01
The problem considered here is a self-similar problem concerning nonlinear diffusion of a strong magnetic field in a conducting nonmagnetic incompressible medium where the magnetic field is produced by a current passing along the symmetry axis. Nonlinear diffusion equations are solved analytically for various particular cases with allowance for the heating of the medium.
Upscaling scheme for long-term ion diffusion in charged porous media
Yang, Yuankai; Wang, Moran
2017-08-01
Description of long-term (over years) ion diffusion at the pore scale is a huge challenge since the characteristic time of diffusion in a typical representative elementary volume is around microseconds, generally ten orders of magnitude lower than the time we were concerned with. This paper presents a numerical upscaling scheme for ion diffusion with electrical double-layer effects (electrodiffusion) considered in charged porous media. After a scaling analysis for the nondimensional governing equations of ion transport at the pore scale, we identify the conditions for decoupling of electrical effect and diffusion, and therefore are able to choose apposite temporal and spatial scales for corresponding directions of the electrodiffusion process. The upscaling scheme is therefore proposed based on a numerical framework for governing equations using a lattice Boltzmann method. The electrical potential or concentration profiles from steady- or unsteady-state electrodiffusion in the long, straight channel, calculated by this upscaling scheme, are compared with the well-meshed full-sized simulations with good agreement. Furthermore, this scheme is used to predict tracer-ion throughdiffusion and outdiffusion in hardened cement pastes. All numerical results show good agreement with the full-sized simulations or experiment data without any fitting parameters. This upscaling scheme bridges the ion diffusion behaviors in different time scales, and may help to improve the understanding of long-term ion transport mechanisms in charged porous media.
Srinivasa Raju, Rallabandi
2016-10-01
The present investigation is concerned with the effects of thermal diffusion (Soret) and diffusion thermo (Dufour) on an unsteady MHD free convective flow with heat and mass transfer of an electrically conducting fluid in the presence of chemical reaction. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. The present numerical results are compared with available data and are found in an excellent agreement. The expressions for velocity, temperature and concentration fields are obtained. With the aid of these, the expressions for the coefficient of skin-friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are derived. Finally the effects of various physical parameters of the flow quantities are studied with the help of graphs and tables.
Nonlinear Dynamics of Ion Concentration Polarization in Porous Media: The Leaky Membrane Model
Dydek, E Victoria
2013-01-01
The conductivity of highly charged membranes is nearly constant, due to counter-ions screening pore surfaces. Weakly charged porous media, or "leaky membranes", also contain a significant concentration of co-ions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena the absence of electro-osmotic flow, a simple Leaky Membrane Model is formulated, based on macroscopic electroneutrality and Nernst-Planck ionic fluxes. The model is solved in cases of unsupported binary electrolytes: steady conduction from a reservoir to a cation-selective surface, transient response to a current step, steady conduction to a flow-through porous electrode, and steady conduction between cation-selective surfaces in cross flow. The last problem is motivated by separations in leaky membranes, such as shock electrodialysis. The article begins with a tribute to Neal Amundson, whose pioneering work on shock waves in chromatography involved similar mat...
Analytical Investigation of Magnetohydrodynamic Flow over a Nonlinear Porous Stretching Sheet
Directory of Open Access Journals (Sweden)
Fazle Mabood
2016-01-01
Full Text Available We investigated the magnetohydrodynamic (MHD boundary layer flow over a nonlinear porous stretching sheet with the help of semianalytical method known as optimal homotopy asymptotic method (OHAM. The effects of different parameters on fluid flow are investigated and discussed. The obtained results are compared with numerical Runge-Kutta-Fehlberg fourth-fifth-order method. It is found that the OHAM solution agrees well with numerical as well as published data for different assigned values of parameters; this thus indicates the feasibility of the proposed method (OHAM.
MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method
Institute of Scientific and Technical Information of China (English)
S. Nadeem; Anwar Hussain
2009-01-01
The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f"(0) with different values of parameters are convergent.
Directory of Open Access Journals (Sweden)
Tudor Barbu
2014-06-01
Full Text Available A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.
Energy Technology Data Exchange (ETDEWEB)
Yamani, Z.; Gurdal, O.; Alaql, A.; Nayfeh, M.H. [Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St. Urbana, Illinois 61801 (United States)
1999-06-01
We use high resolution cross sectional transmission electron microscopy to image the nanostructure of (100) {ital p}-type porous Si. A network of pore tracks subdivide the material into nano-islands and nanocrystallites are resolved throughout the material. With distance from the substrate, electron diffraction develops noncrystalline-like diffuse patterns that dominate the coherent scattering in the topmost luminescent layer. Also, with distance from the substrate, crystalline islands evolve such that their size drops to as small as 1 nm in the topmost luminescence material. Although the topmost luminescent layer is very rich in nanocrystallites, it has the strongest diffuse scattering of all regions. This confirms that diffuse scattering is due to size reduction effects rather than to an amorphous state. {copyright} {ital 1999 American Institute of Physics.}
DEFF Research Database (Denmark)
Rolle, Massimo; Muniruzzaman, Muhammad
Diffusion and compound-specific mixing significantly affect conservative and reactive transport in groundwater at different scales, not only under diffusion-dominated regimes but also under advection-dominated flow through conditions [1]. When dissolved species are charged, besides the magnitude...... of their aqueous diffusion coefficients also the electrostatic interactions significantly affect solute displacement. We investigated electrostatic interactions between ionic species under flow-through conditions resulting in multicomponent ionic dispersion: the dispersive fluxes of the different ions in the pore...... water are cross-coupled due to the effects of Coulombic interactions. Such effects are illustrated in flow-through experiments in saturated porous media. Simple strong electrolytes (i.e., salts and strong acid solutions) were selected as tracers and their transport was studied under different advection...
Marciniak-Czochra, Anna
2013-01-01
We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a non- linear interface law are expected. In this paper we rigorously derive a quadratic effective slip interface law which holds for a range of Reynolds numbers and fracture widths. The porous medium flow is described by the Darcys law. The result shows that the interface slip law can be nonlinear, independently of the regime for the bulk flow. Since most of the interface and boundary slip laws are obtained via upscaling of complex systems, the result indicates that studying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.
Chew, J. V. L.; Sulaiman, J.
2016-06-01
This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.
In situ bioremediation: A network model of diffusion and flow in granular porous media
Energy Technology Data Exchange (ETDEWEB)
Griffiths, S.K.; Nilson, R.H.; Bradshaw, R.W.
1997-04-01
In situ bioremediation is a potentially expedient, permanent and cost- effective means of waste site decontamination. However, permeability reductions due to the transport and deposition of native fines or due to excessive microorganism populations may severely inhibit the injection of supplemental oxygen in the contamination zone. To help understand this phenomenon, we have developed a micro-mechanical network model of flow, diffusion and particle transport in granular porous materials. The model differs from most similar models in that the network is defined by particle positions in a numerically-generated particle array. The model is thus widely applicable to computing effective transport properties for both ordered and realistic random porous media. A laboratory-scale apparatus to measure permeability reductions has also been designed, built and tested.
Speciation of copper diffused in a bi-porous molecular sieve
Energy Technology Data Exchange (ETDEWEB)
Huang, C.-H. [Department of Environmental Engineering, National Cheng Kung University, Tainan 70101, Taiwan (China); Paul Wang, H., E-mail: wanghp@mail.ncku.edu.t [Department of Environmental Engineering, National Cheng Kung University, Tainan 70101, Taiwan (China); Sustainable Environmental Research Center, National Cheng Kung University, Tainan 70101, Taiwan (China); Wei, Y.-L. [Department of Environmental Science and Engineering, Tunghai University, Taichung 40704, Taiwan (China); Chang, J.-E. [Department of Environmental Engineering, National Cheng Kung University, Tainan 70101, Taiwan (China); Sustainable Environmental Research Center, National Cheng Kung University, Tainan 70101, Taiwan (China)
2010-07-21
To better understand diffusion of copper in the micro- and mesopores, speciation of copper in a bi-porous molecular sieve (BPMS) possessing inter-connecting 3-D micropores (0.50-0.55 nm) and 2-D mesopores (4.1 nm) has been studied by X-ray absorption near edge structure (XANES) spectroscopy. It is found that about 77% (16% of CuO nanoparticles and 61% of CuO clusters) and 23% (CuO{sub ads}) of copper can be diffused into the meso- and micropores, respectively, in the BPMS. At least two diffusion steps in the BPMS may be involved: (i) free diffusion of copper in the mesopores and (ii) diffusion-controlled copper migrating into the micropores of the BPMS. The XANES data also indicate that diffusion rate of copper in the BPMS (4.68x10{sup -5} g/s) is greater than that in the ZSM-5 (1.11x10{sup -6} g/s) or MCM-41 (1.17x10{sup -5} g/s).
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-06-01
Full Text Available A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM. The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.
Directory of Open Access Journals (Sweden)
S.P. Anjali Devi
2010-01-01
Full Text Available Viscous and Joule dissipation effects are considered on MHD nonlinear flow and heat transfer past a stretching porous surface embedded in a porous medium under a transverse magnetic field. Analytical solutions of highly nonlinear momentum equation and confluent hypergeometric similarity solution of heat transfer equations in the case when the plate stretches with velocity varying linearly with distance are obtained. The effect of various parameters like suction parameter, Prandtl number, Magnetic parameter, and Eckert number entering into the velocity field, temperature distribution and skin friction co-efficient at the wall are discussed with the aid of graphs.
Frank, T. D.
2008-02-01
We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.
Diffusion and Clustering of Carbon Dioxide on non-porous Amorphous Solid Water
He, Jiao; Vidali, Gianfranco
2016-01-01
Observations by ISO and Spitzer towards young stellar objects (YSOs) showed that CO$_2$ segregates in the icy mantles covering dust grains. Thermal processing of ice mixture was proposed as responsible for the segregation. Although several laboratory studied thermally induced segregation, a satisfying quantification is still missing. We propose that the diffusion of CO$_2$ along pores inside water ice is the key to quantify segregation. We combined Temperature Programmed Desorption (TPD) and Reflection Absorption InfraRed Spectroscopy (RAIRS) to study how CO$_2$ molecules interact on a non-porous amorphous solid water (np-ASW) surface. We found that CO$_2$ diffuses significantly on a np-ASW surface above 65~K and clusters are formed at well below one monolayer. A simple rate equation simulation finds that the diffusion energy barrier of CO$_2$ on np-ASW is 2150$\\pm$50 K, assuming a diffusion pre-exponential factor of 10$^{12}$ s$^{-1}$. This energy should also apply to the diffusion of CO$_2$ on wall of pores...
Theory and simulation of time-fractional fluid diffusion in porous media
Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.
2013-08-01
We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium
Energy Technology Data Exchange (ETDEWEB)
Moatimid, Galal M., E-mail: gal-moa@hotmail.com [Department of Mathematics, Faculty of Education, Ain Shams University, Roxy (Egypt); Alali, Elham M. M., E-mail: dr-elham-alali@hotmail.com; Ali, Hoda S. M., E-mail: hoda-ali-1@hotmail.com [Department of Mathematics, Faculty of Science (Girls Branch), University of Tabuk, Tabuk, P.O. Box 741 (Saudi Arabia)
2014-09-15
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted
Advective-diffusive mass transfer in fractured porous media with variable rock matrix block size.
Sharifi Haddad, Amin; Hassanzadeh, Hassan; Abedi, Jalal
2012-05-15
Traditional dual porosity models do not take into account the effect of matrix block size distribution on the mass transfer between matrix and fracture. In this study, we introduce the matrix block size distributions into an advective-diffusive solute transport model of a divergent radial system to evaluate the mass transfer shape factor, which is considered as a first-order exchange coefficient between the fracture and matrix. The results obtained lead to a better understanding of the advective-diffusive mass transport in fractured porous media by identifying two early and late time periods of mass transfer. Results show that fractured rock matrix block size distribution has a great impact on mass transfer during early time period. In addition, two dimensionless shape factors are obtained for the late time, which depend on the injection flow rate and the distance of the rock matrix from the injection point.
Nonlinear Theory of Anomalous Diffusion and Application to Fluorescence Correlation Spectroscopy
Boon, Jean Pierre; Lutsko, James F.
2015-12-01
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result of competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the cases of fluorescently labeled lipids in the plasma membrane and of fluorescent apoferritin (a spherically shaped oligomer) in a crowded dextran solution and we find that the nonlinear correlation spectra reproduce very well the experimental data indicating sub-diffusive molecular motion.
The constructive technique and its application in solving a nonlinear reaction diffusion equation
Institute of Scientific and Technical Information of China (English)
Lai Shao-Yong; Guo Yun-Xi; Qing Yin; Wu Yong-Hong
2009-01-01
A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.
Diffusion of a Rouse chain in porous media: A mode-coupling-theory study
Ding, Huai; Jiang, Huijun; Zhao, Nanrong; Hou, Zhonghuai
2017-01-01
We use a kinetic mode-coupling theory (MCT) combining with generalized Langevin equation (GLE) to study the diffusion and conformational dynamics of a bead-spring Rouse chain (RC) dissolved in porous media. The media contains fluid particles and immobile matrix ones wherein the latter leads to the lack of translational invariance. The friction kernel ζ (t ) used in the GLE can be obtained directly by adopting a simple density-functional approach in which the density correlators calculated by MCT equations of porous media serve as inputs. Due to cage effects generated by surrounding particles, ζ (t ) shows a very long tail memory in the high volume fraction of fluid and matrix. It is found that the long-time center-of-mass diffusion constant DCM of the RC decreases with the increment of volume fraction, influencing more strongly by the matrix particles than by the fluid ones. The auto-correlation function (ACF) of the end-to-end distance fluctuation can also be calculated theoretically based on GLE. Of particular interest is that the power-law region of ACF has a nearly fixed length in logarithmic scale when it shifts to longer time range, with increasing the volume fraction of media particles. Moreover, the effect of lack of translational invariance has been investigated by comparing the results between fluid-matrix and pure fluid cases under identical total volume fraction.
Flow and Diffusion Equations for Fluid Flow in Porous Rocks for the Multiphase Flow Phenomena
Directory of Open Access Journals (Sweden)
Mohammad Miyan
2015-07-01
Full Text Available The multiphase flow in porous media is a subject of great complexities with a long rich history in the field of fluid mechanics. This is a subject with important technical applications, most notably in oil recovery from petroleum reservoirs and so on. The single-phase fluid flow through a porous medium is well characterized by Darcy’s law. In the petroleum industry and in other technical applications, transport is modeled by postulating a multiphase generalization of the Darcy’s law. In this connection, distinct pressures are defined for each constituent phase with the difference known as capillary pressure, determined by the interfacial tension, micro pore geometry and surface chemistry of the solid medium. For flow rates, relative permeability is defined that relates the volume flow rate of each fluid to its pressure gradient. In the present paper, there is a derivation and analysis about the diffusion equation for the fluid flow in porous rocks and some important results have been founded. The permeability is a function of rock type that varies with stress, temperature etc., and does not depend on the fluid. The effect of the fluid on the flow rate is accounted for by the term of viscosity. The numerical value of permeability for a given rock depends on the size of the pores in the rock as well as on the degree of interconnectivity of the void space. The pressure pulses obey the diffusion equation not the wave equation. Then they travel at a speed which continually decreases with time rather than travelling at a constant speed. The results shown in this paper are much useful in earth sciences and petroleum industry.
Exploring non-linear cosmological matter diffusion coefficients
Velten, Hermano
2014-01-01
Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the nature of the diffusion coefficient $\\sigma$ which measures the magnitude of such transport phenomena. We test dynamics where $\\sigma$ has a phenomenological dependence on the scale factor, the matter density, the dark energy and the expansion rate.
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Diffusion-controlled cementation experiments in porous rock analogues using potash alum and halite
Energy Technology Data Exchange (ETDEWEB)
Hufe, A.; Hilgers, C. [RWTH Aachen Univ. (Germany). Inst. of Reservoir-Petrology; Stanjek, H. [RWTH Aachen Univ. (Germany). Inst. of Interface and Clay Mineralogy
2013-08-01
A good understanding of cementation is critical for reservoir quality predictions. However, studies of core material have shown that cementation may be driven by variations in pore size of the host rock. To better understand the underlying process, we developed a transparent microreactor for diffusion-controlled cementation experiments under the microscope. We studied the effect of different pore sizes and surface charges of solid material at different pH, using rock analogs. High-resolution videos allowed to analyze the nucleation from solution, pore cementation and growth rates of cements. Diffusion - considered the major mass transport during burial diagenesis - was driven along a temperature gradient across the microreactor. Pores were cemented with salt, which is well known to form pore-size dependent seals in silicilastic reservoirs. While halite precipitated primarily in pores bigger than 200 {mu}m, alum nucleated in smaller pores. The growth rate of alum (10{sup -5} mm/s) was one order of magnitude higher than that of halite. However, the dissolution rates of both minerals was similar at about 10{sup -6} mm/s. Authigenic euhdral halite migrated against the bulk diffusion transport and towards the higher-temperature reservoir. Halite growth rates increased by one order of magnitude to 1.8 x 10{sup -5} mm/s, if the phase boundary was vapor-liquid. A comparison nucleation in a 2-phase porous rock analog showed no difference in cementation pattern at a pH 7. However, at a pH of 10.5 the surface energies of the two different solids are altered, and porosity was reduced 60% more by cements in the phase-1 porous layers. Our experiments showed that pore size dependent nucleation and cementation is a process, which may also take place in complex reservoirs. With the successful pore clogging of halite we can now bring our experimental setup to reservoir conditions and establish the processes at elevated p-T conditions. (orig.)
Leyva, J. Francisco; Malaga, Carlos; Plaza, Ramon G.
2013-01-01
This paper introduces a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (J. of Theor. Biol. 188(2) 1997) and it includes a suitable nutrient chemotactic term compatible with such type of diffusion. High resolution numerical simulations using Graphic Processing Units (GPUs) of the new model are presented, showing that the chemotactic term enhance...
Bazaru, Tatiana; Vlad, Valentin I.; Petris, Adrian; Miu, Mihaela
2010-05-01
In this paper, we study the dependence of effective optical linear and nonlinear refractive indices of nano-porous silicon layers on crystalline silicon substrates on fill fraction, at different light wavelengths in visible and near-infrared. Simple approximative formulae, in the frame of Bruggeman's formalism, that describe the dependences of effective optical linear and nonlinear refractive indices of nano-porous silicon on fill fractions and on wavelength, in the range of 620 - 1000 nm, are derived. Experimental results with reflection intensity scan show a good agreement with the data provided by our formulae and the exact results of Boyd-Bruggeman's formalism for the third order nonlinearity, in the case nanoporous silicon with different porosity and at light wavelengths in the mentioned spectral range.
Directory of Open Access Journals (Sweden)
Palle Kiran
2016-03-01
Full Text Available A weak nonlinear oscillatory mode of thermal instability is investigated while deriving a non autonomous complex Ginzburg–Landau equation. Darcy porous medium is considered in the presence of vertical throughflow and time periodic thermal boundaries. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature and solutal fields are treated by a perturbation expansion in powers of amplitude of applied temperature field. The effect of throughflow has either to stabilize or to destabilize the system for stress free and isothermal boundary conditions. Nusselt and Sherwood numbers are obtained numerically and presented the results on heat and mass transfer. It is found that, throughflow and thermal modulation can be used alternatively to control the heat and mass transfer. Further, it is also found that oscillatory flow enhances the heat and mass transfer than stationary flow. Effect of modulation frequency and phase angle on mean Nusselt number is also discussed.
Nonlinear diffusion and viral spread through the leaf of a plant
Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.
2016-10-01
The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.
A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.
Diffusion and Clustering of Carbon Dioxide on Non-porous Amorphous Solid Water
He, Jiao; Emtiaz, Shahnewaj M.; Vidali, Gianfranco
2017-03-01
Observations by ISO and Spitzer toward young stellar objects showed that CO2 segregates in the icy mantles covering dust grains. Thermal processing of the ice mixture was proposed as being responsible for the segregation. Although several laboratories studied thermally induced segregation, a satisfying quantification is still missing. We propose that the diffusion of CO2 along pores inside water ice is the key to quantify segregation. We combined Temperature Programmed Desorption and Reflection Absorption InfraRed Spectroscopy to study how CO2 molecules interact on a non-porous amorphous solid water (np-ASW) surface. We found that CO2 diffuses significantly on an np-ASW surface above 65 K and clusters are formed at well below one monolayer. A simple rate equation simulation finds that the diffusion energy barrier of CO2 on np-ASW is 2150 ± 50 K, assuming a diffusion pre-exponential factor of 1012 s‑1. This energy should also apply to the diffusion of CO2 on the wall of pores. The binding energy of CO2 from CO2 clusters and CO2 from H2O ice has been found to be 2415 ± 20 K and 2250 ± 20 K, respectively, assuming the same prefactor for desorption. CO2–CO2 interaction is stronger than CO2–H2O interaction, in agreement with the experimental finding that CO2 does not wet the np-ASW surface. For comparison, we carried out similar experiments with CO on np-ASW, and found that the CO–CO interaction is always weaker than CO–H2O. As a result, CO wets the np-ASW surface. This study should be of help to uncover the thermal history of CO2 on the icy mantles of dust grains.
Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media
Directory of Open Access Journals (Sweden)
Yu Bai
2015-01-01
Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.
Gettering impurities from crystalline silicon by aluminum diffusion using a porous silicon layer
Energy Technology Data Exchange (ETDEWEB)
Khedher, N.; Hajji, M.; Bessais, B.; Ezzaouia, H.; Bennaceur, R. [Laboratoire des Applications Solaires, Institut National de Recherche Scientifique et Technique, BP. 95, Hammam Lif (Tunisia); Selmi, A. [Laboratoire de Physique des Semi-conducteurs, Faculte des Sciences de Monastir, 5000 Monastir (Tunisia)
2005-06-01
In this paper, we report a study on the possibility of gettering transition metal impurities from solar grade crystalline silicon (Si). Porous silicon layers were formed by the stain-etching method on both sides of the Si wafer. Aluminum diffusion was done throughout the PS layer in an infrared furnace under a (N{sub 2}/O{sub 2}) controlled atmosphere. This enables to getter eventual metal impurities towards the PS layer. The gettering effect was evaluated by measuring the majority carrier density and mobility and the minority carrier diffusion length (L{sub d}) of the Si substrate. For this purpose, Wander Pauw and Hall Effect measurements together with the Light Beam Induced Current (LBIC) technique were used. We noticed that the best gettering corresponds to a heat treatment at 850 C for 30 min; in that case an evident decrease of the majority carrier density and an enhancement of the mobility were observed. After gettering, we found an apparent improvement of the minority carrier diffusion length. These results give evidence of the effectiveness of external gettering treatments by combining (Al-PS) layer for an efficient gettering effect in solar grade monocrystalline Si. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ho, C.K.; Webb, S.W.
1996-05-01
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
A Comparison of PDE-based Non-Linear Anisotropic Diffusion Techniques for Image Denoising
Energy Technology Data Exchange (ETDEWEB)
Weeratunga, S K; Kamath, C
2003-01-06
PDE-based, non-linear diffusion techniques are an effective way to denoise images. In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
Comparison of PDE-based non-linear anistropic diffusion techniques for image denoising
Weeratunga, Sisira K.; Kamath, Chandrika
2003-05-01
PDE-based, non-linear diffusion techniques are an effective way to denoise images.In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
DEFF Research Database (Denmark)
Zhelezny, Petr; Shapiro, Alexander
2006-01-01
is demonstrated. A series of such experiments was carried out. Several samples of carbonaceous and sandstone rock were investigated. The diffusion coefficients in porous media were determined by measuring the concentration of salt in different slices of a sample as a function of time. In cases where stable values...
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Energy Technology Data Exchange (ETDEWEB)
Chirkunov, Yu. A., E-mail: chr101@mail.ru [Novosibirsk State Technical University, Marks Avenue 20, Novosibirsk 630073 (Russian Federation)
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Intracellular water diffusion probed by femtosecond nonlinear CARS microscopy
Potma, E.O; de Boeij, W.P.; Wiersma, D. A.; Elsaesser, T; Mukamel, S; Murnane, MM; Scherer, NF
2001-01-01
We report on a nonlinear coherent anti-Stokes Raman microscope system based on a high repetition rate femtosecond cavity-dumped visible optical parametric oscillator. This microscope enables real-time mapping of water concentration gradients in single living cells at high spatial resolution.
Nonlinear Diffusion Filtering of the GOCE-Based Satellite-Only Mean Dynamic Topography
Cunderlik, Robert; Mikula, Karol
2015-03-01
The paper presents nonlinear diffusion filtering of the GOCE-based satellite-only mean dynamic topography (MDT). Our approach is based on a numerical solution to the nonlinear diffusion equation defined on the discretized Earth’s surface using the regularized surface Perona-Malik Model. For its numerical discretization we use a surface finite volume method. A key idea is that the diffusivity coefficient depends on the edge detector. It allows effectively reduce the stripping noise while preserve important gradients in filtered data. Numerical experiments present nonlinear filtering of the geopotential evaluated from the GO_CONS_GCF_2_ DIR_R5 model on the DTU13 mean sea surface. After filtering the geopotential is transformed into the MDT.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Energy Technology Data Exchange (ETDEWEB)
Andrade, JosÃÂ© E; Rudnicki, John W
2012-12-14
In this project, a predictive multiscale framework will be developed to simulate the strong coupling between solid deformations and fluid diffusion in porous rocks. We intend to improve macroscale modeling by incorporating fundamental physical modeling at the microscale in a computationally efficient way. This is an essential step toward further developments in multiphysics modeling, linking hydraulic, thermal, chemical, and geomechanical processes. This research will focus on areas where severe deformations are observed, such as deformation bands, where classical phenomenology breaks down. Multiscale geometric complexities and key geomechanical and hydraulic attributes of deformation bands (e.g., grain sliding and crushing, and pore collapse, causing interstitial fluid expulsion under saturated conditions), can significantly affect the constitutive response of the skeleton and the intrinsic permeability. Discrete mechanics (DEM) and the lattice Boltzmann method (LBM) will be used to probe the microstructure---under the current state---to extract the evolution of macroscopic constitutive parameters and the permeability tensor. These evolving macroscopic constitutive parameters are then directly used in continuum scale predictions using the finite element method (FEM) accounting for the coupled solid deformation and fluid diffusion. A particularly valuable aspect of this research is the thorough quantitative verification and validation program at different scales. The multiscale homogenization framework will be validated using X-ray computed tomography and 3D digital image correlation in situ at the Advanced Photon Source in Argonne National Laboratories. Also, the hierarchical computations at the specimen level will be validated using the aforementioned techniques in samples of sandstone undergoing deformation bands.
Nonlinear diffusion model for Rayleigh-Taylor mixing
Boffetta, G; Musacchio, S
2010-01-01
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Coupled nonlinear-diffusion color image sharpening based on the chromaticity-brightness model
Saito, Takahiro; Nosaka, Reina; Komatsu, Takashi
2006-01-01
Previously we have presented a selective image sharpening method based on the coupled nonlinear diffusion process composed of a nonlinear diffusion term, a fidelity term and an isotropic peaking term, and it can sharpen only blurred edges without increasing the noise visibility. Our previously presented prototypal color-image sharpening methods based on the coupled nonlinear-diffusion process have been formulated on the linear color models, namely, the channel-bychannel model and the 3D vectorial model. Our prototypal methods can sharpen blurred color step edges, but they do not necessarily enhance contrasts of signal variations in complex texture image regions so well as in simple step-edge regions. To remedy the drawback, this paper extends our coupled nonlinear-diffusion color-image sharpening method to the nonlinear non-flat color model, namely, the chromaticity-brightness model, which is known to be closely relating to human color perception. We modify our time-evolution PDE's for the non-flat space of the chromaticity vector and present its digital implementations. Through experimental simulations, we compare our new color-image sharpening method based on the chromaticity-brightness model with our prototypal color-image sharpening methods based on the linear color models.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Porous iron molybdate nanorods: in situ diffusion synthesis and low-temperature H2S gas sensing.
Chen, Yu-Jin; Gao, Xin-Ming; Di, Xin-Peng; Ouyang, Qiu-Yun; Gao, Peng; Qi, Li-Hong; Li, Chun-Yan; Zhu, Chun-Ling
2013-04-24
In the paper, we developed an in situ diffusion growth method to fabricate porous Fe2(MoO4)3 nanorods. The average diameter and the length of the porous nanorods were 200 nm and 1.2-4 μm, respectively. Moreover, many micropores existed along axial direction of the Fe2(MoO4)3 nanorods. In terms of nitrogen adsorption-desorption isotherms, calculated pore size was in the range of 4-115 nm, agreeing well with the transmission electron microscope observations. Because of the uniquely porous characteristics and catalytic ability at low temperatures, the porous Fe2(MoO4)3 nanorods exhibited very good H2S sensing properties, including high sensitivity at a low working temperature (80 °C), relatively fast response and recovery times, good selectivity, and long-term stability. Thus, the porous Fe2(MoO4)3 nanorods are very promising for the fabrication of high-performance H2S gas sensors. Furthermore, the strategy presented here could be expended as a general method to synthesize other hollow/porous-type transition metal molybdate nanostructures by rational designation in nanoscale.
Complex statistics and diffusion in nonlinear disordered particle chains
Energy Technology Data Exchange (ETDEWEB)
Antonopoulos, Ch. G., E-mail: chris.antonopoulos@abdn.ac.uk [Institute for Complex Systems and Mathematical Biology (ICSMB), Department of Physics, University of Aberdeen, AB24 3UE Aberdeen (United Kingdom); Bountis, T., E-mail: bountis@math.upatras.gr [Center for Research and Applications of Nonlinear Systems (CRANS), Department of Mathematics, University of Patras, 26500 Patras (Greece); Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town 7701 (South Africa); Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); Drossos, L., E-mail: ldrossos@teimes.gr [High Performance Computing Systems Lab (HPCS lab), Department of Computer and Informatics Engineering, Technological Educational Institute of Western Greece, 30300 Antirion (Greece)
2014-06-15
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10{sup 9}, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.
Undithering using linear filtering and non-linear diffusion techniques
Asha, V
2011-01-01
Data compression is a method of improving the efficiency of transmission and storage of images. Dithering, as a method of data compression, can be used to convert an 8-bit gray level image into a 1-bit / binary image. Undithering is the process of reconstruction of gray image from binary image obtained from dithering of gray image. In the present paper, I propose a method of undithering using linear filtering followed by anisotropic diffusion which brings the advantage of smoothing and edge enhancement. First-order statistical parameters, second-order statistical parameters, mean-squared error (MSE) between reconstructed image and the original image before dithering, and peak signal to noise ratio (PSNR) are evaluated at each step of diffusion. Results of the experiments show that the reconstructed image is not as sharp as the image before dithering but a large number of gray values are reproduced with reference to those of the original image prior to dithering.
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
A numerical study of double-diffusive flow in a long rotating porous channel
Alhusseny, Ahmed; Turan, A.
2015-04-01
The problem of double-diffusive flow in a long rotating porous channel has been analysed numerically. The two opposite vertical walls of the channel are maintained at constant but different temperature and concentration, while both horizontal walls are kept insulated. The generalised model is used to mathematically simulate the momentum equations with employing the Boussinesq approximation for the density variation. Moreover, both the fluid and solid phases are assumed to be at a local thermal equilibrium. The Coriolis effect is considered to be the main effect of rotation, which is induced by means of the combined natural heat and mass transfer within the transverse plane. The governing equations are discretised according to the finite volume method with employing the hybrid differencing scheme to calculate the fluxes across the faces of each control volume. The problem of pressure-velocity coupling is sorted out by relying on PISO algorithm. Computations are performed for a wide range of dimensionless parameters such as Darcy-Rayleigh number (100 ≤ Ra* ≤ 10,000), Darcy number (10-6 ≤ Da ≤ 10-4), the buoyancy ratio (-10 ≤ N ≤ 8), and Ekman number (10-7 ≤ Ek ≤ 10-3), while the values of Prandtl and Schmidt numbers are maintained constant and equal to 1.0. The results reveal that the rotation seems to have a dominant role at high levels of porous medium permeability, where it reduces the strength of the secondary flow, and hence the rates of heat and mass transfer. However, this dominance decreases gradually with lessening the permeability for the same level of rotation, but does not completely vanish.
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Hammer, Hans; Lou, Jijie; Wang, Yaqi; Ortensi, Javier; Gleicher, Frederick; Baker, Benjamin; DeHart, Mark; Martineau, Richard
2016-11-01
The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Indian Academy of Sciences (India)
Ranjit Kumar; R S Kaushal; Awadhesh Prasad
2010-10-01
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Institute of Scientific and Technical Information of China (English)
Jean-Michel CORON; Jesús Ildefonso D（I）AZ; Abdelmalek DRICI; Tommaso MINGAZZINI
2013-01-01
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control.They assume that the internal control is only time dependent.The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
Directory of Open Access Journals (Sweden)
Xiaohong Tian
2014-01-01
Full Text Available A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
Garra, R.; Salusti, E.; Droghei, R.
2015-01-01
The evolution of strong transients of temperature and pressure in two adjacent fluid-saturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti (1996). We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quanti...
Improvement of nonlinear diffusion equation using relaxed geometric mean filter for low PSNR images
DEFF Research Database (Denmark)
Nadernejad, Ehsan
2013-01-01
A new method to improve the performance of low PSNR image denoising is presented. The proposed scheme estimates edge gradient from an image that is regularised with a relaxed geometric mean filter. The proposed method consists of two stages; the first stage consists of a second order nonlinear...... anisotropic diffusion equation with new neighboring structure and the second is a relaxed geometric mean filter, which processes the output of nonlinear anisotropic diffusion equation. The proposed algorithm enjoys the benefit of both nonlinear PDE and relaxed geometric mean filter. In addition, the algorithm...... will not introduce any artefacts, and preserves image details, sharp corners, curved structures and thin lines. Comparison of the results obtained by the proposed method, with those of other methods, shows that a noticeable improvement in the quality of the denoised images, that were evaluated subjectively...
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
Kumar, Rakesh
2015-01-01
This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and subject to addition of stagnation point to control the generated vorticity in the boundary layer. The sheet is placed on the right side of the fluid saturated porous medium which is having permeability of specified form. Nonlinear convection waves in the flow field are realized due to the envisaged nonlinear relation between density and temperature. The equations governing the nonlinear convection boundary layer flow are modeled and simplified using similarity transformations. The economized equations are solved for numerical solutions by employing the implicit finite difference scheme also known as Keller-box method. The influence of the associated parameters of the problem on velocity and temperature distributions, skin friction and rate of heat transfer are presented thr...
Institute of Scientific and Technical Information of China (English)
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
Indian Academy of Sciences (India)
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
Cheung, Perry; Fairweather, Joseph D.; Schwartz, Daniel T.
2012-09-01
Simple laboratory methods for determining liquid water distribution in polymer electrolyte membrane fuel cell gas diffusion layers (GDLs) are needed to engineer better GDL materials. Capillary pressure vs. liquid saturation measurements are attractive, but lack the ability to probe the hydraulic interconnectivity and distribution within the pore structure. Hydraulic admittance measurements of simple capillary bundles have recently been shown to nicely measure characteristics of the free-interfaces and hydraulic path. Here we examine the use of hydraulic admittance with a succession of increasingly complex porous media, starting with a laser-drilled sample with 154 asymmetric pores and progress to the behavior of Toray TGP-H090 carbon papers. The asymmetric laser-drilled sample clearly shows hydraulic admittance measurements are sensitive to sample orientation, especially when examined as a function of saturation state. Finite element modeling of the hydraulic admittance is consistent with experimental measurements. The hydraulic admittance spectra from GDL samples are complex, so we examine trends in the spectra as a function of wet proofing (0% and 40% Teflon loadings) as well as saturation state of the GDL. The presence of clear peaks in the admittance spectra for both GDL samples suggests a few pore types are largely responsible for transporting liquid water.
Frost fatigue and spring recovery of xylem vessels in three diffuse-porous trees in situ.
Christensen-Dalsgaard, Karen K; Tyree, Melvin T
2014-05-01
Frost has been shown to cause frost fatigue (reduced cavitation resistance) in branch segments in the lab. Here, we studied the change in cavitation resistance and percent loss of conductivity (PLC) from fall to spring over 2 consecutive years in three diffuse-porous species in situ. We used the cavitron technique to measure P25 , P50 and P90 (the xylem pressure causing a 25, 50 and 90% conductivity loss) and PLC and stained functioning vessels. Cavitation resistance was reduced by 64-87% (in terms of P50 ), depending on the species and year. P25 was impacted the most and P90 the least, changing the vulnerability curves from s- to r-shaped over the winter in all three species. The branches suffered an almost complete loss of conductivity, but frost fatigue did not necessarily occur concurrently with increases in PLC. In two species, there was a trade-off between conduit size and vulnerability. Spring recovery occurred by growth of new vessels, and in two species by partial refilling of embolized conduits. Although newly grown and functioning conduits appeared more vulnerable to cavitation than year-old vessels, cavitation resistance generally improved in spring, suggesting other mechanisms for partial frost fatigue repair. © 2013 John Wiley & Sons Ltd.
Hosoya, Osamu; Chono, Sumio; Saso, Yuko; Juni, Kazuhiko; Morimoto, Kazuhiro; Seki, Toshinobu
2004-12-01
The diffusion coefficient (D) of peptide and protein drugs needs to be determined to examine the permeability through biological barriers and to optimize delivery systems. In this study, the D values of fluorescein isothiocyanate (FITC)-labelled dextrans (FDs) and peptides were determined and the permeability through a porous membrane was discussed. The observed D values of FDs and peptides, except in the case of insulin, were similar to those calculated based on a relationship previously reported between the molecular weight and D of lower-molecular-weight compounds, although the molecular weight range was completely different. The observed D value of insulin was between the calculated values for the insulin monomer and hexamer. The permeability of poly-lysine and insulin through the membrane was determined and the observed values were compared with predicted values by using the relationship between molecular weight and D and an equation based on the Renkin function. The observed permeability of insulin through the membrane was between that of the predicted permeability for the insulin monomer and hexamer. For the permeation of insulin, the determination of D was useful for estimating the permeability because of the irregular relationship between molecular weight and D. The methodology used in this study will be useful for a more quantitative evaluation of the absorption of peptide and protein drugs applied to mucous membranes.
Institute of Scientific and Technical Information of China (English)
邓英尔; 刘慈群
2003-01-01
A mathematical model of two-phase fluid nonlinear flow in the direction ofnormal of ellipse through low-permeability porous media was established according to anonlinear flow law expressed in a continuous function with three parameters, a massconservation law and a concept of turbulent ellipses. A solution to the model was obtainedby using a finite difference method and an extrapolation method. Formulas of calculatingdevelopment index not only before but also after water breaks through an oil well in thecondition of two-phase fluid nonlinear flow in the media were derived. An example wasdiscussed. Water saturation distribution was presented. The moving law of drainage frontwas found. Laws of change of pressure difference with time were recognized. Results showthat there is much difference of water saturation distribution between nonlinear flow andlinear flow; that drainage front by water moves faster, water breaks through sooner and theindex gets worse because of the nonlinear flow ; and that dimensionless pressure differencegets larger at the same dimensionless time and difficulty of oil development becomes biggerby the nonlinear flow . Thus, it is necessary that influence of nonlinear flow on developmentindexes of the oil fields be taken into account. The results provide water-floodingdevelopment of the oil fields with scientific basis.
Institute of Scientific and Technical Information of China (English)
Rajib Basu; G.C.Layek
2013-01-01
Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium.The contributions of Soret and Dufour coefficients are taken into account in the analysis.Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection,while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters.The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of crossdiffusive parameters.The critical Darcy-Rayleigh number decreases with increasing Soret number,resulting in destabilization of the system,while its value increases with increasing Dufour number,resulting in stabilization of the system at the marginal state characterized by stationary convection.The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset.This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures.It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.
DEFF Research Database (Denmark)
Rolle, Massimo
2015-01-01
Diffusion and compound-specific mixing significantly affect conservative and reactive transport in groundwater. The variability of diffusion coefficients for different solutes has a relevant impact on their displacement at different scales, not only under diffusion-dominated regimes but also under...... advection-dominated flow through conditions. When the solutes are charged species, besides the magnitude of their aqueous diffusion coefficients also their electrostatic interactions play a significant role in the displacement of the different species. Under flow-through conditions this leads...... to multicomponent ionic dispersion: the dispersive fluxes of the different ions are cross-coupled due to the effects of Coulombic interactions. Such effects are illustrated in flow-through experiments in saturated porous media. Simple strong electrolytes were selected as tracers and their transport was studied...
Weeratunga, Sisira K.; Kamath, Chandrika
2002-05-01
Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, we focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. We complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. We explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. We also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. Our empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.
Jones, Scott; Heinse, Robert; Or, Dani; Topham, T. Shane; Podolsky, Igor; Bingham, Gail
Optimization of Root Zone Substrates (ORZS) are currently being researched to expand plantbased bio-regenerative life support systems. This NASA funded research investigates the effect of reduced-gravity on porous media fluid management at the root-module and pore scale, necessitated by current limitations in root zone management that may have led to stunted, often unexplained plant vigor. Among them, alterations in substrate water retention and oxygen diffusion are restraining optimal support of plant growth. Our work explores the effect of gravity on the distribution and flow of fluids in porous media. These effects demonstrate unanticipated behavior in fluid transport with fluid distribution in pursuit of a capillary equilibrium within the hysteretic, contingent energy potential of water and continuity of phases for the supply of plant resources to the root. We investigate how accounts of fluid transport are part of a larger story of fluid distribution when gravitational and capillary forces are shifting. We now have data from the International Space Station that were collected in a novel experimental setup developed and tested for measurement of oxygen diffusion in partially saturated porous media under microgravity conditions with a sealed dual-chamber diffusion cell. The experiment flew on the International Space Station between July and September 2007 as part of the ORZS- MIS experimental flight package. In comparing oxygen diffusion measurements in microgravity with earth-based data, results point to enhanced hysteresis in oxygen diffusion dependency on air-filled porosity in microgravity. This indicates altered water distribution patterns relative to earth-based measurements. Considering air invasion during drainage, we hypothesize that a critical air-filled pathway forms at higher saturation in microgravity due to the absence of hydrostatic water distribution. A shift in the critical air-filled porosity in microgravity would require adjustment in plant
Leyva, J. Francisco; Málaga, Carlos; Plaza, Ramón G.
2013-11-01
This paper studies a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.
Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems
Macêdo, E. N.; Cotta, R. M.; Orlande, H. R. B.
A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems
Institute of Scientific and Technical Information of China (English)
Min Yang; Yi-rang Yuan
2008-01-01
In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems.Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O(△t2 + h) and present some numerical examples at the end of the paper.
Inoue, Gen; Yokoyama, Kouji; Ooyama, Junpei; Terao, Takeshi; Tokunaga, Tomomi; Kubo, Norio; Kawase, Motoaki
2016-09-01
The reduction of oxygen transfer resistance through porous components consisting of a gas diffusion layer (GDL), microporous layer (MPL), and catalyst layer (CL) is very important to reduce the cost and improve the performance of a PEFC system. This study involves a systematic examination of the relationship between the oxygen transfer resistance of the actual porous components and their three-dimensional structure by direct measurement with FIB-SEM and X-ray CT. Numerical simulations were carried out to model the properties of oxygen transport. Moreover, based on the model structure and theoretical equations, an approach to the design of new structures is proposed. In the case of the GDL, the binder was found to obstruct gas diffusion with a negative effect on performance. The relative diffusion coefficient of the MPL is almost equal to that of the model structure of particle packing. However, that of CL is an order of magnitude less than those of the other two components. Furthermore, an equation expressing the relative diffusion coefficient of each component can be obtained with the function of porosity. The electrical conductivity of MPL, which is lower than that of the carbon black packing, is considered to depend on the contact resistance.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Institute of Scientific and Technical Information of China (English)
Wang Shaoli; Feng Xinlong; He Yinnian
2011-01-01
This article proposes a diffused hepatitis B virus (HBV) model with CTLimmune response and nonlinear incidence for the control of viral infections.By means of different Lyapunov functions,the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained.Global stability of the positive equilibrium of the model is also considered.The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Self-similar profiles for capillary diffusion driven flow in heterogeneous porous media
Duijn, C.J. van; Neef, M.J. de
1996-01-01
In this paper we consider the process of one-dimensional redistribution of two immiscible and incompressible fluids in a heterogeneous porous medium. We treat in detail the special case in which the initial saturation as well as the properties of the porous medium have a single coinciding discontinu
Energy Technology Data Exchange (ETDEWEB)
Abbas, Z.; Naveed, M., E-mail: rana.m.naveed@gmail.com [Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100 (Pakistan); Sajid, M. [Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad 44000 (Pakistan)
2015-10-15
In this paper, effects of Hall currents and nonlinear radiative heat transfer in a viscous fluid passing through a semi-porous curved channel coiled in a circle of radius R are analyzed. A curvilinear coordinate system is used to develop the mathematical model of the considered problem in the form partial differential equations. Similarity solutions of the governing boundary value problems are obtained numerically using shooting method. The results are also validated with the well-known finite difference technique known as the Keller-Box method. The analysis of the involved pertinent parameters on the velocity and temperature distributions is presented through graphs and tables.
Institute of Scientific and Technical Information of China (English)
Yirang YUAN
2006-01-01
For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.
Texture Image Segmentation Based on Nonlinear Diffusion%基于非线性扩散的纹理分割
Institute of Scientific and Technical Information of China (English)
张煜
2008-01-01
A texture image segmentation based on nonlinear diffusion is presented. The scale of texture can be measured during the process of nonlinear diffusion. A smooth 5-channel vector image with edge preserved, which is composed of inten- sity, scale and orientation of texture image, can be achieved by coupled nonlinear diffusion. A multi-channel statistical region active contour is employed to segment this vector image. The method can be seen as a kind of unsupervised segmentation because parameters are not sensitive to different texture images. Experimental results show its high efficiency in the semi- automatic extraction of texture image.
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Directory of Open Access Journals (Sweden)
Y. J. Choi
2012-01-01
Full Text Available We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+hγ˜, where γ˜ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.
Water Transport in the Micro Porous Layer and Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell
Qin, C.; Hassanizadeh, S. M.
2015-12-01
In this work, a recently developed dynamic pore-network model is presented [1]. The model explicitly solves for both water pressure and capillary pressure. A semi-implicit scheme is used in updating water saturation in each pore body, which considerably increases the numerical stability at low capillary number values. Furthermore, a multiple-time-step algorithm is introduced to reduce the computational effort. A number of case studies of water transport in the micro porous layer (MPL) and gas diffusion layer (GDL) are conducted. We illustrate the role of MPL in reducing water flooding in the GDL. Also, the dynamic water transport through the MPL-GDL interface is explored in detail. This information is essential to the reduced continua model (RCM), which was developed for multiphase flow through thin porous layers [2, 3]. C.Z. Qin, Water transport in the gas diffusion layer of a polymer electrolyte fuel cell: dynamic pore-network modeling, J Electrochimical. Soci., 162, F1036-F1046, 2015. C.Z. Qin and S.M. Hassanizadeh, Multiphase flow through multilayers of thin porous media: general balance equations and constitutive relationships for a solid-gas-liquid three-phase system, Int. J. Heat Mass Transfer, 70, 693-708, 2014. C.Z. Qin and S.M. Hassanizadeh, A new approach to modeling water flooding in a polymer electrolyte fuel cell, Int. J. Hydrogen Energy, 40, 3348-3358, 2015.
Bonilla, Mauricio R; Bhatia, Suresh K
2012-01-10
Molecular transport in nanoconfined spaces plays a key role in many emerging technologies for gas separation and storage, as well as in nanofluidics. The infiltration of fluid mixtures into the voids of porous frameworks having complex topologies is common place to these technologies, and optimizing their performance entails developing a deeper understanding of how the flow of these mixtures is affected by the morphology of the pore space, particularly its pore size distribution and pore connectivity. Although several techniques have been developed for the estimation of the effective diffusivity characterizing the transport of single fluids through porous materials, this is not the case for fluid mixtures, where the only alternatives rely on a time-consuming solution of the pore network equations or adaptations of the single fluid theories which are useful for a limited type of systems. In this paper, a hybrid multicomponent effective medium-correlated random walk theory for the calculation of the effective transport coefficients matrix of fluid mixtures diffusing through porous materials is developed. The theory is suitable for those systems in which component fluxes at the single pore level can be related to the potential gradients of the different species through linear flux laws and corresponds to a generalization of the classical single fluid effective medium theory for the analysis of random resistor networks. Comparison with simulation of the diffusion of binary CO(2)/H(2)S and ternary CO(2)/H(2)S/C(3)H(8) gas mixtures in membranes modeled as large networks of randomly oriented pores with both continuous and discrete pore size distributions demonstrates the power of the theory, which was tested using the well-known generalized Maxwell-Stefan model for surface diffusion at the single pore level.
A two-phase free boundary problem for a nonlinear diffusion-convection equation
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S; Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia (Italy)], E-mail: silvana.delillo@pg.infn.it
2008-04-11
A two-phase free boundary problem associated with a diffusion-convection equation is considered. The problem is reduced to a system of nonlinear integral equations, which admits a unique solution for small times. The system admits an explicit two-component solution corresponding to a two-component shock wave of the Burgers equation. The stability of such a solution is also discussed.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Senthilkumar, D. V.; Muruganandam, P.; Lakshmanan, M.; Kurths, J.
2010-01-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by siz...
Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
Hurtado, Pablo I.; Lasanta, A.; Prados, A.
2013-08-01
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated with a path in mesoscopic phase space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in nondissipative systems. This is a consequence of the quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always Gaussian, as expected from the central limit theorem. On the other hand, strong separation from the Gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem, as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily suppressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion, and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases nonconvex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of
Bourg, Ian C; Sposito, Garrison
2010-03-15
In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D(interlayer) of water tracers and representative cations (Na(+), Cs(+), Sr(2+)) in Na-smectite interlayers. We find that a remarkably simple expression relates D(interlayer) to the pore-scale parameter δ(nanopore) ≤ 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: δ(nanopore) = D(interlayer)/D(0), where D(0) is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H(2)0, Na(+), Sr(2+), and Cs(+) in compacted Na-smectite-rich materials.
Energy Technology Data Exchange (ETDEWEB)
Bourg, I.C.; Sposito, G.
2009-12-01
In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer 'compartments.' We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D{sub interlayer} of water tracers and representative cations (Na{sup +}, Cs{sup +}, Sr{sup 2+}) in Na-smectite interlayers. We find that a remarkably simple expression relates D{sub interlayer} to the pore-scale parameter {delta}{sub nanopore} {<=} 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: {delta}{sub nanopore} = D{sub interlayer}/D{sub 0}, where D{sub 0} is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracer H{sub 2}O, Na{sup +}, Sr{sup 2+} and Cs{sup +}+ in compacted Na-smectite-rich materials.
Energy Technology Data Exchange (ETDEWEB)
Bourg, I.C.; Sposito, G.
2009-12-01
In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer 'compartments.' We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D{sub interlayer} of water tracers and representative cations (Na{sup +}, Cs{sup +}, Sr{sup 2+}) in Na-smectite interlayers. We find that a remarkably simple expression relates D{sub interlayer} to the pore-scale parameter {delta}{sub nanopore} {<=} 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: {delta}{sub nanopore} = D{sub interlayer}/D{sub 0}, where D{sub 0} is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracer H{sub 2}O, Na{sup +}, Sr{sup 2+} and Cs{sup +}+ in compacted Na-smectite-rich materials.
Diffusive approximation of a time-fractional Burgers equation in nonlinear acoustics
Lombard, Bruno
2016-01-01
A fractional time derivative is introduced into the Burgers equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equations. Then a quadrature formula yields a system of local partial differential equations, well-suited to numerical integration. The determination of the quadrature coefficients is crucial to ensure both the well-posedness of the system and the computational efficiency of the diffusive approximation. For this purpose, optimization with constraint is shown to be a very efficient strategy. Strang splitting is used to solve successively the hyperbolic part by a shock-capturing scheme, and the diffusive part exactly. Numerical experiments are proposed to assess the efficiency of the numerical modeling, and to illustrate the e...
Karimbadi, H.; Krauss-Varban, D.
1992-01-01
A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.
Relaxation of charge in monolayer graphene: Fast nonlinear diffusion versus Coulomb effects
Kolomeisky, Eugene B.; Straley, Joseph P.
2017-01-01
Pristine monolayer graphene exhibits very poor screening because the density of states vanishes at the Dirac point. As a result, charge relaxation is controlled by the effects of zero-point motion (rather than by the Coulomb interaction) over a wide range of parameters. Combined with the fact that graphene possesses finite intrinsic conductivity, this leads to a regime of relaxation described by a nonlinear diffusion equation with a diffusion coefficient that diverges at zero charge density. Some consequences of this fast diffusion are self-similar superdiffusive regimes of relaxation, the development of a charge depleted region at the interface between electron- and hole-rich regions, and finite extinction times for periodic charge profiles.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-11-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-12-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
Energy Technology Data Exchange (ETDEWEB)
Abdel-Rahman, Gamal M., E-mail: gamalm60@yahoo.co [Department of Mathematics, Faculty of Science, Benha University, 13518 Benha (Egypt)
2010-06-01
In this paper, the thermal-diffusion and magnetic field effects on a stagnation point flowing over a flat stretching surface have been obtained and studied numerically with the variation of the viscosity under the Soret and Dufour's effects. The governing continuity, momentum, energy and concentration equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. Numerical results were presented for velocity, temperature and concentration profiles for different parameters of the problem as radiation parameter, magnetic field parameter, porous medium parameter, endothermic chemical reaction, heat source parameter, stretching parameter, the Soret and Dufour number and other. Also the effects of the pertinent parameters on the skin friction, the rate of heat and mass transfer are obtained and discussed numerically and illustrated graphically.
Directory of Open Access Journals (Sweden)
Puibasset J.
2016-07-01
Full Text Available The adsorption and phase transitions of confined fluids in nanoporous materials have been studied intensely because of both their fundamental interest and their crucial role in many technologies. Questions relating to the influence of the confinement of fluids, and the disorder or elastic deformation of porous solids on the liquid-gas phase transition are still under debate. Model systems are needed to understand the adsorption phenomenon. In this context, Porous Silicon (PoSi, which is a single crystal obtained by etching a (100 silicon wafer is an excellent candidate. Indeed, it consists of non-connected tubular pores running parallel to the [100] axis perpendicular to the wafer surface, with transverse sections with a polygonal shape of nanometric size whose areas are widely distributed. Once detached from the wafer, free PoSi membranes can be considered a nanoscale disordered honeycomb. Adsorption/desorption experiments have been performed to characterize the structure: they have shown that evaporation occurs collectively, an intriguing observation generally associated with a disordered pore structure with many interconnections through narrow necks. The characterization of fluid mobility inside the pores should give complementary information about the pore structure and topology. This paper focuses on the dynamics of a fluid confined inside the structure of porous silicon, and in particular the self-diffusion measurements (pulsed field gradient spin echo Nuclear Magnetic Resonance (NMR. The results show a strong anisotropy of the self-diffusion tensor, as expected in this highly anisotropic structure. However, a non-zero self-diffusion in the directions perpendicular to the pore axis is observed. In order to interpret these puzzling results, molecular and Brownian dynamics calculations are underway.
Inoue, Gen; Kawase, Motoaki
2016-09-01
It is important to reduce the oxygen diffusion resistance through PEFC porous electrode, because it is the key to reduce the PEFC cost. However, the gas diffusion coefficient of CL is lower than MPL in spite of framework consisted of same carbon blacks. In this study, in order to understand the reasons of the lower gas diffusion performance of CL, the relationship between a carbon black agglomerate structure and ionomer adhesion condition is evaluated by a numerical analysis with an actual reconstructed structure and a simulated structure. As a result, the gas diffusion property of CL strongly depends on the ionomer adhesion shape. In the case of adhesion shape with the same curvature of ionomer interface, each pore can not be connected enough. So the pore tortuosity increases. Moreover, in the case of existence of inefficient large pores formed by carbon black agglomerate and ununiformly coated ionomer, the gas diffusion performance decrease rapidly. As the measurement values in actual CL are almost equal to that with model structure with inefficient large pores. These characteristics can be confirmed by actual cross-section image obtained by FIB-SEM.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
With the aid of a nonlinear transformation, a class of nonlinear convectiondiffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given
Denoising of single-trial matrix representations using 2D nonlinear diffusion filtering.
Mustaffa, I; Trenado, C; Schwerdtfeger, K; Strauss, D J
2010-01-15
In this paper we present a novel application of denoising by means of nonlinear diffusion filters (NDFs). NDFs have been successfully applied for image processing and computer vision areas, particularly in image denoising, smoothing, segmentation, and restoration. We apply two types of NDFs for the denoising of evoked responses in single-trials in a matrix form, the nonlinear isotropic and the anisotropic diffusion filters. We show that by means of NDFs we are able to denoise the evoked potentials resulting in a better extraction of physiologically relevant morphological features over the ongoing experiment. This technique offers the advantage of translation-invariance in comparison to other well-known methods, e.g., wavelet denoising based on maximally decimated filter banks, due to an adaptive diffusion feature. We compare the proposed technique with a wavelet denoising scheme that had been introduced before for evoked responses. It is concluded that NDFs represent a promising and useful approach in the denoising of event related potentials. Novel NDF applications of single-trials of auditory brain responses (ABRs) and the transcranial magnetic stimulation (TMS) evoked electroencephalographic responses denoising are presented in this paper.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Institute of Scientific and Technical Information of China (English)
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
Demekhin, E A; Polyanskikh, S V
2011-01-01
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number sele...
Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space
Indian Academy of Sciences (India)
Li Zhang; Shutang Liu; Chenglong Yu
2014-06-01
In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.
Zhang, Shan-Lin; Li, Cheng-Xin; Li, Chang-Jiu; Liu, Meilin; Yang, Guan-Jun
2016-08-01
Porous metal-supported solid oxide fuel cells (SOFCs) have attracted much attention because their potential to dramatically reduce the cost while enhancing the robustness and manufacturability. In particular, 430 ferritic steel (430L) is one of the popular choice for SOFC support because of its superior performance and low cost. In this study, we investigate the oxidation and diffusion behavior of the interface between a Ni-based anode and porous 430L support exposed to a humidified (3% H2O) hydrogen atmosphere at 700 °C. The Ni-GDC (Ce0.8Gd0.2O2-δ) cermet anodes are deposited on the porous 430L support by atmospheric plasma spraying (APS). The effect of exposure time on the microstructure and phase structure of the anode and the supports is studied and the element diffusion across the support/anode interface is characterized. Results indicate that the main oxidation product of the 430L support is Cr2O3, and that Cr and Fe will diffuse to the anode and the diffusion thickness increases with the exposure time. The diffusion thickness of Cr and Fe reach about 5 and 2 μm, respectively, after 1000 h exposure. However, the element diffusion and oxidation has little influence on the area-specific resistance, indicating that the porous 430L steel and plasma sprayed Ni-GDC anode are promising for durable SOFCs.
Computation of traveling wave fronts for a nonlinear diffusion-advection model.
Mansour, M B A
2009-01-01
This paper utilizes a nonlinear reaction-diffusion-advection model for describing the spatiotemporal evolution of bacterial growth. The traveling wave solutions of the corresponding system of partial differential equations are analyzed. Using two methods, we then find such solutions numerically. One of the methods involves the traveling wave equations and solving an initial-value problem, which leads to accurate computations of the wave profiles and speeds. The second method is to construct time-dependent solutions by solving an initial-moving boundary-value problem for the PDE system, showing another approximation for such wave solutions.
On the sharp front-type solution of the Nagumo equation with nonlinear diffusion and convection
Indian Academy of Sciences (India)
M B A Mansour
2013-03-01
This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Lee, Shiu-Hang; Ellison, Donald C
2008-01-01
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occuring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to devel...
Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel
2017-05-01
The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Das, S.S. [Department of Physics, K.B.D.A.V. College, Nirakarpur, Khordha-752 019 (Odisha) (India); Saran, M.R. [Department of Physics, Maharishi College of Natural Law, Sahid Nagar, Bhubaneswar-751 007 (Odisha) (India); Mohanty, S. [Department of Chemistry, Christ College, Mission Road, Cuttack-753 001 (Odisha) (India); Padhy, R.K. [Department of Physics, ODM Public School, Shishu Vihar, Patia, Bhubaneswar-751 024 (Odisha) (India)
2013-07-01
This paper focuses on the unsteady hydromagnetic mixed convective heat and mass transfer boundary layer flow of a viscous incompressible electrically conducting fluid past an accelerated infinite vertical porous flat plate in a porous medium with suction in presence of foreign species such as H2, He, H2O vapour and NH3. The governing equations are solved both analytically and numerically using error function and finite difference scheme. The flow phenomenon has been characterized with the help of flow parameters such as magnetic parameter (M), suction parameter (a), permeability parameter (Kp), Grashof number for heat and mass transfer (Gr, Gc), Schmidt number (Sc) and Prandtl number (Pr). The effects of the above parameters on the fluid velocity, temperature, concentration distribution, skin friction and heat flux have been analyzed and the results are presented graphically and discussed quantitatively for Grashof number Gr>0 corresponding to cooling of the plate. It is observed that a growing magnetic parameter (M) retards the velocity of the flow field at all points and a greater suction leads to a faster reduction in the velocity of the flow field. Further, as we increase the permeability parameter (Kp) and the Grashof numbers for heat and mass transfer (Gr, Gc) the velocity of the flow field enhances at all points, while a greater suction/Prandtl number leads to a faster cooling of the plate. It is also observed that a more diffusive species has a significant decrease in the concentration boundary layer of the flow field and a growing suction parameter enhances both skin friction (T') and heat flux (Nu) at the wall corresponding to cooling of the plate (Gr>0).
Nonlinear diffusion of indirect excitons in an ideal bilayer with an in-plane harmonic trap
Wang, Li; Wang, Qinglu
2009-06-01
The nonlinear diffusion of the spatially indirect excitons in an ideal bilayer with an in-plane harmonic trap is investigated based on the theories developed by Ivanov [A.L. Ivanov, Europhys. Lett. 59 (2002) 586; A.L. Ivanov, J. Phys.: Condens. Matter 16 (2004) S3629] and Rapaport et al. [R. Rapaport, G. Chen, S. Simon, O. Mitrofanov, L. Pfeiffer, P.M. Platzman, Phys. Rev. B 72 (2005) 075428]. A nonlinear equation for the diffusion of the indirect excitons in this structure is established. The two-dimensional density of the indirect excitons in this structure is calculated. The calculations show that the density adjacent to the trap center for different exciton temperatures can remain very high even long after the photo-excitation because of the confinement of the in-plane harmonic trap, and that the indirect excitons gather several tens of μm away from the trap center. The calculations are in good agreement qualitatively with the experimental results of Voros et al. [Z. Voros, D.W. Snoke, L. Pfeiffer, K. West, Phys. Rev. Lett. 97 (2006) 016803] and prove that an in-plane harmonic trap can indeed keep an exciton gas dense near its center.
Kelly, John V.; O'Brien, Jeff; O'Neill, Feidhlim T.; Gleeson, Michael R.; Sheridan, John T.
2004-10-01
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is non-local as it is assumed that monomers are polymerised to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The numerical method of solution typically involves retaining either two or four harmonics of the Fourier series of monomer concentration in the calculation. In this paper a general set of equations is derived which allows inclusion of higher number of harmonics for any response function. The numerical convergence for varying number of harmonics retained is investigated with special care being taken to note the effect of the; non-local material variance s, the power law degree k, and the rates of diffusion, D, and polymerisation F0. General non-linear material responses are also included.
Nonlinear diffusion of indirect excitons in an ideal bilayer with an in-plane harmonic trap
Energy Technology Data Exchange (ETDEWEB)
Wang Li [Physics Department of Tangshan Teachers College, Tangshan 063000, Hebei (China)], E-mail: wangli@mail.semi.ac.cn; Wang Qinglu [Physics Department of Tangshan Teachers College, Tangshan 063000, Hebei (China)
2009-06-01
The nonlinear diffusion of the spatially indirect excitons in an ideal bilayer with an in-plane harmonic trap is investigated based on the theories developed by Ivanov [A.L. Ivanov, Europhys. Lett. 59 (2002) 586; A.L. Ivanov, J. Phys.: Condens. Matter 16 (2004) S3629] and Rapaport et al. [R. Rapaport, G. Chen, S. Simon, O. Mitrofanov, L. Pfeiffer, P.M. Platzman, Phys. Rev. B 72 (2005) 075428]. A nonlinear equation for the diffusion of the indirect excitons in this structure is established. The two-dimensional density of the indirect excitons in this structure is calculated. The calculations show that the density adjacent to the trap center for different exciton temperatures can remain very high even long after the photo-excitation because of the confinement of the in-plane harmonic trap, and that the indirect excitons gather several tens of {mu}m away from the trap center. The calculations are in good agreement qualitatively with the experimental results of Voros et al. [Z. Voros, D.W. Snoke, L. Pfeiffer, K. West, Phys. Rev. Lett. 97 (2006) 016803] and prove that an in-plane harmonic trap can indeed keep an exciton gas dense near its center.
Energy Technology Data Exchange (ETDEWEB)
Tartakovsky, Daniel
2013-08-30
We developed new CDF and PDF methods for solving non-linear stochastic hyperbolic equations that does not rely on linearization approximations and allows for rigorous formulation of the boundary conditions.
Energy Technology Data Exchange (ETDEWEB)
Potemki, Valeri G. [Moscow State Engineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Automatics and Electronics; Borisevich, Valentine D.; Yupatov, Sergei V. [Moscow State Enineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Technical Physics
1996-12-31
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner`s basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker`s form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author) 7 refs., 10 figs.
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally.
Thermal diffusion of water vapour in porous materials: fact or fiction?
DEFF Research Database (Denmark)
Janssen, Hans
2011-01-01
of all measurements allows concluding that no consistent nor significant thermal diffusion can be observed. This brings these investigations in line with their earlier opponents. This conclusion also agrees with thermodynamics, which confirms the actual existence of thermal diffusion, but also indicates...
Influence of radiation on double conjugate diffusion in a porous cavity
Energy Technology Data Exchange (ETDEWEB)
Azeem,; Idris, Mohd Yamani Idna [Dept. of Computer System & Technology, University of Malaya, Kuala Lumpur (Malaysia); Khan, T. M. Yunus, E-mail: yunus.tatagar@gmail.com [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia); Dept. of Mechanical Engineering, BVB College of Engineering & Technology, Hubli (India); Badruddin, Irfan Anjum, E-mail: irfan-magami@Rediffmail.com; Nik-Ghazali, N. [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia)
2016-05-06
The current work highlights the effect of radiation on the conjugate heat and mass transfer in a square porous cavity having a solid wall. The solid wall is placed at the center of cavity. The left surface of cavity is maintained at higher temperature T{sub w} and concentration C{sub w} whereas the right surface is maintained at T{sub c} and C{sub c} such that T{sub w}>T{sub c} and Cw>Cc. The top and bottom surfaces are adiabatic. The governing equations are solved with the help of finite element method by making use of triangular elements. The results are discussed with respect to two different heights of solid wall inside the porous medium along with the radiation parameter.
Modeling and simulation of liquid diffusion through a porous finitely elastic solid
Zhao, Qiangsheng
2013-01-29
A new theory is proposed for the continuum modeling of liquid flow through a porous elastic solid. The solid and the voids are assumed to jointly constitute the macroscopic solid phase, while the liquid volume fraction is included as a separate state variable. A finite element implementation is employed to assess the predictive capacity of the proposed theory, with particular emphasis on the mechanical response of Nafion® membranes to the flow of water. © 2013 Springer-Verlag Berlin Heidelberg.
Directory of Open Access Journals (Sweden)
Marković Jelena
2007-01-01
Full Text Available The transport of gaseous components through porous media could be described according to the well-known Fick model and its modifications. It is also known that Fick’s law is not suitable for predicting the fluxes in multicomponent gas mixtures, excluding binary mixtures. This model is still frequently used in chemical engineering because of its simplicity. Unfortunately, besides the Fick’s model there is no generally accepted model for mass transport through porous media (membranes, catalysts etc.. Numerous studies on transport through porous media reveal that Dusty Gas Model (DGM is superior in its ability to predict fluxes in multicomponent mixtures. Its wider application is limited by more complicated calculation procedures comparing to Fick’s model. It should be noted that there were efforts to simplify DGM in order to obtain satisfactory accurate results. In this paper linearized DGM, as the simplest form of DGM, is tested under conditions of zero system pressure drop, small pressure drop, and different temperatures. Published experimental data are used in testing the accuracy of the linearized procedure. It is shown that this simplified procedure is accurate enough compared to the standard more complicated calculations.
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient
Directory of Open Access Journals (Sweden)
John D. Towers
2002-10-01
Full Text Available We study the Cauchy problem for the nonlinear (possibly strongly degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(xf(u=partial_x^2 A(u, quad A'(cdotge 0, $$ where the coefficient $gamma(x$ is possibly discontinuous and $f(u$ is genuinely nonlinear, but not necessarily convex or concave. Existence of a weak solution is proved by passing to the limit as $varepsilondownarrow 0$ in a suitable sequence ${u_{varepsilon}}_{varepsilon>0}$ of smooth approximations solving the problem above with the transport flux $gamma(xf(cdot$ replaced by $gamma_{varepsilon}(xf(cdot$ and the diffusion function $A(cdot$ replaced by $A_{varepsilon}(cdot$, where $gamma_{varepsilon}(cdot$ is smooth and $A_{varepsilon}'(cdot>0$. The main technical challenge is to deal with the fact that the total variation $|u_{varepsilon}|_{BV}$ cannot be bounded uniformly in $varepsilon$, and hence one cannot derive directly strong convergence of ${u_{varepsilon}}_{varepsilon>0}$. In the purely hyperbolic case ($A'equiv 0$, where existence has already been established by a number of authors, all existence results to date have used a singular maolinebreak{}pping to overcome the lack of a variation bound. Here we derive instead strong convergence via a series of a priori (energy estimates that allow us to deduce convergence of the diffusion function and use the compensated compactness method to deal with the transport term. Submitted April 29, 2002. Published October 27, 2002. Math Subject Classifications: 35K65, 35D05, 35R05, 35L80 Key Words: Degenerate parabolic equation; nonconvex flux; weak solution; discontinuous coefficient; viscosity method; a priori estimates; compensated compactness
Yang, Haijian
2016-12-10
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Energy Technology Data Exchange (ETDEWEB)
Nanjundappa, C.E., E-mail: cenanju@hotmail.com [Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore-560 056 (India); Shivakumara, I.S., E-mail: shivakumarais@gmail.com [Department of Mathematics, Bangalore University, Bangalore-560 001 (India); Prakash, H.N., E-mail: prakashahn83@gmail.com [Government Pre-University College, B H Road, Tumkur-572 102 (India)
2014-12-15
We investigate the influence of Coriolis force on the onset of thermomagnetic convection in ferrofluid saturating a porous layer in the presence of a uniform vertical magnetic field using both linear and weakly non-linear analyses. The modified Brinkman–Forchheimer-extended Darcy equation with Coriolis term has been used to describe the fluid flow. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary thermomagnetic Convection and weakly non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number Nu as functions of time. The range of thermal Rayleigh number R beyond which the bifurcation becomes subcritical increases with increasing Λ, Da{sup −1} and Ta. The global quantity of the heat transfer rate decreases by increasing the Taylor number Ta. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady streamlines for various parameters.
Yang, Haijian; Sun, Shuyu; Yang, Chao
2017-03-01
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Wang, Wei; Ma, Wanbiao; Lai, Xiulan
2017-01-01
From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R0 of the model without chemotaxis. That is, the infection-free steady state E0 is globally asymptotically stable if R0 virus is uniformly persistent if R0 > 1. In addition, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.
Diffusion of water in nano-porous polyamide membranes: Quasielastic neutron scattering study
Sharma, V. K.; Mitra, S.; Singh, P.; Jurányi, F.; Mukhopadhyay, R.
2010-10-01
Dynamics of water sorbed in a reverse osmosis polyamide membrane (ROPM) as studied by quasielastic neutron scattering (QENS) is reported here. The trimesoylchloride-m-phenylene diamine based ROPM is synthesized by interfacial polymerization technique. QENS data indicates that translational motion of water confined in ROPM gets modified compared to bulk water whereas rotational motion remains unaltered. Translational motion of water in ROPM is found to follow random jump diffusion with lower diffusivity compared to bulk water. Translational diffusivity does not show the Arrhenius behaviour.
Porous silicon used as an oxide diffusion mask to produce a periodic micro doped n{sup ++}/n regions
Energy Technology Data Exchange (ETDEWEB)
Dimassi, Wissem; Jafel, Hayet; Lajnef, Mohamed; Ali Kanzari, M.; Bouaicha, Mongi; Bessais, Brahim; Ezzaouia, Hatem [Laboratoire de Photovoltaique, Centre de Recherche et des Technologies de l' Energie, PB: 95, Hammam Lif 2050 (Tunisia)
2011-06-15
The realization of screen-printed contacts on silicon solar cells requires highly doped regions under the fingers and lowly doped and thin ones between them. In this work, we present a low-cost approach to fabricate selective emitter (n{sup ++}/n doped silicon regions), using oxidized porous silicon (ox-PS) as a mask. Micro-periodic fingers were opened on the porous silicon layer using a micro groove machining process. Optimized phosphorous diffusion through the micro grooved ox-PS let us obtain n{sup ++} doped regions in opened zones and n doped large regions underneath the ox-PS layer. The dark I-V characteristics of the obtained device and Fourier transform infrared (FTIR) spectroscopy investigations of the PS layer show the possibility to use PS as a dielectric layer. The Light Beam Induced Current (LBIC) mapping of the realized device, confirm the presence of a micro periodic n{sup ++}/n type structure. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
DEFF Research Database (Denmark)
Johannesson, Björn; Hosokawa, Yoshifumi; Yamada, Kazuo
2009-01-01
A method to analyse and calculate concentration profiles of different types of ions in the pore solution of porous materials such as concrete subjected to external wetting and drying is described. The equations in use have a solid theoretical meaning and are derived from a porous media technique......, which is a special branch of the more general mixture theory. The effect of chemical action is ignored making the presented model suitable to be implemented into codes dealing solely with chemical equilibrium. The coupled set of equations for diffusion of ionic species, the internal electrical potential...... on the ionic diffusion resistance in the pore solution of the porous material. The Gauss’ law is included in the model in order to be able to calculate the electrical potential which develops due to small deviations from total charge neutrality among the ionic species in the pore solution. The correctness...
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Qin, C.; Hassanizadeh, S.M.; van Oosterhout, L.M.
2016-01-01
In the cathode side of a polymer electrolyte fuel cell (PEFC), a micro porous layer (MPL) added between the catalyst layer (CL) and the gas diffusion layer (GDL) plays an important role in water management. In this work, by using both quasi-static and dynamic pore-network models, water and vapor tra
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
Debussche, Arnaud; Imkeller, Peter
2013-01-01
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
Image segmentation combining non-linear diffusion and the Nystrom extension
Izquierdo, Ebroul
2005-07-01
An approach for image segmentation is presented. Images are first preprocessed using multiscale simplification by nonlinear diffusion. Subsequently image segmentation of the resulting smoothed images is carried out. The actual segmentation step is based on the estimation of the Eigenvectors and Eigenvalues of a matrix derived from both the total dissimilarity and the total similarity between different groups of pixels in the image. This algorithm belong to the class of spectral methods, specifically, the Nystron extension introduced by Fowlkes et al in [1]. Stability analysis of the approximation of the underlying spectral partitioning is presented. Modifications of Fowlkes technique are proposed to improve the stability of the algorithm. The proposed modifications include a criterion for the selection of the initial sample and numerically stable estimations of ill-posed inverse matrices for the solution of the underlying mathematical problem. Results of selected computer experiments are reported to validate the superiority of the proposed approach when compared with the technique proposed in [1].
An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms.
Fernández, José Jesús; Li, Sam
2003-01-01
Cryo-electron tomography is an imaging technique with an unique potential for visualizing large complex biological specimens. It ensures preservation of the biological material but the resulting cryotomograms are extremely noisy. Sophisticated denoising techniques are thus essential for allowing the visualization and interpretation of the information contained in the cryotomograms. Here a software tool based on anisotropic nonlinear diffusion is described for filtering cryotomograms. The approach reduces local noise and meanwhile enhances both curvilinear and planar structures. In the program a novel solution of the partial differential equation has been implemented, which allows a reliable estimation of derivatives and, furthermore, reduces computation time and memory requirements. Several criteria have been included to automatically select the optimal stopping time. The behaviour of the denoising approach is tested for visualizing filamentous structures in cryotomograms.
Directory of Open Access Journals (Sweden)
Jagdev Singh
2014-01-01
Full Text Available The main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive.
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains
Bonforte, Matteo; Vázquez, Juan Luis
2015-10-01
We investigate quantitative properties of the nonnegative solutions to the nonlinear fractional diffusion equation, , posed in a bounded domain, , with m > 1 for t > 0. As we use one of the most common definitions of the fractional Laplacian , 0 zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Harnack inequalities. We also investigate the boundary behaviour and we obtain sharp estimates from above and below. In addition, we obtain similar estimates for fractional semilinear elliptic equations. Either the standard Laplacian case s = 1 or the linear case m = 1 are recovered as limits. The method is quite general, suitable to be applied to a number of similar problems.
KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
KPP reaction-diffusion system with a nonlinear loss inside a cylinder
Giletti, Thomas
2010-09-01
We consider in this paper a reaction-diffusion system in the presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a nonlinear space-dependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique
El-Beltagy, Mohamed A.
2014-01-06
Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.
Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation
Directory of Open Access Journals (Sweden)
B. S. Bhadauria
2014-01-01
Full Text Available The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system.
Diffusion aspects of designing porous growth media for earth and space
DEFF Research Database (Denmark)
Chamindu, Deepagoda; Møldrup, Per; Jensen, M P
2012-01-01
Growing plants in extraterrestrial environments, for example on a space station or in a future lunar or Martian outpost, is a challenge that has attracted increasing interest over the last few decades. Most of the essential plant needs for optimal growth (air, water, and nutrient supply...... to be used in future design models. Also, critical windows of diffusivity (CWD) was defined identifying the air content range where gas diffusivity (hence, oxygen supply) and solute diffusivity or the analogous electrical conductivity (hence, nutrient supply) are above pre-defined, critical minimum values...... be avoided when designing safe plant growth media for space. The CWD concept was also applied to a natural volcanic ash soil (Nishi-Tokyo, Japan), and the natural soil was found competitive or better than the tested commercial growth media. This could bear large perspectives for Martian outpost missions...
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
Prasannakumara, B. C.; Shashikumar, N. S.; Venkatesh, P.
2017-09-01
An analysis has been carried out to study the effect of nonlinear thermal radiation on slip flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet immersed in a porous medium. Water is considered as a base fluid with dust particles along with suspended Aluminum Oxide (Al2O3) nanoparticles. Using appropriate similarity transformations, the coupled nonlinear partial differential equations are reduced into a set of coupled nonlinear ordinary differential equations. The reduced equations are then solved numerically using Runge-Kutta-Fehlberg45 order method with the help of shooting technique to investigate the impact of various pertinent parameters for the velocity and temperature fields. The obtained results are presented in tabular form as well as graphically and discussed in detail. Effect of different parameters on skin friction coefficient and Nusselt number are also discussed.
Variational iteration method for solving the time-fractional diffusion equations in porous medium
Institute of Scientific and Technical Information of China (English)
Wu Guo-Cheng
2012-01-01
The variational iteration method is successfully extended to the case of solving fractional differential equations,and the Lagrange multiplier of the method is identified in a more accurate way.Some diffusion models with fractional derivatives are investigated analytically,and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
Roudbari, Mahnaz Shokrpour; Verhoosel, Clemens V
2016-01-01
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-triv...
Directory of Open Access Journals (Sweden)
Pratibha Joshi
2014-12-01
Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.
Institute of Scientific and Technical Information of China (English)
QIN Xin-qiang; MA Yi-chen; ZHANG Yin
2005-01-01
For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.
Diffusion Controlled Drug Release from Slurry Formed, Porous, Organic and Clay-derived Pellets
Jämstorp Berg, Erik
2012-01-01
Coronary artery disease and chronic pain are serious health issues that cause severe discomfort and suffering in society today. Antithrombotic agents and highly potent analgesics play a critical role in improving the recovery process for patients being treated for these diseases. This thesis focuses on the design and study of pellet-based drug dosage forms which allow diffusion-controlled delivery of drugs with the aim of achieving optimal therapeutic outcomes. A wet slurry process was used t...
Diffusion Controlled Drug Release from Slurry Formed, Porous, Organic and Clay-derived Pellets
Jämstorp Berg, Erik
2012-01-01
Coronary artery disease and chronic pain are serious health issues that cause severe discomfort and suffering in society today. Antithrombotic agents and highly potent analgesics play a critical role in improving the recovery process for patients being treated for these diseases. This thesis focuses on the design and study of pellet-based drug dosage forms which allow diffusion-controlled delivery of drugs with the aim of achieving optimal therapeutic outcomes. A wet slurry process was used t...
Jämstorp, Erik; Strømme, Maria; Frenning, Göran
2011-10-01
A unique structure-function relationship investigation of mechanically strong geopolymer drug delivery vehicles for sustained release of potent substances is presented. The effect of in-synthesis water content on geopolymer pore structure and diffusive drug transport is investigated. Scanning electron microscopy, N2 gas adsorption, mercury intrusion porosimetry, compression strength test, drug permeation, and release experiments are performed. Effective diffusion coefficients are measured and compared with corresponding theoretical values as derived from pore size distribution and connectivity via pore-network modeling. By solely varying the in-synthesis water content, mesoporous and mechanically strong geopolymers with porosities of 8%-45% are obtained. Effective diffusion coefficients of the model drugs Saccharin and Zolpidem are observed to span two orders of magnitude (∼1.6-120 × 10(-8) cm(2) /s), comparing very well to theoretical estimations. The ability to predict drug permeation and release from geopolymers, and materials alike, allows future formulations to be tailored on a structural and chemical level for specific applications such as controlled drug delivery of highly potent substances.
Directory of Open Access Journals (Sweden)
Zhiwu Liao
2011-01-01
Full Text Available Existing Nonlinear Anisotropic Diffusion (NAD methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD, which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical approximate solutions are obtained. The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ＜10 are determined and compared with those by the BAND's finite difference numerical method developed by Newman. At lower values of φ, the decomposition solution with 3 terms gives satisfactory agreement with the numerical solution; at higher values of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved. In general, the solution with 6 terms gives a satisfactory agreement.
Budroni, M. A.
2015-12-01
Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.
Sun, Dajun D; Lee, Ping I
2015-04-06
The importance of rate of supersaturation generation on the kinetic solubility profiles of amorphous systems has recently been shown by us; however, the previous focus was limited to constant rates of supersaturation generation. The objective of the current study is to further examine the effect of nonlinear rate profiles of supersaturation generation in amorphous systems, including (1) instantaneous or infinite rate (i.e., initial degree of supersaturation), (2) first-order rate (e.g., from dissolution of amorphous drug particles), and (3) matrix diffusion regulated rate (e.g., drug release from amorphous solid dispersions (ASDs) based on cross-linked poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels), on the kinetic solubility profiles of a model poorly soluble drug indomethacin (IND) under nonsink dissolution conditions. The previously established mechanistic model taking into consideration both the crystal growth and ripening processes was extended to predict the evolution of supersaturation resulting from nonlinear rates of supersaturation generation. Our results confirm that excessively high initial supersaturation or a rapid supersaturation generation leads to a surge in maximum supersaturation followed by a rapid decrease in drug concentration owing to supersaturation-induced precipitation; however, an exceedingly low degree of supersaturation or a slow rate of supersaturation generation does not sufficiently raise the supersaturation level, which results in a lower but broader maximum kinetic solubility profile. Our experimental data suggest that an optimal area-under-the-curve of the kinetic solubility profiles exists at an intermediate initial supersaturation level for the amorphous systems studied here, which agrees well with the predicted trend. Our model predictions also support our experimental findings that IND ASD in cross-linked PHEMA exhibits a unique kinetic solubility profile because the resulting supersaturation level is governed by a matrix
Energy Technology Data Exchange (ETDEWEB)
Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.
2008-07-02
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.
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Khan, W.A. [Department of Engineering Sciences, National University of Sciences and Technology, Karachi 75350 (Pakistan); Aziz, A. [Department of Mechanical Engineering, School of Engineering and Applied Science, Gonzaga University, Spokane, WA 99258 (United States)
2011-11-15
The Buongiorno model [16] has been used to study the double-diffusive natural convection from a vertical plate to a porous medium saturated with a binary base fluid containing nano-particles. The model identifies the Brownian motion and thermophoresis as the primary mechanisms for enhanced convection characteristics of the nano-fluid. The behavior of the porous medium is described by the Darcy model. The vertical surface has the heat, mass and nano-particle fluxes each prescribed as a power law function of the distance along the wall. The transport equations are transformed into four nonlinear, coupled similarity equations containing eight dimensionless parameters. These equations are solved numerically to obtain the velocity, temperature, solute concentration and nano-particle concentration in the respective boundary layers. Results are presented to illustrate the effects of various parameters including the exponent of the power law describing the imposed surface fluxes on the heat and mass transfer characteristics of the flow. These results are supplemented with the data for the reduced Nusselt number and the two reduced Sherwood numbers, one for the solute and the other for the nano-particles. (authors)
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Weeratunga, S K; Kamath, C
2001-12-20
Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, they focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. They complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. They explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. They also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. The empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.
Tan, Xiaoyu
2016-05-18
In the last decade, many attempts were made to put metal organic frameworks (MOFs) in industrial applications, but most of these efforts weren’t successfully. As one of the few MOFs produced on industrial scale, ZIF-8 has interesting pore size, huge internal surface area and great thermal and chemical stability. Therefore, ZIF-8 might become the first MOF, which will be applied in industrial separation processes. In this thesis, a synthesis study is presented, which leads to a cheap and convenient way to fabricate defect-free and thin ZIF-8 membranes on porous polymeric supports showing high selectivity and high gas permeance. The ZIF-8 layers were produced via a contra-diffusion method. Several polymeric membranes were employed as support in this study, such as PAN, PEI, PSU, PA and PTSC. We studied the influence of the polymeric support properties for the ZIF-8 membrane preparation and optimized the ZIF-8 preparation conditions. The ZIF-8 membranes were characterized via scanning electron microscopy (SEM) and X-ray diffraction (XRD). For gas permeation test, we chose a Wicke-Kallenbach apparatus to measure membrane’s gas permeance and selectivity. One of the best ZIF-8 membranes exhibited a hydrogen permeance of 3.45 × 10-8 mol m-2 s-1 Pa-1 and an ideal selectivity of hydrogen over propane of about 500.
Su, Huaneng; Xu, Qian; Chong, Junjie; Li, Huaming; Sita, Cordellia; Pasupathi, Sivakumar
2017-02-01
In this work, we report a simple strategy to improve the performance of high temperature polymer electrolyte membrane fuel cell (HT-PEMFC) by eliminating the micro-porous layer (MPL) from its gas diffusion electrodes (GDEs). Due to the absence of liquid water and the general use of high amount of catalyst, the MPL in a HT-PEMFC system works limitedly. Contrarily, the elimination of the MPL leads to an interlaced micropore/macropore composited structure in the catalyst layer (CL), which favors gas transport and catalyst utilization, resulting in a greatly improved single cell performance. At the normal working voltage (0.6 V), the current density of the GDE eliminated MPL reaches 0.29 A cm-2, and a maximum power density of 0.54 W cm-2 at 0.36 V is obtained, which are comparable to the best results yet reported for the HT-PEMFCs with similar Pt loading and operated using air. Furthermore, the MPL-free GDE maintains an excellent durability during a preliminary 1400 h HT-PEMFC operation, owing to its structure advantages, indicating the feasibility of this electrode for practical applications.
Directory of Open Access Journals (Sweden)
Prabhakar Reddy B.
2014-05-01
Full Text Available The thermal diffusion and viscous dissipation effects on an unsteady MHD free convection heat and mass transfer flow of an incompressible, electrically conducting, fluid past an infinite vertical porous plate embedded in a porous medium of time dependent permeability under oscillatory suction velocity in the presence of a heat absorbing sink have been studied. It is considered that the influence of a uniform magnetic field acts normal to the flow and the permeability of the porous medium fluctuates with time. The dimensionless governing equations for this investigation have been solved numerically by using the efficient Galerkin finite element method. The numerical results obtained have been presented through graphs and tables for the thermal Grashof number (Gr > 0 corresponding to the cooling of the porous plate and (Gr < 0 corresponding to heating of the porous plate to observe the effects of various material parameters encountered in the problem under investigation. Numerical data for skin-friction, Nusselt and Sherwood numbers are tabulated and then discussed.
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Dr.K.Gnaneswar
2014-09-01
Full Text Available A finite element study of combined heat and mass transfer flow through a porous medium in a circular cylindrical annulus with Soret and Dufour effects in the presence of heat sources has been analyzed. The coupled velocity, energy, and diffusion equations are solved numerically by using Galerkin- finite element technique. Shear stress, Nusslet number and Sherwood number are evaluated numerically for different values of the governing parameters under consideration and are shown in tabular form.
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
Mustaffa, Izadora; Trenado, Carlos; Schwerdtfeger, Karsten; Strauss, Daniel J
2008-01-01
Recent progress in mathematical image processing shows a remarkable success when applying numerical methods to ill-posed partial differential equations (PDE). In particular, nonlinear diffusion filtering (NDF)process is an approach that belongs to such family of differential equations. It has been successfully applied in many recent methods for image processing and computer vision areas, particularly in denoising, smoothing, segmentation, and restoration. In this paper we focus on a novel NDF application, namely denoising of single-trials of auditory brainstem responses (ABRs) and the analysis of transcranial magnetic stimulation (TMS) responses.We show that by applying NDF on a matrix-form image of single-trials, we were able to denoise the single-trials, resulting in a better extraction of information over the ongoing experiment; morphology, eg. the latency of the single-trials according to different stimuli paradigms at different stimulation intensity levels. It is concluded that NDF represents a novel and useful approach for the analysis of single-trials in brain imaging.
Ellison, D C; Baring, M G; Grenier, I A; Lagage, P O; Ellison, Donald C.; Goret, Philippe; Baring, Matthew G.; Grenier, Isabelle A.; Lagage, Pierre-Olivier
1999-01-01
We calculate particle spectra and continuum photon emission from the Cassiopeia A supernova remnant (SNR). The particle spectra, ion and electron, result from diffusive shock acceleration at the forward SNR shock and are determined with a nonlinear Monte Carlo calculation. The calculation self-consistently determines the shock structure under the influence of ion pressure, and includes a simple parameterized treatment of electron injection and acceleration. Our results are compared to photon observations, concentrating on the connection between the Radio and GeV-TeV gamma-ray range, and to cosmic ray ion observations. We include new upper limits from the Cherenkov Array at Themis (CAT) imaging Cherenkov telescope and the Whipple 10m gamma-ray telescope at > 400 GeV. These new limits support the suggestion (e.g. Cowsik & Sarkar 1980; Allen et. al. 1997) that energetic electrons are emitting synchrotron radiation in an extremely high magnetic field (~ 1000 microGauss), far greater than values routinely assi...
Liu, Xunliang; Peng, Fangyuan; Lou, Guofeng; Wen, Zhi
2015-12-01
Fundamental understanding of liquid water transport in gas diffusion media (GDM) is important to improve the material and structure design of polymer electrolyte membrane (PEM) fuel cells. Continuum methods of two-phase flow modeling facilitate to give more details of relevant information. The proper empirical correlations of liquid water transport properties, such as capillary characteristics, water relative permeability and effective contact angle, are crucial to two phase flow modeling and cell performance prediction. In this work, researches on these properties in the last decade are reviewed. Various efforts have been devoted to determine the water transport properties for GDMs. However, most of the experimental studies are ex-situ measurements. In-situ measurements for GDMs and extending techniques available to study the catalyst layer and the microporous layer will be further challenges. Using the Leverett-Udell correlation is not recommended for quantitative modeling. The reliable Leverett-type correlation for GDMs, with the inclusion of the cosine of effective contact angle, is desirable but hard to be established for modeling two-phase flow in GDMs. A comprehensive data set of liquid water transport properties is needed for various GDM materials under different PEM fuel cell operating conditions.
Ali, Iftikhar
2016-01-01
Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation methods, for porous rocks and porous media, that can compliment the field work. Here, a new nonlinear transport model for single phase gas flow in tight porous media is derived, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out of the rock material, and a correction for high flow rates (turbulence). This produces a nonlinear advection-diffusion type of partial differential equation (PDE) with pressure dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. An important application is to the determination of shale rock properties, such as porosity...
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, S. [Nano Scale Device Research Laboratory, Centre for Electronics Design and Technology, Indian Institute of Science, Bangalore 560 012 (India); Pahari, S. [Administrative Department, Jadavpur University, Kolkata 700 032 (India); Sarkar, R. [Department of Computer Science and Engineering, West Bengal University of Technology, BF-142, Salt Lake City, Sector-1, Kolkata 700064 (India); Ghosh, S. [Department of Electronics and Telecommunication Engineering, Bengal Engineering and Science University, Howrah 711 103 (India); Ghatak, K.P. [Department of Electronic Science, University of Calcutta, 92, Achryya Prafulla Chandra Road, Kolkata 700 009 (India)], E-mail: kamakhyaghatak@yahoo.co.in
2008-10-01
We study the diffusivity-mobility ratio (DMR) in heavily doped nonlinear compounds forming band tails on the basis of a newly formulated electron dispersion law and III-V, ternary and quaternary materials form a special case of our generalized analysis. The complex nature of the energy spectrum and creation of a new forbidden zone is the consequence of anisotropic energy band constants and the interaction of the impurity atoms in the tails with spin-orbit splitting of valence bands for the other compounds. Analytically, the presence of non-removable poles in the dispersion relation of the undoped material creates the complex energy spectrum for the corresponding heavily doped sample. The DMR for the heavily doped II-VI, IV-VI and stressed materials has been studied. It has been found taking n-type CdGeAs{sub 2,}, Cd{sub 3}As{sub 2}, InAs, InSb, Hg{sub 1-x}Cd{sub x}Te, In{sub 1-x}Ga{sub x}As{sub y}P{sub 1-y} lattice matched to InP, CdS, PbTe, PbSnTe, Pb{sub 1-x}Sn{sub x}Se and stressed InSb as examples that the DMR increases with the increasing electron concentration with different numerical values and the nature of variations are totally band structure dependent. An experimental method of determining the DMR in heavily doped materials for arbitrary dispersion relations together with three applications in the area of material science in general has been suggested.
Non-linear diffusion of cosmic rays escaping from supernova remnants - I. The effect of neutrals
Nava, L.; Gabici, S.; Marcowith, A.; Morlino, G.; Ptuskin, V. S.
2016-10-01
Supernova remnants are believed to be the main sources of galactic cosmic rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disc volume, where most supernovae explode, and are characterized by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that streaming instability affects the propagation of CRs even in the presence of ion-neutral friction. The diffusion coefficient can be suppressed by more than a factor of ˜2 over a region of few tens of pc around the remnant. The suppression increases for smaller distances. The propagation of ≈10 GeV particles is affected for several tens of kiloyears after escape, while ≈1 TeV particles are affected for few kiloyears. This might have a great impact on the interpretation of gamma-ray observations of molecular clouds located in the vicinity of supernova remnants.
Romanov, Dmitri; Smith, Stanley; Brady, John; Levis, Robert J.
2008-02-01
We have studied the application of the diffusion mapping technique to dimensionality reduction and clustering in multidimensional optical datasets. The combinational (input-output) data were obtained by sampling search spaces related to optimization of a nonlinear physical process, short-pulse second harmonic generation. The diffusion mapping technique hierarchically reduces the dimensionality of the data set and unifies the statistics of input (the pulse shape) and output (the integral output intensity) parameters. The information content of the emerging clustered pattern can be optimized by modifying the parameters of the mapping procedure. The low-dimensional pattern captures essential features of the nonlinear process, based on a finite sampling set. In particular, the apparently parabolic two-dimensional projection of this pattern exhibits regular evolution with the increase of higher-intensity data in the sampling set. The basic shape of the pattern and the evolution are relatively insensitive to the size of the sampling set, as well as to the details of the mapping procedure. Moreover, the experimental data sets and the sets produced numerically on the basis of a theoretical model are mapped into patterns of remarkable similarity (as quantified by the similarity of the related quadratic-form coefficients). The diffusion mapping method is robust and capable of predicting higher-intensity points from a set of low-intensity points. With these attractive features, diffusion mapping stands poised to become a helpful statistical tool for preprocessing analysis of vast and multidimensional combinational optical datasets.
Zhang, Li; Zhang, Fan; Ruan, Shigui
2017-03-01
We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.
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Panpan Jing
2015-06-01
Full Text Available In this letter, we report a novel V-doped SrTiO3 photocatalyst synthesized via electrospinning followed by a thermal diffusion process at low temperature. The morphological and crystalline structural investigations reveal not only that the V-doped SrTiO3 photocatalyst possesses a uniform, porous, fibrous structure, but also that some V5+ ions are introduced into the SrTiO3 lattice. The photocatalytic capability of V-doped SrTiO3 porous nanofibers was evaluated through photodegrading methyl orange (MO in aqueous solution under artificial UV–vis light. The results indicated that V-doped SrTiO3 porous nanofibers have excellent catalytic efficiency. Furthermore, the excellent catalytic activity was maintained even after five cycle tests, indicating that they have outstanding photocatalytic endurance. It is suggested that the excellent photocatalytic performance of doped SrTiO3 nanofibers is possibly attributed to the V5+ ion doping increasing the light utilization as well as to the outstanding porous features, the excellent component and structure stability.
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T.; Finkel, Michael; Blowes, David W.; Cirpka, Olaf A.
2016-09-01
Transport of reactive solutes in groundwater is affected by physical and chemical heterogeneity of the porous medium, leading to complex spatio-temporal patterns of concentrations and reaction rates. For certain cases of bioreactive transport, it could be shown that the concentrations of reactive constituents in multi-dimensional domains are approximately aligned with isochrones, that is, lines of identical travel time, provided that the chemical properties of the matrix are uniform. We extend this concept to combined physical and chemical heterogeneity by additionally considering the time that a water parcel has been exposed to reactive materials, the so-called exposure time. We simulate bioreactive transport in a one-dimensional domain as function of time and exposure time, rather than space. Subsequently, we map the concentrations to multi-dimensional heterogeneous domains by means of the mean exposure time at each location in the multi-dimensional domain. Differences in travel and exposure time at a given location are accounted for as time difference. This approximation simplifies reactive-transport simulations significantly under conditions of steady-state flow when reactions are restricted to specific locations. It is not expected to be exact in realistic applications because the underlying assumption, such as neglecting transverse mixing altogether, may not hold. We quantify the error introduced by the approximation for the hypothetical case of a two-dimensional, binary aquifer made of highly-permeable, non-reactive and low-permeable, reactive materials releasing dissolved organic matter acting as electron donor for aerobic respiration and denitrification. The kinetically controlled reactions are catalyzed by two non-competitive bacteria populations, enabling microbial growth. Even though the initial biomass concentrations were uniform, the interplay between transport, non-uniform electron-donor supply, and bio-reactions led to distinct spatial patterns of
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T; Finkel, Michael; Blowes, David W; Cirpka, Olaf A
2016-09-01
Transport of reactive solutes in groundwater is affected by physical and chemical heterogeneity of the porous medium, leading to complex spatio-temporal patterns of concentrations and reaction rates. For certain cases of bioreactive transport, it could be shown that the concentrations of reactive constituents in multi-dimensional domains are approximately aligned with isochrones, that is, lines of identical travel time, provided that the chemical properties of the matrix are uniform. We extend this concept to combined physical and chemical heterogeneity by additionally considering the time that a water parcel has been exposed to reactive materials, the so-called exposure time. We simulate bioreactive transport in a one-dimensional domain as function of time and exposure time, rather than space. Subsequently, we map the concentrations to multi-dimensional heterogeneous domains by means of the mean exposure time at each location in the multi-dimensional domain. Differences in travel and exposure time at a given location are accounted for as time difference. This approximation simplifies reactive-transport simulations significantly under conditions of steady-state flow when reactions are restricted to specific locations. It is not expected to be exact in realistic applications because the underlying assumption, such as neglecting transverse mixing altogether, may not hold. We quantify the error introduced by the approximation for the hypothetical case of a two-dimensional, binary aquifer made of highly-permeable, non-reactive and low-permeable, reactive materials releasing dissolved organic matter acting as electron donor for aerobic respiration and denitrification. The kinetically controlled reactions are catalyzed by two non-competitive bacteria populations, enabling microbial growth. Even though the initial biomass concentrations were uniform, the interplay between transport, non-uniform electron-donor supply, and bio-reactions led to distinct spatial patterns of
Directory of Open Access Journals (Sweden)
D. R. V. S. R. K. Sastry
2013-01-01
Full Text Available The problem of unsteady magnetohydrodynamic convective flow with radiation and chemical reaction past a flat porous plate moving through a binary mixture in an optically thin environment is considered. The governing boundary layer equations are converted to nonlinear ordinary differential equations by similarity transformation and then solved numerically by MATLAB “bvp4c” routine. The velocity, temperature, and concentration profiles are presented graphically for various values of the material parameters. Also a numerical data for the local skin friction coefficient, the local Nusselt number, and local Sherwood number is presented in tabular forms.
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Kumar Hitesh
2016-01-01
Full Text Available The present paper analyzes the chemically reacting free convection MHD micropolar flow, heat and mass transfer in porous medium past an infinite vertical plate with radiation and viscous dissipation. The non-linear coupled partial differential equations are solved numerically using an implicit finite difference scheme known as Keller-box method. The results for concentration, transverse velocity, angular velocity and temperature are obtained and effects of various parameters on these functions are presented graphically. The numerical discussion with physical interpretations for the influence of various parameters also presented.
Peppin, Stephen S. L.
2009-01-01
Diffusion and permeation are discussed within the context of irreversible thermodynamics. A new expression for the generalized Stokes-Einstein equation is obtained which links the permeability to the diffusivity of a two-component solution and contains the poroelastic Biot-Willis coefficient. The theory is illustrated by predicting the concentration and pressure profiles during the filtration of a protein solution. At low concentrations the proteins diffuse independently while at higher concentrations they form a nearly rigid porous glass through which the fluid permeates. The theoretically determined pressure drop is nonlinear in the diffusion regime and linear in the permeation regime, in quantitative agreement with experimental measurements. © 2009 Walter de Gruyter, Berlin, New York.
Xia, Shaoyan; Huang, Yong; Tan, Xiaodi
2016-03-01
Partial differential equation (PDE)-based nonlinear diffusion processes have been widely used for image denoising. In the traditional nonlinear anisotropic diffusion denoising techniques, behavior of the diffusion depends highly on the gradient of image. However, it is difficult to get a good effect if we use these methods to reduce noise in optical coherence tomography images. Because background has the gradient that is very similar to regions of interest, so background noise will be mistaken for edge information and cannot be reduced. Therefore, nonlinear complex diffusion approaches using texture feature(NCDTF) for noise reduction in phase-resolved optical coherence tomography is proposed here, which uses texture feature in OCT images and structural OCT images to remove noise in phase-resolved OCT. Taking into account the fact that texture between background and signal region is different, which can be linked with diffusion coefficient of nonlinear complex diffusion model, we use NCDTF method to reduce noises of structure and phase images first. Then, we utilize OCT structure images to filter phase image in OCT. Finally, to validate our method, parameters such as image SNR, contrast-to-noise ratio (CNR), equivalent number of looks (ENL), and edge preservation were compared between our approach and median filter, Gaussian filter, wavelet filter, nonlinear complex diffusion filter (NCDF). Preliminary results demonstrate that NCDTF method is more effective than others in keeping edges and denoising for phase-resolved OCT.
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O. Anwar Bég
2016-03-01
Full Text Available A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z coordinate system to a (ξ,η coordinate system in terms of dimensionless x-direction velocity (∂F/∂η and z-direction velocity (G and dimensionless temperature function (H under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.
Zhou, Zuo-Ming; Wang, Xiao-Yan; Lin, Tian-Ming; Jing, Guo-Hua
2014-11-01
Fe3O4 poly (styrene-glycidyl methacrylate) magnetic porous microspheres (MPPMs) were introduced to immobilize Klebsiella sp. FD-3, an iron-reducing bacterium applied to reduce Fe(III)EDTA. The effects of potential inhibitors (S(2-), SO3(2-), NO3(-), NO2(-) and Fe(II)EDTA-NO) on Fe(III)EDTA reduction were investigated. S(2-) reacted with Fe(III)EDTA as an electron-shuttling compound and enhanced the reduction. But Fe(III)EDTA reduction was inhibited by SO3(2-) and Fe(II)EDTA-NO due to their toxic to microorganisms. Low concentrations of NO3(-) and NO2(-) accelerated Fe(III)EDTA reduction, but high concentrations inhibited the reduction, whether by free or immobilized FD-3. The immobilized FD-3 performed better than freely-suspended style. The substrate mass transfer and diffusion kinetics in the porous microspheres were calculated. The value of Thiele modulus and effectiveness factors showed that the intraparticle diffusion was fairly small and neglected in this carrier. Fe(III)EDTA reduction fitted first-order model at low Fe(III)EDTA concentration, and changed to zero-order model at high concentrations. Copyright © 2014 Elsevier Ltd. All rights reserved.
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Uedono, Akira, E-mail: uedono.akira.gb@u.tsukuba.ac.jp [Division of Applied Physics, Faculty of Pure and Applied Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Armini, Silvia; Zhang, Yu [IMEC, Kapeldreef 75, B-3001 Heverlee, Leuven (Belgium); Kakizaki, Takeaki [Division of Applied Physics, Faculty of Pure and Applied Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Krause-Rehberg, Reinhard [Department of Physics, Martin Luther University Halle, 06099 Halle (Germany); Anwand, Wolfgang; Wagner, Andreas [Institute for Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden (Germany)
2016-04-15
Graphical abstract: - Highlights: • Pores with cubic pore side lengths of 1.1 and 3.1 nm coexisted in the low-k film. • For the sample without the SAM sealing process, metal atoms diffused from the top Cu/MnN layer into the OSG film and were trapped by the pores. Almost all pore interiors were covered by those metals. • For the sample damaged by a plasma etch treatment before the SAM sealing process, self-assembled molecules diffused into the OSG film, and they were preferentially trapped by larger pores. - Abstract: Surface sealing effects on the diffusion of metal atoms in porous organosilicate glass (OSG) films were studied by monoenergetic positron beams. For a Cu(5 nm)/MnN(3 nm)/OSG(130 nm) sample fabricated with pore stuffing, C{sub 4}F{sub 8} plasma etch, unstuffing, and a self-assembled monolayer (SAM) sealing process, it was found that pores with cubic pore side lengths of 1.1 and 3.1 nm coexisted in the OSG film. For the sample without the SAM sealing process, metal (Cu and Mn) atoms diffused from the top Cu/MnN layer into the OSG film and were trapped by the pores. As a result, almost all pore interiors were covered with those metals. For the sample damaged by an Ar/C{sub 4}F{sub 8} plasma etch treatment before the SAM sealing process, SAMs diffused into the OSG film, and they were preferentially trapped by larger pores. The cubic pore side length in these pores containing self-assembled molecules was estimated to be 0.7 nm. Through this work, we have demonstrated that monoenergetic positron beams are a powerful tool for characterizing capped porous films and the trapping of atoms and molecules by pores.
Afify, A. A.; Uddin, Md. J.
2016-09-01
A numerical study of a steady two-dimensional double-diffusive free convection boundary layer flow over a vertical surface embedded in a porous medium with slip flow and convective boundary conditions, heat generation/absorption, and solar radiation effects is performed. A scaling group of transformations is used to obtain the governing boundary layer equations and the boundary conditions. The transformed equations are then solved by the fourth- and fifth-order Runge-Kutta-Fehlberg numerical method with Maple 13. The results for the velocity, temperature, and concentration profiles, as well as the skin friction coefficient, the Nusselt number, and the Sherwood number are presented and discussed.
Uwanta, I. J.; Hamza, M. M.
2014-01-01
An investigation is performed to study the effect of suction/injection on unsteady hydromagnetic natural convection flow of viscous reactive fluid between two vertical porous plates in the presence of thermal diffusion. The partial differential equations governing the flow have been solved numerically using semi-implicit finite-difference scheme. For steady case, analytical solutions have been derived using perturbation series method. Suction/injection is used to control the fluid flow in the channel, and an exothermic chemical reaction of Arrhenius kinetic is considered. Numerical results are presented graphically and discussed quantitatively with respect to various parameters embedded in the problem. PMID:27382632
Directory of Open Access Journals (Sweden)
S.N. Gaikwad
2014-01-01
Full Text Available In this paper, we have investigated theoretically the effect of Soret parameter on the onset of double diffusive rotating anisotropic convection in a horizontal sparsely packed porous layer using linear stability theory which is based on the usual normal mode technique. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The effect of anisotropy parameters, Soret parameter, solute Rayleigh number, Taylor number, Lewis number, Darcy and Darcy Prandtl number on stationary and oscillatory convection is shown graphically.
Directory of Open Access Journals (Sweden)
Yong Huang
2012-01-01
Full Text Available The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equation are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.
Directory of Open Access Journals (Sweden)
Kanittha Yimnak
2014-01-01
Full Text Available The meshless local Pretrov-Galerkin method (MLPG with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.
On symmetry groups of a 2D nonlinear diffusion equation with source
Indian Academy of Sciences (India)
Radica Cimpoiasu
2015-04-01
Symmetry analysis of a 2D nonlinear evolutionary equation with mixed spatial derivative and general source term involving the dependent variable and its spatial derivatives is performed. The source terms for which the equation admits nontrivial Lie symmetries are identified for two different forms of the symmetry operator. In one of these cases, the symmetries do not depend on the form of nonlinearities and in the other case, nonlinearities of power, exponential and trigonometric forms are considered. There are no supplementary nonclassical symmetries for the investigated equation. The results reported here generalize the previous results on the 2D heat equation and the 2D Ricci model.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2012-01-01
Full Text Available We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.
Directory of Open Access Journals (Sweden)
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
Bykov, Andrei M; Osipov, Sergei M; Vladimirov, Andrey E
2014-01-01
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (~eV) injected at the viscous subshock, to the escape of the highest energy CRs (~PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the d...
A nonlinear equation for ionic diffusion in a strong binary electrolyte
Ghosal, Sandip; 10.1098/rspa.2010.0028
2012-01-01
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This mathematical framework also describes other important problems in physics such as electron and hole diffusion across semi-conductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here we derive a more general theory by exploiting the ratio of Debye length...
Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems
Directory of Open Access Journals (Sweden)
Oleksii Pliukhin
2015-10-01
Full Text Available A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisfying Dirichlet boundary conditions are obtained. An biological interpretation is presented in order to show that two different types of interaction between biological species can be described.
Ryu, Seungoh
2009-08-01
We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation in the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occurs. We fill this gap by perturbatively incorporating classes of spatially varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity, apply the method to the spherical pore with a simple hemispherical binary distribution of the depletion strength, and obtain bounds for the induced change in the slowest relaxation mode.
Li, Hua; Wu, Tao
2016-10-01
A diffuse-interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg-Landau type of free energy with a double-well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution-gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
Institute of Scientific and Technical Information of China (English)
Chen Bao-ming; Zhang Li-qiang; Wang Bu-xuan
2003-01-01
The influences of Soret effect and Dufour effect on the natural convection and heat and mass transfer for a porous enclosure were investigated by means of the penalty finite element method. Numerical results indicate that the Soret and Dufour effects have significant influences on heat and mass transfer in the presence of large temperature gradient and concentration gradient.
Directory of Open Access Journals (Sweden)
Kishore P.M.
2012-01-01
Full Text Available This investigation is undertaken to study the hydromagnetic flow of a viscous incompressible fluid past an oscillating vertical plate embedded in a porous medium with radiation, viscous dissipation and variable heat and mass diffusion. Governing equations are solved by unconditionally stable explicit finite difference method of DuFort - Frankel’s type for concentration, temperature, vertical velocity field and skin - friction and they are presented graphically for different values of physical parameters involved. It is observed that plate oscillation, variable mass diffusion, radiation, viscous dissipation and porous medium affect the flow pattern significantly.
Ziegler, Ronny; Nielsen, Tim; Koehler, Thomas; Grosenick, Dirk; Steinkellner, Oliver; Hagen, Axel; Macdonald, Rainer; Rinneberg, Herbert
2009-08-20
We report on the nonlinear reconstruction of local absorption and fluorescence contrast in tissuelike scattering media from measured time-domain diffuse reflectance and transmittance of laser as well as laser-excited fluorescence radiation. Measurements were taken at selected source-detector offsets using slablike diffusely scattering and fluorescent phantoms containing fluorescent heterogeneities. Such measurements simulate in vivo data that would be obtained employing a scanning, time-domain fluorescence mammograph, where the breast is gently compressed between two parallel glass plates, and source and detector optical fibers scan synchronously at various source-detector offsets, allowing the recording of laser and fluorescence mammograms. The diffusion equations modeling the propagation of the laser and fluorescence radiation were solved in frequency domain by the finite element method simultaneously for several modulation frequencies using Fourier transformation and preprocessed experimental data. To reconstruct the concentration of the fluorescent contrast agent, the Born approximation including higher-order reconstructed photon densities at the excitation wavelength was used. Axial resolution was determined that can be achieved by various detection schemes. We show that remission measurements increase the depth resolution significantly.
Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin
2017-02-01
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
Directory of Open Access Journals (Sweden)
Victor Kardashov
2002-01-01
Full Text Available This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion. The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients. The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
Weakly nonlinear dynamics in reaction-diffusion systems with Levy flights
Energy Technology Data Exchange (ETDEWEB)
Nec, Y; Nepomnyashchy, A A [Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Golovin, A A [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 (United States)], E-mail: flyby@techunix.technion.ac.il
2008-12-15
Reaction-diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties of the normal complex Ginzburg-Landau equation are generalized for the fractional analogue. In particular, an analogue of the Kuramoto-Sivashinsky equation is derived.
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gra
Institute of Scientific and Technical Information of China (English)
HU Yi-Fan; SUN Jia-Ning; Gidley D.W.
2005-01-01
@@ Two kinds of Cu diffusion barrier layers, sealedfilms and capped fi1ms, on nanoporous low-dielectric-constant filmsare investigated by positronium annihilation lifetime spectroscopy (PALS). We have found that the minimumthickness of Ta to form an effective diffusion barrier is affected by the pore size. The films with large poresrequire thick barrier layers to form effective diffusion barriers. In addition, a possible ultra-thin diffusion barrier,i.e. a plasma-induced densification layer, has also been investigated. The PALS data confirm that a porouslow-dielectric-constant thin film can be shrunk by exposure to plasma. This shrinkage is confined to a surfacelayer of collapsed pores and forms a dense layer. The dense layer tends to behave as Ps (positronium) diffusionbarriers. Indeed, the controlled thin "skin" layer could prevent Cu diffusion into the underlying dielectrics.
Energy Technology Data Exchange (ETDEWEB)
Mainka, J.; Maranzana, G.; Dillet, J.; Didierjean, S.; Lottin, O. [Nancy Univ., Centre national de la recherche scientifique, Vandoeuvre les Nancy (France). Laboratoire d' Energetique et de Mecanique Theorique et Appliquee
2009-07-01
This study provided a preliminary examination of the impact of gas flow rate on the impedance characteristics of a proton exchange membrane fuel cell (PEMFC). The mass transport phenomena within the porous cathode of PEMFCs can be analyzed through electrochemical impedance spectroscopy (EIS). The geometrical description of the electrodes chosen to complete the EIS interpretations is a form of the agglomerate model, where the agglomerates are a mixture of carbon powder and catalyst particles, whereas the electrolyte is assumed to cover only the pore surfaces. Therefore, the reactants access the active catalyst sites by passing successively through the gas diffusion layer (GDL), the pores of the electrode, and finally through a thin electrolyte layer. The fuel cell equivalent electrical circuit is based on a Butler-Volmer formalism that takes into consideration oxygen diffusion in the pores of the GDL and/or the active layer through a Warburg element. The results reveal that in the cathode, the mass transfer limiting layer is most likely the active layer, provided liquid water is present within the pores. Under normal operating conditions, the mass transport resistance of the gas diffusion layer is negligible, as is the fine electrolyte layer coating the agglomerate.
Institute of Scientific and Technical Information of China (English)
YUAN Yi-rang; DU Ning; WANG Wen-qia; HAN Yu-ji; YANG Cheng-shun
2006-01-01
For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.
Institute of Scientific and Technical Information of China (English)
YUAN; Yirang
2006-01-01
For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method,multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
A free boundary problem of a diffusive SIRS model with nonlinear incidence
Cao, Jia-Feng; Li, Wan-Tong; Wang, Jie; Yang, Fei-Ying
2017-04-01
This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole R.
UNCONDITIONAL NONLINEAR EXPONENTIAL STABILITY OF THE MOTIONLESS CONDUCTION-DIFFUSION SOLUTION
Institute of Scientific and Technical Information of China (English)
许兰喜
2000-01-01
Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown that for τ = PC/PT _＜ 1, α = C/R ＞ 1 the motionless state is always stable and for τ＜ 1, α ＜ 1 the sufficient and necessary conditions for stability coincide, where PC, PT, C and R are the Schmidt number, Prandtl number,Rayleigh number for solute and heat, respectively. Moreover, the criteria guarantees the exponential stability.
Some problems on super-diffusions and one class of nonlinear differential equations
Institute of Scientific and Technical Information of China (English)
王永进; 任艳霞
1999-01-01
The historical superprocesses are considered on bounded regular domains with a complete branching form, as a probabilistic argument, the limit property of superprocesses is studied when the domains enlarge to the whole space. As an important application of superprocess, the representation of solutions of involved differential equations is used in term of historical superprocesses. The differential equations including the existence of nonnegative solution, the closeness of solutions and probabilistic representations to the maximal and minimal solutions are discussed, which helps develop the well-known results on nonlinear differential equations.
Ryu, Seungoh; Johnson, David L.
2009-03-01
We consider the diffusion-relaxation dynamics in porous media with partially absorbing boundary conditions. Spectral analysis of Helmholtz equation for the uniform boundary condition has been widely used as a probe of geometry of the medium. The NMR relaxation of the fluid magnetization, for example, is used for a variety of media such as rocks, cement, bones, and cheese. While direct relationship between their geometry and the spectrum forms the basis for such applications, little attention has been paid to the spatial variation of the boundary condition. We report on the way the geometry and such inhomogeneity become intertwined and affect the spectrum. It is often impossible to gauge how severe such interference is in the biological or geophysical experiments. We develop a perturbative theory and numerical techniques and test for cases for which exact solution is obtained.
Directory of Open Access Journals (Sweden)
Yoshua Chávez
2015-01-01
Full Text Available This work is devoted to the study of unbiased diffusion of point-like Brownian particles through channels with radial symmetry of varying cross-section and elliptic shape. The effective one-dimensional reduction is used with distinct forms of a position-dependent diffusion coefficient, D(x, found in literature, to obtain expressions for (I narrow escape times from a single open-ended tube, (II its correspondent effective diffusion coefficient, both as functions of the eccentricity of the tube, ε, where ε = 0 returns the system to a spherical vesicle with two open opposite sides, and (III finally, Lifson-Jackson formula that is used to compute expressions to assess the mean effective diffusion coefficient for a periodic elliptic channel formed by contacting ellipses, also as a function of the eccentricity. Mathematical expressions are presented and contrasted against computational simulations to validate them.
Non-linear diffusion of cosmic rays escaping from supernova remnants I: the effect of neutrals
Nava, Lara; Marcowith, Alexandre; Morlino, Giovanni; Ptuskin, Vladimir S
2016-01-01
Supernova remnants are believed to be the main sources of galactic Cosmic Rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disk volume, where most supernovae explode, and are characterised by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that stream...
Beneš, Michal
2010-01-01
The present paper deals with mathematical models of heat and moisture transport in layered building envelopes. The study of such processes generates a system of two doubly nonlinear evolution partial differential equations with appropriate initial and boundary conditions. The existence of the strong solution in two dimensions on a (short) time interval is proven. The proof rests on regularity results for elliptic transmission problem for composite-like materials.
DEFF Research Database (Denmark)
Johannesson, Björn; Nyman, U.
2010-01-01
A numerical approach for moisture transport in porous materials like concrete is presented. The model considers mass balance equations for the vapour phase and the water phase in the material together with constitutive equations for the mass flows and for the exchange of mass between the two phases....... History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered......-Raphson equilibrium iteration scheme within the time steps. Examples are presented illustrating the performance and potential of the model. Two different types of measurements on moisture content profiles in concrete are used to verify the relevance of the novel proposed model for moisture transport and sorption...
Institute of Scientific and Technical Information of China (English)
YUAN Yi-rang; DU Ning; WANG Wen-qia; CHENG Ai-jie; HAN Yu-ji
2006-01-01
For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems.Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
Lee, Shiu-Hang; Nagataki, Shigehiro
2012-01-01
To better model the efficient production of cosmic rays (CRs) in supernova remnants (SNRs) with the associated coupling between CR production and SNR dynamics, we have generalized an existing cr-hydro-NEI code (i.e., Ellison et al. 2012) to include the following processes: (1) an explicit calculation of the upstream precursor structure including the position dependent flow speed, density, temperature, and magnetic field strength; (2) a momentum and space dependent CR diffusion coefficient; (3) an explicit calculation of magnetic field amplification (MFA); (4) calculation of the maximum CR momentum using the amplified magnetic field; (5) a finite Alfven speed for the particle scattering centers; and (6) the ability to accelerate a superthermal seed population of CRs as well as the ambient thermal plasma. While a great deal of work has been done modeling SNRs, most work has concentrated on either the continuum emission from relativistic electrons or ions, or the thermal emission from the shock heated plasma. Ou...
质子传导膜内受限空间离子扩散过程%Ion diffusion behaviors through porous proton conductive membrane
Institute of Scientific and Technical Information of China (English)
青格乐图; 宋士强; 范永生; 王保国
2013-01-01
To prove the feasibility that nano-scale porous membrane can replace ion exchange membrane used for vanadium redox flow battery (VRB), mass transfer of hydrated-ion in electrolyte solution through a limited space formed by PVDF nano-porous proton conductive membranes was studied. On a self-designed ion diffusion cell, NaCl and water permeation processes were measured under given concentration and hydrodynamic gradient, as well as osmotic pressure. The results obtained can be applied to correlate mass transport behaviors with membrane morphology. The results show that the behavior of ion diffusion through nano-scale limited space is similar to that in a bulk electrolyte solution; apparent diffusion coefficients are independent of ion concentration. In contrast, apparent diffusion coefficients of ion permeation through ion exchange membrane obviously increase with concentration gradient. For a given osmotic pressure, PVDF nano-porous proton conductive membranes have smaller water permeation rate than that of Nafion 117, and negative influence is also much smaller. Self-made PVDF proton conductive membrane can effectively reject VO2+ , providing selectivity over 300 for H+ /VO2+ electrolyte at ambient temperature, which means that it is possible to replace ion exchange membrane in flow battery application.%以具有纳米尺度孔径的聚偏氟乙烯(PVDF)质子传导膜为对象,研究电解质溶液中水合离子在受限空间内的传递行为,证明使用纳米尺度多孔膜代替离子交换膜用于液流电池过程的可行性.利用渗透实验分别研究浓度场、压力场,以及不同渗透压条件下膜中离子扩散和水迁移现象,分析传质行为与膜结构和组成之间的关系.结果表明离子在纳米尺度孔径的PVDF膜中的扩散过程与溶液中类似,表观离子扩散系数不受浓度差推动力的影响；离子交换膜中的表观离子扩散系数随浓度差推动力提高而增加.在渗透压作用下,自制PVDF
The paper proposes three alternative, diffusion-limited mathematical models to account for volatile organic compound (VOC) interactions with indoor sinks, using the linear isotherm model as a reference point. (NOTE: Recent reports by both the U.S. EPA and a study committee of the...
The paper proposes three alternative, diffusion-limited mathematical models to account for volatile organic compound (VOC) interactions with indoor sinks, using the linear isotherm model as a reference point. (NOTE: Recent reports by both the U.S. EPA and a study committee of the...
Directory of Open Access Journals (Sweden)
Isaac Lare Animasaun
2016-06-01
Full Text Available The problem of unsteady convective with thermophoresis, chemical reaction and radiative heat transfer in a micropolar fluid flow past a vertical porous surface moving through binary mixture considering temperature dependent dynamic viscosity and constant vortex viscosity has been investigated theoretically. For proper and correct analysis of fluid flow along vertical surface with a temperature lesser than that of the free stream, Boussinesq approximation and temperature dependent viscosity model were modified and incorporated into the governing equations. The governing equations are converted to systems of ordinary differential equations by applying suitable similarity transformations and solved numerically using fourth-order Runge–Kutta method along with shooting technique. The results of the numerical solution are presented graphically and in tabular forms for different values of parameters. Velocity profile increases with temperature dependent variable fluid viscosity parameter. Increase of suction parameter corresponds to an increase in both temperature and concentration within the thin boundary layer.
Watkins, N. W.; Credgington, D.; Sanchez, R.; Chapman, S. C.
2007-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototpe) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in indices quantifying Earth's auroral currents and in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work [1] in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects. I will discuss how this resolves some contradictions seen in earlier work. Such Noah-Joseph hybrid ("ambivalent" [2]) behaviour is highly topical in physics but is typically studied in the paradigm of the continuous time random walk (CTRW) [2,3] rather than LFSM. I will clarify the physical differences between these two pictures and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm [4] with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time (c.f. [2,3]). Intriguingly the self-similarity exponent extracted from the CTRW differs from that seen in LFSM. In the CTRW it is the ratio of μ to a temporal exponent, in LFSM it is an additive function of them. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold-related to the burst size measure introduced by Takalo and Consolini into solar- terrestrial physics
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Eitzinger Bernhard
2015-09-01
Full Text Available La distribution de la taille des pores détermine la perméabilité d’air et la capacité de diffusion d’un papier à cigarettes, et par conséquent elle a une influence signifiante sur les échanges gazeux à travers le papier à cigarettes, non seulement d’une cigarette allumée, mais aussi d’une cigarette qui s’éteint. Pour le dessin des cigarettes, et notamment des papiers à cigarettes, il faut comprendre comment la distribution de la taille des pores du papier à cigarettes est influencée par la structure et les qualités du papier, ainsi que comment la distribution de la taille des pores influence la perméabilité d’air et la capacité de diffusion.
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Lasseter, T.J.; Karakas, M.
1982-01-01
A simple numerical method has been developed that largely eliminates numerical diffusion errors associated with saturation discontinuities or shocks for two-phase flow in one and two dimensions. The important aspect of the approach is the computation of a variable weighting factor for the interface fractional flow between grid blocks. The approach appears to be generalizable to the multicomponent, multidimensional case including gravity and capilarity. 5 refs.
Ginn, T. R.; Murphy, E. M.; Chilakapati, A.; Seeboonruang, U.
2001-03-01
Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.
Directory of Open Access Journals (Sweden)
Evgeny G. Bugaev
2015-09-01
Full Text Available Geological, geophysical and seismogeological studies are now conducted in a more detail and thus provide for determining seismic sources with higher accuracy, from the first meters to first dozens of meters [Waldhauser, Schaff, 2008]. It is now possible to consider uncertainty ellipses of earthquake hypocenters, that are recorded in the updated Earthquake Catalogue, as surfaces of earthquake focus generators. In our article, it is accepted that a maximum horizontal size of an uncertainty ellipse corresponds to an area of a focus generator, and seismic events are thus classified into two groups, earthquakes with nonstiff and stiff foci. Criteria of such a classification are two limits of elastic strain and brittle strain in case of uniaxial (3⋅10–5 or omnidirectional (10–6 compression. The criteria are established from results of analyses of parameters of seismic dislocations and earthquake foci with regard to studies of surface parameters and deformation parameters of fault zones. It is recommendable that the uniaxial compression criterion shall be applied to zones of interaction between tectonic plates, and the unilateral compression criterion shall be applied to low active (interplate areas. Sample cases demonstrate the use of data sets on nonstiff and stiff foci for separate evaluation of magnitude reoccurrence curves, analyses of structured and dissipated seismicity, review of the physical nature of nonlinearity of recurrence curves and conditions of preparation of strong earthquakes. Changes of parameters of the recurrence curves with changes of data collection square areas are considered. Reviewed are changes of parameters of the recurrence curves during preparation for the Japan major earthquake of 11 March 2011 prior to and after the major shock. It is emphasized that it is important to conduct even more detailed geological and geophysical studies and to improve precision and sensitivity of local seismological monitoring networks
Suresh, P V; Jayanti, Sreenivas
2016-10-01
Adoption of hydrogen economy by means of using hydrogen fuel cells is one possible solution for energy crisis and climate change issues. Polymer electrolyte membrane (PEM) fuel cell, which is an important type of fuel cells, suffers from the problem of water management. Cross-flow is induced in some flow field designs to enhance the water removal. The presence of cross-flow in the serpentine and interdigitated flow fields makes them more effective in proper distribution of the reactants on the reaction layer and evacuation of water from the reaction layer than diffusion-based conventional parallel flow fields. However, too much of cross-flow leads to flow maldistribution in the channels, higher pressure drop, and membrane dehydration. In this study, an attempt has been made to quantify the amount of cross-flow required for effective distribution of reactants and removal of water in the gas diffusion layer. Unit cells containing two adjacent channels with gas diffusion layer (GDL) and catalyst layer at the bottom have been considered for the parallel, interdigitated, and serpentine flow patterns. Computational fluid dynamics-based simulations are carried out to study the reactant transport in under-the-rib area with cross-flow in the GDL. A new criterion based on the Peclet number is presented as a quantitative measure of cross-flow in the GDL. The study shows that a cross-flow Peclet number of the order of 2 is required for effective removal of water from the GDL. Estimates show that this much of cross-flow is not usually produced in the U-bends of Serpentine flow fields, making these areas prone to flooding.
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Guin, J.A.
1998-12-31
The overall objective of this project was to investigate the diffusion of coal and petroleum asphaltenes in the pores of a supported catalyst. Experimental measurements together with mathematical modeling was conducted to determine how the diffusion rate of asphaltenes, as well as some model compounds, depended on molecule sizes and shapes. The process of diffusion in the pores of a porous medium may occur by several mechanisms. Hindered diffusion occurs when the sizes of the diffusion molecules are comparable to those of the porous pores through which they are diffusing. Hindered diffusion phenomena have been widely observed in catalytic hydrotreatment of asphaltenes, heavy oils, coal derived liquids, etc. Pore diffusion limitations can be greater in spent catalysts due to the deposition of coke and metals in the pores. In this work, a general mathematical model was developed for the hindered diffusion-adsorption of solute in a solvent onto porous materials, e. g. catalysts, from a surrounding bath. This diffusion model incorporated the nonuniformities of pore structures in the porous media. A numerical method called the Method of Lines was used to solve the nonlinear partial differential equations resulting from the mathematical model. The accuracy of the numerical solution was verified by both a mass balance in the diffusion system and satisfactory agreement with known solutions in several special cases.
Petra, N.; Alexanderian, A.; Stadler, G.; Ghattas, O.
2015-12-01
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer a parameter field (e.g., the log permeability field in a porous medium flow model problem) from synthetic observations at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. Due to the infinite-dimensional character of the parameter field, we seek an optimization method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and the sensor dimension. To facilitate this goal, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the resulting covariance operator to define the OED objective function. We use randomized trace estimation to compute the trace of this covariance operator. The resulting OED problem includes as constraints the system of PDEs characterizing the MAP point, and the PDEs describing the action of the covariance (of the Gaussian approximation to the posterior) to vectors. We control the sparsity of the sensor configurations using sparsifying penalty functions, and solve the resulting penalized bilevel optimization problem via an interior-point quasi-Newton method, where gradient information is computed via adjoints. We elaborate our OED method for the problem of determining the optimal sensor configuration to best infer the log permeability field in a porous medium flow problem. Numerical results show that the number of PDE
Deridder, Sander; Desmet, Gert
2011-01-07
The results of a numerical simulation study of the diffusion and retention in fully porous spheres and cylinders are compared with some of the high order accuracy analytical solutions for the effective diffusion coefficient that have been derived from the effective medium theory (EMT) theory in part I of the present study. A variety of different ordered (spheres and cylinders) and disordered (cylinders) packings arrangements has been considered. The agreement between simulations and theory was always excellent, lying within the (very tight) accuracy limits of the simulations over the full range of retention factor and diffusion constant values that is practically relevant for most LC applications. Subsequently filling up the spheres and cylinders with a central solid core, while keeping the same packing geometry and the same mobile phase (same thermodynamic retention equilibrium), it was found that the core induces an additional obstruction which reduces the effective intra-particle diffusion coefficient exactly with a factor γ(part)=2/(2+ρ³) for spherical particles and γ(part)=1/(1+ρ²) for cylinders (ρ is the ratio of the core to the particle diameter, ρ=d(core)/d(part)). These expressions hold independently of the packing geometry, the value of the diffusion coefficients and the equilibrium constant or the size of the core. The expressions also imply that, if considering equal mobile phase conditions, the presence of the solid core will never reduce the particle contribution to the B-term band broadening with more than 33% (50% in case of cylindrical pillars). Copyright © 2010 Elsevier B.V. All rights reserved.
Hallbauer-Zadorozhnaya, Valeriya; Santarato, Giovanni; Abu Zeid, Nasser
2015-08-01
In this paper, two separate but related goals are tackled. The first one is to demonstrate that in some saturated rock textures the non-linear behaviour of induced polarization (IP) and the violation of Ohm's law not only are real phenomena, but they can also be satisfactorily predicted by a suitable physical-mathematical model, which is our second goal. This model is based on Fick's second law. As the model links the specific dependence of resistivity and chargeability of a laboratory sample to the injected current and this in turn to its pore size distribution, it is able to predict pore size distribution from laboratory measurements, in good agreement with mercury injection capillary pressure test results. This fact opens up the possibility for hydrogeophysical applications on a macro scale. Mathematical modelling shows that the chargeability acquired in the field under normal conditions, that is at low current, will always be very small and approximately proportional to the applied current. A suitable field test site for demonstrating the possible reliance of both resistivity and chargeability on current was selected and a specific measuring strategy was established. Two data sets were acquired using different injected current strengths, while keeping the charging time constant. Observed variations of resistivity and chargeability are in agreement with those predicted by the mathematical model. These field test data should however be considered preliminary. If confirmed by further evidence, these facts may lead to changing the procedure of acquiring field measurements in future, and perhaps may encourage the design and building of a new specific geo-resistivity meter. This paper also shows that the well-known Marshall and Madden's equations based on Fick's law cannot be solved without specific boundary conditions.
Haspot, Boris
2016-06-01
We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.
Lin, Zhi; Zhang, Qinghai
2017-09-01
We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.
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Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
Arifuzzaman, S. M.; Rana, B. M. Jewel; Ahmed, R.; Ahmmed, S. F.
2017-06-01
High order chemically reactive micropolar fluid flow through an infinite vertical porous medium with thermal diffusion, mass diffusion, MHD, thermal radiation and heat sink has been studied. A flow model is established by employing the well-known boundary layer approximations. In order to obtain non-dimensional system of equations, a similarity transformation is applied on the flow model. The stability and convergence analysis have been analyzed. The obtained non-dimensional equations have been solved by explicit finite difference method. The effects of various parameters entering into the problem on velocity, angular velocity, temperature and concentration are shown graphically.
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Breton, J.P. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1962-06-15
The present-day theories of separation by gaseous diffusion (Present and de BETHUNE, KYNCH, BOSANQUET) are all based on the same model in which the pores are cylindrical capillaries. In the theory presented here, we substitute for this model that of a disordered and isotropic bed of identical spheres, which describes more accurately most of the porous media. We take as our starting point DERIAGUINE and BAKANOV'S permeability theory, which expresses the flow of a simple gas in such a bed when the latter is of high porosity. We first generalise this theory in the case of medium and low porosities; then, we go on to a mixture of two gases, from which we deduce our separation theory. Finally we compare our results with those of Present and de BETHUNE. (author) [French] Les theories actuelles de la separation par diffusion gazeuse (PRESENT et de BETHUNE, KYNCH, BOSANQUET) reposent toutes sur le modele des pores capillaires cylindriques. Dans la theorie presentee ici, nous substituons a ce modele celui d'un empilement desordonne et isotropes de spheres identiques, qui decrit plus correctement la plupart des milieux poreux. Nous partons de la theorie de la permeabilite de DERIAGUINE et BAKANOV, qui exprime l'ecoulement d'un gaz simple dans un tel empilement dans le cas ou la porosite en est elevee. Nous generalisons d'abord cette theorie du cas des porosites moyennes ou faibles, puis, passant a un melange de deux gaz, nous en deduisons une theorie de la separation. Pour terminer, nous comparons nos resultats a ceux de PRESENT et de BETHUNE. (auteur)
Monga, O.; Garnier, P.; Pot, V.; Coucheney, E.; Nunan, N.; Otten, W.; Chenu, C.
2013-10-01
This paper deals with the simulation of microbial degradation in soil within pore space at microscopic scale. Pore space was described using sphere network coming from a geometrical modeling algorithm. The biological model was improved regarding previous work in order to include transformation of dissolved organic compounds and diffusion processes. Our model was tested using experimental results of a simple substrate decomposition (Fructose) within a simple media (the sand). Diverse microbial communities were inoculated. Separated incubations in microcosms were carried out using 5 different bacterial communities at 2 different water potentials of -10 cm and -100 cm of water. We calibrated the biological parameters by means of experimental data obtained at high water content and we tested the model without any parameters change at low water content. Same as for experimental data, our simulation results showed the decrease in water content involved the decrease of mineralisation. The model was able to simulate the decrease of connectivity between substrate and microorganism due the decrease of water content.
Monga, O.; Garnier, P.; Pot, V.; Coucheney, E.; Nunan, N.; Otten, W.; Chenu, C.
2014-04-01
This paper deals with the simulation of microbial degradation of organic matter in soil within the pore space at a microscopic scale. Pore space was analysed with micro-computed tomography and described using a sphere network coming from a geometrical modelling algorithm. The biological model was improved regarding previous work in order to include the transformation of dissolved organic compounds and diffusion processes. We tested our model using experimental results of a simple substrate decomposition experiment (fructose) within a simple medium (sand) in the presence of different bacterial strains. Separate incubations were carried out in microcosms using five different bacterial communities at two different water potentials of -10 and -100 cm of water. We calibrated the biological parameters by means of experimental data obtained at high water content, and we tested the model without changing any parameters at low water content. Same as for the experimental data, our simulation results showed that the decrease in water content caused a decrease of mineralization rate. The model was able to simulate the decrease of connectivity between substrate and microorganism due the decrease of water content.
Directory of Open Access Journals (Sweden)
O. Monga
2013-10-01
Full Text Available This paper deals with the simulation of microbial degradation in soil within pore space at microscopic scale. Pore space was described using sphere network coming from a geometrical modeling algorithm. The biological model was improved regarding previous work in order to include transformation of dissolved organic compounds and diffusion processes. Our model was tested using experimental results of a simple substrate decomposition (Fructose within a simple media (the sand. Diverse microbial communities were inoculated. Separated incubations in microcosms were carried out using 5 different bacterial communities at 2 different water potentials of −10 cm and −100 cm of water. We calibrated the biological parameters by means of experimental data obtained at high water content and we tested the model without any parameters change at low water content. Same as for experimental data, our simulation results showed the decrease in water content involved the decrease of mineralisation. The model was able to simulate the decrease of connectivity between substrate and microorganism due the decrease of water content.
Nonlinear Diffusion Equations.
1985-06-01
Rabies will inevitably return t Bri so we cons id, red a domain with the shape of Britain :in , a single- rbiJ fox on the coastline. Travelling waves w...9. A. Friedman and J.B. McLeod, Strict inequality in iso- perimetric inequalities, Proc. Roy. Soc. Edin., to 6 appear. 10. A. Friedman and J.B
Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations
Jakobsen, Simone Cifani And Espen R
2010-01-01
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection diffusion equations, and some fractional Porous medium equations. In this paper we define weak entropy solutions for this class of equations and prove well-posedness under weak regularity assumptions on the solutions, e.g. uniqueness is obtained in the class of bounded integrable functions. Then we introduce a monotone conservative numerical scheme and prove convergence toward an Entropy solution in the class of bounded integrable functions of bounded variation. We then extend the well-posedness results to non-local terms based on general L\\'evy type operators, and establish some connections to fully non-linear HJB equations. Finally, we present some numerical experiments to give the reader an idea about the qualitative behavior of solutions of these equations.
Fullerene-doped porous glasses
Joshi, M. P.; Kukreja, L. M.; Rustagi, K. C.
We report the doping of C60 in porous glass by diffusion in solution phase at room temperature. The presence of C60 in the doped porous glass was confirmed spectroscopically. We also report the changes in optical absorption spectrum and intensity-dependent transmission of 30 ns laser pulses at 527 nm in these materials.
Fullerene-doped porous glasses
Energy Technology Data Exchange (ETDEWEB)
Joshi, M.P. [Center for Adv. Technol., Indore (India). Nonlinear Optics Group; Kukreja, L.M. [Center for Adv. Technol., Indore (India). Nonlinear Optics Group; Rustagi, K.C. [Center for Adv. Technol., Indore (India). Nonlinear Optics Group
1997-07-01
We report the doping of C{sub 60} in porous glass by diffusion in solution phase at room temperature. The presence of C{sub 60} in the doped porous glass was confirmed spectroscopically. We also report the changes in optical absorption spectrum and intensity-dependent transmission of 30 ns laser pulses at 527 nm in these materials. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Vu, T.H.
2009-10-15
This thesis documents the relationship between the porous microstructure of cement based materials and theirs gaseous diffusivity properties relative to the aqueous phase location and the global saturation level of the material. The materials studied are cement pastes and mortars. To meet the thesis objective, the materials are characterized in detail by means of several experimental methods: mercury intrusion porosimetry, water porosimetry, thermo-poro-metry, nitrogen sorption and water desorption. In addition, diffusion tests realized on materials maintained in controlled humidity chambers allow obtaining the effective hydrogen diffusivity as function of the microstructure and the saturation state of material with a gas chromatography. The experimental results are then used as a data base that is compared to a modeling approach. The model developed consists of a combination of ordinary diffusion (Fick regime) and Knudsen diffusion of hydrogen. The model also accounts for the effects of the liquid curtains, the impact of tortuosity on gas diffusion, and the saturation level of the porous system. (author)
Directory of Open Access Journals (Sweden)
Ruofeng Rao
2013-01-01
Full Text Available The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω, Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Hydrophobic, Porous Battery Boxes
Bragg, Bobby J.; Casey, John E., Jr.
1995-01-01
Boxes made of porous, hydrophobic polymers developed to contain aqueous potassium hydroxide electrolyte solutions of zinc/air batteries while allowing air to diffuse in as needed for operation. Used on other types of batteries for in-cabin use in which electrolytes aqueous and from which gases generated during operation must be vented without allowing electrolytes to leak out.
Voltammetry at porous electrodes: A theoretical study
Barnes, Edward O; Li, Peilin; Compton, Richard G
2014-01-01
Theory is presented to simulate both chronoamperometry and cyclic voltammetry at porous electrodes fabricated by means of electro-deposition around spherical templates. A theoretical method to extract heterogeneous rate constants for quasireversible and irreversible systems is proposed by the approximation of decoupling of the diffusion within the porous electrode and of bulk diffusion to the electrode surface.
Institute of Scientific and Technical Information of China (English)
李岚溪; 胥海伦; 刘东; 叶会文
2016-01-01
Due to the losing efficacy of the dust-cleaning at the top of the cartridge filters and the overlarge pressure at the bottom, this paper proposes to interfere the dust-cleaning fluid flow in the cartridge filters with gas diffusers based on porous media. The influence of the inlet-pressure and the diffusers based on porous media on these characteristics is simulated. Results are as follows. At the same inlet-pressure of the nozzles, the dust-cleaning performance shows the best when the porosity of the porous media is 0.87. At the same porosity of the porous media, the dust-cleaning performance shows the best when the inlet-pressure of the nozzles is 0.5MPa.%现有滤筒除尘器清灰存在滤筒顶部失效，底部压力太大的缺点，提出采用多孔介质气体散射器进行干扰滤筒除尘器内清灰的流场，并采用数值方法进行计算，结果表明：喷嘴进口压力相同情况下，多孔介质气流散射器孔隙率为0.87时清灰性能最好；多孔介质气流散射器孔隙率相同情况下，喷嘴进口压力为0.5MPa时清灰性能最好。
Surface second-harmonic generation in Sr0.6Ba0.4NbO3 with a nonlinear diffusion mechanism
Zhang, T. H.; Yang, J.; Kang, H. Z.; Feng, L.; Xu, J. J.; Zhang, C. P.; Ren, X. K.; Wang, B. H.; Lu, Y. Z.; Jia, F.; Shao, W. W.
2006-04-01
Surface second-harmonic generation excited by photorefractive surface electromagnetic wave with a diffusion mechanism of nonlinearity has been observed at the surface of the negative c axis of a Sr0.6Ba0.4NbO3 (SBN:60) experimentally. The second-harmonic 532nm wavelength light is generated by 1064nm laser in a passive guiding manner in the experiment, for the wavelength of the fundamental beam is insensitive to the SBN crystal. The transfer efficiency of surface second-harmonic generation is 1%/W.
Directory of Open Access Journals (Sweden)
Jordan Hristov
2016-01-01
Full Text Available The article addresses a reappraisal of the famous Ward–Tordai equation describing the equilibrium of surfactants at air/liquid interfaces under diffusion control. The new derivation is entirely developed in the light of fractional calculus. The unified approach demonstrates that this equation can be clearly reformulated as a nonlinear ordinary time-fractional equation of order 1/2. The work formulates versions with different isotherms. A simple solution of the case with the Henry’s isotherm and a discussion of a Cauchy problem involving the Freundlich isotherm are provided.
Das, T.; Panda, M.; Panda, S.; Panda, B. K.
2017-05-01
In this work, the variation of optical properties in the AlGaN/GaN quantum well after thermal annealing is studied. The potential profile change of the quantum well resulting from the interdiffusion of Ga and Al atoms across the interface of the well and the barrier during the thermal treatments is assumed to follow Fick's law. The results show that the thermal annealing can induce an increase of the optical susceptibilities in the AlGaN/GaN quantum well. However the third-order nonlinear optical susceptibilities are red shifted with increasing in diffusion lengths.
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-01-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population. PMID:28195135
Johnston, Stuart T.; Baker, Ruth E.; McElwain, D. L. Sean; Simpson, Matthew J.
2017-02-01
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.
Institute of Scientific and Technical Information of China (English)
Xiu Hui YANG; Fu Cai LI; Chun Hong XIE
2005-01-01
In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions:({ut-α(u,v)△u=g(u,v),vt-b(u,v)△v=h(u,v),(e)u/(e)(g)=d(u,v),(e)u/(e)(g)=f(u,v),)Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.
ZnO/porous-Si and TiO{sub 2}/porous-Si nanocomposite nanopillars
Energy Technology Data Exchange (ETDEWEB)
Wang, Dong, E-mail: dong.wang@tu-ilmenau.de; Yan, Yong; Schaaf, Peter [Chair Materials for Electronics, Institute of Materials Engineering and Institute of Micro- and Nanotechnologies MacroNano, TU Ilmenau, Gustav-Kirchhoff-Str. 5, 98693 Ilmenau (Germany); Sharp, Thomas [Oxford Instruments Plasma Technology Ltd., Yatton, Bristol BS49 4AP (United Kingdom); Schönherr, Sven; Ronning, Carsten [Institute for Solid State Physics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena (Germany); Ji, Ran [SUSS MicroTec Lithography GmbH, Schleissheimer Str. 90, 85748 Garching (Germany)
2015-01-01
Porous Si nanopillar arrays are used as templates for atomic layer deposition of ZnO and TiO{sub 2}, and thus, ZnO/porous-Si and TiO{sub 2}/porous-Si nanocomposite nanopillars are fabricated. The diffusion of the precursor molecules into the inside of the porous structure occurs via Knudsen diffusion and is strongly limited by the small pore size. The luminescence of the ZnO/porous-Si nanocomposite nanopillars is also investigated, and the optical emission can be changed and even quenched after a strong plasma treatment. Such nanocomposite nanopillars are interesting for photocatalysis and sensors.
van Milligen, B Ph
2014-01-01
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained with a variety of models. {We present and use a simplified numerical model which does not contain any turbulence, Taylor dispersion, or fractality. With it, we show that the non-linearity in the intermediate regime nevertheless occurs. Furthermore,} we show that that the intermediate regime can be regarded as a phase transition between random, diffusive transport at low flow velocity and ordered transport controlled by the geometry of the pore space at high flow velocities. This phase transition explains the first-order behavior in the intermediate regime. A new quantifier, the ratio of the amount of solute in dominantly advective versus dominantly diffusive pore channels, plays the role of `order parameter' of this phase transition. Taylor dispersion, often invoked to exp...
Energy Technology Data Exchange (ETDEWEB)
Tsuo, Y.S.; Menna, P.; Pitts, J.R. [National Renewable Energy Lab., Golden, CO (United States)] [and others
1996-05-01
The authors have studied a novel extrinsic gettering method that uses the large surface areas produced by a porous-silicon etch as gettering sites. The annealing step of the gettering used a high-flux solar furnace. They found that a high density of photons during annealing enhanced the impurity diffusion to the gettering sites. The authors used metallurgical-grade Si (MG-Si) prepared by directional solidification casing as the starting material. They propose to use porous-silicon-gettered MG-Si as a low-cost epitaxial substrate for polycrystalline silicon thin-film growth.
Studies of Tracer Dispersion and Fluid Flow in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Rage, T.
1996-12-31
This doctoral thesis explores the connection between the topology of a porous medium and its macroscopic transport properties and is based on computerized simulation. In porous media, both diffusion and convection contribute to the dispersion of a tracer and their combined effect is emphasized. The governing equations are solved numerically, using finite differences and Monte Carlo technique. The influence of finite Reynolds number on the outcome of echo-experiments is discussed. Comparing experiments and simulations it is found that nonlinear inertial forces lead to a visible deformation of a returned tracer at surprisingly small Reynolds numbers. In a study of tracer dispersion and fluid flow in periodic arrays of discs it is demonstrated that the mechanisms of mechanical dispersion in periodic media and in natural (non-periodic) porous media are essentially different. Measurements of the percolation probability distribution of a sandstone sample is presented. Local porosity theory predicts that this simple geometric function of a porous medium is of dominant importance for its macroscopic transport properties. It is demonstrated that many aspects of transport through fractures can be studied by using simple but realistic models and readily available computer resources. An example may be the transport of hydrocarbon fluids from the source rock to a reservoir. 165 refs., 44 figs., 1 table
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Directory of Open Access Journals (Sweden)
Toshihiro Isobe
2014-09-01
Full Text Available Epoxy/porous SiO2 composites were prepared with the pore surface modified using various silane coupling agents. The N2 adsorption and desorption isotherm shows that the porous SiO2 used for raw materials has sufficiently high pore volume. Their pore sizes, calculated using Barrett–Joyner–Halenda method as less than 20 nm was markedly smaller than the mean free path of the gases used for this study. The respective degrees of gas selectivity CO2/N2, CH4/N2, and O2/N2 were measured. Results show that the epoxy/porous SiO2 composite surface-modified by APTES only exhibits CO2/N2 gas selectivity at a lower pressure drop. It originates in the affinity between amino group of the APTES and CO2 gas. The epoxy/porous SiO2 composite treated by APTES also shows gas separation capability. The 80% N2/20% CO2 mix gas was converted into 68.2% N2/31.8% CO2 gas after gas separation tests at 25 °C. The gas separation capability was maintained at high temperatures. The 80% N2/20% CO2 mix gas was converted into 70.8% N2/29.2% CO2 gas at 100 °C.
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
Gordon, Peter V
2012-01-01
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source.
Denisyuk, Yu. N.; Andreoni, A.; Bondani, M.; Potenza, M. A. S.
2000-09-01
Results of experiments on recording three-dimensional holographic images of extended diffuse objects using an SHG hologram generating the second harmonic are presented. In this case, the object image is formed by the second-harmonic radiation whose wavelength is smaller than the wavelength of object and reference waves recorded on a hologram by a factor of two. Elements of the theory of an SHG hologram are considered. A holographic image of a transparency object illuminated with diffuse light is obtained. It is shown that the resolving power of this image is close to the limit determined by diffraction effects. An experiment on defocusing the reconstructed image showed that it was localized in one spatial plane and, therefore, was three-dimensional.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if \\emph{the absorption is small enough}, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.
Boundary control of fluid flow through porous media
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar
2010-01-01
The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design....
Energy Technology Data Exchange (ETDEWEB)
Samet Y. Kadioglu; Robert R. Nourgaliev; Vincent A. Mousseau
2008-03-01
We perform a comparative study for the harmonic versus arithmetic averaging of the heat conduction coefficient when solving non-linear heat transfer problems. In literature, the harmonic average is the method of choice, because it is widely believed that the harmonic average is more accurate model. However, our analysis reveals that this is not necessarily true. For instance, we show a case in which the harmonic average is less accurate when a coarser mesh is used. More importantly, we demonstrated that if the boundary layers are finely resolved, then the harmonic and arithmetic averaging techniques are identical in the truncation error sense. Our analysis further reveals that the accuracy of these two techniques depends on how the physical problem is modeled.
Energy Technology Data Exchange (ETDEWEB)
Le Meur, G.; Rochais, D.; Domingues, G. [CEA Centre d' Etudes du Ripault (SRCC/LMC), 37 - Tours (France); Basini, V. [CEA Cadarache (DEC/SPUA/LMPC), 13 - Saint-Paul-lez-Durance (France). Dept. d' Etudes des Combustibles
2006-07-01
This work presents the results of a measurements campaign of the thermal diffusivity of the porous pyrocarbon layer (90 {mu}m thickness) of a HTR (high temperature reactor) fuel particulate. The photo-reflectance microscopy technique is used and allows to characterize the microscopic skeleton of the layer. The effective thermal diffusivity of the layer is estimated using a numerical homogenization technique which integrates the properties of gases confined inside the porosities. (J.S.)
DEFF Research Database (Denmark)
Johannesson, Björn
2010-01-01
There exist, mainly, two different continuum approaches to calculate transient multi species ionic diffusion. One of them is based on explicitly assuming a zero current in the diffusing mixture together with an introduction of a streaming electrical potential in the constitutive equations...... are compared with existing results from the solutions of the Gauss’ law method. For the studied case the calculated concentrations of the ionic species, using the two different methods, differed very little....
Snaar, J.E.M.
2002-01-01
The structure and dynamics of water diffusion and -transport at a microscale in heterogeneous porous media have been ^{}investigated using various ^{1}H NMR techniques. In particular in biological porous media the dynamics are usually very complex
Energy Technology Data Exchange (ETDEWEB)
Telles, Rubens S.
1990-12-31
This work discusses the problem of hydrodynamic dispersion on natural convection in porous medium near impermeable surfaces. The study considers the convection caused by density variation due to temperature and concentration gradients combination. The parametrization of the phenomenon is obtained through scale analysis. It is also presented four possible situations according to the intensity of dispersion term. In search of similarity solutions the similarity variables and parameters associated to dispersion are found through scale analysis. The Runge-Kutta algorithm and the `shooting` method are used to solve the equations resulting from the similarity transformations. Several cases are solved covering an extensive range of the governing parameters. 22 refs., 43 figs., 13 tabs.
Institute of Scientific and Technical Information of China (English)
Chang Jiang ZHU; Zhi Yong ZHANG; Hui YIN
2006-01-01
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:{ψt = -(1 - α)ψ - θx + αψxx, (E)θt = -(1 - α)θ + vψx + (χθ)x + αθxx,with initial data(ψ,θ)(x, 0) = (ψ0(x),θ0(x)) → (χ±,θ±) as x →±∞, (Ⅰ)where α and v are positive constants such that α＜ 1, v ＜ 4α(1 - α). Under the assumption that|ψ+ - ψ-| + |θ+ - θ-| is sufficiently small, we show the global existence of the solutions to Cauchy problem (E) and (I) if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method.
Salusti, E; Garra, R
2016-01-01
We here analyze the propagation of transients of fluid-rock temperature and pressure through a thin boundary layer, where a steady trend is present, between two adjacent homogeneous rocks. We focus on the effect of convection on transients crossing such thin layer. In comparison with early models where this boundary was assumed a sharp mathematical plane separating the two rocks, here we show a realistic analysis of such boundary layer that implies a novel nonlinear model. Its solutions describe large amplitude, quick and sharp transients characterized by a novel drift and variations of the signal amplitude, leading to a nonlinear wave propagation. Possible applications are in volcanic, hydrologic, hydrothermal systems as well as for deep oil drilling. In addition, this formalism could easily be generalized for the case of a signal arriving in a rock characterized by a steady trend of pressure and/or temperature. These effects, being proportional to the initial conditions, can also give velocity variations no...
Banerjee, Tanmoy; Biswas, Debabrata
2013-12-01
We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.
Gărăjeu, M.; Suquet, P.
2007-04-01
Composite materials often exhibit local fluctuations in the volume fraction of their individual constituents. This paper studies the influence of such small fluctuations on the effective properties of composites. A general asymptotic expansion of these properties in terms of powers of the amplitude of the fluctuations is given first. Then, this general result is applied to porous materials. As is well-known, the effective yield surface of ductile voided materials is accurately described by Gurson's criterion. Suitable extensions for viscoplastic solids have also been proposed. The question addressed in the present study pertains to nonuniform distributions of voids in a typical volume element or in other words to the presence of matrix-rich and pore-rich zones in the material. It is shown numerically and analytically that such deviations from a uniform distribution result in a weakening of the macroscopic carrying capacity of the material.
Nonequilibrium Thermodynamics of Porous Electrodes
Ferguson, Todd R
2012-01-01
We review classical porous electrode theory and extend it to non-ideal active materials, including those capable of phase transformations. Using principles of non-equilibrium thermodynamics, we relate the cell voltage, ionic fluxes, and Faradaic charge-transfer kinetics to the variational electrochemical potentials of ions and electrons. The Butler-Volmer exchange current is consistently expressed in terms of the activities of the reduced, oxidized and transition states, and the activation overpotential is defined relative to the local Nernst potential. We also apply mathematical bounds on effective diffusivity to estimate porosity and tortuosity corrections. The theory is illustrated for a Li-ion battery with active solid particles described by a Cahn-Hilliard phase-field model. Depending on the applied current and porous electrode properties, the dynamics can be limited by electrolyte transport, solid diffusion and phase separation, or intercalation kinetics. In phase-separating porous electrodes, the model...
El-Amin, Mohamed
2011-05-14
In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.
EL-Dabe, N. T.; Attia, H. A.; Essawy, M. A. I.; Ramadan, A. A.; Abdel-Hamid, A. H.
2016-11-01
The steady MHD axisymmetric flow of an incompressible viscous electrically conducting nanofluid impinging on a permeable plate is investigated with heat and mass transfer. An external uniform magnetic field as well as a uniform inflow, in the presence of either suction or injection, are applied normal to the plate. The effects of heat (generation/absorption) and chemical reaction have been accentuated. This study indicates the incorporated influence of both the thermophoresis phenomenon and the Brownian behavior. Numerical solutions for the governing non-linear momentum, energy and nanoparticle equations have been obtained. The rates of heat and mass transfer are presented and discussed.
Institute of Scientific and Technical Information of China (English)
A.M.Abd-Alla; S.M.Abo-Dahab; H.D.El-Shahrany
2013-01-01
In this paper,the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically.The material is represented by the constitutive equations for a second-order fluid.Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented.The analytical expressions for the pressure gradient,pressure rise,friction force,stream function,shear stress,and velocity are obtained in the physical domain.The effects of the non-dimensional wave amplitude,porosity,magnetic field,rotation,and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically.Numerical results are given and illustrated graphically in each case considered.Comparison was made with the results obtained in the presence and absence of rotation,magnetic field,and porosity.The results indicate that the effects of the non-dimensional wave amplitude,porosity,magnetic field,rotation,and the dimensionless time-mean flow are very pronounced in the phenomena.
Energy Technology Data Exchange (ETDEWEB)
Karniadakis, George Em [Brown University
2014-03-11
The main objective of this project is to develop new computational tools for uncertainty quantifica- tion (UQ) of systems governed by stochastic partial differential equations (SPDEs) with applications to advection-diffusion-reaction systems. We pursue two complementary approaches: (1) generalized polynomial chaos and its extensions and (2) a new theory on deriving PDF equations for systems subject to color noise. The focus of the current work is on high-dimensional systems involving tens or hundreds of uncertain parameters.
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
Towards a non-linear theory for induced seismicity in shales
Salusti, Ettore; Droghei, Riccardo
2014-05-01
We here analyze the pore transmission of fluid pressure pand solute density ρ in porous rocks, within the framework of the Biot theory of poroelasticity extended to include physico-chemical interactions. In more details we here analyze the effect of a strong external stress on the non-linear evolution of p and ρ in a porous rock. We here focus on the consequent deformation of the rock pores, relative to a non-linear Hooke equation among strain, linear/quadratic pressure and osmosis in 1-D. We in particular analyze cases with a large pressure, but minor than the 'rupture point'. All this gives relations similar to those discussed by Shapiro et al. (2013), which assume a pressure dependent permeability. Thus we analyze the external stress necessary to originate quick non-linear transients of combined fluid pressure and solute density in a porous matrix, which perturb in a mild (i.e. a linear diffusive phenomenon) or a more dramatic non-linear way (Burgers solitons) the rock structure. All this gives a novel, more realistic insight about the rock evolution, fracturing and micro-earthquakes under a large external stress.
Institute of Scientific and Technical Information of China (English)
徐琛梅
2008-01-01
In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.
Thermal and optical properties of porous silicon
Directory of Open Access Journals (Sweden)
Silva A. Ferreira da
2001-01-01
Full Text Available Thermal diffusivity and optical absorption have been investigated for porous silicon, at room temperature, using photoacoustic spectroscopy. The experimental results obtained conform well with the existing studies recently published. The value obtained for thermal diffusivity is 0.045 ± 0.002 cm²/s.The absorption onsets show energy structures, differing from the ordinary semiconductor of bulk type.
Luminescence decay of porous silicon
Chen, X.; Uttamchandani, D.; Sander, D.; O'Donnell, K. P.
1993-04-01
The luminescence decay pattern of porous silicon samples prepared by electrochemical etching is characterised experimentally by a non-exponential profile, a strong dependence on temperature and an absence of spectral diffusion. We describe this luminescence as carrier-dopping-assisted recombination. Following the correlation function approach to non-dispersive transport developed by Scher and co-workers [Physics Today 41 (1991) 26], we suggest a simple derivation of analytical functions which accurately describes the anomalous luminescence decay of porous silicon, and show that this model includes exponential and Kohlrausch [Pogg. Ann. Phys. 119 (1863) 352] (stretched-exponential) relaxations as special cases.
Flow of polymer fluids through porous media
Zami-Pierre, Frédéric; Davit, Yohan; Loubens, Romain de; Quintard, Michel
2016-01-01
Non-Newtonian fluids are extensively used in enhanced oil recovery. However, understanding the flow of such fluids in complex porous media remains a challenging problem. In the presented study, we use computational fluid dynamics to investigate the creeping flow of a particular non-Newtonian fluid through porous media, namely a power-law fluid with a newtonian behavior below a critical shear rate. We show that the nonlinear effects induced by the rheology only weakly impact the topological st...
Silicon infrared diffuser for wireless communication
Massera, Ettore; Rea, Ilaria; Nasti, Ivana; Maddalena, Pasqualino; di Francia, Girolamo
2006-09-01
We show what we believe to be a novel way to use silicon in infrared radio communication as a suitable material for the realization of optical diffusers in the range of 850-1600 nm. A crystalline silicon wafer is made porous by means of electrochemical etching. The porous silicon produced is optically characterized, and measurements report a high reflectance in the band of interest. We also study the angular distribution of diffused radiation by the porous silicon surface at different angles of incident radiation. Measurements show that radiation diffuses in a quasi-Lambertian manner, confirming the good performance of this material as an incident radiation diffuser.
A non-Linear transport model for determining shale rock characteristics
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
Indian Academy of Sciences (India)
Satish M Manocha
2003-02-01
Carbon in dense as well as porous solid form is used in a variety of applications. Activated porous carbons are made through pyrolysis and activation of carbonaceous natural as well as synthetic precursors. Pyrolysed woods replicate the structure of original wood but as such possess very low surface areas and poor adsorption capacities. On activation, these exhibit increased adsorption volumes of 0.5–0.8 cm3 /gm and surface areas of 700–1800 m2 /gm depending on activation conditions, whether physical or chemical. Former carbons possess mixed pore size distribution while chemically activated carbons predominantly possess micropores. Thus, these carbons can be used for adsorption of wide distributions of molecules from gas to liquid. The molecular adsorption within the pores is due to single layer or multilayer molecule deposition at the pore walls and hence results in different types of adsorption isotherm. On the other hand, activated carbon ﬁbres with controlled microporous structure and surface area in the range of 2500 m2 /gm can be developed by controlled pyrolysis and physical activation of amorphous carbon ﬁbres. Active carbon ﬁbres with unmatchable pore structure and surface characteristics are present and futuristic porous materials for a number of applications from pollution control to energy storage.
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
Ho, Clifford K
2006-01-01
This book presents a compilation of state-of-the art studies on gas and vapor transport processes in porous and fractured media. A broad set of models and processes are presented, including advection/diffusion, the Dusty Gas Model, enhanced vapor diffusion, phase change, coupled processes, solid/vapor sorption, and vapor-pressure lowering. Numerous applications are also presented that illustrate these processes and models in current problems facing the scientific community. This book fills a gap in the general area of transport in porous and fractured media; an area that has historically been dominated by studies of liquid-phase flow and transport. This book identifies gas and vapor transport processes that may be important or dominant in various applications, and it exploits recent advances in computational modeling and experimental methods to present studies that distinguish the relative importance of various mechanisms of transport in complex media.
AULISA, EUGENIO
2009-08-01
Motivated by the reservoir engineering concept of the well Productivity Index, we introduced and analyzed a functional, denoted as "diffusive capacity", for the solution of the initial-boundary value problem (IBVP) for a linear parabolic equation.21 This IBVP described laminar (linear) Darcy flow in porous media; the considered boundary conditions corresponded to different regimes of the well production. The diffusive capacities were then computed as steady state invariants of the solutions to the corresponding time-dependent boundary value problem. Here similar features for fast or turbulent nonlinear flows subjected to the Forchheimer equations are analyzed. It is shown that under some hydrodynamic and thermodynamic constraints, there exists a so-called pseudo steady state regime for the Forchheimer flows in porous media. In other words, under some assumptions there exists a steady state invariant over a certain class of solutions to the transient IBVP modeling the Forchheimer flow for slightly compressible fluid. This invariant is the diffusive capacity, which serves as the mathematical representation of the so-called well Productivity Index. The obtained results enable computation of the well Productivity Index by resolving a single steady state boundary value problem for a second-order quasilinear elliptic equation. Analytical and numerical studies highlight some new relations for the well Productivity Index in linear and nonlinear cases. The obtained analytical formulas can be potentially used for the numerical well block model as an analog of Piecemann. © 2009 World Scientific Publishing Company.
Thermal behavior of a porous electric heater
Energy Technology Data Exchange (ETDEWEB)
Naji, M.; Al-Nimr, M.A. [Jordan University of Science and Technology, Irbid (Jordan). Dept. of Mechanical Engineering
2002-03-01
The performance of a proposed porous electric heater is investigated. The porous heater exchanges heat with the working fluid through its large volumetric surface area. As a result, it produces lower surface temperature as compared with the conventional heater for the same imposed heating power. Two mathematical models are presented to describe the thermal behavior of both heaters. Axial diffusion is included in the governing equation of the solid conventional heater. The predictions of both models are compared at different operating conditions where it is found that porous heaters have much better thermal performance than the conventional heaters. (author)
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon
2006-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon
2007-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
HALL CURRENT EFFECTS ON FREE CONVECTION MHD FLOW PAST A POROUS PLATE
Directory of Open Access Journals (Sweden)
G. Ramireddy
2011-06-01
Full Text Available Heat and mass transfer along a vertical porous plate under the combined buoyancy force effects of thermal and species diffusion is investigated in the presence of a transversely applied uniform magnetic field and the Hall currents are taken into account. The governing fundamental equations on the assumption of a small magnetic Reynolds number are approximated by a system of non-linear ordinary differential equations, which are integrated by fourth-order Runge–Kutta method. Velocity, temperature and concentration are shown on graphs. The numerical values of the local shear stress, the local Nusselt number Nu and the local Sherwood number Sh are entered in tables. The effects of the magnetic parameter, Hall parameter and the relative buoyancy force effect between species and thermal diffusion on the velocity, temperature and concentration are discussed. The results are compared with those known from the literature.
Institute of Scientific and Technical Information of China (English)
张锡文; 郝鹏飞; 何枫; 王学芳
2001-01-01
多孔扩散型消声器由于其体积小、消声性能高而广泛应用到排气噪声的降低上，其外壳对消声器的消声性能具有重要作用.本文对此类消声器外壳的孔型、孔径和孔距以及外壳同消声材料的配合方面进行了细致的实验研究，特别对外壳与消声材料的配合与其排放噪声以及外部流场之间的关系进行了探讨，得到了一些有用的结论，对消声器性能的提高具有一定指导意义。%The porous diffusion type silencer is widely used to reduce the air flow noise because of its small volume and high noise attenuating ability.The out case of the silencer plays a very important role in reducing noise.The effect of the hole's shape,diameter and the distance between neighboring holes as well as the matchup between the case and the sound absorbing material tube are investigated experimentally.The relation between the out-flow noise and the gas velocity distribution is carefully studied for two different kinds of matchup between the case and the sound absorbing material tube.Some useful results are gotten,which may be valuable to the design of the silencer.
DEFF Research Database (Denmark)
Riiber, Jacob; Tamke, Martin; Ramsgaard Thomsen, Mette
2012-01-01
The Porous Ascend project investigates how algorithmic and generative approaches allows for the utilization of complex, and by other means inaccessible, ways of devising the schema by which we arrange the parts of an architectural object. It does so by pursuing to physically realize a structure...... of folded elements, based on the concept of applying recursion to the geometry of the non-periodic Penrose tiling. Within this process the project explores questions regarding the making of bespoke digital design tools, digital production, material behaviour and assemblage strategies. The project points...... with an outside and an efficient distribution of specific material behaviour....
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Response of porous SMA: a micromechanical study
Directory of Open Access Journals (Sweden)
V. Sepe
2014-07-01
Full Text Available Lately porous shape memory alloys (SMA have attracted great interest as low weight materials characterized by high energy dissipation capability. In the present contribution a micromechanical study of porous SMA is proposed, introducing the simplifying hypothesis of periodic distribution of voids. The mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense SMA matrix and prescribing suitable periodicity and continuity conditions. The constitutive behavior and the dissipation energy capability of the porous Nitinol are examined for several porosity levels. Numerical applications are performed in order to test the ability of the proposed procedure to well capture the overall behavior and the key features of the special heterogeneous material.
Mamou, M.; Vasseur, P.
1999-09-01
The Darcy model with the Boussinesq approximations is used to study double-diffusive instability in a horizontal rectangular porous enclosure subject to two sources of buoyancy. The two vertical walls of the cavity are impermeable and adiabatic while Dirichlet or Neumann boundary conditions on temperature and solute are imposed on the horizontal walls. The onset and development of convection are first investigated using the linear and nonlinear perturbation theories. Depending on the governing parameters of the problem, four different regimes are found to exist, namely the stable diffusive, the subcritical convective, the oscillatory and the augmenting direct regimes. The governing parameters are the thermal Rayleigh number, RT, buoyancy ratio, N, Lewis number, Le, normalized porosity of the porous medium, [epsilon], aspect ratio of the enclosure, A, and the thermal and solutal boundary condition type, [kappa], applied on the horizontal walls. On the basis of the nonlinear perturbation theory and the parallel flow approximation (for slender or shallow enclosures), analytical solutions are derived to predict the flow behaviour. A finite element numerical method is introduced to solve the full governing equations. The results indicate that steady convection can arise at Rayleigh numbers below the supercritical value, indicating the development of subcritical flows. At the vicinity of the threshold of supercritical convection the nonlinear perturbation theory and the parallel flow approximation results are found to agree well with the numerical solution. In the overstable regime, the existence of multiple solutions, for a given set of the governing parameters, is demonstrated. Also, numerical results indicate the possible occurrence of travelling waves in an infinite horizontal enclosure.
Adsorption Kinetics in Nanoscale Porous Coordination Polymers
Energy Technology Data Exchange (ETDEWEB)
Nune, Satish K.; Thallapally, Praveen K.; McGrail, Benard Peter; Annapureddy, Harsha V. R.; Dang, Liem X.; Mei, Donghai; Karri, Naveen; Alvine, Kyle J.; Olszta, Matthew J.; Arey, Bruce W.; Dohnalkova, Alice
2015-10-07
Nanoscale porous coordination polymers were synthesized using simple wet chemical method. The effect of various polymer surfactants on colloidal stability and shape selectivity was investigated. Our results suggest that the nanoparticles exhibited significantly improved adsorption kinetics compared to bulk crystals due to decreased diffusion path lengths and preferred crystal plane interaction.
Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium.
Uddin, Ziya; Harmand, Souad
2013-02-07
The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size.
Harfash, Akil J.; Alshara, Ahmed K.
2015-05-01
The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium are tested. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. Then, the accuracy of the linear instability thresholds are tested using a three dimensional simulation. It is shown that the strong stabilising effect of gravity field. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.
Theoretical characterization of the gravity influence on the displacement flows in porous media
Rosa, Reinaldo; Baroni, Mariana; de Wit, Anne; Pontes, Jose; da Silva, Antonio
Structural characterization of miscible displacement in porous media (Hele-Shaw cell-type) is of special interest to understand, among several processes, fingering time evolution of gravitydriven thin coating films. When the heavy solution lies on top of the lighter one in the gravity field, a complex convective fingerlike deformation of the front is observed experimentally. In this paper, nonlinear interactions between chemical reactions and miscible density fingering are studied by direct numerical simulations taking into account different gravity conditions in a Darcy-Boussinesq system. The nonlinear pattern formation of the fingers for different values of g (the planetary gravitational acceleration) is characterized by two complementary analytical methods: linear stability analysis and gradient pattern analysis. Both methods are very sensitive to fine response of the fingering process when the gravitational field is slightly changed. Here, for the first time, is presented the theoretical fine variation of the density fingering fronts in a porous media as a function of the gravitational acceleration (we used typical values, in m/s2, at the surface of the known solar system planets (3.69, 4.00, 4.70, 8.75, 9.82, 9.89, 10.99, 11.08, 25.99). Finally, due to new discoveries, in reaction-diffusion processes, which have been made under space conditions, we discuss the importance of this result in future space missions under distinct planetary gravitational acceleration.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
Seismic fault preserving diffusion
Lavialle, Olivier; Pop, Sorin; Germain, Christian; Donias, Marc; Guillon, Sebastien; Keskes, Naamen; Berthoumieu, Yannick
2007-02-01
This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non-linear diffusion filtering leading to a better detection of seismic faults. The non-linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.
Amine Functionalized Porous Network
Eddaoudi, Mohamed
2015-05-28
Amine groups can be introduced in porous materials by a direct (one pot) or post-synthetic modification (PSM) process on aldehyde groups, and the resulting porous materials have increased gas affinity.
Pescarmona, G P; Scalerandi, M; Delsanto, P P; Condat, C A
1999-12-01
A new approach for modelling the spatio-temporal evolution of tumors is presented. To test its validity, a very basic model is considered, which, in spite of its simplicity, is capable of generating a multiplicity of morphologies and growth and migration rates. From an in-vivo scenario of basic life processes, cancer cell proliferation is described as a competition for basic nutrients. The chosen mathematical treatment and simulation techniques permit a direct implementation of the local nonlinear couplings existing between the various cell populations and the free and bound nutrient concentration. A discussion of the results and proposed improvements and applications of the model is also presented.
Solutions of fractional diffusion problems
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2010-10-01
Full Text Available Using the concept of majorant functions, we prove the existence and uniqueness of holomorphic solutions to nonlinear fractional diffusion problems. The analytic continuation of these solutions is studied and the singularity for two cases are posed.
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Energy Technology Data Exchange (ETDEWEB)
Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas
1999-10-01
We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity
Hamon, F. P.; Mallison, B.; Tchelepi, H.
2016-12-01
In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem
Method to prepare nanoparticles on porous mediums
Vieth, Gabriel M [Knoxville, TN; Dudney, Nancy J [Oak Ridge, TN; Dai, Sheng [Knoxville, TN
2010-08-10
A method to prepare porous medium decorated with nanoparticles involves contacting a suspension of nanoparticles in an ionic liquid with a porous medium such that the particles diffuse into the pores of the medium followed by heating the resulting composition to a temperature equal to or greater than the thermal decomposition temperature of the ionic liquid resulting in the removal of the liquid portion of the suspension. The nanoparticles can be a metal, an alloy, or a metal compound. The resulting compositions can be used as catalysts, sensors, or separators.
Ogawa, Naohisa
2011-01-01
The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the thickness of the tube is sufficiently small compared with its curvature radius. We discuss how geomerical quantities appear in a quasi-one-dimensional diffusion equation.
Energy Technology Data Exchange (ETDEWEB)
BARTON,THOMAS J.; BULL,LUCY M.; KLEMPERER,WALTER G.; LOY,DOUGLAS A.; MCENANEY,BRIAN; MISONO,MAKOTO; MONSON,PETER A.; PEZ,GUIDO; SCHERER,GEORGE W.; VARTULI,JAMES C.; YAGHI,OMAR M.
1999-11-09
Tailoring of porous materials involves not only chemical synthetic techniques for tailoring microscopic properties such as pore size, pore shape, pore connectivity, and pore surface reactivity, but also materials processing techniques for tailoring the meso- and the macroscopic properties of bulk materials in the form of fibers, thin films and monoliths. These issues are addressed in the context of five specific classes of porous materials: oxide molecular sieves, porous coordination solids, porous carbons, sol-gel derived oxides, and porous heteropolyanion salts. Reviews of these specific areas are preceded by a presentation of background material and review of current theoretical approaches to adsorption phenomena. A concluding section outlines current research needs and opportunities.
Directory of Open Access Journals (Sweden)
Mohammed Almakki
2017-07-01
Full Text Available The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.
An Iterative Implicit Scheme for Nanoparticles Transport with Two-Phase Flow in Porous Media
El-Amin, Mohamed
2016-06-01
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is solved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Numerical example for regular heterogenous permeability is considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graphically.
Scaling percolation in thin porous layers
Médici, E. F.; Allen, J. S.
2011-12-01
Percolation in porous media is a complex process that depends on the flow rate, material, and fluids properties as well as the boundary conditions. Traditional methods of characterizing percolation rely upon visual observation of a flow pattern or a pressure-saturation relation valid only in the limit of no flow. In this paper, the dynamics of fluid percolation in thin porous media is approached through a new scaling. This new scaling in conjunction with the capillary number and the viscosity ratio has resulted in a linear non-dimensional correlation of the percolation pressure and wetted area in time unique to each porous media. The effect of different percolation flow patterns on the dynamic pressure-saturation relation can be condensed into a linear correlation using this scaling. The general trend and implications of the scaling have been analyzed using an analytical model of a fluid percolating between two parallel plates and by experimental testing on thin porous media. Cathode porous transport layers (PTLs), also known as gas diffusion layers, of a proton exchange membrane (PEM) fuel cell having different morphological and wetting properties were tested under drainage conditions. Images of the fluid percolation evolution and the percolation pressure in the PTLs were simultaneously recorded. A unique linear correlation is obtained for each type of PTL samples using the new scaling. The correlation derived from this new scaling can be used to quantitatively characterize porous media with respect to percolation. While the characterization method discussed herein was developed for the study of porous materials used in PEM fuel cells, the method and scaling are applicable to any porous media.
A design strategy for magnetorheological dampers using porous valves
Energy Technology Data Exchange (ETDEWEB)
Hu, W; Robinson, R; Wereley, N M [Smart Structures Laboratory, Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering, University of Maryland, College Park, MD 20742 (United States)], E-mail: wereley@umd.edu
2009-02-01
To design a porous-valve-based magnetorheological (MR) damper, essential design parameters are presented. The key elements affecting the damper performance are identified using flow analysis in porous media and an empirical magnetic field distribution in the porous valve. Based on a known MR fluid, the relationship between the controllable force of the damper and the porous valve characteristics, i.e. porosity and tortuosity, is developed. The effect of the porosity and tortuosity on the field-off damping force is exploited by using semi-empirical flow analysis. The critical flow rate for the onset of nonlinear viscous damping force is determined. Using the above design elements, an MR damper using by-pass porous valve is designed and tested. The experimental damper force and equivalent damping are compared with the predicted results to validate this design strategy.
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole
2008-01-01
. To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...
The Dam Bursts for Porous Liquids.
James, Stuart L
2016-07-01
In 2007 the idea was put forward that, through careful molecular design, it should be possible to synthesize liquids which contain permanent, well-defined molecule-sized cavities (pores). Such "porous liquids" could be a kind of liquid zeolite, or liquid MOF (metal-organic framework), exhibiting the size and shape-selective sorption (or dissolution) associated with microporous solids as well as the fluidity of liquids - a new and potentially useful combination of properties. However, these materials remained essentially hypothetical until recently. In 2014 and 2015 three papers were published which describe convincing examples of porous liquids, and studies have shown that they do exhibit some remarkable properties, such as very fast gas diffusion and high gas solubilities. The examples reported so far are almost certainly only the tip of the iceberg. Now that porous liquids are 'real', a new area of materials science may open up, with clear potential for long-term applications in chemical processes.
Cross-diffusion effects in isothermal double diffusive
Energy Technology Data Exchange (ETDEWEB)
Becerril, R. [Michoacan Univ. Michoacana de San Nicolas de Hidalgo, Michoacan (Mexico). Inst. de Fisica y Mathematicas
2000-11-01
The nonlinear coefficients of the amplitude equations for the stationary, oscillatory and codimension-2 point bifurcations are calculated for isothermal double diffusive convection with cross-diffusion. The locations of the tricritical point for the stationary instability and the codimension-2 point are also found. Thereby the separation between these points in parameter space can be calculated as a function of rescaled cross-diffusion constants.
Mass transport in a microchannel bioreactor with a porous wall.
Chen, Xiao Bing; Sui, Yi; Lee, Heow Pueh; Bai, Hui Xing; Yu, Peng; Winoto, S H; Low, Hong Tong
2010-06-01
A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.
Nonlinear sequential laminates reproducing hollow sphere assemblages
Idiart, Martín I.
2007-07-01
A special class of nonlinear porous materials with isotropic 'sequentially laminated' microstructures is found to reproduce exactly the hydrostatic behavior of 'hollow sphere assemblages'. It is then argued that this result supports the conjecture that Gurson's approximate criterion for plastic porous materials, and its viscoplastic extension of Leblond et al. (1994), may actually yield rigorous upper bounds for the hydrostatic flow stress of porous materials containing an isotropic, but otherwise arbitrary, distribution of porosity. To cite this article: M.I. Idiart, C. R. Mecanique 335 (2007).
Laser-induced growth of nanocrystals embedded in porous materials
Capoen, Bruno; Chahadih, Abdallah; El Hamzaoui, Hicham; Cristini, Odile; Bouazaoui, Mohamed
2013-06-01
Space localization of the linear and nonlinear optical properties in a transparent medium at the submicron scale is still a challenge to yield the future generation of photonic devices. Laser irradiation techniques have always been thought to structure the matter at the nanometer scale, but combining them with doping methods made it possible to generate local growth of several types of nanocrystals in different kinds of silicate matrices. This paper summarizes the most recent works developed in our group, where the investigated nanoparticles are either made of metal (gold) or chalcogenide semiconductors (CdS, PbS), grown in precursor-impregnated porous xerogels under different laser irradiations. This review is associated to new results on silver nanocrystals in the same kind of matrices. It is shown that, depending on the employed laser, the particles can be formed near the sample surface or deep inside the silica matrix. Photothermal and/or photochemical mechanisms may be invoked to explain the nanoparticle growth, depending on the laser, precursor, and matrix. One striking result is that metal salt reduction, necessary to the production of the corresponding nanoparticles, can efficiently occur due to the thermal wrenching of electrons from the matrix itself or due to multiphoton absorption of the laser light by a reducer additive in femtosecond regime. Very localized semiconductor quantum dots could also be generated using ultrashort pulses, but while PbS nanoparticles grow faster than CdS particles due to one-photon absorption, this better efficiency is counterbalanced by a sensitivity to oxidation. In most cases where the reaction efficiency is high, particles larger than the pores have been obtained, showing that a fast diffusion of the species through the interconnected porosity can modify the matrix itself. Based on our experience in these techniques, we compare several examples of laser-induced nanocrystal growth in porous silica xerogels, which allows
Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer
Directory of Open Access Journals (Sweden)
S. N. Gaikwad
2016-01-01
Full Text Available The linear and nonlinear stability analysis of double diffusive reaction-convection in a sparsely packed anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically. The linear analysis is based on the usual normal mode method and the nonlinear theory on the truncated representation of Fourier series method. The Darcy-Brinkman model is employed for the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Darcy number, Damkohler number, anisotropy parameters, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effect of Darcy number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary, oscillatory and finite amplitude convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory and finite amplitude modes. Further, the transient behavior of the Nusselt and Sherwood numbers are investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta method.
Curry, D. M.; Cox, J. E.
1972-01-01
Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.
Curry, D. M.; Cox, J. E.
1972-01-01
Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.
Institute of Scientific and Technical Information of China (English)
段毅文
2003-01-01
The consecutive diffusion reaction in porous catalyst particles is a very important kind of chemical reactions,such as hydrolysis,halogenating,and oxidizing reactions.The fractional geometry symmetry model has been used to analyze these kinds of reactions.And it will widen the recognized area in single particle chemical reaction engineering in order to obtain the various factors for a heterogeneous catalysis reaction in an amorphous porous catalyst particle.Also,the relationship,that is Dui=(φ2i)/(m+1),between fractional number m and experimental data in the porous catalyst bed has been obtained.%在多孔固体催化剂颗粒中的串连扩散反应是非常重要的一类化学反应,如水解反应,卤化反应和氧化反应等.分数几何对称模型已用于分析这类反应的一般规律.为了得到多孔固体催化剂颗粒内非均相催化反应的各因素,这个模型将拓宽单颗粒化学反应工程的认识领域.而且,在多孔固体催化剂颗粒填充床中分数参数m和实验数据间的关系Dui=(φ2i)/(m+1)也已推得.
Confocal imaging of protein distributions in porous silicon optical structures
Energy Technology Data Exchange (ETDEWEB)
De Stefano, Luca [Institute for Microelectronics and Microsystems, Department of Naples, National Council of Research, Via P Castellino 111, 80131 Naples (Italy); D' Auria, Sabato [Institute of Protein Biochemistry, National Council of Research, Via P Castellino 111, 80131 Naples (Italy)
2007-10-03
The performances of porous silicon optical biosensors depend strongly on the arrangement of the biological probes into their sponge-like structures: it is well known that in this case the sensing species do not fill the pores but instead cover their internal surface. In this paper, the direct imaging of labelled proteins into different porous silicon structures by using a confocal laser microscope is reported. The distribution of the biological matter in the nanostructured material follows a Gaussian behaviour which is typical of the diffusion process in the porous media but with substantial differences between a porous silicon monolayer and a multilayer such as a Bragg mirror. Even if semi-quantitative, the results can be very useful in the design of the porous silicon based biosensing devices.
Nonlinear property of slightly compressible media permeated with air-filled bubbles
Institute of Scientific and Technical Information of China (English)
Bo QIN
2009-01-01
Based on the nonlinear oscillation of an air- filled bubble in weakly compressible media at prestressed state, the effective medium method is used to study the nonlinear property of the slightly compressible media permeated with air bubbles. It is this nonlinear oscilla- tion of air bubbles that results in the nonlinear property of the porous media. Numerical results have confirmed that the nonlinearity of the porous media is usually high, though the optimal porosity is very small. Moreover, the nonlinear property is greatly affected by the prestressed state, porosity, and shear modulus of the matrix media.
Rb optical resonance inside a random porous medium
Villalba, S; Laliotis, A; Lenci, L; Barreiro, S; Lezama, A
2012-01-01
We studied absorption and fluorescence of Rb atoms confined to the interstitial cavities of a random porous glass. Due to the diffusive light propagation in the porous sample, resonant light absorption is almost entirely compensated by atomic fluorescence at low atomic densities. For higher densities, radiation trapping increases the probability of non-radiative decay via atom-wall collisions. A simple connection of the fluorescence/absorption yield to the sample porosity is given.
On some applications of diffusion processes for image processing
Energy Technology Data Exchange (ETDEWEB)
Morfu, S., E-mail: smorfu@u-bourgogne.f [Laboratoire d' Electronique, Informatique et Image (LE2i), UMR Cnrs 5158, Aile des Sciences de l' Ingenieur, BP 47870, 21078 Dijon Cedex (France)
2009-06-29
We propose a new algorithm inspired by the properties of diffusion processes for image filtering. We show that purely nonlinear diffusion processes ruled by Fisher equation allows contrast enhancement and noise filtering, but involves a blurry image. By contrast, anisotropic diffusion, described by Perona and Malik algorithm, allows noise filtering and preserves the edges. We show that combining the properties of anisotropic diffusion with those of nonlinear diffusion provides a better processing tool which enables noise filtering, contrast enhancement and edge preserving.
Hydrodynamic dispersion within porous biofilms
Davit, Y.
2013-01-23
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher\\'s equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels\\' network; (2) the solute\\'s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport. © 2013 American Physical Society.
Caserta, A; Salusti, E
2016-01-01
In this paper we propose the application of a new model of transients of pore pressure p and solute density \\r{ho} in geologic porous media. This model is rooted in the non-linear waves theory, the focus of which is advection and effect of large pressure jumps on strain (due to large p in a non-linear version of the Hooke law). It strictly relates p and \\r{ho} evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e. the non-linear Burgers solitons. We therefore propose that the actual transport process in porous rocks for large signals is not the linear diffusion, but could be governed by solitons. A test of an eventual presence of solitons in a rock is here proposed, and then applied to Pierre Shale, Bearpaw Shale, Boom Clay and Oznam-Mugu silt and clay. A quick analysis showing the presence of solitons for nuclear waste disposal and salty water intrusions is also analyzed. Finally, in a kind of "theoretical exp...
Modelling the initial stage of porous alumina growth during anodization
Aryslanova, E. M.; Alfimov, A. V.; Chivilikhin, S. A.
2013-05-01
Artificially on the surface of aluminum there may be build a thick layer of Al2O3, which has a porous structure. In this paper we present a model of growth of porous alumina in the initial stage of anodizing, identifying dependencies anodizing parameters on the rate of growth of the film and the distance between the pores and as a result of the created model equations were found for changes in the disturbance of alumina for the initial stage of anodizing aluminum oxide porous border aluminum-alumina and alumina-electrolyte, with the influence of surface diffusion of aluminum oxide.
Configurational diffusion of coal macromolecules
Energy Technology Data Exchange (ETDEWEB)
Guin, J.A.; Curtis, C.W.; Tarrer, A.R.; Kim, S.; Hwang, D.; Chen, C.C.; Chiou, Z.
1991-01-01
The objective of our research was to obtain fundamental information regarding the functional dependence of the diffusion coefficient of coal molecules on the ratio of molecule to pore diameter. That is, the objective of our study was to examine the effect of molecule size and configuration on hindered diffusion of coal macromolecules through as porous medium. To best accomplish this task, we circumvented the complexities of an actual porous catalyst by using a well defined porous matrix with uniform capillaric pores, i.e., a track-etched membrane. In this way, useful information was obtained regarding the relationship of molecular size and configuration on the diffusion rate of coal derived macromolecules through a pore structure with known geometry. Similar studies were performed using a pellet formed of porous alumina, to provide a link between the idealized membranes and the actual complex pore structure of real catalyst extrudates. The fundamental information from our study will be useful toward the tailoring of catalysts to minimize diffusional influences and thereby increase coal conversion and selectivity for desirable products. (VC)
Mechanical Properties of Zirconium Ceramics with Hierarchical Porous Structure
Kulkov, S.; Shutilova, E.; Buyakova, S.
2016-07-01
The work studies porous ceramics produced from ultra-fine powders. The porosity of ceramic samples was from 15 to 80%. The ceramic materials had cellular structure. A distinctive feature of all deformation diagrams obtained in the experiment was their nonlinearity at low deformations, which was described by the parabolic law. It was shown that the observed nonlinear elasticity for low deformations on deformation diagrams is due to mechanical instability of cellular elements in a ceramic frame.
Directory of Open Access Journals (Sweden)
A.M. Rashad
2015-01-01
Full Text Available The thermal-diffusion and diffusion-thermo effects on heat and mass transfer by transient free convection flow of over an impulsively started isothermal vertical plate embedded in a saturated porous medium were numerically investigated, considering a homogeneous chemical reaction of first order. The transient, nonlinear and coupled governing equations are solved using an implicit finite-difference scheme. The effects of various parameters on the transient velocity, temperature, and concentration profiles as well as heat and mass transfer rates are analyzed. Numerical results for the unsteady-state velocity, temperature and concentration profiles as well as the axial distributions and the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
An analytical model for porous single crystals with ellipsoidal voids
Mbiakop, A.; Constantinescu, A.; Danas, K.
2015-11-01
A rate-(in)dependent constitutive model for porous single crystals with arbitrary crystal anisotropy (e.g., FCC, BCC, HCP, etc.) containing general ellipsoidal voids is developed. The proposed model, denoted as modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous material to estimate the response of the nonlinear porous single crystal. Periodic multi-void finite element simulations are used in order to validate the MVAR for a large number of parameters including cubic (FCC, BCC) and hexagonal (HCP) crystal anisotropy, various creep exponents (i.e., nonlinearity), several stress triaxiality ratios, general void shapes and orientations and various porosity levels. The MVAR model, which involves a priori no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in the rate-dependent context. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids. Finally, a simple way of calibrating the MVAR with just two adjustable parameters is depicted in the rate-independent context so that an excellent agreement with the FE simulation results is obtained. In this last case, this proposed model can be thought as a generalization of the Gurson model in the context of porous single crystals and general ellipsoidal void shapes and orientations.
Hierarchical Porous Structures
Energy Technology Data Exchange (ETDEWEB)
Grote, Christopher John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-07
Materials Design is often at the forefront of technological innovation. While there has always been a push to generate increasingly low density materials, such as aero or hydrogels, more recently the idea of bicontinuous structures has gone more into play. This review will cover some of the methods and applications for generating both porous, and hierarchically porous structures.
Energy Technology Data Exchange (ETDEWEB)
Tsuo, Y.S.; Menna, P.; Al-Jassim, M. [National Renewable Energy Lab., Golden, CO (United States)] [and others
1995-08-01
We have studied a novel extrinsic gettering method that utilizes the very large surface areas, produced by porous silicon etch on both front and back surfaces of the silicon wafer, as gettering sites. In this method, a simple and low-cost chemical etching is used to generate the porous silicon layers. Then, a high-flux solar furnace (HFSF) is used to provide high-temperature annealing and the required injection of silicon interstitials. The gettering sites, along with the gettered impurities, can be easily removed at the end the process. The porous silicon removal process consists of oxidizing the porous silicon near the end the gettering process followed by sample immersion in HF acid. Each porous silicon gettering process removes up to about 10 {mu}m of wafer thickness. This gettering process can be repeated so that the desired purity level is obtained.
Formation of titanium carbide coating with micro-porous structure
Luo, Yong; Ge, Shirong; Jin, Zhongmin; Fisher, John
2010-03-01
Micro-porous titanium carbide coating was successfully synthesized in a vacuum gas carburizing furnace by using a sequential diffusion technology. The composition and structure of the as-synthesized TiC were examined by X-ray diffraction, X-ray photoelectron spectroscopy (XPS) and glow discharge mass spectrometry (GDMS), and scanning electron microscopy (SEM). All of the XRD, XPS and GDMS analysis results indicate that carbon atoms effectively diffused into the titanium alloys and formed a uniform acicular TiC coating with micro-porous structure.
On the viscous dissipation modeling of thermal fluid flow in a porous medium
Salama, Amgad
2011-02-24
The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e.; viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism. © 2011 Springer-Verlag.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Observation of time-varying photoconductivity and persistent photoconductivity in porous silicon
DEFF Research Database (Denmark)
Frello, T.; Veje, E.; Leistiko, Otto
1996-01-01
of at least two competing mechanisms, one is tentatively related to photoinduced creation of charge carriers in the silicon substrate followed by diffusion into the porous silicon layer, and the other is tentatively related to desorption of hydrogen from the porous silicon. ©1996 American Institute of Physics....
Variability on Raman Shift to Stress Coefficient of Porous Silicon
Institute of Scientific and Technical Information of China (English)
LEI Zhen-Kun; KANG Yi-Lan; CEN Hao; HU Ming
2006-01-01
Porous silicon film is a capillary-like medium, which is able to reveal different meso-elastic modulus with porosity. During the preparation of porous silicon samples, the capillary force is a non-classic force related to the liquid evaporation which directly influences the evolution of residual stress. In this study, a non-linear relation of Raman shift to stress coefficient and the porosity is obtained from the elastic modulus measured with nano-indentation by Bellet et al. fJ. Appl. Phys. 60 (1996) 3772] Dynamic capillarity during the drying process of porous silicon is investigated using micro-Raman spectroscopy, and the results reveal that the residual stress resulted from the capillarity increased rapidly. Indeed, the dynamic capillarity has a close relationship with a great deal of micro-pore structures of the porous silicon.
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Salamon, David; Da Silva Teixeira, Sandra; Dutczak, S.M.; Stamatialis, Dimitrios
2014-01-01
Nowadays, diffusion through scaffold and tissue usually limits transport, and forms potentially hypoxic regions. Several methods are used for preparation of 3D hydroxyapatite scaffolds, however, production of a scaffold including porous hollow fibers for nutrition delivery is difficult and