On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

Caracterización del hormigón en relación a la difusión de gases y su correlación con el radón

Radon gas (Rn) is a natural radioactive gas present in some soils and able to penetrate buildings through the building envelope in contact with the soil. Radon can accumulate within buildings and consequently be inhaled by their occupants. Because it is a radioactive gas, its disintegration process produces alpha particles that, in contact with the lung epithelia, can produce alterations potentially giving rise to cancer. Many international organizations related to health protection, such as WHO, confirm this causality. One way to avoid the accumulation of radon in buildings is to use the building envelope as a radon barrier. The extent to which concrete provides such a barrier is described by its radon diffusion coefficient (DRn), a parameter closely related to porosity (ɛ) and tortuosity factor (τ). The measurement of the radon diffusion coefficient presents challenges, due to the absence of standard procedures, the requirement to establish adequate airtightness in testing apparatus (referred to here as the diffusion cell), and due to the fact that measurement has to be carried out in an environment certified for use of radon calibrated sources. In addition to this calibrated radon sources are costly. The measurement of the diffusion coefficient for non-radioactive gas is less complex, but nevertheless retains a degree of difficulty due to the need to provide reliably airtight apparatus for all tests. Other parameters that can characterize and describe the process of gas transport through concrete include the permeability coefficient (K) and the electrical resistivity (ρe), both of which can be measured relatively easily with standardized procedure. The use of these parameters would simplify the characterization of concrete behaviour as a radon barrier. Although earlier studies exist, describing correlation among these parameters, there is, as has been observed in the literature, little common ground between the various research efforts. For precisely this reason, prior to any attempt to measure radon diffusion, it was deemed necessary to carry out further research in this area, as a foundation to the current work, to explore potential relationships among the following parameters: porosity-tortuosity, oxygen diffusion coefficient, permeability coefficient and resistivity. Permeability coefficient measurement (m2) presents a more straightforward challenge than diffusion coefficient measurement. Some authors identify a relationship between both coefficients, including Gaber (1988), who proposes: k= a•Dn Equation 1 Where: a=A/(8ΠD020), A = sample cross-section, D020 = diffusion coefficient in air (m2/s). Other studies (Klink et al. 1999, Gaber and Schlattner 1997, Gräf and Grube et al. 1986), experimentally relate both coefficients of different types of concrete confirming that this relationship exists, as represented by the simplified expression: k≈Dn Equation 2 In each particular study a different value for n was established, varying from 1.3 to 2.5, but this requires determination of a value for n in a more general way because these proposed models cannot estimate diffusion coefficient. If diffusion coefficient has to be measured to be able to establish n, these relationships are not interesting. The measurement of electric resistivity is easier than diffusion coefficient measurement. Correlation between the parameters can be established via Einstein´s law that relates movement of electrical charges to media conductivity according to the expression: D_e=k/ρ Equation 3 Where: De = diffusion coefficient (cm2/s), K = constant, ρ = electric resistivity (Ω•cm). The tortuosity factor is used to represent the uneven geometry of concrete pores, which are described as being not straight, but tortuous. This factor was first introduced in the literature to relate global porosity with fluid transport in a porous media, and can be formulated in a number of different ways. For example, it can take the form of equation 4 (Mason y Malinauskas), which combines molecular and Knudsen diffusion using the tortuosity factor: D=ε^τ (3/2r √(πM/8RT+1/D_0 ))^(-1) Equation 4 Where: r = medium radius obtained from MIP (µm), M = gas molecular mass, R = ideal gases constant, T = temperature (K), D0 = coefficient diffusion in the air (m2/s). Few studies provide any insight as to how to obtain the tortuosity factor. The work of Andrade (2012) is exceptional in this sense, as it outlines how the tortuosity factor can be deduced from pore size distribution (from MIP) from the equation: ∅_th=∅_0•ε^(-τ). Equation 5 Where: Øth = threshold diameter (µm), Ø0 = minimum diameter (µm), ɛ = global porosity, τ = tortuosity factor. Alternatively, the following equation may be used to obtain the tortuosity factor: DO2=D0*ɛτ Equation 6 Where: DO2 = oxygen diffusion coefficient obtained experimentally (m2/s), DO20 = oxygen diffusion coefficient in the air (m2/s). This equation has been inferred from Archie´s law ρ_e=〖a•ρ〗_0•ɛ^(-m) and from the Einstein law mentioned above, using the values of oxygen diffusion coefficient obtained experimentally. The principal objective of the current study was to establish correlations between the different parameters that characterize gas transport through concrete. The achievement of this goal will facilitate the assessment of the useful life of concrete, as well as open the door to the pro-active planning for the use of concrete as a radon barrier. Two further objectives were formulated within the current study: 1.- To develop a method for measurement of gas coefficient diffusion in concrete. 2.- To model an analytic estimation of radon diffusion coefficient from parameters related to concrete porosity and tortuosity factor. In order to assess the possible correlations, parameters have been measured using the standardized procedures or purpose-built in the laboratory for the study of equations 1, 2 y 3. To measure the gas diffusion coefficient, a diffusion cell was designed and manufactured, with the design evolving over several cycles of research, leading ultimately to a unit that is reliably air tight. The analytic estimation of the radon diffusion coefficient DRn in concrete is based on concrete global porosity (ɛ), whose values may be experimentally obtained from a mercury intrusion porosimetry test (MIP), and from its tortuosity factor (τ), derived using the relations expressed in equations 5 y 6. The conclusions of the study are: Several models based on regressions, for concrete with a relative humidity of 50%, have been proposed to obtain the diffusion coefficient following the equations K=Dn, K=a*Dn y D=n/ρe. The final of these three relations is the one with the determination coefficient closest to a value of 1: D=(19,997*LNɛ+59,354)/ρe Equation 7 The values of the obtained oxygen diffusion coefficient adjust quite well to those experimentally measured. The proposed method for the measurement of the gas coefficient diffusion is considered to be adequate. The values obtained for the oxygen diffusion coefficient are within the range of those proposed by the literature (10-7 a 10-8 m2/s), and are consistent with the other studied parameters. Tortuosity factors obtained using pore distribution and the expression Ø=Ø0*ɛ-τ are inferior to those from resistivity ρ=ρ0*ɛ-τ. The closest relationship to it is the one with porosity of pore diameter 1 µm (τ=2,07), being 7,21% inferior. Tortuosity factors obtained from the expression DO2=D0*ɛτ are similar to those from resistivity: for global tortuosity τ=2,26 and for the rest of porosities τ=0,7. Estimated radon diffusion coefficients are within the range of those consulted in literature (10-8 a 10-10 m2/s).ABSTRACT El gas radón (Rn) es un gas natural radioactivo presente en algunos terrenos que puede penetrar en los edificios a través de los cerramientos en contacto con el mismo. En los espacios interiores se puede acumular y ser inhalado por las personas. Al ser un gas radioactivo, en su proceso de desintegración emite partículas alfa que, al entrar en contacto con el epitelio pulmonar, pueden producir alteraciones del mismo causando cáncer. Muchos organismos internacionales relacionados con la protección de la salud, como es la OMS, confirman esta causalidad. Una de las formas de evitar que el radón penetre en los edificios es utilizando las propiedades de barrera frente al radón de su propia envolvente en contacto con el terreno. La principal característica del hormigón que confiere la propiedad de barrera frente al radón cuando conforma esta envolvente es su permeabilidad que se puede caracterizar mediante su coeficiente de difusión (DRn). El coeficiente de difusión de un gas en el hormigón es un parámetro que está muy relacionado con su porosidad (ɛ) y su tortuosidad (τ). La medida del coeficiente de difusión del radón resulta bastante complicada debido a que el procedimiento no está normalizado, a que es necesario asegurar una estanquidad a la celda de medida de la difusión y a que la medida tiene que ser realizada en un laboratorio cualificado para el uso de fuentes de radón calibradas, que además son muy caras. La medida del coeficiente de difusión de gases no radioactivos es menos compleja, pero sigue teniendo un alto grado de dificultad puesto que tampoco está normalizada, y se sigue teniendo el problema de lograr una estanqueidad adecuada de la celda de difusión. Otros parámetros que pueden caracterizar el proceso son el coeficiente de permeabilidad (K) y la resistividad eléctrica (ρe), que son más fáciles de determinar mediante ensayos que sí están normalizados. El uso de estos parámetros facilitaría la caracterización del hormigón como barrera frente al radón, pero aunque existen algunos estudios que proponen correlaciones entre estos parámetros, en general existe divergencias entre los investigadores, como se ha podido comprobar en la revisión bibliográfica realizada. Por ello, antes de tratar de medir la difusión del radón se ha considerado necesario realizar más estudios que puedan clarificar las posibles relaciones entre los parámetros: porosidad-tortuosidad, coeficiente de difusión del oxígeno, coeficiente de permeabilidad y resistividad. La medida del coeficiente de permeabilidad (m2) es más sencilla que el de difusión. Hay autores que relacionan el coeficiente de permeabilidad con el de difusión. Gaber (1988) propone la siguiente relación: k= a•Dn Ecuación 1 En donde: a=A/(8ΠD020), A = sección de la muestra, D020 = coeficiente de difusión en el aire (m2/s). Otros estudios (Klink et al. 1999, Gaber y Schlattner 1997, Gräf y Grube et al. 1986) relacionan de forma experimental los coeficientes de difusión de radón y de permeabilidad de distintos hormigones confirmando que existe una relación entre ambos parámetros, utilizando la expresión simplificada: k≈Dn Ecuación 2 En cada estudio concreto se han encontrado distintos valores para n que van desde 1,3 a 2,5 lo que lleva a la necesidad de determinar n porque no hay métodos que eviten la determinación del coeficiente de difusión. Si se mide la difusión ya deja de ser de interés la medida indirecta a través de la permeabilidad. La medida de la resistividad eléctrica es muchísimo más sencilla que la de la difusión. La relación entre ambos parámetros se puede establecer a través de una de las leyes de Einstein que relaciona el movimiento de cargas eléctricas con la conductividad del medio según la siguiente expresión: D_e=k/ρ_e Ecuación 3 En donde: De = coeficiente de difusión (cm2/s), K = constante, ρe = resistividad eléctrica (Ω•cm). El factor de tortuosidad es un factor de forma que representa la irregular geometría de los poros del hormigón, al no ser rectos sino tener una forma tortuosa. Este factor se introduce en la literatura para relacionar la porosidad total con el transporte de un fluido en un medio poroso y se puede formular de distintas formas. Por ejemplo se destaca la ecuación 4 (Mason y Malinauskas) que combina la difusión molecular y la de Knudsen utilizando el factor de tortuosidad: D=ε^τ (3/2r √(πM/8RT+1/D_0 ))^(-1) Ecuación 4 En donde: r = radio medio obtenido del MIP (µm), M = peso molecular del gas, R = constante de los gases ideales, T = temperatura (K), D0 = coeficiente de difusión de un gas en el aire (m2/s). No hay muchos estudios que proporcionen una forma de obtener este factor de tortuosidad. Destaca el estudio de Andrade (2012) en el que deduce el factor de tortuosidad de la distribución del tamaño de poros (curva de porosidad por intrusión de mercurio) a partir de la ecuación: ∅_th=∅_0•ε^(-τ) Ecuación 5 En donde: Øth = diámetro umbral (µm), Ø0 = diámetro mínimo (µm), ɛ = porosidad global, τ = factor de tortuosidad. Por otro lado, se podría utilizar también para obtener el factor de tortuosidad la relación: DO2=D0*-τ Ecuación 6 En donde: DO2 = coeficiente de difusión del oxígeno experimental (m2/s), DO20 = coeficiente de difusión del oxígeno en el aire (m2/s). Esta ecuación está inferida de la ley de Archie ρ_e=〖a•ρ〗_0•ɛ^(-m) y la de Einstein mencionada anteriormente, utilizando valores del coeficiente de difusión del oxígeno DO2 obtenidos experimentalmente. El objetivo fundamental de la tesis es encontrar correlaciones entre los distintos parámetros que caracterizan el transporte de gases a través del hormigón. La consecución de este objetivo facilitará la evaluación de la vida útil del hormigón así como otras posibilidades, como la evaluación del hormigón como elemento que pueda ser utilizado en la construcción de nuevos edificios como barrera frente al gas radón presente en el terreno. Se plantean también los siguientes objetivos parciales en la tesis: 1.- Elaborar una metodología para la medida del coeficiente de difusión de los gases en el hormigón. 2.- Plantear una estimación analítica del coeficiente de difusión del radón a partir de parámetros relacionados con su porosidad y su factor de tortuosidad. Para el estudio de las correlaciones posibles, se han medido los parámetros con los procedimientos normalizados o puestos a punto en el propio Instituto, y se han estudiado las reflejadas en las ecuaciones 1, 2 y 3. Para la medida del coeficiente de difusión de gases se ha fabricado una celda que ha exigido una gran variedad de detalles experimentales con el fin de hacerla estanca. Para la estimación analítica del coeficiente de difusión del radón DRn en el hormigón se ha partido de su porosidad global (ɛ), que se obtiene experimentalmente del ensayo de porosimetría por intrusión de mercurio (MIP), y de su factor de tortuosidad (τ), que se ha obtenido a partir de las relaciones reflejadas en las ecuaciones 5 y 6. Las principales conclusiones obtenidas son las siguientes: Se proponen modelos basados en regresiones, para un acondicionamiento con humedad relativa de 50%, para obtener el coeficiente de difusión del oxígeno según las relaciones: K=Dn, K=a*Dn y D=n/ρe. La propuesta para esta última relación es la que tiene un mejor ajuste con R2=0,999: D=(19,997*LNɛ+59,354)/ρe Ecuación 7 Los valores del coeficiente de difusión del oxígeno así estimados se ajustan a los obtenidos experimentalmente. Se considera adecuado el método propuesto de medida del coeficiente de difusión para gases. Los resultados obtenidos para el coeficiente de difusión del oxígeno se encuentran dentro del rango de los consultados en la literatura (10-7 a 10-8 m2/s) y son coherentes con el resto de parámetros estudiados. Los resultados de los factores de tortuosidad obtenidos de la relación Ø=Ø0*ɛ-τ son inferiores a la de la resistividad (ρ=ρ0*ɛ-τ). La relación que más se ajusta a ésta, siendo un 7,21% inferior, es la de la porosidad correspondiente al diámetro 1 µm con τ=2,07. Los resultados de los factores de tortuosidad obtenidos de la relación DO2=D0*ɛτ son similares a la de la resistividad: para la porosidad global τ=2,26 y para el resto de porosidades τ=0,7. Los coeficientes de difusión de radón estimados mediante estos factores de tortuosidad están dentro del rango de los consultados en la literatura (10-8 a 10-10 m2/s).

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

A model for chloride transport in concrete is proposed. The model accounts for transport several transport mechanisms such as diffusion, advection, migration, etc. This work shows the chloride transport equations at the macroscopic scale in non-saturated concrete. The equations involve diffusion, migration, capillary suction, chloride combination and precipitation mechanisms. The material is assumed to be infinitely rigid, though the porosity can change under influence of chloride binding and precipitation. The involved microscopic and macroscopic properties of the materials are measured by standardized methods. The variables which must be imposed on the boundaries are temperature, relative humidity and chloride concentration. The output data of the model are the free, bound, precipitated and total chloride ion concentrations, as well as the pore solution content and the porosity. The proposed equations are solved by means of the finite element method (FEM) implemented in MATLAB (classical Galerkin formulation and the streamline upwind Petrov-Galerkin (SUPG) method to avoid spatial instabilities for advection dominated flows).

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

Corrosion of steel bars embedded in concrete has a great influence on structural performance and durability of reinforced concrete. Chloride penetration is considered to be a primary cause of concrete deterioration in a vast majority of structures. Therefore, modelling of chloride penetration into concrete has become an area of great interest. The present work focuses on modelling of chloride transport in concrete. The differential macroscopic equations which govern the problem were derived from the equations at the microscopic scale by comparing the porous network with a single equivalent pore whose properties are the same as the average properties of the real porous network. The resulting transport model, which accounts for diffusion, migration, advection, chloride binding and chloride precipitation, consists of three coupled differential equations. The first equation models the transport of chloride ions, while the other two model the flow of the pore water and the heat transfer. In order to calibrate the model, the material parameters to determine experimentally were identified. The differential equations were solved by means of the finite element method. The classical Galerkin method was employed for the pore solution flow and the heat transfer equations, while the streamline upwind Petrov Galerkin method was adopted for the transport equation in order to avoid spatial instabilities for advection dominated problems. The finite element codes are implemented in Matlab® . To retrieve a good understanding of the influence of each variable and parameter, a detailed sensitivity analysis of the model was carried out. In order to determine the diffusive and hygroscopic properties of the studied concretes, as well as their chloride binding capacity, an experimental analysis was performed. The model was successfully compared with experimental data obtained from an offshore oil platform located in Brazil. Moreover, apart from the main objectives, numerous results were obtained throughout this work. For instance, several diffusion coefficients and the relation between them are discussed. It is shown how the electric field set up between the ionic species depends on the gradient of the species’ concentrations. Furthermore, the capillary hysteresis effects are illustrated by a proposed model, which leads to the determination of several microstructure properties, such as the pore size distribution and the tortuosity-connectivity of the porous network. El fenómeno de corrosión del acero de refuerzo embebido en el hormigón ha tenido gran influencia en estructuras de hormigón armado, tanto en su funcionalidad estructural como en aspectos de durabilidad. La penetración de cloruros en el interior del hormigón esta considerada como el factor principal en el deterioro de la gran mayoría de estructuras. Por lo tanto, la modelización numérica de dicho fenómeno ha generado gran interés. El presente trabajo de investigación se centra en la modelización del transporte de cloruros en el interior del hormigón. Las ecuaciones diferenciales que gobiernan los fenómenos a nivel macroscópico se deducen de ecuaciones planteadas a nivel microscópico. Esto se obtiene comparando la red porosa con un poro equivalente, el cual mantiene las mismas propiedades de la red porosa real. El modelo está constituido por tres ecuaciones diferenciales acopladas que consideran el transporte de cloruros, el flujo de la solución de poro y la transferencia de calor. Con estas ecuaciones se tienen en cuenta los fenómenos de difusión, migración, advección, combinación y precipitación de cloruros. El análisis llevado a cabo en este trabajo ha definido los parámetros necesarios para calibrar el modelo. De acuerdo con ellas, se seleccionaron los ensayos experimentales a realizar. Las ecuaciones diferenciales se resolvieron mediante el método de elementos finitos. El método clásico de Galerkin se empleó para solucionar las ecuaciones de flujo de la solución de poro y de la transferencia de calor, mientras que el método streamline upwind Petrov-Galerkin se utilizó para resolver la ecuación de transporte de cloruros con la finalidad de evitar inestabilidades espaciales en problemas con advección dominante. El código de elementos finitos está implementado en Matlab® . Con el objetivo de facilitar la comprensión del grado de influencia de cada variable y parámetro, se realizó un análisis de sensibilidad detallado del modelo. Se llevó a cabo una campaña experimental sobre los hormigones estudiados, con el objeto de obtener sus propiedades difusivas, químicas e higroscópicas. El modelo se contrastó con datos experimentales obtenidos en una plataforma petrolera localizada en Brasil. Las simulaciones numéricas corroboraron los datos experimentales. Además, durante el desarrollo de la investigación se obtuvieron resultados paralelos a los planteados inicialmente. Por ejemplo, el análisis de diferentes coeficientes de difusión y la relación entre ellos. Así como también se observó que el campo eléctrico establecido entre las especies iónicas disueltas en la solución de poro depende del gradiente de concentración de las mismas. Los efectos de histéresis capilar son expresados por el modelo propuesto, el cual conduce a la determinación de una serie de propiedades microscópicas, tales como la distribución del tamaño de poro, además de la tortuosidad y conectividad de la red porosa.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion Bt of known Hurst index H, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around H ? 0.30, a value in the subdiffusive regime.

Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Source terms for calculations of vaporizing and burning fuel sprays with non-unity Lewis numbers in gases with temperature-dependent thermal conductivities

Liquid-fueled burners are used in a number of propulsion devices ranging from internal combustion engines to gas turbines. The structure of spray flames is quite complex and involves a wide range of time and spatial scales in both premixed and non-premixed modes (Williams 1965; Luo et al. 2011). A number of spray-combustion regimes can be observed experimentally in canonical scenarios of practical relevance such as counterflow diffusion flames (Li 1997), as sketched in figure 1, and for which different microscalemodelling strategies are needed. In this study, source terms for the conservation equations are calculated for heating, vaporizing and burning sprays in the single-droplet combustion regime. The present analysis provides extended formulation for source terms, which include non-unity Lewis numbers and variable thermal conductivities.