A moving-boundary problem for concrete carbonation: Global existence and uniqueness of weak solutions

This paper deals with a one-dimensional coupled system of semi-linear parabolic equations with a kinetic condition on the moving boundary. The latter furnishes the driving force for the moving boundary. The main result is a global existence and uniqueness theorem of positive weak solutions. The system under consideration is modelled on the so-called carbonation of concrete - a prototypical chemical-corrosion process in a porous solid - concrete - which incorporates slow diffusive transport, interfacial exchange between wet and dry parts of the pores and, in particular, a fast reaction in thin layers, here idealized as a moving-boundary surface in the solid. We include simulation results showing that the model captures the qualitative behaviour of the carbonation process.     

A moving two-reaction zones model: global existence of solutions

We address some aspects concerning the analysis of a moving-boundary system modeling concrete carbonation. The model is based on the fact that carbonation might be considered as a reaction which is localized on two distinct a priori unknown internal zones which progress into concrete. We report on the existence of local and global weak solutions. The main feature of the problem is that the nonlinear coupling of the system occurs due to the moving boundary and nonlinearity of the involved productions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large time behavior of a solution of carbon dioxide transport model in concrete carbonation process

In [7] we show the global existence and uniqueness of a solution of carbon dioxide transport model in concrete carbonation process. This model is governed by a parabolic-type equation which has a non-local term depending on the unknown function itself. In this paper, we show the large time behavior of that solution.     

An immersed-boundary method for compressible viscous flows and its application in the gas-kinetic BGK scheme

An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible and compressible viscous flows with complex stationary and moving boundaries on stationary Cartesian grids. In this method the ghost-cell technique is used to satisfy the boundary condition on the immersed boundary. A novel idea, “local boundary determination”, is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments. Thus, the singular behavior of the ghost cell is eliminated. Furthermore, the so-called “fresh-cell” problem that occurs when implementing the IB method in a moving-boundary simulation is resolved by a simple temporal extrapolation. The method is first applied in the gas-kinetic BGK scheme to simulate the Taylor–Couette flow, wherein the second-order spatial accuracy of the method is validated and the “super-convergence” of the BGK scheme is observed. After that the flow between a circular cylinder and a square cylinder is used as a test case to showcase the advantage of this method in resolving the singularity problem. Then the supersonic flow around a stationary cylinder, the incompressible flow around an oscillating cylinder and the compressible flow around a moving airfoil are simulated to verify that this method can be used to simulate compressible flows and handle moving boundaries. These numerical tests demonstrate the good performance of the proposed immersed-boundary method for the study of incompressible/compressible flow problems with complex stationary/moving boundaries.     

Gaussian moving averages,semimartingales and option pricing

We provide a characterization of the Gaussian processes with stationary increments that can be represented as a moving average with respect to a two-sided Brownian motion. For such a process we give a necessary and sufficient condition to be a semimartingale with respect to the filtration generated by the two-sided Brownian motion. Furthermore, we show that this condition implies that the process is either of finite variation or a multiple of a Brownian motion with respect to an equivalent probability measure. As an application we discuss the problem of option pricing in financial models driven by Gaussian moving averages with stationary increments. In particular, we derive option prices in a regularized fractional version of the Black–Scholes model.     

The influence of the oceans on the atmospheric burden of carbon dioxide

An important component in the climatic balance of atmospheric carbon dioxide is the interaction of the atmospheric and oceanic systems of the earth. Transport across the ocean surface and vertical mixing into the deep oceans provide mechanisms whereby carbon dioxide released by fossil fuel combustion is eventually transferred into the ocean depths. Mathematical treatments enable one to calculate the time-scale for accumulation of carbon dioxide in the atmosphere and it is shown that a simple two-reservoir model is equivalent to a more intricate three-reservoir system for calculations over the next century at least. The physical parameters needed to apply these models are considered and results concerning past and future trends are presented.     

Adhesive contact problem for viscoplastic materials

We examine a mathematical model that describes a quasistatic adhesive contact between a viscoplastic body and deformable foundation. The material’s behaviour is described by the rate-type constitutive law which involves functions with a non-polynomial growth. The contact is modelled by the normal compliance condition with limited penetration and adhesion, a subdifferential friction condition also depending on adhesion, and the evolution of bonding field is governed by an ordinary differential equation. We present the variational formulation of this problem which is a system of an almost history-dependent variational–hemivariational inequality for the displacement field and an ordinary differential equation for the bonding field. The results on existence and uniqueness of solution to an abstract almost history-dependent inclusion and variational–hemivariational inequality in the reflexive Orlicz–Sobolev space are proved and applied to the adhesive contact problem.     

Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems

Although the numerical solution of one-dimensional phase-change, or Stefan, problems is well documented, a review of the most recent literature indicates that there are still unresolved issues regarding the start-up of a computation for a region that initially has zero thickness, as well as how to determine the location of the moving boundary thereafter. This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes. We demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used, and is numerically second-order accurate in both time and space, a point that has been consistently overlooked for this type of moving-boundary problem.     

Lower Bounds for Kinetic Planar Subdivisions

We revisit the notion of kinetic efficiency for noncanonically defined discrete attributes of moving data, like binary space partitions and triangulations. Under reasonable computational models, we obtain lower bounds on the minimum amount of work required to maintain any binary space partition of moving segments in the plane or any Steiner triangulation of moving points in the plane. Such lower bounds—the first to be obtained in the kinetic context—are necessary to evaluate the efficiency of kinetic data structures when the attribute to be maintained is not canonically defined. Received June 10, 1999, and in revised form March 9, 2000. {\it Online publication August\/ 11, 2000.}     

Computational adequacy for recursive types in models of intuitionistic set theory

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models.     

Towards Riccati-Feedback Control of Complex Flows with Moving Interfaces

Problems featuring moving interfaces appear in many applications. They can model solidification and melting of pure materials, crystal growth and other multi-phase problems. The control of the moving interface enables to, for example, influence production processes and, thus, the product material quality. We consider the two-phase Stefan problem that models a solid and a liquid phase separated by the moving interface. In the liquid phase, the heat distribution is characterized by a convection-diffusion equation. The fluid flow in the liquid phase is described by the Navier–Stokes equations which introduces a differential algebraic structure to the system. The interface movement is coupled with the temperature through the Stefan condition, which adds additional algebraic constraints. Our formulation uses a sharp interface representation and we define a quadratic tracking-type cost functional as a target of a control input. We compute an open loop optimal control for the Stefan problem using an adjoint system. For a feedback representation, we linearize the system about the trajectory defined by the open loop control. This results in a linear-quadratic regulator problem, for which we formulate the differential Riccati equation with time varying coefficients. This Riccati equation defines the corresponding feedback gain. Further, we present the feedback formulation that takes into account the structure and the differential algebraic components of the problem. Also, we discuss how the complexities that come, for example, with mesh movements, can be handled in a feedback setting. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of the bicarbonate system in the blood

In this paper, we describe a mathematical model about the reaction-diffusion kinetics of bicarbonate system, which it plays a key role in regulating blood pH. It is very important to know the determinants of blood pH in both experimental and theoretical studies, in order to help to investigate the hidden mechanism of acid-base disorders in the clinical setting. We explore the dynamics of the bicarbonate system under the closed condition. This condition yields that the total amount of carbon dioxide is conserved and the difference in concentrations between anions and cations is conserved. For the stability of the model, we hypothesize that the amount of initial concentrations perturbed around an equilibrium point is less than a certain constant depending on a rate constant. With an application of Liapunov's method, we prove that the model in the form of reaction-diffusion system is globally stable under the hypothesis. We also provide the blood pH profile, which is computed in our model with the experimentally observed rate constants.     

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

In this paper, we are interested in the long time behavior of approximate solutions to a free boundary model which appears in the modeling of concrete carbonation [1]. In particular, we study the long time regime of the moving interface. The numerical solutions are obtained by an implicit in time and finite volume in space scheme. We show the existence of solutions to the scheme and, following [2‐3], we prove that the approximate free boundary increases in time following a ‐law. Finally, we supplement the study through numerical experiments.     

中国碳排放的省域差异及影响因素的实证研究

参照IPCC(2006)以及国家气候变化对策协调小组办公室和国家发改委能源研究所)的方法,估算了我国30个省(直辖市、自治区)的1997—2011年期间的二氧化碳排放量.数据显示,我国各省(直辖市、自治区)的二氧化碳排放量从整体上基本都呈现出上升趋势,地区差异比较显著.总体上来讲,我国的二氧化碳排放量呈现出由东到西依次递减的规律特征,东部地区的二氧化碳排放量最多,中部地区次之,西部地区二氧化碳排放量最少,而且东部地区的二氧化碳排放在绝对量上大大超过中西两大区域.产业结构和经济发展是影响各地区二氧化碳排放量的主要因素,能源消费结构和出口贸易对各地区碳排放量的影响不显著.     

基于组合赋权法的我国CO2排放量影响因素的评价研究

为客观和准确地挖掘和评价我国CO₂排放量影响因素,选取技术投入、对外贸易开放程度、产业结构、能源消费结构、经济增长水平、人口规模和绿色植被用地面积等因素作为评价依据,构建我国CO₂排放量影响因素指标体系。在此基础上,基于组合赋权法构建我国CO₂排放量影响因素评价模型,实证分析2000~2011年我国CO₂排放量影响因素。组合赋权法结果显示:技术投入、产业结构、能源消费结构、经济增长和绿色植被用地面积是影响我国CO₂排放量的主要因素。组合赋权法在我国CO₂排放量影响因素评价分析的运用,提高了评价的客观性和科学性,为进一步确定CO₂排放量影响因素提供有价值的参考。     

Cavity Volume and Free Energy in Many-Body Systems

Most models for the spread of an invasive species into a new environment are based on Fisher’s reaction–diffusion equation. They assume that habitat quality is independent of the presence or absence of the invading population. Ecosystem engineers are species that modify their environment to make it (more) suitable for them. A potentially more appropriate modeling approach for such an invasive species is to adapt the well-known Stefan problem of melting ice. Ahead of the front, the habitat is unsuitable for the species (the ice); behind the front, the habitat is suitable (the open water). The engineering action of the population moves the boundary ahead (the melting). This approach leads to a free boundary problem. In this paper, we study the well-posedness of a novel free boundary model for the spread of ecosystem engineers that was recently derived from an individual random walk model. The Stefan condition for the moving boundary is replaced by a biologically derived two-sided condition that models the movement behavior of individuals at the boundary as well as the process by which the population moves the boundary to expand their territory. Our proofs consist of several new and novel ideas that can be used in broader contexts. We assign a convex functional to this problem so that the evolution system governed by this convex potential is exactly the system of evolution equations describing the above model. We then apply variational and fixed-point methods to deal with this free boundary problem.

     

On the Existence of Weak Solutions for a 1-D Free-Boundary Concrete Carbonation Problem

In this paper we deal with a one-dimensional free-boundary problem arising in the modeling of concrete carbonation process. More precisely, we investigate global existence, uniqueness and large-time behavior of weak solutions for the problem under consideration. We also obtain the existence of a weak solution when the measure of the initial domain vanishes.