Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Grain size distributions of Magneli phases and metallic titanium in chondritic porous interplanetary dust particles

A mineralogical survey of chondritic interplanetary dust particles (IDPs)showed that these micrometeorites differ significantly in form and texture from components of carbonaceous chondrites and contain some mineral assemblages which do not occur in any meteorite class1. Models of chondritic IDP mineral evolution generally ignore the typical (ultra-) fine grain size of consituent minerals which range between 0.002-0.1µm in size2. The chondritic porous (CP) subset of chondritic IDPs is probably debris from short period comets although evidence for a cometary origin is still circumstantial3. If CP IDPs represent dust from regions of the Solar System in which comet accretion occurred, it can be argued that pervasive mineralogical evolution of IDP dust has been arrested due to cryogenic storage in comet nuclei. Thus, preservation in CP IDPs of "unusual meteorite minerals", such as oxides of tin, bismuth and titanium4, should not be dismissed casually. These minerals may contain specific information about processes that occurred in regions of the solar nebula, and early Solar System, which spawned the IDP parent bodies such as comets and C, P and D asteroids6. It is not fully appreciated that the apparent disparity between the mineralogy of CP IDPs and carbonaceous chondrite matrix may also be caused by the choice of electron-beam techniques with different analytical resolution. For example, Mg-Si-Fe distributions of Cl matrix obtained by "defocussed beam" microprobe analyses are displaced towards lower Fe-values when using analytical electron microscope (AEM)data which resolve individual mineral grains of various layer silicates and magnetite in the same matrix6,7. In general, "unusual meteorite minerals" in chondritic IDPs, such as metallic titanium, Tin01-n(Magneli phases) and anatase8 add to the mineral data base of fine-grained Solar System materials and provide constraints on processes that occurred in the early Solar System.

Mineralogy of chondritic porous aggregates : current status

Chondritic porous aggregates (CPA's) belong to an important subset of small particles (usually between 5 and 50 micrometers) collected from the stratosphere by high flying aircraft. These aggregates are approximately chondritic in elemental abundance and are composed of many thousands of small­er, submicrometer particles. CPA particles have been the subject of intensive study during the past few years [1-3] and there is strong evidence that they are a new class of extraterrestrial material not represented in the meteorite collection [3,4]. However, CPA's may be related to carbonaceous chondrites and in fact, both may be part of a continuum of primitive extraterrestrial materials [5]. The importance of CPA's stems from suggestions that they are very primitive solar system material possibly derived from early formed proto­ planets, chondritic parent bodies, or comets [3, 6]. To better understand the origin and evolution of these particles, we have attempted to summarize all of the mineralogical data on identified CPA's published since about 1976.

A multi-stage history for carbonaceous material in extraterrestrial chondritic porous aggregate W7029*A and a new cosmothermometer

A new set of primitive extraterrestrial materials collected in the Earth's stratosphere include Chondritic Porous Aggregates (CPA's) [1]. CPAs have a complex and variable mineralogy [1-3] that include 'organic compounds' [4,5] and poorly graphitised carbon (PGC)[6]. This study presents a continuation of our detailed Analytical Electron Microscope study on carbon-rich CPA W7029*A from the JSC Cosmic Dust Collection. This CPA is an uncontaminated sample that survived atmospheric entry without appreciable alteration [7] and which contains ~44% carbonaceous material. The carbonaceous composition of selected particles was confirmed by Electron Energy Loss Spectroscopy and Selected Area Electron Diffraction (SAED). Possible carbonaceous contaminants introduced by specimen preparation techniques are easily recognised from indigenous CPA carbon particles [8] and do not bias our interpretations.

Conduction-radiation effect on natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

The effect of conduction-convection-radiation on natural convection flow of Newtonian optically thick gray fluid, confined in a non-Darcian porous media square cavity is numerically studied. For the gray fluid consideration is given to Rosseland diffusion approximation. Further assuming that (i) the temperature of the left vertical wall is varying linearly with height, (ii) cooled right vertical and top walls and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the Alternate Direct Implicit method together with the Successive Over Relaxation technique. The investigation of the effect of governing parameters namely the Forschheimer resistance (Γ), the Planck constant (Rd), and the temperature difference (Δ), on flow pattern and heat transfer characteristics has been carried out. It was seen that the reduction of flow and heat transfer occurs as the Forschheimer resistance is increased. On the other hand both the strength of flow and heat transfer increases as the temperature ratio, Δ, is increased.

Titanium-oxide magneli phases in four chondritic porous interplanetary dust particles

Detailed analytical electron microscope analyses of four fine-grained chondritic porous interplanetary dust particles (IDPs)reveal the presence of titanium oxide Magneli phases, TinO2n-1 (n=4,5,6), and rare Ti-metal. The titanium minerals are indigenous to these chondritic IDPs. The association of Magneli phases, Ti-metal, and carbonaceous material in chondritic IDPs, along with the grain size distributions support in situ solid carbon gasification in these extraterrestrial particles. The active catalyst in this process is titanium metal that we infer may be of interstellar origin. This favorable catalysis uniquely leads to the formation of Magneli phases. As chondritic IDPs may be solid debris of short-period comets, our data indicate that nuclei of short-period comets may show distinctive chemical reactions that lead to Ti-mineral assemblages that typically include Magneli phases. The proposed model provides a plausible mechnism to explain the higher solid carbon content of chondritic IDPs relative to bulk carbon abundances typical for carbonaceous chondrite matrices that represent another type of more evolved, that is, metamorphosed, undifferentiated solar system bodies.

Metastable carbon in two chondritic porous interplanetary dust particles

An understanding of carbonaceous matter in primitive extraterrestrial materials is an essential component of studies on dust evolution in the interstellar medium and the early history of the Solar System. We have suggested previously that a record of graphitization is preserved in chondritic porous (CP) aggregates and carbonaceous chondrites1,2 and that the detailed mineralogy of CP aggregates can place boundary conditions on the nature of both physical and chemical processes which occurred at the time of their formation2,3. Here, we report further analytical electron microscope (AEM) studies on carbonaceous material in two CP aggregates which suggest that a record of hydrocarbon carbonization may also be preserved in these materials. This suggestion is, based upon the presence of well-ordered carbon-2H (lonsdaleite) in CP aggregates W7029*A and W7010*A2. This carbon is a metastable phase resulting from hydrous pyrolysis below 300-350°C and may be a precursor to poorly graphitized carbons (PGCs) in primitive extraterrestrial materials2. © 1987 Nature Publishing Group.

Layer silicates in a chondritic porous interplanetary dust particle

Analytical electron microscopy on individual grains from a portion of a chondritic porous interplanetary dust particle (aggregate W7029C1 from the NASA Johnson Space Center Cosmic Dust Collection) shows that layer silicates compose 50 percent of the silicate fraction examined. These layer silicates can be classified into two distinct crystallochemical groups: (1) fine-grained, polycrystalline smectite minerals; and (2) well-ordered, single crystals of kaolinite and Mg-poor talc. The layer silicates in this portion of sample W7029(asterisk)A are dissimilar to those described in other chondritic porous aggregates. The predominant layer silicate assemblage in W7029(asterisk)A indicates that heating of the aggregate during atmospheric entry was brief and probably to a temperature less than 300C. Comparison with terrestrial phyllosilicate occurrences suggests that some layer silicates in aggregate W7029(asterisk)A may have been formed by alteratiton from preexisting silicate minerals at low temperatures (less than 25C) after aggregate formation.

Diagenesis in interplanetary dust - chondritic porous aggregate w7029-star-a

In previous Analytical Electron Microscope studies of extraterrestrial Chondritic Porous Aggregate (CPA) W7029* A, we have reported on the presence of layer silicates(Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1983) and metal oxides (Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1984). We present here a continuation ofthis detailed mineralogical study and propose a scenario which may account for the variety and types of phases observed in this CPA. At least 50% ofCPA W7029*A is carbonaceous material, primarily poorly graphitised carbon (POC) with morphologies similar to POC in acid residues of carbonaceous chondrites (Smith and Busek, 1981; Lumpkin, 1983). The basal spacing of graphite in CPA W7029*A ranges from 3.47-3.52 A and compares with doo, of graphite in the Allende residues (Smith and Buseck, 1981; Lumpkin, 1983). Low-temperature phases comprise - 20% of CPA W7029*A and include layer silicates, Bi,O" a-FeOOH(Rietmeijer and Mackinnon, 1984a; Mackinnon and Rietmeijer, 1983), BaSO.,.Ti.O, plates, pentlandite-violarite and bornite. Clusters of Mg-rich olivine and pyroxene make up - 12% of the aggregate...

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

In situ SANS study of the surface and pore filling adsorption of subcritical and supercritical CO2 in porous silica as a function of pore size

We applied small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) to monitor evolution of the CO2 adsorption in porous silica as a function of CO2 pressure and temperature in pores of different sizes. The range of pressures (0 < P < 345 bar) and temperatures (T=18 OC, 35 OC and 60 OC) corresponded to subcritical, near critical and supercritical conditions of bulk fluid. We observed that the adsorption behavior of CO2 is fundamentally different in large and small pores with the sizes D > 100 Å and D < 30 Å, respectively. Scattering data from large pores indicate formation of a dense adsorbed film of CO2 on pore walls with the liquid-like density (ρCO2)ads≈0.8 g/cm3. The adsorbed film coexists with unadsorbed fluid in the inner pore volume. The density of unadsorbed fluid in large pores is temperature and pressure dependent: it is initially lower than (ρCO2)ads and gradually approaches it with pressure. In small pores compressed CO2 gas completely fills the pore volume. At the lowest pressures of the order of 10 bar and T=18 OC, the fluid density in smallest pores available in the matrix with D ~ 10 Å exceeds bulk fluid density by a factor of ~ 8. As pressure increases, progressively larger pores become filled with the condensed CO2. Fluid densification is only observed in pores with sizes less than ~ 25 – 30 Å. As the density of the invading fluid reaches (ρCO2)bulk~ 0.8 g/cm3, pores of all sizes become uniformly filled with CO2 and the confinement effects disappear. At higher densities the fluid in small pores appears to follow the equation of state of bulk CO2 although there is an indication that the fluid density in the inner volume of large pores may exceed the density of the adsorbed layer. The equivalent internal pressure (Pint) in the smallest pores exceeds the external pressure (Pext) by a factor of ~ 5 for both sub- and supercritical CO2. Pint gradually approaches Pext as D → 25 – 30 Å and is independent of temperature in the studied range of 18 OC ≤ T ≤ 60 OC. The obtained results demonstrate certain similarity as well as differences between adsorption of subcritical and supercritical CO2 in disordered porous silica. High pressure small angle scattering experiments open new opportunities for in situ studies of the fluid adsorption in porous media of interest to CO2 sequestration, energy storage, and heterogeneous catalysis.

A framework for a dense matching algorithm : Results using matching metrics and order statistic filters

An algorithm for computing dense correspondences between images of a stereo pair or image sequence is presented. The algorithm can make use of both standard matching metrics and the rank and census filters, two filters based on order statistics which have been applied to the image matching problem. Their advantages include robustness to radiometric distortion and amenability to hardware implementation. Results obtained using both real stereo pairs and a synthetic stereo pair with ground truth were compared. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.