On the statistical estimation of diffusion processes: a survey

Data available on continuos-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).

On the statistical estimation of diffusion processes - a partial survey

Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the employment of Martingale Estimating Functions, and the application of Generalized Method of Moments (GMM).

Foreign direct investment spillovers: what can we learn from portuguese data?

This paper investigates the impact of foreign direct investment on the productivity performance of domestic firms in Portugal. The data comprise nine manufacturing sectors for the period 1992-95. Relatively to previous studies, model specification is improved by taking into consideration several aspects: the influence of the “technological gap” on spill-overs diffusion and the choice of its most appropriate interval; sectoral variation in the coefficients of the spill-overs effect; identification of constant, idiosyncratic sectoral factors by means of a fixed effects model; and the search for inter-sectoral positive spillover effects. The relationship between domestic firms productivity and the foreign presence does take place in a positive way, only if a proper technology differential between the foreign and domestic producers exists and the sectoral characteristics are favourable. In broad terms, spillovers diffusion is associated to modern industries in which the foreign owned establishments have a clear, but not too sharp, edge on the domestic ones. Besides, other specific sectoral influences can be pertinent; agglomerative location factors being one example.

Estimation of random coefficients logit demand models: an application to the Brazilian fixed income fund market

Estimation of demand and supply in differentiated products markets is a central issue in Empirical Industrial Organization and has been used to study the effects of taxes, merges, introduction of new goods, market power, among others. Logit and Random Coefficients Logit are examples of demand models used to study these effects. For the supply side it is generally supposed a Nash equilibrium in prices. This work presents a detailed discussion of these models of demand and supply as well as the procedure for estimation. Lastly, is made an application to the Brazilian fixed income fund market.

Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media

Estudo da desidratação de tomates em pedaços com pré-tratamento osmótico

Vegetables drying plays an important role in the field of food dehydration, being a very old practice that was originated from sun drying items of food in order to preserve them to be consumed during the periods of scarcity. One of these vegetables is the tomato, that was originally grown in South America. Tomatoes are easily perishable after being picked up from the tree and this makes the process of tomato dehydration a challenge due to the high amount of water (95%) contained in them. The present research work was mainly intended to develop alternative processes for tomato conservation, by drying slices of skinned and unskinned tomatoes in the in natura form or in the osmotically pre-dehydrated form. Firstly, the best conditions of the osmotic pre-dehydration process were defined including temperature, immersion time and concentration of the osmotic solution, based on the results of water loss, solids gain and weigh reduction of the pre-dehydration tomatoes at different processing conditions. The osmotic solution used was made up of NaCl (5 and 10%) and sucrose (25 and 35%) at different combinations. For a fixed conditions of osmotic pre-dehydration, the drying tests of the pre-processed and in natura tomatoes were carried out in a stove with air circulation and a convective dryer with trays, at two levels of temperature. The sensorial analysis of the osmotically pre-treated and unskinned dehydrated tomatoes was carried out as well as a study on the their shelf-live. The results obtained showed that the drying of the tomatoes took place as a result of the internal control of the water transport, and did not show a constant rate, while two distinct periods of the decreasing phase were observed. The osmotic pre treatment substancially reduced the initial amount of humidity in the tomatoes, thus reducing the necessary time for the product to attain levels of intermediate humidity. The impermeability of the tomato skin was identified as well as the unfavorable influence of the pre-treatment on the unskinned tomatoes, whose solid gain brought about a decrease in the water activity with subsequent reduction of the drying rate. Despite the various simplifications carried out during the development of this study, the proposed diffusive model adjusted to the experimental data satisfactorily, thus making it possible to determine the effective coefficients of diffusion, whose results were consistent and compatible with those found in the current literature. Concerning the higher rates of evaporation and the lowest processing time, the best results were obtained in the drying of the unskinned, in natura tomatoes and of the skinned, pre-dehydrated tomatoes, at 60ºC, both processed in the convective drier. The results of the sensorial analysis of the unskinned and pre-treated product did not prove to be satisfactory. Regarding the shelf-live of the tomatoes, for a period of 45 days, no physicochemical or microbiological alteration of the product was noted

Development and validation of a stability-indicative agar diffusion assay to determine the potency of linezolid in tablets in the presence of photodegradation products

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Measurement of oxygen atom diffusion in Nb and Ta by anelastic spectroscopy

Impurity interstitial atoms present in metals with BCC structure can diffuse in the metallic matrix by jumps to energetically equivalent crystallographic sites. Anelastic spectroscopy (internal friction) is based on the measurement of mechanical loss or internal friction as a function of temperature. Due to its selective and nondestructive nature, anelastic spectroscopy is well suited for the study of diffusion of interstitial elements in metals. Internal friction measurements were made using the torsion pendulum technique with oscillation frequency of a few Hz, temperature interval from 300 to 700 K, heating rate of about 1 K/min, and vacuum better than 10-5 mbar. The polycrystalline Nb and Ta samples used were supplied by Aldrich Inc. The results obtained showed thermally activated relaxation structures due to stress-induced ordering of oxygen atoms around the Nb (or Ta) atoms of the metallic matrix. The results were interpreted by three methods and led to activation enthalpy values for the diffusion of oxygen in Nb and Ta of 1.15 eV and 1.10 eV, respectively.

Determination of the oxygen and nitrogen interstitial diffusion coeficient in niobium by mechanical spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Diffusion of Interstitial Elements in Ti Alloys used as Biomaterials

Titanium alloys are excellent implant materials for orthopedic applications due to their desirable properties, such as good corrosion resistance, low elasticity modulus, and excellent biocompatibility. The presence of interstitial elements (such as oxygen and nitrogen) causes strong changes in the material's mechanical properties, mainly in its elastic properties. Study of the interaction among interstitial elements present in metals began with Snoek's postulate, that a stress-induced ordering of interstitials gives rise to a peak in the mechanical relaxation (internal friction) spectra. In the mechanical relaxation spectra, each species of interstitial solute atom gives rise to a distinct Snoek's peak, whose temperature and position depend on the measurement frequency. This effect is very interesting because its peculiar parameters are directly related to the diffusion coefficient (D) for the interstitial solute. This paper presents a study of diffusion of heavy interstitial elements in Ti-35Nb-7Zr-5Ta alloys using mechanical spectroscopy. Pre-exponential factors and activation energies are calculated for oxygen and nitrogen in theses alloys.

Oxygen diffusion in superconducting oxides

Since the discovery of high-temperature superconductivity of cuprate oxides, it has been clear that it is strongly affected by the oxygen content, which is also a crucial factor to determine other physical properties of high T-c superconductors. Non-stoichiometric (interstitial) oxygen strongly influences the physical properties of various superconducting oxides, in particular by creating conducting holes. It is now ascertained that the amount of holes injected depends not only on the content of interstitial oxygen, but also on its ordering. Rearrangement of the oxygen ordering may occur even below room temperature due to the unusual high mobility of these atoms. This way, mechanical spectroscopy is one of the most adequate techniques for the study of the mobility (diffusion) of oxygen atoms. This technique allows the determination of the jump frequency of an atomic species precisely, regardless of the model or the different possible types of jumps. In order to evaluate the mobility and the effect of oxygen content on these oxides, ceramic samples we prepared and submitted to several oxygen removal cycles alternately with mechanical relaxation measurements. As for SBCO, it was assumed that the peak was due to O(1)-O(5) jumps of oxygen atoms at the chain terminals or in chain fragments in the orthorhombic phase. In the case of BSCCO, the results showed complex anelastic relaxation structures, which were attributed to interstitial oxygen atom jumps between two adjacent CuO planes.

Oxygen diffusion in Ti-10Mo alloys measured by mechanical spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Oxygen Diffusion in Ti-20Mo Alloys, used as Biomaterial, Measured by Mechanical Spectroscopy

Titanium alloys are favorable implant materials for orthopedic applications, due to their desirable properties such as good corrosion resistance, low elasticity modulus, and excellent biocornpatibility. The research on titanium alloys is concentrated in the beta type, as the Ti-20Mo alloys and the addition of interstitial elements in these metals cause changes in their mechanical properties. The mechanical spectroscopy measurements have been frequently used in order to verify the behavior of these interstitials atoms in metallic alloys. This paper presents the study of oxygen diffusion in Ti-20Mo alloys using mechanical spectroscopy measurements. A thermally activated relaxation structure was observed in the sample after oxygen doping. It was associated with the interstitial diffusion of oxygen atoms in a solid solution in the alloy. The diffusion coefficient for the oxygen diffusion in the alloy was obtained by the frequency dependence of the peak temperature and by using a simple mathematical treatment of the relaxation structure and the Arrhenius law.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)