Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams

Illumination uniformity of a spherical capsule directly driven by laser beams has been assessed numerically. Laser facilities characterized by ND = 12, 20, 24, 32, 48 and 60 directions of irradiation with associated a single laser beam or a bundle of NB laser beams have been considered. The laser beam intensity profile is assumed super-Gaussian and the calculations take into account beam imperfections as power imbalance and pointing errors. The optimum laser intensity profile, which minimizes the root-mean-square deviation of the capsule illumination, depends on the values of the beam imperfections. Assuming that the NB beams are statistically independents is found that they provide a stochastic homogenization of the laser intensity associated to the whole bundle, reducing the errors associated to the whole bundle by the factor  , which in turn improves the illumination uniformity of the capsule. Moreover, it is found that the uniformity of the irradiation is almost the same for all facilities and only depends on the total number of laser beams Ntot = ND × NB.

Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization

Computational homogenization by means of the finite element analysis of a representative volume element of the microstructure is used to simulate the deformation of nanostructured Ti. The behavior of each grain is taken into account using a single crystal elasto-viscoplastic model which includes the microscopic mechanisms of plastic deformation by slip along basal, prismatic and pyramidal systems. Two different representations of the polycrystal were used. Each grain was modeled with one cubic finite element in the first one while many cubic elements were used to represent each grain in the second one, leading to a model which includes the effect of grain shape and size in a limited number of grains due to the computational cost. Both representations were used to simulate the tensile deformation of nanostructured Ti processed by ECAP-C as well as the drawing process of nanostructured Ti billets. It was found that the first representation based in one finite element per grain led to a stiffer response in tension and was not able to predict the texture evolution during drawing because the strain gradient within each grain could not be captured. On the contrary, the second representation of the polycrystal microstructure with many finite elements per grain was able to predict accurately the deformation of nanostructured Ti.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Ecological Homogenization of Urban USA

A visually apparent but scientifically untested outcome of land-use change is homogenization across urban areas, where neighborhoods in different parts of the country have similar patterns of roads, residential lots, commercial areas, and aquatic features. We hypothesize that this homogenization extends to ecological structure and also to ecosystem functions such as carbon dynamics and microclimate, with continental-scale implications. Further, we suggest that understanding urban homogenization will provide the basis for understanding the impacts of urban land-use change from local to continental scales. Here, we show how multi-scale, multi-disciplinary datasets from six metropolitan areas that cover the major climatic regions of the US (Phoenix, AZ; Miami, FL; Baltimore, MD; Boston, MA; Minneapolis–St Paul, MN; and Los Angeles, CA) can be used to determine how household and neighborhood characteristics correlate with land-management practices, land-cover composition, and landscape structure and ecosystem functions at local, regional, and continental scales.

Homogenization of elliptic problems in thin domains with oscillatory boundaries

Los dominios finos, es decir, dominios sustancialmente más pequeños en alguna o varias de sus direcciones que en el resto, aparecen en muchos campos de la ciencia. Por ejemplo, dinámica de fluídos (lubricación, conducción de fluídos en tubos delgados, dinámica de oceanos...), mecánica de sólidos (barras delgadas, placas o cáscaras) o incluso en fisiología (circulación de la sangre). Así, el amplio número de posibles aplicaciones a situaciones reales ha hecho que la investigación de modelos de ecuaciones en derivadas parciales en dominios finos se convierta en un tema muy estudiado en los últimos años. Desde un punto de vista matemático, el estudio de las soluciones de una EDP en un dominio fino es un caso particular de la cuestión general relativa a cómo la variación de los dominios afecta al comportamiento de las soluciones de la EDP. En este marco, obtener la ecuación límite del modelo considerado, comparar la solución de la ecuación límite y las soluciones del problema en el dominio fino, analizar los coeficientes de la ecuación límite y comprender cómo la geometría del dominio afecta a la ecuación límite son algunos de los objetivos que deberían ser alcanzados. De hecho, es importante señalar que este tipo de cuestiones no sólo proporcionan importantes resultados teóricos sino que son muy relevantes desde el punto de vista de las aplicaciones. Por ejemplo, ser capaz de reducir el problema original a un problema mucho más sencillo, problema límite, que refleje las principales características del problema de partida puede ser muy útil para ingenieros y físicos...

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Ultra high pressure homogenization (UHPH) inactivation of Bacillus amyloliquefaciens spores in phosphate buffered saline (PBS) and milk

Ultra high pressure homogenization (UHPH) opens up new areas for dynamic high pressure assisted thermal sterilization of liquids. Bacillus amyloliquefaciens spores are resistant to high isostatic pressure and temperature and were suggested as potential surrogate for high pressure thermal sterilization validation. B. amyloliquefaciens spores suspended in PBS buffer (0.01 M, pH 7.0), low fat milk (1.5%, pH 6.7), and whole milk (3.5%, pH 6.7) at initial concentration of similar to 10(6) CFU/mL were subjected to UHPH treatments at 200, 300, and 350 MPa with an inlet temperature at similar to 80 degrees C. Thermal inactivation kinetics of B. amyloliquefaciens spores in PBS and milk were assessed with thin wall glass capillaries and modeled using first-order and Weibull models. The residence time during UHPH treatments was estimated to determine the contribution of temperature to spore inactivation by UHPH. No sublethal injury was detected after UHPH treatments using sodium chloride as selective component in the nutrient agar medium. The inactivation profiles of spores in PBS buffer and milk were compared and fat provided no clear protective effect for spores against treatments. Treatment at 200 MPa with valve temperatures lower than 125 degrees C caused no reduction of spores. A reduction of 3.5 log(10)CFU/mL of B. amyloliquefaciens spores was achieved by treatment at 350 MPa with a valve temperature higher than 150 degrees C. The modeled thermal inactivation and observed inactivation during UHPH treatments suggest that temperature could be the main lethal effect driving inactivation.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Climatic fluctuations and homogenization of Northeast Brazil using precipitation data.

Before using the basic precipitation data in any agroclimatic study to assess the productivity it is important to check the data series for homogeneity. For this purpose data of 105 locations for the period 1912-1981 over northeast Brazil were used. The preliminary study indicate nonhomogeneity in the time series during 1940's at few locations. The amplitude of variation of time series when taken as 10-year moving average show quite different for different regions. It appears that this amplitude is related to time of onset of effective rains in some extent. There is also great diversity in the fluctuations. They present a great regional diversity. Some diversity. Some of the data in the low latitudes indicate presence of four cycles namely 52, 26, 13 & 6.5. years. The 52-year cycle is also evident in the case of onset of southwest Monsoon over a low latitude zone (Kerala Coast) in India. In the case of south Africa the prominent cycles are 60, 30, 15 & 10 similar situation appears to be present in the higher latitudes of northeast Brazil.

Landscape properties mediate the homogenization of bird assemblages during climatic extremes

Extreme weather events, such as drought, have marked impacts on biotic communities. In many regions, a predicted increase in occurrence of such events will be imposed on landscapes already heavily modified by human land use. There is an urgency, therefore, to understand the way in which the effects of such events may be exacerbated, or moderated, by different patterns of landscape change. We used empirical data on woodlanddependent birds in southeast Australia, collected during and after a severe drought, to document temporal change in the composition of bird assemblages in 24 landscapes (each 100 km2) representing a gradient in the cover of native wooded vegetation (from 60% to <2%). We examined (a) whether drought caused region-wide homogenization of the composition of landscape bird assemblages, and (b) whether landscape properties influenced the way assemblages changed in response to drought. To quantify change, we used pairwise indices of assemblage dissimilarity, partitioned into components that represented change in the richness of assemblages and change in the identity of constituent species (turnover). There was widespread loss of woodland birds in response to drought, with only partial recovery following drought-breaking rains. Region-wide, the composition of landscape assemblages became more different over time, primarily caused by turnover-related differentiation. The response of bird assemblages to drought varied between landscapes and was strongly associated with landscape properties. The extent of wooded vegetation had the greatest influence on assemblage change: landscapes with more native vegetation had more stable bird assemblages over time. However, for the component processes of richness- and turnoverrelated compositional change, measures of landscape productivity had a stronger effect. For example, landscapes with more riparian vegetation maintained more stable assemblages in terms of richness. These results emphasize the importance of the total extent of native vegetation, both overall cover and that occurring in productive parts of the landscape, for maintaining bird communities whose composition is resistant to severe drought. While extreme climatic events cannot be prevented, their effects can be ameliorated by managing the pattern of native vegetation in anthropogenic landscapes, with associated benefits for maintaining ecological processes and human well-being.

Abundance of introduced species at home predicts abundance away in herbaceous communities

Many ecosystems worldwide are dominated by introduced plant species, leading to loss of biodiversity and ecosystem function. A common but rarely tested assumption is that these plants are more abundant in introduced vs. native communities, because ecological or evolutionary-based shifts in populations underlie invasion success. Here, data for 26 herbaceous species at 39 sites, within eight countries, revealed that species abundances were similar at native (home) and introduced (away) sites – grass species were generally abundant home and away, while forbs were low in abundance, but more abundant at home. Sites with six or more of these species had similar community abundance hierarchies, suggesting that suites of introduced species are assembling similarly on different continents. Overall, we found that substantial changes to populations are not necessarily a pre-condition for invasion success and that increases in species abundance are unusual. Instead, abundance at home predicts abundance away, a potentially useful additional criterion for biosecurity programmes.

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 multi-scaling approach to predict hydraulic damage of poromaterials

The purpose of this paper is to introduce the concept of hydraulic damage and its numerical integration. Unlike the common phenomenological continuum damage mechanics approaches, the procedure introduced in this paper relies on mature concepts of homogenization, linear fracture mechanics, and thermodynamics. The model is applied to the problem of fault reactivation within resource reservoirs. The results show that propagation of weaknesses is highly driven by the contrasts of properties in porous media. In particular, it is affected by the fracture toughness of host rocks. Hydraulic damage is diffused when it takes place within extended geological units and localized at interfaces and faults.