The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Variations of local heat transfer coefficient in piped flow of viscous liquids

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

Mapping material distribution in a heterogeneous sand tank by image analysis

Water flow and solute transport through soils are strongly influenced by the spatial arrangement of soil materials with different hydraulic and chemical properties. Knowing the specific or statistical arrangement of these materials is considered as a key toward improved predictions of solute transport. Our aim was to obtain two-dimensional material maps from photographs of exposed profiles. We developed a segmentation and classification procedure and applied it to the images of a very heterogeneous sand tank, which was used for a series of flow and transport experiments. The segmentation was based on thresholds of soil color, estimated from local median gray values, and of soil texture, estimated from local coefficients of variation of gray values. Important steps were the correction of inhomogeneous illumination and reflection, and the incorporation of prior knowledge in filters used to extract the image features and to smooth the results morphologically. We could check and confirm the success of our mapping by comparing the estimated with the designed sand distribution in the tank. The resulting material map was used later as input to model flow and transport through the sand tank. Similar segmentation procedures may be applied to any high-density raster data, including photographs or spectral scans of field profiles.

Local total and radiative heat-transfer coefficients during the heat treatment of a workpiece in a fluidised bed

The heat-transfer coefficients around a workpiece immersed in an electrically heated heat treatment fluidised bed were studied. A suspension probe designed to simulate a workpiece of complex geometry was developed to measure local total and radiative heat-transfer coefficients at a high bed temperature. The probe consisted of an energy-storage region separated by insulation from the fluidised bed, except for the measuring surface, and a multi-thermocouple measurement system. Experiments in the fluidised bed were performed for a fluidising medium of 120-mesh alumina, a wide temperature range of 110–1050 °C and a fluidising number range of 1.18–4.24. It was found that the workpiece surface temperature has a more significant effect on heat transfer than the bed temperature. The total heat-transfer coefficient at the upper surface of the workpiece sharply decreased at the start of heating, and then steadily increased as heating progressed, while a sharp decrease became a rapid increase and then a slow increase for the radiative heat-transfer coefficient. A great difference in the heat-transfer coefficients around the workpiece was observed.

Effective diffusion coefficients behavior in osmotic dehydration of apple slices considering shrinking and local concentration dependence

The mass transfer during osmotic dehydration of apple slices immersed in 40, 50 and 60% (w/w) aqueous sucrose solutions was investigated to evaluate the influence of solution concentration on diffusivities. In the mathematical model, the diffusion coefficients were functions of the local water and sucrose concentration. The mass transfer equations were, simultaneously, solved for water and sucrose using an implicit numerical method. Material coordinates following the shrinkage of the solid were used. The predicted concentration profiles were integrated and compared to experimental data, showing a reasonable agreement with the measured data. on average, the effective diffusion coefficients for water and sucrose decreased as the osmotic solution concentration increased; that is the behavior of the binary coefficients in water-sucrose solutions. However, the diffusivities expressed as a function of the local concentration in the slices varied between the treatments. Water diffusion coefficients showed a remarkable variation throughout the slice and unusual behavior, which was associated to the cellular structure changes observed in tissue immersed in osmotic solutions. Cell structure changes occurred in different ways: moderate plasmolysis at 40%, accentuated plasmolysis at 50% and generalized damage of the cells at 60%. Intact vacuoles were observed after a long time of exposure (30 h) to 40 and 50% solutions. Effects of the concentration on tissue changes make it difficult to generalize the behavior of diffusion coefficients.

Local shell-side coefficients in shell and tube exchanges the use of a mass transfer technique

A diffusion-controlled electrochemical mass transfer technique has been employed in making local measurements of shell-side coefficients in segmentally baffled shell and tube heat exchangers. Corresponding heat transfer data are predicted through the Chilton and Colburn heat and mass transfer analogy. Mass transfer coefficients were measured for baffle spacing lengths of individual tubes in an internal baffle compartment. Shell-side pressure measurements were also made. Baffle compartment average coefficients derived from individual tube coefficients are shown to be in good agreement with reported experimental bundle average heat transfer data for a heat exchanger model of similar geometry. Mass transfer coefficients of individual tubes compare favourably with those obtained previously by another mass transfer technique. Experimental data are reported for a variety of segmental baffle configurations over the shell-side Reynolds number range 100 to 42 000. Baffles with zero clearances were studied at three baffle cuts and two baffle spacings. Baffle geometry is shown to have a large effect on the distribution of tube coefficients within the baffle compartment. Fluid "jetting" is identified with some baffle configurations. No simple characteristic velocity is found to correlate zonal or baffle compartment average mass transfer data for the effect of both baffle cut and baffle spacing. Experiments with baffle clearances typical of commercial heat exchangers are also reported. The effect of leakage streams associated with these baffles is identified. Investigations were extended to double segmental baffles for which no data had previously been published. The similarity in the shell-side characteristics of this baffle arrangement and two parallel single segmental baffle arrangements is demonstrated. A general relationship between the shell-side mass transfer performance and pressure drop was indicated by the data for all the baffle configurations examined.

Contemporary New Zealand coefficients for the Trauma Injury Severity Score: TRISS(NZ)

Aims – To develop local contemporary coefficients for the Trauma Injury Severity Score in New Zealand, TRISS(NZ), and to evaluate their performance at predicting survival against the original TRISS coefficients. Methods – Retrospective cohort study of adults who sustained a serious traumatic injury, and who survived until presentation at Auckland City, Middlemore, Waikato, or North Shore Hospitals between 2002 and 2006. Coefficients were estimated using ordinary and multilevel mixed-effects logistic regression models. Results – 1735 eligible patients were identified, 1672 (96%) injured from a blunt mechanism and 63 (4%) from a penetrating mechanism. For blunt mechanism trauma, 1250 (75%) were male and average age was 38 years (range: 15-94 years). TRISS information was available for 1565 patients of whom 204 (13%) died. Area under the Receiver Operating Characteristic (ROC) curves was 0.901 (95%CI: 0.879-0.923) for the TRISS(NZ) model and 0.890 (95% CI: 0.866-0.913) for TRISS (P<0.001). Insufficient data were available to determine coefficients for penetrating mechanism TRISS(NZ) models. Conclusions – Both TRISS models accurately predicted survival for blunt mechanism trauma. However, TRISS(NZ) coefficients were statistically superior to TRISS coefficients. A strong case exists for replacing TRISS coefficients in the New Zealand benchmarking software with these updated TRISS(NZ) estimates.

Vertical structure and horizontal gradients of aerosol extinction coefficients over coastal India inferred from airborne lidar measurements during the Integrated Campaign for Aerosol, Gases and Radiation Budget (ICARB) field campaign

Quantitative estimates of the vertical structure and the spatial gradients of aerosol extinction coefficients have been made from airborne lidar measurements across the coastline into offshore oceanic regions along the east and west coasts of India. The vertical structure revealed the presence of strong, elevated aerosol layers in the altitude region of similar to 2-4 km, well above the atmospheric boundary layer (ABL). Horizontal gradients also showed a vertical structure, being sharp with the e(-1) scaling distance (D-0H) as small as similar to 150 km in the well-mixed regions mostly under the influence of local source effects. Above the ABL, where local effects are subdued, the gradients were much shallower (similar to 600-800 km); nevertheless, they were steep compared to the value of similar to 1500-2500 km reported for columnar AOD during winter. The gradients of these elevated layers were steeper over the east coast of India than over the west coast. Near-simultaneous radio sonde (Vaisala, Inc., Finland) ascents made over the northern Bay of Bengal showed the presence of convectively unstable regions, first from surface to similar to 750-1000 m and the other extending from 1750 to 3000 m separated by a stable region in between. These can act as a conduit for the advection of aerosols and favor the transport of continental aerosols in the higher levels (> 2 km) into the oceans without entering the marine boundary layer below. Large spatial gradient in aerosol optical and hence radiative impacts between the coastal landmass and the adjacent oceans within a short distance of < 300 km (even at an altitude of 3 km) during summer and the premonsoon is of significance to the regional climate.

Plant species diversity of buffer zones in agricultural landscapes: in search of determinants from the local to regional scale

Buffer zones are vegetated strip-edges of agricultural fields along watercourses. As linear habitats in agricultural ecosystems, buffer strips dominate and play a leading ecological role in many areas. This thesis focuses on the plant species diversity of the buffer zones in a Finnish agricultural landscape. The main objective of the present study is to identify the determinants of floral species diversity in arable buffer zones from local to regional levels. This study was conducted in a watershed area of a farmland landscape of southern Finland. The study area, Lepsämänjoki, is situated in the Nurmijärvi commune 30 km to the north of Helsinki, Finland. The biotope mosaics were mapped in GIS. A total of 59 buffer zones were surveyed, of which 29 buffer strips surveyed were also sampled by plot. Firstly, two diversity components (species richness and evenness) were investigated to determine whether the relationship between the two is equal and predictable. I found no correlation between species richness and evenness. The relationship between richness and evenness is unpredictable in a small-scale human-shaped ecosystem. Ordination and correlation analyses show that richness and evenness may result from different ecological processes, and thus should be considered separately. Species richness correlated negatively with phosphorus content, and species evenness correlated negatively with the ratio of organic carbon to total nitrogen in soil. The lack of a consistent pattern in the relationship between these two components may be due to site-specific variation in resource utilization by plant species. Within-habitat configuration (width, length, and area) were investigated to determine which is more effective for predicting species richness. More species per unit area increment could be obtained from widening the buffer strip than from lengthening it. The width of the strips is an effective determinant of plant species richness. The increase in species diversity with an increase in the width of buffer strips may be due to cross-sectional habitat gradients within the linear patches. This result can serve as a reference for policy makers, and has application value in agricultural management. In the framework of metacommunity theory, I found that both mass effect(connectivity) and species sorting (resource heterogeneity) were likely to explain species composition and diversity on a local and regional scale. The local and regional processes were interactively dominated by the degree to which dispersal perturbs local communities. In the lowly and intermediately connected regions, species sorting was of primary importance to explain species diversity, while the mass effect surpassed species sorting in the highly connected region. Increasing connectivity in communities containing high habitat heterogeneity can lead to the homogenization of local communities, and consequently, to lower regional diversity, while local species richness was unrelated to the habitat connectivity. Of all species found, Anthriscus sylvestris, Phalaris arundinacea, and Phleum pretense significantly responded to connectivity, and showed high abundance in the highly connected region. We suggest that these species may play a role in switching the force from local resources to regional connectivity shaping the community structure. On the landscape context level, the different responses of local species richness and evenness to landscape context were investigated. Seven landscape structural parameters served to indicate landscape context on five scales. On all scales but the smallest scales, the Shannon-Wiener diversity of land covers (H') correlated positively with the local richness. The factor (H') showed the highest correlation coefficients in species richness on the second largest scale. The edge density of arable field was the only predictor that correlated with species evenness on all scales, which showed the highest predictive power on the second smallest scale. The different predictive power of the factors on different scales showed a scaledependent relationship between the landscape context and local plant species diversity, and indicated that different ecological processes determine species richness and evenness. The local richness of species depends on a regional process on large scales, which may relate to the regional species pool, while species evenness depends on a fine- or coarse-grained farming system, which may relate to the patch quality of the habitats of field edges near the buffer strips. My results suggested some guidelines of species diversity conservation in the agricultural ecosystem. To maintain a high level of species diversity in the strips, a high level of phosphorus in strip soil should be avoided. Widening the strips is the most effective mean to improve species richness. Habitat connectivity is not always favorable to species diversity because increasing connectivity in communities containing high habitat heterogeneity can lead to the homogenization of local communities (beta diversity) and, consequently, to lower regional diversity. Overall, a synthesis of local and regional factors emerged as the model that best explain variations in plant species diversity. The studies also suggest that the effects of determinants on species diversity have a complex relationship with scale.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson's ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.

Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

Are the available boiling heat transfer coefficients suitable for silicon microchannel heat sinks?

The typical MEMS fabrication of micro evaporators ensures the perfect smooth wall surface that is lack of nucleation sites, significantly decreasing the heat transfer coefficients compared with miniature evaporators fabricated using copper or stainless steel. In the present paper, we performed the boiling heat transfer experiment in silicon triangular microchannel heat sink over a wide parameter range for 102 runs. Acetone was used as the working fluid. The measured boiling heat transfer coefficients versus the local vapor mass qualities are compared with the classical Chen’s correlation and other correlations for macro and miniature capillary tubes. It is found that most of these correlations significantly over-predict the measured heat transfer coefficients. New correlations are given. There are many reasons for such deviations. The major reason is coming from the perfect smooth silicon surface that lowers the heat transfer performances. New theory is recommended for the silicon microchannel heat sink that should be different from metallic capillary tubes.