Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

Pair production by and electric field in (1+1)-dimensional de Sitter space

We use the method of Bogolubov transformations to compute the rate of pair production by an electric field in (1+1)-dimensional de Sitter space. The results are in agreement with those obtained previously using the instanton methods. This is true even when the size of the instanton is comparable to the size of the de Sitter horizon.

Three-dimensional interpolation of soil data: fertility and pedomorphological features in southern Brazil

The graphical representation of spatial soil properties in a digital environment is complex because it requires a conversion of data collected in a discrete form onto a continuous surface. The objective of this study was to apply three-dimension techniques of interpolation and visualization on soil texture and fertility properties and establish relationships with pedogenetic factors and processes in a slope area. The GRASS Geographic Information System was used to generate three-dimensional models and ParaView software to visualize soil volumes. Samples of the A, AB, BA, and B horizons were collected in a regular 122-point grid in an area of 13 ha, in Pinhais, PR, in southern Brazil. Geoprocessing and graphic computing techniques were effective in identifying and delimiting soil volumes of distinct ranges of fertility properties confined within the soil matrix. Both three-dimensional interpolation and the visualization tool facilitated interpretation in a continuous space (volumes) of the cause-effect relationships between soil texture and fertility properties and pedological factors and processes, such as higher clay contents following the drainage lines of the area. The flattest part with more weathered soils (Oxisols) had the highest pH values and lower Al3+ concentrations. These techniques of data interpolation and visualization have great potential for use in diverse areas of soil science, such as identification of soil volumes occurring side-by-side but that exhibit different physical, chemical, and mineralogical conditions for plant root growth, and monitoring of plumes of organic and inorganic pollutants in soils and sediments, among other applications. The methodological details for interpolation and a three-dimensional view of soil data are presented here.

Reheating in inflationary cosmologies: Geometric coupling of the "inflaton" to quantum fields

We propose a simple geometrical prescription for coupling a test quantum scalar field to an "inflaton" (classical scalar field) in the presence of gravity. When the inflaton stems from the compactification of a Kaluza-Klein theory, the prescription leaves no arbitrariness and amounts to a dimensional reduction of the Klein-Gordon equation. We discuss the possible relevance of this coupling to "reheating" in inflationary cosmologies.

Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems

Thermal fluctuations around inhomogeneous nonequilibrium steady states of one-dimensional rigid heat conductors are analyzed in the framework of generalized fluctuating hydrodynamics. The effect of an external source of noise is also considered. External fluctuations come from temperature and position fluctuations of the source. Contributions of each kind of noise to the temperature correlation function are computed and compared through the study of its asymptotic behavior.

Three-dimensional radiobiological dosimetry of kidneys for treatment planning in peptide receptor radionuclide therapy.

PURPOSE: Peptide receptor radionuclide therapy (PRRT) delivers high absorbed doses to kidneys and may lead to permanent nephropathy. Reliable dosimetry of kidneys is thus critical for safe and effective PRRT. The aim of this work was to assess the feasibility of planning PRRT based on 3D radiobiological dosimetry (3D-RD) in order to optimize both the amount of activity to administer and the fractionation scheme, while limiting the absorbed dose and the biological effective dose (BED) to the renal cortex. METHODS: Planar and SPECT data were available for a patient examined with (111)In-DTPA-octreotide at 0.5 (planar only), 4, 24, and 48 h post-injection. Absorbed dose and BED distributions were calculated for common therapeutic radionuclides, i.e., (111)In, (90)Y and (177)Lu, using the 3D-RD methodology. Dose-volume histograms were computed and mean absorbed doses to kidneys, renal cortices, and medullae were compared with results obtained using the MIRD schema (S-values) with the multiregion kidney dosimetry model. Two different treatment planning approaches based on (1) the fixed absorbed dose to the cortex and (2) the fixed BED to the cortex were then considered to optimize the activity to administer by varying the number of fractions. RESULTS: Mean absorbed doses calculated with 3D-RD were in good agreement with those obtained with S-value-based SPECT dosimetry for (90)Y and (177)Lu. Nevertheless, for (111)In, differences of 14% and 22% were found for the whole kidneys and the cortex, respectively. Moreover, the authors found that planar-based dosimetry systematically underestimates the absorbed dose in comparison with SPECT-based methods, up to 32%. Regarding the 3D-RD-based treatment planning using a fixed BED constraint to the renal cortex, the optimal number of fractions was found to be 3 or 4, depending on the radionuclide administered and the value of the fixed BED. Cumulative activities obtained using the proposed simulated treatment planning are compatible with real activities administered to patients in PRRT. CONCLUSIONS: The 3D-RD treatment planning approach based on the fixed BED was found to be the method of choice for clinical implementation in PRRT by providing realistic activity to administer and number of cycles. While dividing the activity in several cycles is important to reduce renal toxicity, the clinical outcome of fractionated PRRT should be investigated in the future.

THREE DIMENSIONAL CHARACTERIZATION OF SOIL MACROPOROSITY BY X-RAY MICROTOMOGRAPHY

Analysis of the soil pore system represents an important way of characterizing soil structure. Properties such as the shape and number of pores can be determined through soil pore evaluations. This study presents a three-dimensional (3D) characterization of the shape and number of pores of a sub-tropical soil. To do so, a second generation X-ray microtomograph equipped with a plain type detector was employed. A voltage of 120 kV and current of 80 mA was applied to the X-ray tube. The soil samples analyzed were collected at three different depths (0-10, 10-20, and 20-30 cm). The results obtained allowed qualitative (images) and quantitative (3D) analyses of the soil structure, revealing the potential of the microtomographic technique, as well as the study of differences in soil macroporosity at different depths. Macroporosity was 5.14 % in the 0-10 cm layer, 5.10 % in the 10-20 cm layer, and 6.64 % in the 20-30 cm layer. The macroporosity of unclassified pores (UN) was 0.30 % (0-10 and 10-20 cm) and 0.40 % (20-30 cm), while equant pores (EQ) had values of 0.01 % at the three depths under analysis.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.