Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Reference values for whole body and cerebral multi-frequency bio-impedance data in neonates less than 12 h postpartum

Multiple frequency bio-electrical impedance analysis (MFBIA) may be useful for monitoring fluid balance in newborn infants or to provide early prediction of the outcome following perinatal asphyxia. A reference range of data is needed for identification of babies with abnormal impedance values. This was a cross-sectional observational study in 84 term and near-term healthy neonates less than 12 h postpartum. Whole body and cerebral MFBIA measurements were performed at the bedside in the post-natal ward. Gestational age, post-natal age, gender, birthweight, head circumference and foot length measures were recorded. Reference values for impedance at the characteristic frequency (Z(C)) and resistance at zero frequency (R-0) are reported for whole body and cerebral impedance. Significant correlations (p < 0.05) were observed between whole body impedance and birthweight, footlength and head circumference. Females had a significantly higher whole body R0 than males. Cerebral impedance did not correlate significantly with any of the demographic measures and therewere no gender differences observed for cerebral impedance. The reference range for whole body multi-frequency bio-impedance values in term and near-term infants within the first 12 h postpartum can be calculated from the footlength (FL) using the following equations: Z(C) = (942.9 - 4.818* FL) +/- 124.6 Omega; R-0 = (1042 - 4.520(*)FL) +/- 135.5 Omega. For cerebral impedance the reference range is 29.5-48.7 Omega for Z(C) and 33.7-58.0 Omega for R-0.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.