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Phi analysis method of thermal design of structure foundations
Published in Jean-François Thimus, Ground Freezing 2000 - Frost Action in Soils, 2020
The Phi method evaluates conical heat transfer through the foundation into the deep subgrade. Incremental depth analysis occurs on spherical sector surfaces with their center the same as the vertex of the cone. The surface of the cone is assumed stable at 0°C or below. Separate analysis surrounding the cone is required to assure that thawing will not occur across this conical boundary.
A Unified Method for Calculating Parasitic Capacitive and Resistive Coupling in VLSI Circuits
Published in Thomas Noulis, Noise Coupling in System-on-Chip, 2018
Alkis A. Hatzopoulos, Michael G. Dimopoulos
Eventually, the lower boundary resistance Rm− is computed by Rm−=Rs/(aβ) where the coefficients α, β are used to normalize the area of the spherical sector to that of the contact by the following way. The values of α and β are determined as follows. A CS is placed above the contact at a relatively large distance in comparison to the dimensions of the contact. This ensures that the curvature of the corresponding sphere becomes negligible in respect to the dimensions of the contact and the base circle of the spherical sector will better approximate the flat contact. The particular value used in this work is d=4rc. The spherical sector corresponds to a sphere of radius d centered at the CS having a total surface area equal to ASP=4πd2. The surface area of the sector is ASCT=2πd2(1−cosθ). Thus, the ratio a of the latter to the area of the sphere is a=ASCTASP=2πd2(1−cosθ)4πd2=1−cosθ2
SPH Modelling of a Dike Failure with Detection of the Landslide Sliding Surface and Damage Scenarios for an Electricity Pylon
Published in International Journal of Computational Fluid Dynamics, 2022
Andrea Amicarelli, Emanuela Abbate, Antonella Frigerio
The quadratic invariants of the velocity-gradient tensor are numerically computed within the domain of a simplified 3D rotational landslide. This is the 3D generalisation of the 2D rotational landslide of Section 3.3. In the 3D configuration, the main landslide body is a spherical sector (instead of the 2D circular sector of Section 3.3) and the buffer zone is a sector of a spherical shell (instead of the 2D circular crown of Section 3.3). The buffer zone is confined by an inner rotating sphere, representing the landslide-body bottom, and an outer fixed sphere, which is the fixed-soil top. In the buffer zone of depth Δx, a circular Couette flow is established: it is a fluid spherical shell rotating and deforming in laminar regime. The code SPHERA, included the numerical developments for the shear-stress boundary terms of Section 2.2, is first validated on three configurations of the spherical Couette flows, by comparison with the available closed-form solutions (Appendix A, Section A1). Then, the configuration representing the buffer zone of the simplified 3D rotational landslide is used to compute the SPH quadratic invariants of the velocity-gradient tensor, as described in the following.
Three-dimensional wireless ad hoc networks with random nodes distribution
Published in International Journal of Electronics, 2021
To guarantee the delivery of data packets to the destination node, it is assumed that the source and intermediate nodes relay the packets to their nearest neighbour that lies within a spherical cone with angle (apex angle) in the direction of the destination. The virtual straight line connecting the source and destination nodes is called a reference path, and the route to the destination is viewed as a deviation from the reference path. In reference to Figure 5, the volume of a spherical cone (or spherical sector) of angle and radius can be expressed as:
Design and evaluation of a unipolar aerosol particle charger with built-in electrostatic precipitator
Published in Instrumentation Science & Technology, 2018
Tongzhu Yu, Yixin Yang, Jianguo Liu, Huaqiao Gui, Jiaoshi Zhang, Yin Cheng, Peng Du, Jie Wang, Wenyu Wang, Huanqin Wang
The mean number concentration of ions in the corona chamber, Nin, which can be expressed as follows: where A is the inner surface area of the spherical sector where the ion is deposited, which can be expressed as follows: where r is the radius of the spherical sector, h is the height of the arch, and a is the radius of the arch bottom circle. Zi is the ions electrical mobility (1.425 cm2/V · s for negative ions[34]). If the space-charge effect is neglected, the electric field strength can be estimated using the following equation: where d is the distance between the corona needle and the spherical sector apex.