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The Light Field of a Luminaire
Published in R. H. Simons, A. R. Bean, Lighting Engineering, 2008
The area of the spherical cap is equal to the solid angle subtended by the cap at the centre of the sphere multiplied by the radius squared (see Section 1.4.1), Figure 1.22(a): areaofcap=2πR2(1−sinβ)
Preliminary Mathematics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
If one of the bounding parallel planes is tangent to the sphere, the surface bounded is called as a spherical zone of one base. The entire 3D portion is called as a spherical cap. A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere. Figure 3.9 shows a spherical cap with altitude h, radius r, and circumference of base, c.
Nucleation on a sphere: the roles of curvature, confinement and ensemble
Published in Molecular Physics, 2018
Jack O. Law, Alex G. Wong, Halim Kusumaatmaja, Mark A. Miller
Recently, Gómez et al. developed a continuum Landau theory for phase nucleation on curved surfaces [1], which predicts that, in the absence of elasticity or finite thickness, curvature affects the free energy barrier to nucleation by altering the relationship between the perimeter of the nucleus and its area. On a plane, assuming isotropic growth, . However, on surfaces with positive (negative) Gaussian curvature, the area grows faster (slower) as a function of P than on a plane. This will naturally change the shape of the free energy profile described in Equation (4). On the sphere, the perimeter of a spherical cap of area is given by where is the total surface area of the sphere. As shown in Figure 3, this modification is sufficient to capture the shape of the barrier.
Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect
Published in Molecular Physics, 2018
Satoshi Nakagawa, Isman Kurniawan, Koichi Kodama, Muhammad Saleh Arwansyah, Kazutomo Kawaguchi, Hidemi Nagao
We introduce a function related to the molecular crowding effect as where ρi is the i-th density of hydrophobic CG particle in the different proteins given in Equation (3). ρ* is the critical density of hydrophobic CG particle. b = 20 is used in this work. In this work, we assume that the critical density becomes equal to the average number of the hydrophobic amino acid residue in a local volume. We consider that the local volume is defined as a spherical cap or a spherical segment of one base which is a portion of a sphere cut off by a plane and assume the sphere with the radius σ and the height of the cap with σ − d. We can estimate ρ* = 6.2 by using the spherical cap of the local volume defined by d and σ with the ratio of the hydrophobic CG particle to the total number shown in the capture of Figure 1. This assumption means when hydrophobic CG particles bind to recessed surface of other proteins, the intermolecular interaction becomes weak due to the molecular crowding effect.
Experimental and Numerical Analysis of Thermal Interaction Between Two Droplets in Spray Cooling of Heated Surfaces
Published in Heat Transfer Engineering, 2018
Paolo E. Santangelo, Mauro A. Corticelli, Paolo Tartarini
The code was implemented in Matlab®, featuring a modular and flexible architecture. A structured nonuniform mesh was employed and refined where the higher temperature gradients and the larger heat fluxes were expected (i.e., at the interfaces and below the droplets), as shown in Figure 4. The 3-dimensional energy-diffusion equation was discretized by the finite-volume method, using the Crank-Nicolson technique for time-advancement [37]. An explicit approach was applied to compute evaporated mass, as well as heat-transfer coefficient at each node and time step. Notably, the evaporated flux at the droplet/air interface was calculated for each top-cell area, thus re-building and re-meshing the whole droplet at every time step. The elements constituting droplets featured different heights to match a spherical-cap geometry. The code proved capable of keeping the relative error between actual droplet volume and reconstructed volume lower than 0.2% over the whole simulation. The structured mesh of the system was preserved by building a number of virtual vertical layers outside the droplets equal to the ones within them.