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Electric Field Intensity
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
As shown in Figure 5.4, the repulsion is likely to cause the net charge to reside at points of spheres most distant from each other. The force of repulsion is set equal to the weight of a sphere. The diameter of a 1 cm3 sphere is 1.24 cm, so the force can be treated as that between two point charges 2.48 cm apart (i.e., twice the sphere diameter apart). Using Coulomb’s law, this requires a charge of 7.8 × 10−8 C. Compared to the total mobile charge of 13,600 C, this amounts to removing just one valence electron out of every 5.7 trillion (5.7 × 1012) from each copper sphere. The final result is that removal of just one out of roughly six trillion of free electrons from each copper sphere would cause enough electric repulsion on the top sphere to lift it, overcoming the gravitational pull of the entire Earth.
Light, Life, and Measurement
Published in Thomas M. Nordlund, Peter M. Hoffmann, Quantitative Understanding of Biosystems, 2019
Thomas M. Nordlund, Peter M. Hoffmann
Using the particle-in-a-box model we can, in fact, count the number of free electrons, place them in the energy levels, and calculate transition energies. What photon energy would be required to promote an electron in the highest-occupied state to the next higher state? Let’s assume the 1-nm3 silver particle is a 1-nm cube. Remember the energies depend only on the (de Broglie) wavelength of the particle, which is not very different for a 1-nm3 sphere. The energies for the cube are () Enml=π2ℏ22ML2(n2+m2+l2)
Application of ICRP Biokinetic Models to Depleted Uranium
Published in Alexandra C. Miller, Depleted Uranium, 2006
This is used to define the aerodynamic equivalent diameter, dae, which is widely used in occupational health, and in both the HRTM and the ICRP 30 lung model. It is the diameter of a unit density (1 g cm−3) sphere with the same settling velocity as the particle: () ug=ρde2C(de)g18μχ=dae2C(dae)g18μ
A novel drying tower technology for zero liquid discharge of desulfurization technology
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Xiandong Liu, Man Zhang, Xuan Yao, Boyu Deng, Hao Kong, Guohua Wei, Hairui Yang
The schematic diagram and real picture of the novel drying tower are shown in Figure 3 and the main design parameters are listed in Table 1. The drying capacity of wastewater is 240 kg/h according to demand of power plant. Heating resource is the second air with temperature of 230°C and outlet air temperature is set as 165°C. Through the heat balance considering heat loss of 5%, the amount of needed heating air can be calculated. Average flow velocity at bottom cross section is chosen as 6 m/s to realize fluidization state and thus bottom diameter of cone section is designed as 1 m. The angle of cone section is chosen as 14 degrees to allow particles easily fall back to bottom section instead stagnate on the wall. The height of cone section and cylinder section is chosen as 1 m and 4 m to make wastewater evaporate fully. To intensify the inner circulation, air distributor is designed to have higher open ratio in the central circular part with diameter of 0.4 m, which causes more air flow flux. Inert Al2O3 sphere with diameter of 2 mm and density of 3000 kg/m3 is chosen as the bed materials. Initial packing height of these particles is 0.24 m, which corresponds with total bed material mass of 380 kg. Wastewater is injected into the tower through three slit nozzles, which locates in the height of 0.6 m above air distributor and are uniformly distributed in the circumferential direction.
The wild Fox–Artin arc in invariant sets of dynamical systems
Published in Dynamical Systems, 2018
T. V. Medvedev, O. V. Pochinka
Various topological constructions emerge naturally in the modern theory of dynamical systems. For instance, the Cantor set, discovered as an example of a set with cardinality of the continuum and zero Lebesgue measure, clarified the structure of expanding attractors and contracting repellers. Fractals, being self-similar objects with fractional dimension, are naturally found in complex dynamics. For example, the basin boundary of an attracting point can be the Julia set. The lakes of Wada, showing the phenomenon of a curve dividing the plane into more than two domains, were used in the construction of the Plykin attractor on the 2-sphere. A curve contained in the 2-torus and having an irrational winding number, being an injectively immersed subset but not a topological submanifold, was realized as an invariant manifold of a fixed point of the Anosov diffeomorphism of the 2-torus. The mildly wild embedding of a frame of Debrunner–Fox, representing a wild collection of tame arcs in , was realized as a frame of one-dimensional saddle points separatrices of Morse–Smale diffeomorphism on the 3-sphere.
Cost-effectiveness of patient-specific motion management strategy in lung cancer radiation therapy planning
Published in The Engineering Economist, 2019
Shan Liu, Shouyi Wang, W. Art Chaovalitwongse, Stephen R. Bowen
Wang et al. (2014) developed a new expert-informed feature selection and regularization technique to construct a sparse multivariate prediction model from patient-specific data (i.e., baseline diagnostic factors and respiratory patterns). The prediction model can inform physicians of how likely it is that the patient will benefit from respiratory gating so that the motion management decision during the imaging stage can be optimized. A multiple linear regression model was developed to predict quantitative imaging improvement (%ΔSUVpeak or %ΔSUVmax) by the extracted respiratory motion features. To construct a valid prediction model unbiased by overfitting and unburdened by complexity, a stepwise feature selection approach was implemented to prune unnecessary predictor variables and discover the most important predictor variables for prediction (Miller 2002). A leave-one-out cross-validation approach was applied to evaluate the prediction performance of the learned regression model (Efron 1983). Prior results in Wang et al. (2014) show that the standard deviation of predicted %ΔSUVpeak error (i.e., actual %ΔSUVpeak − predicted %ΔSUVpeak) is around 8% in the 22-patient cohort. Whereas SUVmax represents the volume element (voxel) with the highest image intensity value, SUVpeak is defined as a voxel neighborhood with the highest image intensity average over a 1-cm3 sphere (Wahl et al. 2009). Because SUVmax is more ubiquitously used in clinical oncology settings due to its simpler definition and utility as a prognostic marker of treatment response, we have adopted it in our prediction modeling for this study.