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Multi-Particle Motion
Published in Rob Appleby, Graeme Burt, James Clarke, Hywel Owen, The Science and Technology of Particle Accelerators, 2020
Rob Appleby, Graeme Burt, James Clarke, Hywel Owen
The self-forces within a bunch give rise to a number of phenomena, many of them unwanted. These include defocusing (leading to a change in the betatron tunes), energy loss, and so on. It is conventional to divide the space-charge forces into collisional interactions – those in which particles collide individually – and the overall smooth space-charge force. The boundary between these regimes is given by the Debye length, which describes the distance over the field of a single particle is screened. The Debye length is
HfO2 Thin Film for Microelectromechanical Systems Application
Published in Iniewski Krzysztof, Integrated Microsystems, 2017
An exponential fit to ΔC/C0 gives the exponential factor mqEs/kBT (4.9), and hence the hopping distance (s) can be evaluated using the value m = 0.20. The obtained hopping distance (shown in Table 33.1) is greater than the interatomic distance, which indicates that the mobile charges used in this model are electronic in nature [18]. The density of defects in the dielectric film may be then extracted using N ≈ 1/s3 and then the Debye length is calculated using Equation 33.5. DC conductivity experiments (J–E characteristics) give σ as a function of electric field and we set the electric field to 1 MV/cm to calculate the conductivity in our devices.
Dictionary
Published in Mario P. Iturralde, Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990
Debye length. A theoretical length which describes the maximum separation at which a given electron will be influenced by the electric field of a given positive ion. Sometimes referred to as the Debye shielding distance or plasma length. It is well known that charged particles interact through their own electric fields. In addition, Debye has shown that the attractive force between an electron and ion which would otherwise exist for very large separations is indeed cut off for a critical separation due to the presence of other positive and negative charges in-between. This critical separation or Debye length decreases for increased plasma density.
Electroosmotically driven flow of micropolar bingham viscoplastic fluid in a wavy microchannel: application of computational biology stomach anatomy
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Anber Saleem, Mishal Nayab Kiani, Sohail Nadeem, Salman Akhtar, Mehdi Ghalambaz, Alibek Issakhov
Figures 12–16 provides the relation between P, as displayed in Figure 12. A rise in the Debye-length parameter expressively increases the pressure difference, as shown in Figure 13. However, Figure 14. Figure 15 reveals that an increase in the coupling number reduces the pressure difference Figure 16; however, an inverse linear relationship could be observed in all plots.
Effects of hypertension and FAAH inhibitor treatment of rats with primary and secondary hypertension considering the physicochemical properties of erythrocytes
Published in Toxicology Mechanisms and Methods, 2020
Izabela Dobrzyńska, Barbara Szachowicz-Petelska, Anna Pędzińska-Betiuk, Zbigniew A. Figaszewski, Elżbieta Skrzydlewska
Introducing the results of measurements of electrical charge dependence of the cell membrane as a function of pH to the theoretical equations that I derived to describe the charge dependence on solution composition, I determined the total concentrations of CTA and CTB and their association constants with KAH and KBOH. Mathematical calculations based on the model describing the adsorption of electrolyte ions on the surfaces of cell membranes enabled quantitative assessment of the parameters characterizing the membrane (CTA, CTB, KAH and KBOH). The determined constants were substituted in the above equation, resulting in theoretical curves. The theoretical values for the zeta potential can be determined from the following formula: a is the particle radius and κ−1 is the Debye length.
Surface charge, glycocalyx, and blood-brain barrier function
Published in Tissue Barriers, 2021
Fruzsina R. Walter, Ana R. Santa-Maria, Mária Mészáros, Szilvia Veszelka, András Dér, Mária A. Deli
In the direction perpendicular to the hypothetical membrane surface (z), mobile counterions of the electrolyte forming the diffuse double layer screen the electric field of the “fix” (membrane-bound) charges, and in a low-potential limit, decrease V(z) exponentially by a space constant called Debye length (λD): V(z) = V0·exp(-z/λD), where V0 is the surface potential.149 Inside the membrane, the surface charge of the membrane lipids, together with water molecules occluded at the membrane surface, gives rise to the elusive dipole potential, which could not be measured precisely, so far, with the available experimental techniques.