Poisson, equation

Poisons, systemic Poisson s equation Poisson s ratio... 

In order to solve the preceding set of equations, Poisson s method is applied to... 

In addition to the electron and hole continuity equations, Poisson s equation must be satisfied. 

According to this equation, Poisson s ratio is 1/2 when G. 

Scalar and vector fields that depend on more than one independent variable, which we write in the notation T fx, y), TCx, t), TCr), TCr, t), etc., are very often obtained as solutions to PDEs. Some classic equations of mathematical physics that we will consider are the wave equation, the heat equation, Laplace s equation, Poisson s equation, and the SchrOdinger equation for some exactly solvable quantum-mechanical problems. 

Selvadurai APS (2000a) Partial differential equations in mechanics, vol 1. Fundamentals, Laplace s equation, diffiision equation, wave equation. Springer, Berhn Selvadurai APS (2(XX)b) Partial differential equations in mechanics, vol 2. The biharmonic equation, Poisson s equation. Springer, Berhn... 

In any semiconductor device the charge densities are governed by three differential equations, Poisson s equation which expresses the minimization of electrostatic potential energy and continuity equations that express the conservation of charges. Typically, multilayer stacks of thin-film solar cells are simulated in the dimension parallel to the surface normal of the stack. For such a one-dimensional device model, these equations become... 

This is called the Coulomb gauge, and the resulting equation (Poisson s equation). 

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

Marmur [12] has presented a guide to the appropriate choice of approximate solution to the Poisson-Boltzmann equation (Eq. V-5) for planar surfaces in an asymmetrical electrolyte. The solution to the Poisson-Boltzmann equation around a spherical charged particle is very important to colloid science. Explicit solutions cannot be obtained but there are extensive tabulations, known as the LOW tables [13]. For small values of o, an approximate equation is [9, 14]... 

The model used is the RPM. The average electrostatic potential ifr) at a distance r away from an ion / is related to tire charge density p.(r) by Poisson s equation... 

Weinert M 1981 Soiution of Poisson s equation beyond Ewaid-type methods J. Math. Phys. 22 2433... 

Sadygov R G and Yarkony D R 1998 On the adiabatic to diabatic states transformation in the presence of a conical intersection a most diabatic basis from the solution to a Poisson s equation. I J. Chem. Rhys. 109 20... 

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

The set of coupled Poisson equations (50) can, in principle, be solved with any appropriate choice of boundary conditions for Pi j(qx)- There is one choice. 

This justifies the use of the simpler language over the one. The solution of the Poisson equation and the boundary conditions used are explained in detail elsewhere [55]. Here, we will present some selected results. 

If a gaussian function is chosen for the charge spread function, and the Poisson equation is solved by Fourier transformation (valid for periodic... 

The Poisson equation relates spatial variation of the potential 4> at position r to the density of the charge distribution, p, in a medium with a dielectric constant e... 

Fig. 1. Explanation of the principles of the finite-difference method for solution of the Poisson-Boltzmann equation...

Tanford, C., Kirkwood, J. G. Theory of protein titration curves. I. General equations for impenetrable spheres. J. Am. Chem. Soc. 79 (1957) 5333-5339. 6. Garrett, A. J. M., Poladian, L. Refined derivation, exact solutions, and singular limits of the Poisson-Boltzmann equation. Ann. Phys. 188 (1988) 386-435. Sharp, K. A., Honig, B. Electrostatic interactions in macromolecules. Theory and applications. Ann. Rev. Biophys. Chem. 19 (1990) 301-332. 

Sharp, K. A., Honig, B. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. J. Phys. Chem. 94 (1990) 7684-7692. Zhou, H.-X. Macromolecular electrostatic energy within the nonlinear Poisson-Boltzmann equation. J. Chem. Phys. 100 (1994) 3152-3162. 

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