Because electrostatic forces are crucial in biological systems, molecular dynamics simulations of biological systems require a method of computing electrostatic forces that is accurate and rapid. We propose a surface charge method, apply it to a system of arbitrary number of charged dielectric spheres, and obtain an exact solution for an arbitrary configuration of the spheres. The precision depends only on the number of terms kept in a series expansion and can therefore be controlled at will. It appears that the first few terms are usually adequate. The exact result exhibits a phenomenon that we call asymmetric screening. Namely, the magnitude of attractive interactions is decreased (relative to point charges in an infinite solvent) while the magnitude of repulsive interactions is increased (again, relative to point charges in an infinite solvent). This effect might aid in the adoption of correct conformations and in intermolecular recognition. Evaluation of the energy involves only matrix inversion. The surface charge method can be transformed easily to a numerical method for use with arbitrary surfaces. With modest additions, the model also describes an electrorheological fluid. Such a system provides the cleanest opportunity to apply the model.
The concept of the breaking strength of a polymer chain is analyzed by means of a study of the dynamics of a rectilinear chain of monomers connected by Hookian bonds. A formalism is then developed whereby the average time to breaking of the chain can be calculated as a function of temperature and strain. An approximation to the exact solution of the resulting equations is discussed. It is concluded that correlations in space and time in the motion of the chain lead to breaking times that are not simple functions of the chain length. The predicted breaking times are appreciably smaller than those that would be found in a chain in which the thermal motions of the monomers were uncorrelated.
A new method is presented for solving electrostatic boundary value problems with dielectrics or conductors and is applied to systems with spherical geometry. The strategy of the method is to treat the induced surface charge density as the variable of the boundary value problem. Because the potential is expressed directly in terms of the induced surface charge density, the potential is automatically continuous at the boundary. The remaining boundary condition produces an algebraic equation for the surface charge density, which when solved leads to the potential. The surface charge method requires the enforcement of only one boundary condition, and produces the induced surface charge in addition to the potential with no additional labor. The surface charge method also can be applied in nonspherical geometries and provides a starting place for efficient numerical solutions.
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