Range Of Interparticle Distances Research Articles

Application of a Three-Dimensional Immersed Boundary Method for Free Convection From Single Spheres and Aggregates

AbstractA three-dimensional immersed boundary method (IBM) is applied for the solution of the thermal interactions between spherical particles in a viscous Newtonian fluid. At first, the free convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed as a function of the Grashof number. A new correlation for the heat transfer rate from a single sphere is obtained, which is valid in the ranges 0.5 ≤ Pr ≤ 200 and 0 ≤ Gr ≤ 500. Second, the free convection heat transfer rate from pairs of spheres (bispheres) and from small spherical clusters immersed in air (Pr = 0.72) is investigated using this numerical technique. For bispheres, their orientation and the thermal plume interactions within a range of interparticle distances may cause the enhancement of the heat transfer rate above the values observed for two isolated spheres. For the simple triangular particle clusters, where the particles are in contact, it was observed that the average heat transfer rate per sphere decreases with the increased number of spheres in the cluster.

Hyperspherical approach to the calculation of few-body atomic resonances

Direct solution of the Schr\odinger equation for the doubly excited resonant $^{1}\mathrm{S}^{\mathrm{e}}$ state of the helium atom is obtained with the help of the complex rotation method (which reduces the resonance problem to that of bound states with complex energy) and the correlation function hyperspherical harmonic (CFHH) method. In the CFHH method the solution is a product of a correlation function and a smooth factor expanded into hyperspherical harmonic functions. Given a proper correlation function, chosen from physical considerations, the method generates resonant wave functions, accurate in the whole range of interparticle distances. Since the method is nonvariational no stabilization procedure is needed. The calculated energy and width are shown to be strictly independent of the angle of complex rotation, hence there is no need for the angle optimization procedure as well. The results are compared with variational and other precise computations.

Theory of plasmon‐assisted electron pairing in semiconductors

AbstractIt is shown that plasmon‐assisted superconductivity can occur in an electron plasma of a modulationdoped quantum well structure or in an optically excited, cool quasi‐equilibrium electron–hole plasma in stressed quantum wells. For our analysis the quasi‐classical approximation (QCA) for non‐equilibrium Keldysh‐Green functions for carriers of a degenerate plasma is used. The screening is described in RPA, simplified further for some of the calculations by a damped plasmon‐pole approximation (PPA). Because the plasmon coupling is strong the appropriately modified Eliashberg equations are derived and analyzed for the complex frequency‐dependent normal and anomalous self‐energies. The plasmon frequency in a semiconductor plasma with a typical density of 1018 cm−3 is of the order of some 10 meV. If the spectral density of the plasmon is not too broad, a pairing instability is found also in the range of interparticle distances with rs < 1, where QCA and RPA are valid. Depending on the material, transition plasma temperatures of up to 30 K are obtained which can be enhanced further by quantum confinement and special properties of the band structure. The underlying virtual exchange of plasmons can only be obtained in a fully dynamical description, and is absent in the commonly used quasi‐static quasi‐particle approximations.

Nonvariational calculation of the relativistic and finite-size corrections for the helium ground state.

Relativistic and finite-size corrections are calculated by using an accurate direct solution of the Schr\"odinger equation [the correlation function hyperspherical harmonic (CFHH) method] for the ground state of the helium atom. In the CFHH method the solution is a product of a correlation function and of a smooth factor expanded into hyperspherical harmonic functions. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which leads in turn to precise estimates of the relativistic operators. Our nonvariational results are compared with those obtained in recent variational calculations.

Precise nonvariational calculation of the two-photon annihilation rate of the positronium negative ion.

A direct (nonvariational) solution of the Schr\"odinger equation for the ground state of the positronium negative ion is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Given the proper correlation function chosen from physical considerations, the CFHH method generates wave functions accurate in the whole range of interparticle distances that lead, in turn, to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. The correlation function used was chosen to have proper electron-positron and electron-electron cusps as well as asymptotic behavior. The inclusion of 225 hyperspherical functions yields the nonextrapolated ground-state energy value of 0.262 005 058 atomic units, which is lower than the nonextrapolated energy values 0.262 004 895 and 0.262 005 056 calculated in works of Ho [J. Phys. B 16, 1503 (1983)] and Bhatia and Drachman [Phys. Rev. A 28, 2523 (1983)] but higher than the best variational value 0.262 005 069 obtained by Petenlenz and Smith [Phys. Rev. A 36, 5125 (1987)]. The accuracy of our value of 2.086 10 \ifmmode\pm\else\textpm\fi{}0.000 06 ${\mathrm{nsec}}^{\mathrm{\ensuremath{-}}1}$ for the two-photon annihilation rate is higher by an order of magnitude than obtained in the previous literature.

Correlation-function hyperspherical-harmonic calculation of the microdt molecular ion.

Direct solution of the Schrodinger equation for the ground and excited S states of the μdt molecular ion is obtained with the help of the correlation-function hyperspherical-harmonic method. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which lead in turn to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results are compared with those obtained in other precision calculations

The relationship between bimolecular rate coefficients for irreversible and reversible diffusion influenced reactions

A formulation of the theory for diffusion influenced reversible reaction A + B ⇌ C in solution is used to study the effect of the back reaction on the bimolecular forward rate coefficient. The formula recently derived by Szabo that relates the forward rate coefficient in the presence of the back reaction to that in its absence is shown to be valid not only when the reaction occurs at the distance of closest approach but also when it can occur over a range of interparticle distances.

Precise nonvariational calculation of excited states of helium with the correlation-function hyperspherical-harmonic method.

Direct solution of the Schrodinger equation for resonant S states of the Helium atom is obtained with the help of the complex rotation method (which reduces the resonant problem to that of bound states) and the correlation function hyperspherical harmonic method (CFHHM). In the CFHH method the bound state solution is a product of a correlation function and of a smooth factor expanded into hyperspherical harmonic functions. Given a proper correlation function, chosen from physical considerations, the method generates resonant wave functions, accurate in the whole range of interparticle distances. Calculated energies are compared to those obtained by variational and other precise computations.

Correlation-function hyperspherical harmonic calculations of the pp micro, dd micro, and tt micro molecular ions.

The direct solution of the Schr\"odinger equation for the ground state of the pp\ensuremath{\mu}, dd\ensuremath{\mu}, and tt\ensuremath{\mu} molecular ions is obtained with the help of the correlation-function hyperspherical harmonic method. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which leads in turn to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results are compared with those obtained in other precision calculations.

Modelling of the Radial Distribution Function of the Hard‐Sphere Liquid in a Quasi‐Crystalline Model

AbstractThe radial distribution function of the hard‐sphere system, which is obtained by the exact solution of the Percus‐Yevick equation, is described within the framework of the quasi‐crystalline model of liquids (crystal lattice with lattice sites smeared out by the Gaussian law). The b.c.c. lattice is found to allow to receive a practically ideal description of all oscillations of the RDF (with an exception of several first peaks) over a range of interparticle distances up to the 16 sphere diameters. Other lattices give a significantly worse description. It is proposed that the quasi‐crystalline model reflects the correlations in the particle positions connected with regularities of the random close packing.