Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

Solution Branches for Non-linear Equilibrium Problems--Bifurcation and Domain Perturbations

Consider the following simple, but typical, example of a non-linearequilibrium (differential equation) problem: u = –f(u) for (x, y) D, u = 0 for (x, y) D. Usually the eigenvalues of the (small u) linearized problemare simple, and each simple eigen value generates two solutionbranches for the full problem. However, the full problem nearlyalways has many other solution branches, and this paper describeshow to find these other branches and why they arise.     

Uniform Asymptotic Representation of Solutions of the Basic Semiconductor-Device Equations

In this paper we analyse the basic semiconductor-device equationsmodelling a symmetric one-dimensional voltage-controlled diodeunder the assumptions of zero recombination-generation and constantmobilities. Employing the singular-perturbation formulationwith the normed Debye length as perturbation parameter we derivethe zeroth-order terms of the matched asymptotic expansion ofthe solutions, which are sums of uniformly smooth outer terms(reduced solutions) and exponentially varying inner terms (layersolutions). The main result of the paper is that, if the perturbationparameter is sufficiently small, then there exists a solutionof the semiconductor-device problem which is approximated uniformlyby the zeroth-order term of the expansion, even for large appliedvoltages. This result shows the validity of the asymptotic expansionsof the solutions of the semiconductor-device problem in physicallyrelevant high-injection situations.     

Pair approximation for polarization interaction and adiabatic nuclear and electronic sampling method for fluids with dipole polarizability

The adiabatic nuclear and electronic sampling method (ANES), originally formulated as an efficient Monte Carlo algorithm for systems with fluctuating charges, is applied to the simulation of a polarizable water model with induced dipole moments. Structural, thermodynamic and dipolar properties obtained by ANES and a newer algorithm, the pair approximation for polarization interaction (PAPI), are compared with full iteration. With the best parameters, the inaccuracy of both approximate methods was found to be comparable with the uncertainty of the full iteration. The PAPI method with iteration radius equal to the second minimum of the oxygen—oxygen correlation function is, depending on the convergence tolerance, 10–15 times faster than the full iteration for 256 molecules, and yields very accurate structure and thermodynamics with deviation about 0.3%. When the iteration radius is increased to the cutoff distance, exact results are recovered at the cost of decreased efficiency. The ANES method with small nuclear displacements proved to inefficiently sample the configurational space. Simulations at low electronic temperatures with large nuclear displacements are inaccurate for up to 100 electronic moves, and increasing this number would make the simulations as slow as the full iteration. The most accurate and efficient adiabatic ANES simulations are those with infinite electronic temperature, large nuclear displacements and 1–10 electronic moves. The extra freedom of induced dipoles in the ANES method at high electronic temperatures modifies the observed dipolar properties; however, the question of whether the dielectric constant is also modified needs further consideration.     

Theoretical determination of the vibrational levels of NH+ 3 and its isotopomers

The vibrational levels associated with the electronic ground state X²A₂″ of NH⁺ ₃ have been determined up to 5000 cm^?1 by perturbation and variational calculations with full dimensionality of the molecule. For the variational part a new version of MULTIMODE was used which uses the ab initio electronic energy and its first derivative to define the potential energy function. These quantities were generated by the B97-1 density functional and RCCSD(T) approaches. For ND⁺ ₃, ND₂H⁺ and NDH⁺ ₂ the vibrational levels were calculated only by perturbation theory. The rotational constants for all the isotopomers were determined and the first transition dipole moments for NH⁺ ₃ and ND⁺ ₃ were plotted. A critical comparison of the perturbation and variational techniques suggests a possible further modification to the MULTIMODE algorithm for large systems.     

The numerical solution of an inverse scattering problem for acoustic waves

In a previous paper, the authors presented a dual space methodfor the numerical solution of the two-dimensional inverse scatteringproblem for acoustic waves in an inhomogeneous medium. Here,by making major modifications to the dual space method, a dramaticimprovement in the numerical performance of this method is achievedfor solving the inverse scattering problem.     

Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.