A contour integral method is proposed to solve nonlinear eigenvalue problems numerically. The target equation is F (λ)x = 0, where the matrix F (λ) is an analytic matrix function of λ. The method can extract only the eigenvalues λ in a domain defined by the integral path, by reducing the original problem to a linear eigenvalue problem that has identical eigenvalues in the domain. Theoretical aspects of the method are discussed, and we illustrate how to apply of the method with some numerical examples.

The Sakurai-Sugiura projection method, which solves a generalized eigenvalue problem to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory. A new interpretation based on the filter diagonalization was given, and the corresponding filter function was derived explicitly. The block version of the method was also proposed, which enabled to resolve degenerated eigenvalues. Two numerical examples were provided to illustrate the method.

The most stable structures of Arn+, n=3–27, are determined with the analytical gradient method for the diatomics-in-molecules Hamiltonian. The oscillator strength distribution is evaluated. The charge is found to be localized on the central three atoms, which form the trimeric ion core. The first solvation shell evolves around the ion core and is completed at n=25. The calculation shows that the photoabsorption band is in the visible region, which originates from the 2Σu+→ 2Σg+ transition of the Ar3+ ion core, and is red-shifted with the increase of the cluster size, reproducing the experimental results. The red-shift is explained in terms of the solvated ion core model, in which the excited state of the ion core interacts strongly with the surrounding solvent atoms.

No abstract

A coupled fermentation/pervaporation process for reliable production of concentrated ethanol was studied using ethanol permselective silicalite membranes coated with two types of silicone rubber, KE-45 and KE-108, as a hydrophobic material. Ethanol recovery was greatly improved by using a membrane coated with KE-45 silicone rubber. The recovered ethanol concentration in the permeate was 67% (w/w), and the amount of recovered ethanol from the broth was more than 10 times higher than that using a noncoated membrane. Succinic acid and glycerol, by-products created during fermentation, interfered with the pervaporation performance of the coated membrane when used to separate an ethanol/water solution.

We propose a numerical method using contour integral to solve polynomial eigenvalue problems (PEPs). The method finds eigenvalues contained in a certain domain which is defined by a surrounding integral path. By evaluating the contour integral numerically along the path, the method reduces the original PEP into a small generalized eigenvalue problem, which has the identical eigenvalues in the domain. Error analysis indicates that the error of the eigenvalues is not uniform: inner eigenvalues are less erroneous. Four numerical examples are presented, which confirm the theoretical predictions.

No abstract

A full electron calculation for the photosynthetic reaction center of Rhodopseudomonas viridis was performed by using the fragment molecular orbital (FMO) method on a massive cluster computer. The target system contains 20,581 atoms and 77,754 electrons, which was divided into 1,398 fragments. According to the FMO prescription, the calculations of the fragments and pairs of the fragments were conducted to obtain the electronic state of the system. The calculation at RHF/6-31G* level of theory took 72.5 hours with 600 CPUs. The CPUs were grouped into several workers, to which the calculations of the fragments were dispatched. An uneven CPU grouping, where two types of workers are generated, was shown to be efficient.