Optimal Control of the Obstacle for an Elliptic Variational Inequality

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H ¹ ₀ (Ω) so that the state is close to the desired profile while the H ¹ (Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established. Accepted 11 September 1996     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.

     

Interaction of He Atoms with XeF2 Observed in Crossed Molecular Beams

The interactional shape of XeF₂ with respect to energy and distance was observed by He atom scattering in molecular beam experiments. The heterogeneous second virial coefficient and the binary coefficient of diffusion were calculated from the resulting interaction potential.     

Structure and Curie temperature of Y2Fe17-xCrx

The structures of Y2Fe17-xCrx are simulated by the ab initio potentials. The site preference of Cr atom in Y2Fe17 is evaluated and the order is determined as 4f, 12j, which is close to the experimental result. Based on the site preference behavior, the calculated parameters and the atom sites of Y-Fe-Cr system are studied. The result corresponds well to observed data. Further, the DOS of the relaxed structures are calculated and the variation in Curie temperature is explained qualitatively by the spin-fluctuation theory.     

Wegner estimate for sparse and other generalized alloy type potentials

We prove a Wegner estimate for generalized alloy type models at negative energies (Theorems 8 and 13). The single site potential is assumed to be non-positive. The random potential does not need to be stationary with respect to translations from a lattice. Actually, the set of points to which the individual single site potentials are attached, needs only to satisfy a certain density condition. The distribution of the coupling constants is assumed to have a bounded density only in the energy region where we prove the Wegner estimate.     

An Inverse Problem for the Matrix Schrödinger Equation

By modifying and generalizing some old techniques of N. Levinson, a uniqueness theorem is established for an inverse problem related to periodic and Sturm-Liouville boundary value problems for the matrix Schrödinger equation.     

The Ansatz Method for Analyzing Schrödinger’s Equation with Three Anharmonic Potentials in D Dimensions

In this letter, by applying a suitable ansatz to the wave functions, the solutions of the D-dimensional radial Schrödinger equation with some anharmonic potentials are obtained.     

Interaction between aromatic amine cations and nonpolar solvents: Infrared spectra of isomeric aniline -Ar n ( ) complexes

Infrared (IR) photodissociation spectra of the aniline⁺-Ar_n cations, An ⁺ - Ar _n (n = 1, 2), are analyzed in the vicinity of the N-H stretch fundamentals. The complexes are produced in an electron impact (EI) ion source which produces predominantly the most stable cluster isomers. Two isomers of An⁺-Ar are identified by their characteristic N-H stretch frequencies: the planar proton-bound global minimum, in which the Ar ligand forms a nearly linear H-bond to the amino group, and the less stable π-bound local minimum, in which the Ar atom is attached to the π-electron system of the aromatic ring. This result is the first unambiguous detection of the most stable H-bound An⁺-Ar dimer. All previous spectroscopic studies of An⁺-Ar employed resonance enhanced multiphoton ionization (REMPI) of neutral An-Ar and identified only the less stable π-bound cation due to restrictions arising from the Franck-Condon principle. The EI-IR spectrum of An⁺-Ar₂ shows that the most stable structure of this trimer features two equivalent H-bonds (C_2v symmetry). The interpretation of the experimental data is supported by quantum chemical calculations. The ab initio potential of An⁺-Ar calculated at the UMP2/6-311G(2df, 2pd) level features H-bound global minima ( D _e = 513 cm^-1) and π-bound local minima ( D _e = 454 cm^-1), with a barrier of V _b ≈ 140 cm^-1 for isomerization from the π-bound toward the H-bound minimum. Received 4 February 2002 Published online 13 September 2002     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.