One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).     

Existence and nonexistence of curved front solution of a biological equation

This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential.     

Classical study of the influence of induced rotation and anisotropy effects on energy transfer between an atom and a diatomic molecule

The lagrangian equations of motion for a mass 4 atom colliding with a mass 2 diatomic molecule are solved numerically in order to investigate the validity of some approximations often used in energy transfer theory. The results are shown to be very sensitive to the details of the intermolecular potential; the effect of induced rotation can change the vibrational energy transfer by an order of magnitude.     

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.     

A closed-form solution of the Schroedinger equation describing the harmonic oscillator with time dependent frequency and acted on by a time dependent perturbative force

A new form of the semiclassical quantum conditions in non-separable systems is proposed. In two dimensions (2D) it has the form (? = 1)

where C_Σ is the path of a classical trajectory closed in phase space, N_x and N_y are the number of circuits in the x and y ‘senses’ on the invariant toroid and J_x and J_y are the ‘good’ action variables on the toroid; these action variables, J_x and J_y , must have the values 2π(n ₁ + ½) and 2π(n ₂ + ½) respectively where n ₁ and n ₂ are the integer quantum numbers. Closed classical trajectories occur only for the exceptional toroids with rational frequency ratios. In the general case we imply that the trajectory has closed on itself to some arbitrary accuracy. Results for the 2D potentials studied are in agreement with previously published work. It is shown how the method may be extended to 3D systems.     

Time reversal of noise sources in a reverberation room

Usually, time reversal is studied with pulsed emissions. Here, the properties of time reversal of the acoustic field emitted by noise sources in a reverberation room are studied numerically, theoretically, and experimentally. A time domain numerical simulation of a two-dimensional enclosure shows that the intensity of a time-reversed noise is strongly enhanced right on the initial source position. A theory based on the link that exists between time reversal of noise and the "well-known" time reversal of short pulse is developed. One infers that the focal spot size equals half a wavelength and the signal to noise ratio only depends on the number of transceivers in the time reversal mirror. This last property is characteristic of the time reversal of noise. Experimental results are obtained in a 5 X 3 X 3 m3 reverberation room. The working frequency range varies from 300 Hz to 2 kHz. The ability of the time reversal process to physically reconstruct the image of two noise sources is studied. To this end, care is given to the technique to separate two close random sources, and also to the influence of temperature fluctuations on the focusing quality.     

A simple and efficient evolution operator for time-dependent Hamiltonians: the Taylor expansion

No compact expression of the evolution operator is known when the Hamiltonian operator is time dependent, like when Hamiltonian operators describe, in a semiclassical limit, the interaction of a molecule with an electric field. It is well known that Magnus [N. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)] has derived a formal expression where the evolution operator is expressed as an exponential of an operator defined as a series. In spite of its formal simplicity, it turns out to be difficult to use at high orders. For numerical purposes, approximate methods such as "Runge-Kutta" or "split operator" are often used usually, however, to a small order (<5), so that only small time steps, about one-tenth or one-hundredth of the field cycle, are acceptable. Moreover, concerning the latter method, split operator, it is only very efficient when a diagonal representation of the kinetic energy operator is known. The Taylor expansion of the evolution operator or the wave function about the initial time provides an alternative approach, which is very simple to implement and, unlike split operator, without restrictions on the Hamiltonian. In addition, relatively large time steps (up to the field cycle) can be used. A two-level model and a propagation of a Gaussian wave packet in a harmonic potential illustrate the efficiency of the Taylor expansion. Finally, the calculation of the time-averaged absorbed energy in fluoroproprene provides a realistic application of our method.     

A0 mode interaction with a plate free edge: theory and experiments at very low frequency by thickness product

When a plane acoustic wave reaches a medium with an impedance infinite or null, it experiences a phase shift of zero or pi and its amplitude on the edge is maximum or vanishes. The case of a flexion wave (A0 Lamb wave) at a free end is also simple; its amplitude is multiplied by a factor 2 square root 2 and the phase shift is pi/2. The evanescent wave at the origin of these phenomena, perfectly described by the classical flexural plate theory, is identified as the imaginary A1 mode of the exact Rayleigh-Lamb theory. The experiences confirm the theoretical predictions.     

Mutation in the flavin mononucleotide domain modulates magnetic circular dichroism spectra of the iNOS ferric cyano complex in a substrate-specific manner

We have obtained low-temperature magnetic circular dichroism (MCD) spectra for ferric cyano complexes of the wild type and E546N mutant of a human inducible nitric oxide synthase (iNOS) oxygenase/flavin mononucleotide (oxyFMN) construct. The mutation at the FMN domain has previously been shown to modulate the MCD spectra of the l-arginine-bound ferric iNOS heme (Sempombe, J.; et al. J. Am. Chem. Soc. 2009, 131, 6940-6941). The addition of l-arginine to the wild-type protein causes notable changes in the CN(-)-adduct MCD spectrum, while the E546N mutant spectrum is not perturbed. Moreover, the MCD spectral perturbation observed with l-arginine is absent in the CN(-) complexes incubated with N-hydroxy-L-arginine, which is the substrate for the second step of NOS catalysis. These results indicate that interdomain FMN-heme interactions exert a long-range effect on key heme axial ligand-substrate interactions that determine substrate oxidation pathways of NOS.