Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

Solvent effects on oxygen atom transfer reaction between manganese(V)-oxo corrole and alkene

Pseudo-first order reaction rate constants of 5,10,15-tris（pentafluorophenyl）corrole Mn（V）-oxo (F₁₅CMn（V）-oxo),5,15-bis（pentafluorophenyl）-10-（phenyl）corrole Mn（V）-oxo(F₁₀CMn（V）-oxo),5,15- bis（phenyl）-10-（pentafluorophenyl）corrole Mn（V）-oxo（F₅CMn（V）-oxo） and 5,10,15-tris（phenyl）corrole Mn（V）-oxo（F₀CMn（V）-oxo） with a series of alkene substrates in different solvents were determined by UV-vis spectroscopy.The results indicated that the oxygen atom transfer pathway between Mn（V）-oxo corrole and alkene is solvent-dependent.     

Phase mismatch effects on the dynamics of a semilinear photorefractive oscillator with reflection-type gratings

This paper describes the effect of pump waves misalignement on the performance of the semilinear photorefractive coherent oscillator with the reflection gratings. The oscillation intensity and its modulation frequency are calculated numerically for different misalignement angles, coupling strengths and pump intensity ratios. It is shown that a small angular detuning of the pump wave, less than one milliradian, extends the range of pump ratios and the range of coupling strengths for which a non-degenerate oscillation occurs. The results of experiments with the BaTiO₃-based semilinear oscillator are in qualitative agreement with the calculated data.     

Polarization control in spun and telecommunication optical fibers

We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are determined by the polarization state of the injected backward pump. In randomly birefringent telecommunication fibers, we show that an unpolarized signal beam can be repolarized into any particular polarization state, without loss of energy.     

Algebraic time-reversal operation

We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) é U(4) é K(4)=A(4)ùS(4) é S(4) ? T_dU(5)\supset U(4)\supset K(4)=A(4)\wedge S(4)\supset S(4)\approx T_d. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.     

β-Octafluorinated tetrakis(ethoxycarbonyl)porphyrin

Tetrakis(alloxycarbonyl)porphyrin and its β-octafluoro-substituted derivatives were synthesized via Lindsey method and transformed to their zinc complexes.Single crystal X-ray structures of corresponding Zn(Ⅱ) porphyrins revealed that β-octafluorination will give more compactness of porphyrin moieties in the crystal structure owing to the hydrogen bonding interactions involving β-fluorine atoms.An unusual six-coordinated Zn(Ⅱ) was found via intramolecular coordination of oxygen atom of meso-substituents with central Zn(Ⅱ).     

Effects of angular pump mismatch for the semi-linear oscillator

We investigate, analytically and numerically, the influence of an angular mismatch of counter-propagating pump beams on the threshold of oscillation for the photorefractive semi-linear oscillator driven by non-local non-linear response. Our analysis includes the frequency degenerate and non-degenerate regimes within a wide range of the variable input parameters—the coupling strength, the pump ratio, and the feedback mirror reflectivity. The limiting case of mirrorless oscillation is considered as well. The main outcome of our studies is the possibility of strong reduction of the oscillation threshold owing to the angular mismatch. Furthermore, increasing the mismatch induces pronounced bifurcations of the oscillation parameters, including transitions between degenerate and non-degenerate oscillation modes. The main findings are verified by direct simulations of the dynamic equations.     

Velocity locking of incoherent nonlinear wave packets

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.     

Enhanced alignment and orientation of polar molecules by vibrational resonant adiabatic passage

The authors show that polar molecules can be adiabatically aligned and oriented by laser pulses more efficiently when the laser frequencies are vibrationally resonant. The aligned molecules are found in a superposition of vibrational pendular states, each associated with the alignment of the rotor in one vibrational state. The authors construct the dressed potential associated with this mechanism. Values of detunings and field amplitudes are given to optimize the degree of alignment and orientation for the CO molecule.