Unbiased estimate of forces from measured correlation functions,including the case of strong multiplicative noise

Starting from appropriate short-time correlation function measurements, we propose a dynamical “learning” method to derive the deterministic and stochastic forces underlying an observed process, even if this process contains strong multiplicative noise. To do this we extend the ideas of our previous paper [1] to establish mathematical relationships in this more general case between the joint distribution function of the process and its corresponding Ito-Langevin equation. A numerical example for a simulated process containing strong multiplicative noise shows good agreement with the theory.     

Theory of two-photon lasers I

We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.     

Chapman-Kolmogorov equation for discrete chaos

We derive an equation of the Chapman-Kolmogorov type for multi-dimensional discrete mappings under the impact of additive and multiplicative noise with arbitrary distribution.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

Modulated traveling waves in nonequilibrium systems: The ‘blinking state’

For the first time we give an explanation of the mechanism underlying the generation of modulated traveling wave states in nonequilibrium systems, frequently denoted as blinking state. The blinking state is generated by two nonlinearly interacting oscillatory modes with slightly different eigenfrequencies. Frequency locking between these modes generate spatial patterns experimentally known as confined states.     

Anisotropy in Tendon Investigated in Vivo by a Portable NMR Scanner, the NMR-MOUSE

Ordered tissue like tendon is known to exhibit the magic-angle phenomenon in magnetic resonance investigations. Due to the anisotropic structure the transverse relaxation time T₂ depends on the orientation of the tendon in the magnetic field. In medical imaging, relaxation measurements of tendon orientation are restricted by the size of the object and the space available in the magnet. For humans, tendon orientation can only be varied within small limits. As a consequence, the magic-angle phenomenon may lead to a misjudgement of tendon condition. It is demonstrated that the NMR-MOUSE (mobile universal surface explorer), a hand-held NMR sensor, can be employed to investigate the anisotropy of T₂ in Achilles tendon in vivo. The NMR-MOUSE provides a convenient tool for analyzing the correlation of T₂ and the physical condition of tendon.