Photon correlations from ultra-strong optical nonlinearities

We study the full field and frequency filtered output photon statistics of a resonator in thermal equilibrium with a bath and containing an arbitrarily large quartic nonlinearity. According to the general theory of photodetection, we derive general input-output relations valid for the ultra-anharmonic regime, where the nonlinearity becomes comparable to the energy of the resonator, and show how the emission properties are modified as compared to the generally assumed simple anharmonic regime. We analyse the impact of the nonlinearity on the full statistics of the emission and its spectral properties. In particular we derive a semi-analytical expression for the frequency resolved two-photon correlations or two-photon spectrum of the system in terms of the master equation coefficients and density matrix. This provides a very clear insight into the level structure and emission possibilities of the system.Comment: 10 pages, 7 figure

Covariance approach to the free photon field

We introduce photon theory following the same principles as for introduction of the quantum theory of a single particle, using a C*-algebraic approach based on covariance systems. The basic symmetries are additivity of the fields and additivity of test functions. We write down in explicit form a state of this covariance system. It turns out to reproduce the traditional Fock representation of the free photon field, with a Lorentz invariant vacuum. Properties of smeared-out photons are discussed.Comment: Latex, 24 pages, to appear in: "Probing the structure of Quantum Mechanics: nonlinearity, nonlocality, computation and axiomatics", eds. D. Aerts, M. Czachor, and T. Durt (World Scientific, 2002

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm

Numerical Analysis of Geometric and Material Nonlinearity of Beams in the Plane

The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package

Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller

LARGE DEFORMATION THEORY IN GEOMECHANICS - INFLUENCE OF KINEMATIC NONLINEARITY ON THE RESULTS OF SOME CHARACTERISTIC GEOTECHNICAL CALCULATIONS

The geotechnical engineering calculations are usually carried out according to the small deformation and displacement theory (infinitesimal strain theory) i.e. first-order theory. A linear relationship between componental displacements and deformations is adopted. The well-known conditions for equilibrium are defined for an undeformed system i.e. undeformed structure. Therefore, the geometric and static linearity assumptions are usually valid in geotechnical engineering calculations. These linearities are collectively referred to as kinematic linearity. In other words, engineers believe that results of quite satisfactory accuracy are obtained if only material nonlinearity is taken into account in the engineering calculations, regardless of the type of geotechnical problem being analysed. Therefore, it is not necessary to apply the large (finite) deformation theory with the assumption of material nonlinearity. The main aim of this paper is to verify the previous statement in the case of some characteristic problems of Geotechnics. In the first part of this paper, the large deformation theory, which is mostly unknown to the wider professional public, is briefly presented. After that, simple numerical analyses of some characteristic problems of Geotechnics were carried out in the well-known software FLAC 2D software with the aim of comparing the results obtained for the cases of kinematic linearity and kinematic nonlinearity. The obtained results point to the fact that kinematic nonlinearity should not always be ignored in the usual geotechnical engineering calculations. Therefore, engineers are urged to be careful