Search results for "nonlinear"
showing 10 items of 3684 documents
Theory of tailor automata
2019
Abstract In the paper, a fragment of the new theory of tailor automata is presented, within which a deterministic finite automaton was defined. The proposed automaton provides a theoretical model of an informally characterized biomolecular automaton. The idea of working of which is founded on the concept of alternating cut of some double-stranded fragments of DNA, with the use of a restriction enzyme and ligations of some double-stranded fragments of DNA, with the use of the ligase enzyme.
Energy localization in a nonlinear discrete system
1996
International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.
Modulational instability and two-dimensional dynamical structures
2008
A process of nonlinear structure formation on a two-dimensional lattice is proposed. The basic model consists of a two-dimensional lattice equipped at each node with a molecule or dipole rotating in the lattice plane. The interactions involved in the model are reduced to a periodic lattice. Such a discrete system can be applied to the problem of molecule adsorption on a substrate crystal surface, for instance. The continuum approximation of the model leads to a 2-D sine-Gordon system including nonlinear couplings, which itself can be reduced to a 2-D nonlinear Schrodinger equation in the low amplitude limit. Spatio-temporal structure formation is investigated by means of numerical simulatio…
Advanced Ultrasonic Structural Monitoring of Waveguides
2008
Ultrasonic Guided Waves (UGWs) are a useful tool in those structural health monitoring applications that can benefit from built-in transduction, moderately large inspection ranges and high sensitivity to small flaws. This paper describes two methods, based on linear and nonlinear acoustics for structural damage detection based on UGWs. The linear method combine the advantages of UGW inspection with the outcomes of the Discrete Wavelet Transform (DWT) that is used for extracting defect-sensitive features that can be combined to perform a multivariate diagnosis of damage. In particular, the DWT is exploited to generate a set of relevant wavelet coefficients to construct a uni-dimensional or m…
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
2001
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
Enhanced supercontinuum generation in tapered tellurite suspended core fiber
2015
Abstract We demonstrate 400-THz (0.6–3.3 µm) bandwidth infrared supercontinuum generation in a 10 cm-long tapered tellurite suspended core fiber pumped by nJ-level 200-fs pulses from an optical parametric oscillator. The increased nonlinearity and dispersion engineering extended by the moderate reduction of the fiber core size are exploited for supercontinuum optimization on both frequency edges (i.e., 155-THz overall gain), while keeping efficient power coupling into the untapered fiber input. The remaining limitation of supercontinuum bandwidth is related to the presence of the high absorption beyond 3 µm whereas spectral broadening is expected to fully cover the glass transmission window…
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
2013
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
MAPPINGS OF FINITE DISTORTION: $L^n \log^{\alpha} L$ -INTEGRABILITY
2003
Recently, systematic studies of mappings of finite distortion have emerged as a key area in geometric function theory. The connection with deformations of elastic bodies and regularity of energy minimizers in the theory of nonlinear elasticity is perhaps a primary motivation for such studies, but there are many other applications as well, particularly in holomorphic dynamics and also in the study of first order degenerate elliptic systems, for instance the Beltrami systems we consider here.
Nonlinear dynamics of a two-photon Fabry–Pérot laser
2000
Abstract The steady-state emission, stability and temporal dynamics of a single-mode two-photon laser with a Fabry–Perot cavity is investigated and compared with that of a ring-cavity laser. It is found that the Fabry–Perot cavity makes the laser less efficient than the ring cavity because of spatial hole burning, but the domain of stability is larger for the Fabry–Perot laser. The intensity and phase dynamics are numerically investigated and distinctive features are found in the phase dynamics as compared with one-photon lasers.
Generation of Bound States of Three Ultrashort Pulses With a Passively Mode-Locked High-Power Yb-Doped Double-Clad Fiber Laser
2004
We report the generation of high-power ultrashort bound states of three pulses in an ytterbium-doped double-clad fiber laser. The laser is mode-locked through nonlinear polarization rotation technique in a unidirectional cavity configuration. A pair of diffraction grating is incorporated in the cavity to compensate for the normal dispersion of the fiber. The laser generates chirped bound states of three pulses with either equal or different time separations, with more than 500-pJ energy per pulse. These pulses are subsequently compressed to 100 fs with a compression factor of more than 40.