Search results for "Linear"
showing 10 items of 7165 documents
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.
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
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.
Diode-pumped self-Q-switched erbium-doped all-fibre laser
2004
A diode-pumped self-Q-switched erbium-doped fibre laser is developed and studied. The laser has an all-fibre configuration containing a piece of an active heavily erbium-doped fibre and two fibre Bragg grating mirrors and does not require any additional intracavity elements to obtain short pulses. Analysis of the laser operation suggests that the most probable mechanism of passive Q-switching of the laser cavity is absorption from the excited state of erbium resulting in the thermally induced nonlinear change in the refractive index in the erbium-doped fibre.
Pharmacological distribution diagrams: a tool for de novo drug design.
1996
Abstract Discriminant analysis applied to SAR studies using topological descriptors allows us to plot frequency distribution diagrams: a function of the number of drugs within an interval of values of discriminant function vs. these values. We make use of these representations, pharmacological distribution diagrams (PDDs), in structurally heterogeneous groups where generally they adopt skewed Gaussian shapes or present several maxima. The maxima afford intervals of discrimianant function in which exists a good expectancy to find new active drugs. A set of β-blockers with contrasted activity has been selected to test the ability of PDDs as a visualizing technique, for the identification of n…
Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities
2013
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired…