Search results for "Linear"
showing 10 items of 7165 documents
Slowing down of light pulses using backward-wave four-wave mixing with local response
2015
The slowing down of light pulses is achieved using backward-wave four-wave mixing in a medium with local response. A Bi12TiO20 crystal with an external dc field is used in the experiment as a proof-of-concept material. The delay and shape transformation of output pulses are studied and compared for the transmitted and phase conjugate channels. It is shown that the phase conjugate pulse achieves a longer delay under typical experimental conditions with equal intensities of the pump beams. This advantage of the phase conjugate beam is especially pronounced for short pulses with half-widths smaller than the response time of the medium. The agreement of the experimental results with numerical c…
Fractional mechanical model for the dynamics of non-local continuum
2009
In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…
The Vlasov Limit for a System of Particles which Interact with a Wave Field
2008
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.
Stabilisation of dispersion-managed soliton transmissions by nonlinear gain
1999
Nonlinear gain is shown to be effective in suppressing the radiative background that may not be separated from the signal when the average dispersion is close to zero in dispersion-managed soliton transmissions. By correctly combining nonlinear gain and filtering, the instability introduced by guiding filters can be avoided.
Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.
2000
We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…
Test of the semischematic model for a liquid of linear molecules
1998
We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].
On the sources of the late integrated Sachs-Wolfe effect
2000
In some scenarios, the peculiar gravitational potential of linear and mildly nonlinear structures depends on time and, as a result of this dependence, a late integrated Sachs-Wolfe effect appears. Here, an appropriate formalism is used which allows us to improve on the analysis of the spatial scales and locations of the main cosmological inhomogeneities producing this effect. The study is performed in the framework of the currently preferred flat model with cosmological constant, and it is also developed in an open model for comparisons. Results from this analysis are used to discuss the contribution of Great Attractor-like objects, voids, and other structures to the CMB anisotropy.
Some aspects of the orientation of galaxies in clusters
2013
The analysis of Tully's groups of galaxies belonging to the Local Supercluster (LSC) was performed. In the 1975 Hawley and Peebles presented the method for investigations of the galaxies orientation in the large structures. In our previous papers statistical test proposed by Hawley and Peebles for investigation of this problem was analyzed in details and some improvements were suggested. On this base the new method of the analysis of galactic alignment in clusters was proposed. Using this method, God{\l}owski (2012) analyzed the orientation of galaxies inside Tully's group founding no significant deviations from isotropy both in orientation of position angles and $\delta_D$ and $\eta$ angle…
Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations
2012
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \gamma depends on the initial conditions, characterized by th…
A dynamical systems study of the inhomogeneous Lambda-CDM model
2010
We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-…