Search results for "Linear"
showing 10 items of 7165 documents
Sum Frequency Generation Spectra from Velocity-Velocity Correlation Functions: New Developments and Applications
2018
At the interface, the properties of water can be rather different from those observed in the bulk. In this chapter we present an overview of our computational approach to understand water structure and dynamics at the interface including atomistic and electronic structure details. In particular we show how Density Functional Theory-based molecular dynamics simulations (DFT-MD) of water interfaces can provide a microscopic interpretation of recent experimental results from surface sensitive vibrational Sum Frequency Generation spectroscopy (SFG). In our recent work we developed an expression for the calculation of the SFG spectra of water interfaces which is based on the projection of the at…
Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms
2013
We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and…
Linear Methods in Nilpotent Groups
1982
The subject of this chapter is commutator calculation. It will be recalled that the commutator [x, y] of two elements x, y of a group is defined by the relation $$ [x,y] = {{x}^{{ - 1}}}{{y}^{{ - 1}}}xy. $$ . We then have $$ [xy,z] = {{[x,z]}^{y}}[y,z],\quad [x,yz] = [x,z]{{[x,y]}^{z}}. $$ . These relations are rather similar to the conditions for bilinearity of forms, and there are a number of ways of formalizing this similarity. Once this is done, commutator calculations can be done by linear methods. Several examples of theorems proved by this method will be given in this chapter.
The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures
2018
The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoulli beam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of mul…
The Soliton Concept in Lattice Dynamics
1996
In previous chapters we have considered nonlinear waves in the macroworld. We have examined different systems which provide the simplest examples of onedimensional systems or devices, where the localized waves or pulses called solitons can be simply and coherently created, easily observed, and manipulated on a macroscopic scale. At the microscopic level the localized nonlinear wave modes have a spatial extension ranging from less than a few microns to a few angstroms. These excitations, which correspond to large-amplitude atomic or molecular motions, are mainly created by thermal processes, sometimes by some external stimulus; their experimental manifestation is indirect; their observation …
Slow-light solitons: Influence of relaxation
2008
We have applied the transformation of the slow-light equations to the Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the presence of relaxation and found that the spontaneous emission from the upper atomic level is strongly suppressed. Our solution proves that the spatial shape of the soliton is well preserved even if the relaxation time is much shorter than the soliton time length. This fact is of great importance for applications of the slow-light soliton concept in optical information processing. We also demonstrate that relaxation plays a role of resistance to the sol…
A three domain controller for a high frequency high power four quadrant power converter for superconducting magnets
2002
The paper describes the implementation of a controller that orchestrates the functioning of three subsystems that implement a high energy converter (/spl plusmn/1500 A, /spl plusmn/15 V) that supplies a superconducting magnet to be used in particle accelerators. The performance of the whole system, in accordance to specifications, is documented with experimental results.
Extension of Electron Monte Carlo Dose Calculation in Eclipse to Siemens Linear Accelerators
2009
Initially, the implementation of the macro Monte Carlo (MC) method into Eclipse (Varian Medical Systems), named eMC, was carried out for Varian accelerators only. In this work eMC algorithm has been modified to allow also accurate dose calculations for electron beams for Siemens accelerators.
Nonlinear nonviscous hydrodynamical models for charge transport in the framework of extended thermodynamic methods
2002
This paper develops a procedure, based on methods of extended thermodynamics, to design nonlinear hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. Models obtained in this way allow the study of the motion of electric charges in the presence of arbitrary external electric fields and may be useful when one wishes to study phenomena in a neighborhood of a stationary nonequilibrium process: indeed, the drift velocity of the charge gas with respect to the crystal lattice is not regarded as a small parameter.
Continuous-wave Lyman-alpha generation with solid-state lasers.
2009
A coherent continuous-wave Lyman-alpha source based on four-wave sum-frequency mixing in mercury vapor has been realized with solid-state lasers. The third-order nonlinear susceptibility is enhanced by the 6(1)S - 7(1)S two-photon resonance and the near 6(1)S-6(3)P one-photon resonance. The phase matching curve for this four-wave mixing scheme is observed for the first time. In addition we investigate the two-photon enhancement of the Lyman-alpha yield and observe that the maxima of Lyman-alpha generation are shifted compared to the two-photon resonances of the different isotopes.