Search results for " Integra"
showing 10 items of 2527 documents
On-axis diffractional behavior of two-dimensional pupils
2010
We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precisio…
Shapes of a gas bubble rising in the vertical Hele–Shaw cell with magnetic liquid
2005
Abstract Dynamics of the bubble rising in the vertical Hele–Shaw cell with magnetic liquid in the normal magnetic field is studied. Linear stability analysis of the circular shape is carried out. Development of the instability with respect to the lowest symmetric mode is simulated by the boundary integral equation technique.
Rotational Motion of Linear Molecules in Three Dimensions. A Path-Integral Monte Carlo Approach
1994
Abstract A path-integral Monte Carlo (PIMC) simulation method for the rotational motion of linear molecules in three dimensions is presented. The technique is applied to an H2 impurity in a static crystal-field. The resulting orientational distributions from quantum and classical simulations are obtained and discussed. The algorithm suffers from the “sign problem” of quantum simulations. However, as can be seen by comparing the low temperature simulation result to the variational solution of the Schrodinger equation, the PIMC method captures the quantum fluctuations.
Bright and dark optical solitons in fiber media with higher-order effects
2002
We consider N-coupled higher-order nonlinear Schrodinger (N-CHNLS) equations which govern the simultaneous propagation of N optical fields in fiber media with higher-order effects. Bright and dark soliton solutions are derived using Hirota bilinear method for the general cross-coupling ratio between the parameters of self-phase modulation and cross-phase modulation effects. By means of coupled amplitude-phase formulation also, similar kind of dark soliton solutions are obtained. It is found that the parametric conditions for the simultaneous propagation of N dark solitons from both the methods are the same.
Simplicial Wheeler-DeWitt equation in 2+1 spacetime dimensions.
1993
We introduce an equation which rue suggest to be a simplicial counterpart to the Wheeler-DeWitt equation in 2 + 1 spacetime dimensions. Our approach is based on the use of the Ashtekar variables
A simple microsuperspace model in 2 + 1 spacetime dimensions
1992
Abstract We quantize the closed Friedmann model in 2 + 1 spacetime dimensions using euclidean path-integral approach and a simple microsuperspace model. A relationship between integration measure and operator ordering in the Wheeler-DeWitt equation is found within our model. Solutions to the Wheeler-DeWitt equation are exactly reproduced from the path integral using suitable integration contours in the complex plane.
Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons
2001
Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.
The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
2018
We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularisation parameter $\varepsilon$. This is done by transforming the system of differential equations for this integral and all its sub-topologies to a form linear in $\varepsilon$, where the $\varepsilon^0$-part is strictly lower triangular. This system is easily solved order by order in the dimensional regularisation parameter $\varepsilon$. This is an example of an elliptic multi-scale integral involving several elliptic sub-topologies. Our methods are applicable to similar problems.
Stationary problems for equation of the KdV type and dynamical r-matrices
1995
We study a quite general family of dynamical $r$-matrices for an auxiliary loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax representations and to find variables of separation for a wide set of the integrable natural Hamiltonian systems. As an example, we discuss the Henon-Heiles system and a quartic system of two degrees of freedom in detail.
The $\varepsilon$-form of the differential equations for Feynman integrals in the elliptic case
2018
Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The $\varepsilon$-form is obtained by a (non-algebraic) change of basis for the master integrals.