On symmetries,reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion

This paper studies the compressional dispersive Alfvén (CDA) waves where Noether symmetries will be calculated from which the corresponding conservation laws will be obtained via Noether's theorem. Furthermore, one case of double reduction is performed via the association of a conserved vector with a Noether symmetry (with zero gauge). The conserved quantities of optical solitons in the presence of intermodal dispersion that is governed by the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. The invariance-multiplier method is adopted to carry out the analysis, from which the conserved densities are then retrieved. Finally, the conserved quantities are obtained using the 1-soliton solution of the governing equation.     

Analysis of BPSK homodyne receivers based on modified balanced optical phase-locked loop in the presence of non-negligible loop propagation delay

Optical homodyne receivers based on modified balanced optical phase-locked loop is analyzed taking into account loop propagation delay. This modified loop contains all the components of a standard BOPLL in conjunction of an additional phase modulator. This modified loop offers a much improved tracking performance and also shows good improvements in the reduction performance over previously reported methods, like, relaxed line-width requirement and improved lock-in range. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser line-width with the optimum phase deviations in the presence of non-negligible loop propagation delay. It is found that in order to maintain a 10⁻¹⁰ BER system performance with ξ = 1, R = 1 A/W, P_R = −53 dBm, Δυ = 1 MHz, phase modulator sensitivity K_PM = 10 rad/V and 10° phase deviation between the two transmitted bits, the loop delay must be kept below 3 ns. Further, the required line-width with the non-negligible loop delay time is evaluated and found to be (2.1 × 10⁻³)/τ, where τ (s) is the loop delay. This number corresponds to BER = 10⁻¹⁰, imperfect phase recovery power penalty of 1 dB and phase modulator sensitivity K_PM = 20 rad/V.     

Experimental gravity induced coexistence curve of methyl fluoride near the critical point

Abstract

The top part of the coexistence curve of methyl fluoride in the critical region has been determined first by direct observation of the disappearance of the meniscus of the fluid situated in a high-pressure light scattering cell and subsequently from the measured maximum depolarization ratio of an appreciable number of isochores close to the critical point. The experimental data obtained from direct observations yield a coexistence curve which nearly coincides with that found recently from pVT measurements. However, the data obtained from light scattering experiments describe a gravity induced coexistence curve which lies above the previous one and which shows a minimum at the critical point. The complete experimental data have been used to evaluate the critical parameters p_c, ρ_c and T_c and the critical exponent β.     

Ultraslow solitons due to large quintic nonlinearity in coupled quantum well structures driven by two control laser beams

In this paper, we have shown the existence of large amounts of quintic nonlinearity in asymmetric three-coupled quantum wells, which arise due to a probe pulse and two controlling laser beams. The possibilities of generation and propagation of ultraslow bright optical solitons in these systems have been examined in situations of both Kerr and quintic nonlinearities. We have also demonstrated numerically that these solitons are stable. The modulation instability of a continuous or quasi-continuous wave probe beam has been also investigated and the role of quintic nonlinearity in suppressing this instability has been addressed.     

Simple technique for alignment of a dispersive ring laser cavity

A simple technique for the alignment of a dispersive ring cavity consisting of a reflection-grating and two mirrors is described. Lasing on different rotational–vibrational transitions of CO₂ molecule is achieved in the ring configuration.     

Sub-barrier fission fragment angular distributions for the system19F+232Th

The measurements of fission fragment angular distributions for the system¹⁹F+²³²Th have been extended to the sub-barrier energies of 89.3, 91.5 and 93.6 MeV. The measured anisotropies, within errors are nearly the same over this energy region. However, the deviation of the experimental values of anisotropies from that of standard statistical model predictions increases as the bombarding energy is lowered.     

Testing for the Absence of Random Effects in a Two-way Nested Design with Mixed Effects Model: A Nonparametric Approach

Two-way nested design with mixed effects model arises in many practical situations. In the classical analysis of variance set-up, a test for the absence of the random effects is obtained under the assumption that the random effects and the errors are normally distributed. The present paper avoids this assumption and provides an asymptotically distribution-free test procedure for the above problem. The asymptotic null distribution of the test statistic is obtained. Actual implementation of the test is straight forward given the prior information on quantiles of the intra-block differences of observations. In the absence of such information, working test procedures are proposed. The performances of these tests are compared with the classical analysis of variance test through simulations. The tests are then illustrated by some real data sets.     

Motion of test particles around domain walls

We present a detailed analysis of the motion of test particles around domain walls. The study of the trajectories of the test particles has been done using the Hamilton-Jacobi formalism. In most of the cases we show that the particles can not be trapped by the walls.     

Harder–Narasimhan reduction for principal bundles over a compact Kähler manifold

Generalizing the Harder–Narasimhan filtration of a vector bundle it is shown that a principal G-bundle over a compact K?hler manifold admits a canonical reduction of its structure group to a parabolic subgroup of G. Here G is a complex connected reductive algebraic group; in the special case where , this reduction is the Harder–Narasimhan filtration of the vector bundle associated to by the standard representation of . The reduction of in question is determined by two conditions. If P denotes the parabolic subgroup, L its Levi factor and the canonical reduction, then the first condition says that the principal L-bundle obtained by extending the structure group of the P-bundle using the natural projection of P to L is semistable. Denoting by the Lie algebra of the unipotent radical of P, the second condition says that for any irreducible P-module V occurring in , the associated vector bundle is of positive degree; here is considered as a P-module using the adjoint action. The second condition has an equivalent reformulation which says that for any nontrivial character of P which can be expressed as a nonnegative integral combination of simple roots (with respect to any Borel subgroup contained in P), the line bundle associated to for is of positive degree. The equivalence of these two conditions is a consequence of a representation theoretic result proved here. Received: 10 November 1999 / Revised version: 31 October 2001 / Published online: 26 April 2002     

Krull–Schmidt reduction of principal bundles in arbitrary characteristic

Let M be an irreducible projective variety defined over an algebraically closed field k, and let E_G be a principal G-bundle over M, where G is a connected reductive linear algebraic group defined over k. We show that for E_G there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, the principal G-bundle E_G admits a reduction of structure group to H. Furthermore, this reduction is unique up to an automorphism of E_G.