Effects of Lorentz local field correction on propagation properties of few-cycle pulse in dense Λ-type atomic medium

By solving numerically the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, we investigate the effects of Lorentz local field correction (LFC) on the propagation properties of few-cycle laser pulse in a dense A-type three-level atomic medium. We find that: when the area of the input pulse is larger, split of pulse occurs and the number of the sub-pulses with LFC is larger than that without LFC; at the same distance, the time interval between the first sub-pulse and the second sub-pulse in the case without LFC is longer than that with LFC, the time of pulse appearing in the case without LFC is later than that in the case with LFC, and the two phenomena are more obvious with propagation distance increasing; time evolution rules of the populations of levels vertical bar 1 >, vertical bar 2 > and vertical bar 3 > in the two cases with and without LFC are much different. When the area of the input pulse is smaller, effects of LFC on time evolutions of the pulse and populations are remarkably smaller than those in the case of larger area pulse. (c) 2008 Elsevier B.V. All rights reserved.

Poverty alleviation among fishermen within the floodplains of Kaduna River: implication for introducing commercial fish farming at village level in Doko local government area of Niger State, Nigeria

A diagnostic survey was conducted among the fishermen in six selected villages in Doko Local Government Area of Niger State. One hundred and fifty fishermen were randomly selected and interviewed to find out whether or not they had interest in commercial fish farming aimed at improving their livelihood. The dwindling fish catches in the natural flood plain ponds and Ex-bow Lakes continue to have a serious negative effect on the socio-economic well being of the village communities in question. A break on natural regular annual flooding of the plains had resulted into very low natural fish recruitment. Data analysis using simple descriptive statistics revealed that land tenure system, educational status, inadequate infrastructural facilities, religious taboos, existing fish species among others were found to be favourable indices for commercial fish farming. However, serious conflicts among the fishermen concerning the ownership status of these natural fish ponds are found to be major obstacles to commercial fish farming despite that the traditional ownership of the ponds were vested in the lands of individuals and village communities. Extensive fish farming and small-scale fish farming in the ponds and Ex-bow Lake with improved management practices are considered to be profitable venture. Despite the fact that fish seeds supply and extension effort are still inadequate, the fish farmers have indicated willingness to adopt commercial fish farming in the Ex-bow Lakes and flood plains in order to restore abundant fish production thereby providing for their food security and also increasing the daily income

Impact assessment of Niger State fisheries legislation on fisheries conservation in Edozhigi local government area (L.G.A.) of Niger State

A preliminary survey was conducted among the fishermen in five selected villages in Edozhigi L.G.A. of Niger State. One hundred and fifty fishermen were randomly selected and interviewed to find out the impact of Niger State fisheries legislation on fisheries conservation resources in the area. The analysis of data collected using descriptive statistics indicated that undersized mesh of gill nets, beach seines and traps are being used unabated. Also, fenced barriers across the entrance of flood plain ponds and Ex-bow lakes from the main stream are in the area. The fisheries rules and regulations implementers are rarely seen or not seen at all in the area. The decreasing nature of fish catches was detected. It is observed that government policy on fish conversation is neglected due to inadequate or lack of funding for meaningful extension and implementation of the fisheries rules and regulations

Ordinary mod p representations of the metaplectic cover of p-adic SL_2

We classify the genuine ordinary mod p representations of the metaplectic group SL(2,F)-tilde, where F is a p-adic field, and compute its genuine mod p spherical and Iwahori Hecke algebras. The motivation is an interest in a possible correspondence between genuine mod p representations of SL(2,F)-tilde and mod p representations of the dual group PGL(2,F), so we also compare the two Hecke algebras to the mod p spherical and Iwahori Hecke algebras of PGL(2,F). We show that the genuine mod p spherical Hecke algebra of SL(2,F)-tilde is isomorphic to the mod p spherical Hecke algebra of PGL(2,F), and that one can choose an isomorphism which is compatible with a natural, though partial, correspondence of unramified ordinary representations via the Hecke action on their spherical vectors. We then show that the genuine mod p Iwahori Hecke algebra of SL(2,F)-tilde is a subquotient of the mod p Iwahori Hecke algebra of PGL(2,F), but that the two algebras are not isomorphic. This is in contrast to the situation in characteristic 0, where by work of Savin one can recover the local Shimura correspondence for representations generated by their Iwahori fixed vectors from an isomorphism of Iwahori Hecke algebras.

The local-field corrective effect on Rabi oscillation of ultrashort pulse excitation in semiconductor GaAs

Rabi oscillation of the thin bulk semiconductor GaAs, which takes into account the effect of the local-field correction induced by the interacting excitons, is investigated by numerically solving the semiconductor Bloch equations. It is found, for a 2 pi few-cycle pulse excitation, that two incomplete Rabi-floppings emerge due to the competition between the Rabi frequency of the incident pulse and the internal-field matrices. Furthermore, for a sub-cycle 2 pi pulse excitation a complete Rabi-flopping can occur because of the absolute phase effect. We ascribe these characteristics of the Rabi oscillation to the renormalized Rabi frequency.

Local and Global Externalities, Environmental Policies and Growth

33 p.

Multiscale model reduction methods for deterministic and stochastic partial differential equations

Partial differential equations (PDEs) with multiscale coefficients are very difficult to solve due to the wide range of scales in the solutions. In the thesis, we propose some efficient numerical methods for both deterministic and stochastic PDEs based on the model reduction technique.

For the deterministic PDEs, the main purpose of our method is to derive an effective equation for the multiscale problem. An essential ingredient is to decompose the harmonic coordinate into a smooth part and a highly oscillatory part of which the magnitude is small. Such a decomposition plays a key role in our construction of the effective equation. We show that the solution to the effective equation is smooth, and could be resolved on a regular coarse mesh grid. Furthermore, we provide error analysis and show that the solution to the effective equation plus a correction term is close to the original multiscale solution.

For the stochastic PDEs, we propose the model reduction based data-driven stochastic method and multilevel Monte Carlo method. In the multiquery, setting and on the assumption that the ratio of the smallest scale and largest scale is not too small, we propose the multiscale data-driven stochastic method. We construct a data-driven stochastic basis and solve the coupled deterministic PDEs to obtain the solutions. For the tougher problems, we propose the multiscale multilevel Monte Carlo method. We apply the multilevel scheme to the effective equations and assemble the stiffness matrices efficiently on each coarse mesh grid. In both methods, the $\KL$ expansion plays an important role in extracting the main parts of some stochastic quantities.

For both the deterministic and stochastic PDEs, numerical results are presented to demonstrate the accuracy and robustness of the methods. We also show the computational time cost reduction in the numerical examples.

Intense local plasma heating by stopping of ultrashort ultraintense laser pulse in dense plasma

Self-trapping, stopping, and absorption of an ultrashort ultraintense linearly polarized laser pulse in a finite plasma slab of near-critical density is investigated by particle-in-cell simulation. As in the underdense plasma, an electron cavity is created by the pressure of the transmitted part of the light pulse and it traps the latter. Since the background plasma is at near-critical density, no wake plasma oscillation is created. The propagating self-trapped light rapidly comes to a stop inside the slab. Subsequent ion Coulomb explosion of the stopped cavity leads to explosive expulsion of its ions and formation of an extended channel having extremely low plasma density. The energetic Coulomb-exploded ions form shock layers of high density and temperature at the channel boundary. In contrast to a propagating pulse in a lower density plasma, here the energy of the trapped light is deposited onto a stationary and highly localized region of the plasma. This highly localized energy-deposition process can be relevant to the fast ignition scheme of inertial fusion.

Local air pollution and global climate change taxes: a distributional analysis

25 p.

How are Italian and Spanish cities tackling climate change? A local comparative study

27 p.