A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Group velocity of probe light pulse in an open lambda system

The group velocity of the probe light pulse (GVPLP) propagating through an open Lambda-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light. elds or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.

Nuclear weak interaction rates during stellar evolution and collapse

Nuclear weak interaction rates, including electron and positron emission rates, and continuum electron and positron capture rates , as well as the associated v and –/v energy loss rates are calculated on a detailed grid of temperature and density for the free nucleons and 226 nuclei with masses between A = 21 and 60. Gamow-Teller and Fermi discrete-state transition matrix element systematics and the Gamow-Teller T^< →/← T^> resonance transitions are discussed in depth and are implemented in the stellar rate calculations. Results of the calculations are presented on an abbreviated grid of temperature and density and comparison is made to terrestrial weak transition rates where possible. Neutron shell blocking of allowed electron capture on heavy nuclei during stellar core collapse is discussed along with several unblocking mechanisms operative at high temperature and density. The results of one-zone collapse calculations are presented which suggest that the effect of neutron shell blocking is to produce a larger core lepton fraction at neutrino trapping which leads to a larger inner-core mass and hence a stronger post-bounce shock.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.

Experimental studies of weak superconductivity

Experimental investigations were made of the nature of weak superconductivity in a structure having well-defined, controllable characteristics and geometry. Controlled experiments were made possible by using a thin-film structure which was entirely metallic and consisted of a superconducting film with a localized section that was weak in the sense that its transition temperature was depressed relative to the rest of the film. The depression of transition temperature was brought about by underlaying the superconductor with a normal metal.

The DC and AC electrical characteristics of this structure were studied. It was found that this structure exhibited a non-zero, time-average supercurrent at finite voltage to at least .2 mV, and generated an oscillating electric potential at a frequency given by the Josephson relation. The DC V-I characteristic and the amplitude of the AC oscillation were found to be consistent with a two- fluid (normal current-supercurrent) model of weak super-conductivity based on e thermodynamically irreversible process of repetitive phase-slip, and featuring a periodic time dependence in the amplitude of the superconducting order parameter.

The observed linewidth of the AC oscillation could be accounted for by incorporating Johnson noise in the two-fluid model.

Experimentally it was found that the behavior of a short (length on the order of the coherence distance) weak superconductor could be characterized by its critical current and normal-state resistance, and an empirical expression was obtained for the time dependence of the super-current and voltage.

It was found that the results could not be explained on the basis of the theory of the Josephson junction.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Nd : YAG ceramic laser obtained high slope-efficiency of 62% in high power applications

By using quite uniformly nine-stacks side-around arranged compact pumping system, a high power Nd:YAG ceramic quasi-CW laser with high slope efficiency of 62% has been demonstrated. With 450 W quasi-CW stacked laser diode bars pumping at 808 nm, performance of the Nd: YAG ceramic laser with different output coupling mirrors has been investigated. Optimum output power of 236 W at 1064 nm was obtained and corresponding optical-to-optical conversion efficiency was as high as 52.5%. The laser system operated quite stably and no saturation phenomena have been observed, which means higher output laser power could be obtained if injecting higher pumping power. The still-evolving Nd: YAG ceramics are potential super excellent media for high power practical laser applications. (c) 2005 Optical Society of America.

Highly efficient Nd:YAG ceramic CW laser with 59.8% slope-efficiency

In this paper, a highly efficient Ti:sapphire end-pumped 1 at.-% Nd:YAG ceramic laser that is comparable in efficiency with Nd:YAG single crystal lasers has been developed. Optical absorption and emission spectra for Nd:YAG ceramics have been measured. With 673-mW pumping, 295-mW laser output at 1064 nm has been obtained. The laser threshold is only 13 mW. Deducted the transmitted light, the corresponding optical-to-optical conversion efficiency is 58.4%. The lasing characteristics of Nd:YAG ceramic are nearly equal to those of Nd:YAG single crystal.

Incidência de tuberculose por município, Brasil 2001-2003: uma abordagem sobre o programa de controle e fatores determinantes da doença

Esta pesquisa avaliou a situação da tuberculose no Brasil, no período de 2001 a 2003, segundo indicadores do processo de operacionalização do Programa Nacional de Controle de Tuberculose (PNCT), e estimou os efeitos de fatores determinantes da taxa de incidência da doença. Para a avaliação utilizou-se a análise de cluster não-hierárquica, visando agrupar os municípios brasileiros de acordo com a morbidade por tuberculose (TB) e AIDS, e pelo desempenho do PNCT. Estes clusters foram mapeados, comparando-se a distribuição nos municípios, em regiões metropolitanas, municípios prioritários, e segundo o tamanho da população. O qui-quadrado de Pearson foi utilizado para testar associação nas categorias. A modelagem longitudinal multinível foi usada para identificar e estimar os efeitos dos determinantes da doença. Os agregados foram: anos, municípios e regiões metropolitanas. O modelo foi de intercepto e inclinação aleatória. Foram retidas as variáveis capazes de diminuir a variância dos níveis, pois, desta forma, explicam a variabilidade hierárquica da doença. Incluiu-se renda, densidade populacional, proporção de cura, taxa de incidência de AIDS e as grandes regiões brasileiras. A avaliação mostrou que a situação epidemiológica preocupante ocorreu nos municípios com Baixa TB e Alta AIDS, e Alta TB e AIDS. O cluster de Muito baixa TB e AIDS concentrou 50% dos municípios, o que pode configurar problemas de notificação. São 6 clusters de desempenho do programa. Bom e Bom com baixo DOTS predominando nos municípios pequenos, não prioritários e fora das regiões metropolitanas. No desempenho Moderado houve maior proporção de municípios prioritários. Clusters Regular e Fraco concentraram 10% dos municípios, com abandono de tratamento elevado e cura muito baixa. O cluster Muito Fraco caracterizou-se pela falta de dados nos indicadores de desempenho. O modelo multinível identificou a AIDS como fator impactante na tuberculose, anteriormente não encontrado em outros estudos; a interação entre renda e AIDS, e importante contribuição das regiões metropolitanas na distribuição da tuberculose, que se manifesta heterogeneamente nas grandes regiões do país. A análise discriminou municípios, e mostrou não haver associação entre maior morbidade e melhor desempenho do PNCT, retratando inadequação da vigilância à realidade epidemiológica do Brasil. O programa necessita ser reforçado, no sentido de considerar a AIDS ao estabelecer suas estratégias de controle. Ademais, os aspectos de baixa renda da população e densidade populacional, já analisados em diversas pesquisas, também se manifestaram de forma importante nestes resultados.

The Carpathian range represents a weak genetic barrier in South-East Europe

Background: In the present study we have assessed whether the Carpathian Mountains represent a genetic barrier in East Europe. Therefore, we have analyzed the mtDNA of 128 native individuals of Romania: 62 of them from the North of Romania, and 66 from South Romania. Results: We have analyzed their mtDNA variability in the context of other European and Near Eastern populations through multivariate analyses. The results show that regarding the mtDNA haplogroup and haplotype distributions the Romanian groups living outside the Carpathian range (South Romania) displayed some degree of genetic differentiation compared to those living within the Carpahian range (North Romania). Conclusion: The main differentiation between the mtDNA variability of the groups from North and South Romania can be attributed to the demographic movements from East to West (prehistoric or historic) that differently affected in these regions, suggesting that the Carpathian mountain range represents a weak genetic barrier in South-East Europe.

Length-weight relationships of demersal fishes from the upper continental slope off Colombia

Parameters of the length–weight relationship of the form W=aLb are presented for 45 demersal fish species caught on the upper continental slope of the Caribbean Sea off Colombia. The b values varied between 2.13 and 4.97, with the mean b = 3.042 (95% CI, 2.887- 3.196).