The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.

Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.

In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.

Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.

Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

Technique for diagnosing x-ray laser beam quality by use of the moire signal

We present what we believe is a novel technique based on the moire effect for fully diagnosing the beam quality of an x-ray laser. Using Fresnel diffraction theory, we investigated the intensity profile of the moire pattern when a general paraxial beam illuminates a pair of Ronchi gratings in the quasi-far field. Two formulas were derived to determine the beam quality factor M-2 and the effective radius of curvature R-e from the moire pattern. On the basis of the results, the far-field divergence, the waist location, and the radius can be calculated further. Finally, we verified the approach by use of numerical simulation. (C) 1999 Optical Society of America [S0740-3232(99)01502-1].

Analysis of beam-quality degradation in nonlinear frequency conversion

Based on the ripple transfers of electric-field amplitude and phase in frequency tripling, simple formulas are derived for the harmonic laser's beam-quality factor M-3omega(2), with an arbitrary fundamental incidence to ideal nonlinear crystals. Whereas the harmonic beam's quality is generally degraded, the beam's divergence is similar to that of the fundamental after nonlinear frequency conversion. For practical crystals with periodic surface ripples that are caused by their machining, a multiorder diffractive model is presented with which the focusing properties of harmonic beams can be studied. Predictions of the theories are shown to be in excellent agreement with full numerical simulations. (C) 2002 Optical Society of America.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

板条热容激光器的二维热特性

固体热容激光器（SSHCL）作为高功率固体激光器的一个重要发展方向,引起人们广泛关注。数值模拟激光介质板条在热容方式下工作的温度和应力分布是了解该类激光器工作特性的一种有效手段,采用平面应力近似法导出了半导体激光器抽运热容激光介质板的二维温度和应力分布公式,同时也对二维抽运光吸收密度、介质板温度分布和折射率变化进行了分析与讨论。数值计算的结果表明二维效应的温度分布和应力分布要比一维效应给出的分布更均匀。

Time response of optical switching properties of Sb thin films under focused laser pulses

The time response of optical switching properties of Sb thin films under focused laser pulses is investigated. The results show that the response course can be divided into onset, opening, and closing stages. Formulas for their lengths are given. The onset and opening times decrease with increasing pumping light power density. The closing time is about 150 ns. For optical memory, if the power density of the readout and recording lasers changes from 5 x 10(9) to 15 x 10(9) W/m(2), the onset time changes from 2.5 to 0.30 mus, and the opening time is on the nanosecond scale. (C) 2003 Society of Photo-Optical Instrumentation Engineers.

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

Propagation of flat-topped beams

The propagation of flat-topped beams passing through paraxial ABCD optical system is investigated based on the propagation formulas of Gaussian beam. The focal shift of focused coherent flat-topped beam is also studied in detail. Analytical expressions of the M-2 factor and the far-field intensity distribution for flat-topped beams are derived on the basis of second-order moments. (C) 2007 Elsevier Ltd. All rights reserved.

Formulação supersimétrica de processos estocásticos com ruído multiplicativo

Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi.

偏振光斯托克斯参量的高速实时测量技术

为了满足对高速变化的偏振态的测量,提出一种能够对偏振态实现高速测量的技术。阐述了利用1/4波片与起偏器测量偏振光的斯托克斯参量常规的原理和方法,根据高速测量的要求推导出了新的斯托克斯参量计算公式,并依据此公式设计了基于多通道偏振态高速测量的方案,设计了具体的方法并编写了控制与算法程序。测试表明,该系统的测量速度达到了每秒700次偏振态测量,测量速度主要由电子线路的性能决定,测得的结果稳定可靠实现了光纤传输偏振态的高速测量。

Collective dynamics of glass-forming polymers at intermediate length scales: a synergetic combination of neutron scattering, atomistic simulations and theoretical modelling

Qens/wins 2014 - 11th International Conference on Quasielastic Neutron Scattering and 6th International Workshop on Inelastic Neutron Spectrometers / editado por:Frick, B; Koza, MM; Boehm, M; Mutka, H

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

O gozo no feminino

Esta pesquisa faz uma reflexão sobre a incidência do feminino e o gozo que lhe é próprio, na clínica psicanalítica e no social. A hipótese que sustenta o trabalho é a de que, na estrutura neurótica, quando o sujeito ocupa a posição feminina e experimenta o gozo Outro, pode vivenciar uma espécie de loucura, de sem-razão, que se expressa através de fenômenos aparentemente semelhantes aos de uma psicose. Freud deixou em aberto a questão do Dark Continent que habita as mulheres. Lacan partindo das elaborações freudianas pode avançar na questão ao separar feminino e mulher, utilizando-se das fórmulas da sexuação. O uso dessas fórmulas permitiu a Lacan conceituar o feminino como o que está fora da norma fálica e pode ser experimentado por qualquer um que se situe na posição do não-todo fálico. Esta pesquisa apresenta um estudo do gozo através da obra de Freud e Lacan para distinguir o gozo do Outro barrado, do gozo do Outro não barrado. Os casos clínicos aqui apresentados exemplificam alguns efeitos da experiência da alteridade: o gozo místico, a relação de devastação entre mãe e filha, e a experiência do gozo feminino no encontro com o Outro sexo.