On the size distribution of Poisson Voronoi cells

Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells. Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed.     

Population dynamics: Poisson approximation and its relation to the Langevin process

We discuss how to simulate a stochastic evolution process in terms of difference equations with Poisson distributions of independent events when the problem is naturally described by discrete variables. For large populations the Poisson approximation becomes a discrete integration of the Langevin approximation [T. G. Kurtz, J. Appl. Prob. 7, 49 (1970); 8, 344 (1971)]. We analyze when the latter gives a reasonable representation of the original evolution for finite size systems. A simple example of an epidemic process is used to organize the discussion and to perform statistical tests that underline the goodness of the proposed method.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to the??-factoryDA??NE. For this collider about 5·10¹⁴ d E _??/E _?? photons per second are expected in the photon energyE _?? range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

Quantum key distribution system against the probabilistic faint after-gate attack

In practical quantum key distribution (QKD) systems, a single photon-detector (SPD) is one of the most vulnerable components. Faint after-gate attack is a universal attack against the detector. However, the original faint after-gate attack can be discovered by monitoring the photocurrent. This paper presents a probabilistic generalization of the attack, which we refer to as probabilistic faint after-gate attack, by introducing probability control modules. Previous countermeasures for photocurrent monitoring may fail in detecting the eavesdropper under some specific probabilities. To mitigate this threat, we provide a method to determine the detectable boundary in the limitation of precision of photocurrent monitoring, and investigate the security of QKD systems under such boundaries using the weak randomness model.     

Efficient standing-wave model for DFB lasers by nonlinear carrier approximation

A nonlinear approximation scheme is proposed to describe the time-dependent longitudinal carrier distribution with a view toward finding the efficient solution scheme of the previously proposed standing-wave model for simulation of DFB lasers. It shows its advantage over the existing linear scheme in terms of the modal accuracy in cases where the optical power is large enough to trigger the saturation effect. The validity of this improved scheme is demonstrated through comparisons made on the static and dynamic performances of $\lambda /4$ -phase shifted DFB lasers.     

Soliton in fiber lasers beyond the Ginzburg-Landau equation approximation

Operation of a passively mode-locked fiber laser beyond the Ginzburg-Landau Equation (GLE) approximation is numerically investigated. It is found that even in the Maxwell-Bloch formalism stable solitary waves can still be obtained in the laser due to the cavity pulse peak clamping effect. We further show that the gain bandwidth plays a significant role in determining the detailed property of the formed solitary pulses.     

Application of the coherent photon seeding technique to synchronously pumped and hybridly mode-locked dye lasers

The mode-locking performances of synchronously pumped and hybridly mode-locked dye lasers self-stabilized by coherent photon seeding (CPS) are investigated experimentally. The variation of the optimum values of the feedback parameters and the pulse quality of the stabilized laser with the cavity detuning is studied over a wide range of this parameter. The results presented for the case of pure synchronous pumping complement those previously reported for the generation of transform-limited pulses of variable length. The first experiment on the application of CPS to a conventional dual-jet hybridly mode-locked laser confirms the predictions of the numerical modelling.     

The bi-directional amplifier in the constant intensity approximation and its application to KrF lasers

Bi-directional and folded laser amplifiers are analysed in the constant intensity approximation. Simple analytical expressions are developed for gain, output intensity and extraction efficiency. The analysis is applied to electron-beam pumped KrF lasers and expressions for saturation intensity, small-signal gain coefficient and intrinsic efficiency in terms of gas composition and pump power per unit volume are given. The problem of fluorine burn-up in KrF lasers is discussed. Under certain conditions the analysis is shown to be equally applicable to oscillators and comparison is made with previous experimental results and computer code predictions.     

Ioffe-time distribution of quarks in the photon

We have analysed the Ioffe-time distribution of quarks in virtual photons using Operator Product Expansion of the correlation function that determines the matrix element of the corresponding quark string operator. The distribution for a transversally polarised photon admits a spectral representation which can be continued to the on-shell region p ² = 0. The resulting model Ioffe-time distribution turns out to be larger than parametrisations of the available F ₂ ^γ data, because its slope at the origin is unphysically large. We suggest that this problem is linked to the use of purely quark interpolating currents and it affects the calculation of Ioffe-time distribution of quarks for any hadronic state.     

On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

The Allan factor (AF) is a statistic widely used to assess if the rate of occurrences of an event tends to cluster and show persistence in a range of space and/or time scales. For a homogeneous Poisson process, the relationship between AF and the space/time is expected to be constant, thus denoting the lack of clustering and persistence in the occurrence process. However, in time series analysis, conclusions about the persistence of the underlying process have been usually drawn by visual inspection of the diagrams of AF estimates versus scale, without applying any formal statistical test. This study investigates the sampling distribution function of the AF estimator when the underlying process is homogeneous Poissonian. Monte Carlo simulations show that the distribution of the AF estimator is described by a gamma distribution whose mean and variance can be deduced by the delta method. Therefore, the derived analytical distribution of the AF estimator can be used to build a formal statistical test to evaluate the significance of the AF fluctuation against the Poissonian hypothesis across a range of space/time scales. As an example, we apply the AF-based test to analyse the time series of the number of rainfall observations exceeding fixed high thresholds in order to study the properties of the rate of occurrence of the extreme values over a wide range of time scales.     

On tangential star products for the coadjoint Poisson structure

We derive necessary conditions on a Lie algebra from the existence of a star product on a neighbourhood of the origin in the dual of the Lie algebra for the coadjoint Poisson structure which is both differential and tangential to all the coadjoint orbits. In particular we show that when the Lie algebra is semisimple there are no differential and tangential star products on any neighbourhood of the origin in the dual of its Lie algebra.Research partially supported by EC contract CHRX-CT920050     

On the kinematic approximation to specular reflectivity data

The kinematic approximation to specular reflectivity is very useful for understanding neutron and X-ray scattering observations, because it provides a simple analytical formula that relates the scattering-length density profile of a layered surface or interface, β(z), to the data, R (q_z ). Although its derivation from the wave equation, or the optical transfer model, for large q_z , is straightforward, the origin of the q_z -factor in the denominator is less obvious when the problem is viewed in the limit of Fraunhofer diffraction from the outset. This paper, which is principally educational, aims to bring clarity to the issue.     

On Poisson geometries related to noncommutative emergent gravity

We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space–time is realized as quantized symplectic submanifold embedded in R^D${\mathbb{R}}^D$, whose effective metric depends on the embedding as well as on the Poisson structure. We study solutions of the equations of motion for the Poisson structure, focusing on a natural class of solutions such that the effective metric coincides with the embedding metric. This leads to i$i$-(anti-) self-dual complexified Poisson structures in four space–time dimensions with Lorentzian signature. Solutions on manifolds with conformally flat metric are obtained and tools are developed which allow to systematically re-derive previous results, e.g. for the Schwarzschild metric. It turns out that the effective gauge coupling is related to the symplectic volume density, and may vary significantly over space–time. To avoid this problem, we consider in a second part space–time manifolds with compactified extra dimensions and split noncommutativity, where solutions with constant gauge coupling are obtained for several physically relevant geometries.     

Deconvolution method for recovering the photon time-of-flight distribution from time-resolved measurements

A nonparametric deconvolution algorithm for recovering the photon time-of-flight distribution (TOFD) from time-resolved (TR) measurements is described. The algorithm combines wavelet denoising and a two-stage deconvolution method based on generalized singular value decomposition and Tikhonov regularization. The efficacy of the algorithm was tested on simulated and experimental TR data and the results show that it can recover the photon TOFD with high fidelity. Combined with the microscopic Beer-Lambert law, the algorithm enables accurate quantification of absorption changes from arbitrary time-of-flight windows, thereby optimizing the depth sensitivity provided by TR measurements.     

Shielded distribution approximation for a wall-bounded classical fluid

We investigate lower order distribution functions in classical fluids in the presence of large-scale inhomogeneities, in particular those imposed by wall contacts. The consequences of the effective shielding of a wall by the nearest particle of the set being considered are determined in the context of two distribution function hierarchies, kinematic and dynamic in origin. The effects of both flat and spherical, hard and soft walls are considered, as well as those of curved and double walls. A few correction sequences to the basic shielding approximation are discussed.Supported in part by the Department of Energy under contract DE-AC02-76 ERO 3077.     

Some relations for the far-field distribution of semiconductor lasers with gain-guiding

Simple relations for the phase distribution of the fundamental mode of gain-guided lasers are derived, yielding simple, approximate analytic expressions for the far-field distribution parallel to the junction in the case of strong astigmatism. It is shown that the shape of the far-field distribution is essentially determined solely by the distribution of the effective refractive index parallel to the active layer. The relations may be used for any shape of the effective refractive index distribution to yield simple arguments as to why there are lasers which exhibit far-field distributions with double as well as triple maxima. Because of the simplicity of the expressions for the far-field distribution it is also possible to make an estimate of the shape of the carrier profile, once the near-field and far-field intensity distributions are known. In addition, a general relation between the normalized fundamental mode gain and the shape of the far-field distribution is given.     

On the photon arrival-time-energy uncertainty relation

A lower bound is obtained for the photon arrival-time-energy uncertainty relation.