Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose distribution yielding the Planck law of black-body radiation. The fractional part is the dark part (we call is dark variable) with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. The Planck variable can be decomposed into an infinite sum of independent binary random variables representing the binary photons (more accurately photo-molecules or photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons follow the Fermi statistics. Consequently, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of binary photons. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave-particle fluctuations of fermions. These fluctuations combine to give the wave-particle fluctuations of the original bosonic photons expressed by the Einstein fluctuation formula.Comment: 29 page

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page

A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

SFB 880: aeroacoustic research for low noise take-off and landing

This paper gives an overview about prediction capabilities and the development of noise reduction technologies appropriate to reduce high lift noise and propeller noise radiation for future low noise transport aircraft with short take-off and landing capabilities. The work is embedded in the collaborative research centre SFB 880 in Braunschweig, Germany. Results are presented from all the acoustics related projects of SFB 880 which cover the aeroacoustic simulation of the effect of flow permeable materials, the characterization, development, manufacturing and operation of (porous) materials especially tailored to aeroacoustics, new propeller arrangements for minimum exterior noise due to acoustic shielding as well as the prediction of vibration excitation of aircraft structures, reduced by porous materials

Computational chain for virtual fly-over simulations applied to fan noise

To ensure an aircraft’s compliance with noise regulations, expensive fly-over tests are required. Up until now, there is no numerical alternative to the experimental Standard procedure. In this paper, a step is taken toward enabling a ”virtual fly-over” in the future. The authors restricted themselves to the study of tonal fan noise from ist generation in the fan stage to its propagation to observer positions at ground level. As one large simulation tackling the entire problem at full-scale Reynolds numbers would have been computationally too demanding, a computational chain is established. This computational chain splits the large task into smaller subtasks linked by interfaces. Each of these subtasks can then be solved by a suitable calculation technique. For the presented case, the subtasks include the mean flow computation, the noise generation, and the noise propagation. The computational chain - including the involved tools and interfaces - is discussed in detail and first results are presented for isolated and installed engine configurations

Application of an Aircraft Design-To-Noise Simulation Process

System noise has been integrated as an additional design objective within conceptual aircraft design. The DLR system noise prediction tool PANAM accounts for individual noise sources depending on their geometry and operating conditions. PANAM is integrated into the existing aircraft design framework PrADO from the Technical University of Braunschweig in order to realize a design-to-noise simulation process. In addition, a ray-tracing tool from DLR, SHADOW, is incorporated into the simulation framework in order to account for structural engine noise shielding. The overall simulation process is then applied to identify promising low-noise aircraft concepts. The presented application aims at fan noise reduction through shielding. For the selected reference aircraft, the fan is a major noise source during both landing and takeoff. It is demonstrated, that the aircraft designers influence on the environmental vehicle characteristics is significant at the conceptual design phase. Usually, a trade-off between extensive engine noise shielding and economical flight performance is inevitable. The new design-to-noise process is well suitable to assess all four measures of ICAOs balanced approach