From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: Firstly we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting `freezing of dimensionality' rules out the occurrence of hyperchaos. Secondly we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome - one particle followed by the other - consecutive barriers of the periodic potential resulting in collective directed motion

Random Time Forward Starting Options

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options {\bf Random Time Forward Starting (RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur

Low noise optical receivers

the paper describes low noise first stage optical receivers.Analysis of operating conditions affecting signal-to-noise ratio has been carried out.Each preamplifier was carefully optimised to work with particular type of the detector

Logistyczna sprawność produktu – projektowanie wspomagające logistykę

Projekt okładki : Grochowska, DariaThis monograph considers the subject of design for logistics and its outcome in the form of a logistically efficient product. It is a comprehensive study which not only provides an analysis of selected theoretical problems but also discusses research methods and methodologies in the field [...]. The monograph is intended as the first step in research on identification of conditions underlying design for logistics and characterization of the concept logistic efficiency of products. One should hope that in spite of the many boundary conditions and constraints discussed herein, the introduced model of logistic efficiency of products will contribute to the strengthening of the competitiveness of manufacturing companies by demonstrating to designers the extent to which their work impacts on the effectiveness and efficiency of logistic processes down the line. The monograph also does the groundwork for the transformation of production processes for the fourth industrial revolution - Industry 4.0, where product design that considers technology, assembly, quality, and logistics will play a critical role

Anharmonic softening of Raman active phonons in Iron-Pnictides; estimating the Fe isotope effect due to anharmonic expansion

We present Raman measurements on the iron-pnictide superconductors CeFeAsO_{1-x}F_{x} and NdFeAsO{1-x}F_{x}. Modeling the Fe-As plane in terms of harmonic and a cubic anharmonic Fe-As interaction we calculate the temperature dependence of the energy and lifetime of the Raman active Fe B_{1g} mode and fit to the observed energy shift. The shifts and lifetimes are in good agreement with those measured also in other Raman studies which demonstrate that the phonon spectrum is well represented by phonon-phonon interactions without any significant electronic contribution. We also estimate the anharmonic expansion from Fe (56->54) isotope substitution to \Delta a=5.1 10^{-4}\AA and \Delta d_{Fe-As}= 2.510^{-4}\AA and the shift of harmonic zero point fluctuations of bond lengths <=3 10^{-5}\AA^2, giving a total relative average decrease of electronic hopping integrals of |\delta t|/t<= 2.0 10^{-4}. The results poses a serious challenge for any theory of superconductivity in the pnictides that does not include electron-phonon interactions to produce a sizable Fe-isotope effect.Comment: 7 pages, 6 figure

Applications of the Cracow X-ray microprobe in tomography

A nuclear microprobe at the IFJ PAN in Cracow has found numerous applications in different fields of research, mostly in biophysics, medical sciences, geology, and material research. In order to extend the research possibilities, a new X-ray microprobe was constructed. This new microprobe consists of three experimental lines dedicated to: (i) X-ray irradiation of biological specimens, (ii) elemental analysis of samples by micro X-ray fluorescence or total reflection X-ray fluorescence methods and (iii) computer microtomography. In this paper the computer microtomography line was described. The line consists of an open type Hamamatsu L9191 X-ray tube with microfocusing to about 2 μm, a high resolution X-ray sensitive CCD camera, and a precise goniometer composed of six piezoelectric motors. Depending on the required X-ray energy, the Hamamatsu tube is used with Ti, Mo, Ag, or W targets. A small focus size and short focus-to-object distance enable to obtain images of samples with a magnification of more than 1000× and resolution of the order of 2 μm. The computer microtomography measurements are carried out using home developed codes combined with commercial software. Details of the microprobe construction and preliminary results of the computer microtomography experiments are presented

Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study

Multipolar Expansions for the Relativistic N-Body Problem in the Rest-Frame Instant Form

Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyperplanes (intrinsic rest frame of the isolated system) turn out to be the natural framework for describing multipole kinematics. In particular, concepts like the {\it barycentric tensor of inertia} can be defined in special relativity only by means of the quadrupole moments of the isolated system.Comment: 46 pages, revtex fil

Density-potential mappings in quantum dynamics

In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an explicit relation between the boundary conditions on the density and the convergence properties of the fixed-point procedure via the spectral properties of the associated Sturm-Liouville operator. We show precisely under which conditions discrete and continuous spectra arise and give explicit examples. These conditions are then used to show that in the most physically relevant cases the fixed point procedure converges. This is further demonstrated with an example.Comment: 20 pages, 8 figures, 3 table