The fractional Fourier transform as a simulation tool for lens‐based X‐ray microscopy

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X‐ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on‐line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL‐based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non‐monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.     

Inelastic scattering and nucleon transfer in the system232Th+206Pb near the Coulomb barrier

Nucleon transfer accompanied by Coulomb excitation was studied in the system²⁰⁶Pb+²³²Th atE _Lab=6.4 MeV/u. Particle-particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and nucleon transfer reactions. The mean excitation energy was measured by means of aγ-ray energy and multiplicity filter consisting of 6 NaI detectors. Large cross sections for one-neutron and two-neutron pick-up from²³²Th are observed. The impact-parameter dependence of the neutron transfer is analyzed in terms of semiclassical barrier penetration models. Using realistic neutron potentials with a diffuse surface, the experimental data are in accordance with the assumption of a “cold” transfer to states near the yrast line.     

A Monte Carlo model for networks between professionals and society

We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, P(k)∼k^-γ$P(k)\sim k^{-\gamma }$, with γ$\gamma$ ranging from 0.2$0.2$ to 0.5$0.5$, small-world properties, with a network diameter following D(N)∼logN$D(N)\sim \log N$ and relative high clustering, following C(N)∼1/N$C(N)\sim 1/N$ and C(k)∼k^-α$C(k)\sim k^{-\alpha }$, with α$\alpha$ close to 3. We compare our results with data from real-world protein interaction networks.     

The effect of diotic and dichotic level-randomization on the binaural masking-level difference

Detection thresholds for tones in narrow-band noise were measured for two binaural configurations: N(o)S(o) and N(o)S(pi). The 30-Hz noise band had a mean overall level of 65 dB SPL and was centered on 250, 500, or 5000 Hz. Signals and noise were simultaneously gated for 500, 110, or 20 ms. Three conditions of level randomization were tested: (1) no randomization; (2) diotic randomization--the stimulus level (common to both ears) was randomly chosen from an uniformly distributed 40-dB range every presentation interval; and (3) dichotic randomization--the stimulus levels for each ear were each independently and randomly chosen from the 40-dB range. Regardless of binaural configuration, level randomization had small effects on thresholds at 500 and 110 ms, implying that binaural masking-level differences (BMLDs) do not depend on interaural level differences for individual stimuli. For 20-ms stimuli, both diotic and dichotic randomization led to markedly poorer performance than at 500- and 110-ms durations; BMLDs diminished with no randomization and dichotic randomization but not with diotic randomization. The loss of BMLDs at 20 ms, with degrees-of-freedom (2WT) approximately 1, implies that changes in intracranial parameters occurring during the course of the observation interval are necessary for BMLDs when mean-level and mean-intracranial-position cues have been made unhelpful.     

Entanglement of macroscopic test masses and the standard quantum limit in laser interferometry

We show that the generation of entanglement of two heavily macroscopic mirrors is feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the standard quantum limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.     

Tailoring enhanced chaos in optically injected semiconductor lasers

We demonstrate theoretically and experimentally that the injection of two optical signals into a semiconductor laser can be a feasible and practical method of enhancing chaos, influencing the stability map and generating various nonlinear dynamics.     

Induced Cycles in Graphs

The maximum number vertices of a graph G inducing a 2-regular subgraph of G is denoted by \(c_\mathrm{ind}(G)\). We prove that if G is an r-regular graph of order n, then \(c_\mathrm{ind}(G) \ge \frac{n}{2(r-1)} + \frac{1}{(r-1)(r-2)}\) and we prove that if G is a cubic, claw-free graph on order n, then \(c_\mathrm{ind}(G) > \frac{13}{20}n\) and this bound is asymptotically best possible.     

Stratification and domination in graphs II

A graph G is 2-stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class.) We color the vertices in one color class red and the other color class blue. Let F be a 2-stratified graph with one fixed blue vertex v specified. We say that F is rooted at v. The F-domination number of a graph G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that every blue vertex v of G belongs to a copy of F rooted at v. In this paper we investigate the F-domination number when (i) F is a 2-stratified path P₃ on three vertices rooted at a blue vertex which is a vertex of degree 1 in the P₃ and is adjacent to a blue vertex and with the remaining vertex colored red, and (ii) F is a 2-stratified K₃ rooted at a blue vertex and with exactly one red vertex.