Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|\eta_\mathrm{r}|$, where $\eta_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $\tau_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $\omega_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $\epsilon=10$.Comment: 20 pages, 11 figures, to be published in Journal of the Physical Society of Japa

Site-occupancy factors in the Debye scattering equation : a theoretical discussion on significance and correctness

The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809-823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543-1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)-(iii)

Branching Lévy processes with inhomogeneous breeding potentials

The object of study in this thesis is a number of different models of branching Levy processes in inhomogeneous breeding potential. We employ some widely-used spine techniques to investigate various features of these models for their subsequent comparison. The thesis is divided into 5 chapters. In the first chapter we introduce the general framework for branching Markov processes within which we are going to present all our results. In the second chapter we consider a branching Brownian motion in the potential β|·|p, β> 0, p ≥0. We give a new proof of the result about the critical value of p for the explosion time of the population. The main advantage of the new proof is that it can be easily generalised to other models. The third chapter is devoted to continuous-time branching random walks in the potential β|·|p, β> 0, p ≥0. We give results about the explosion time and the right most particle behaviour comparing them with the known results for the branching Brownian motion. In the fourth chapter we look at general branching Levy processes in the potential β|·|p, β> 0, p ≥0. Subject to certain assumptions we prove some results about the explosion time and the rightmost particle. We exhibit how the corresponding results for the branching Brownian motion and and the branching random walk fit into the general structure. The last chapter considers a branching Brownian motion with branching taking place at the origin on the local time scale. We present some results about the population dynamics and the right most particle behaviour. We also prove the Strong Law of Large Numbers for this model.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Bound and free waves in non-collinear second harmonic generation

We analyze the relationship between the bound and the free waves in the noncollinear SHG scheme, along with the vectorial conservation law for the different components arising when there are two pump beams impinging on the sample with two different incidence angles. The generated power is systematically investigated, by varying the polarization state of both fundamental beams, while absorption is included via the Herman and Hayden correction terms. The theoretical simulations, obtained for samples which are some coherence length thick show that the resulting polarization mapping is an useful tool to put in evidence the interference between bound and free waves, as well as the effect of absorption on the interference patternComment: 10 pages, 7 figure. to be published on Optics Expres

Taxon ordering in phylogenetic trees by means of evolutionary algorithms

<p>Abstract</p> <p>Background</p> <p>In in a typical "left-to-right" phylogenetic tree, the vertical order of taxa is meaningless, as only the branch path between them reflects their degree of similarity. To make unresolved trees more informative, here we propose an innovative Evolutionary Algorithm (EA) method to search the best graphical representation of unresolved trees, in order to give a biological meaning to the vertical order of taxa.</p> <p>Methods</p> <p>Starting from a West Nile virus phylogenetic tree, in a (1 + 1)-EA we evolved it by randomly rotating the internal nodes and selecting the tree with better fitness every generation. The fitness is a sum of genetic distances between the considered taxon and the <it>r </it>(radius) next taxa. After having set the radius to the best performance, we evolved the trees with (<it>λ </it>+ <it>μ</it>)-EAs to study the influence of population on the algorithm.</p> <p>Results</p> <p>The (1 + 1)-EA consistently outperformed a random search, and better results were obtained setting the radius to 8. The (<it>λ </it>+ <it>μ</it>)-EAs performed as well as the (1 + 1), except the larger population (1000 + 1000).</p> <p>Conclusions</p> <p>The trees after the evolution showed an improvement both of the fitness (based on a genetic distance matrix, then close taxa are actually genetically close), and of the biological interpretation. Samples collected in the same state or year moved close each other, making the tree easier to interpret. Biological relationships between samples are also easier to observe.</p

Tamm Plasmon Resonance as Optical Fingerprint of Silver/Bacteria Interaction

The incorporation of responsive elements into photonic crystals is an effective strategy for fabricating active optical components to be used as sensors, actuators, and modulators. In particular, the combination of simple multilayered dielectric mirrors with optically responsive plasmonic materials has proven to be successful. Recently, Tamm plasmon (TP) modes have emerged as powerful tools for these purposes. These modes arise at the interface between a distributed Bragg reflector (DBR) and a plasmonic layer and can be excited at a normal incidence angle. Although the TP field is located usually at the DBR/metal interface, recent studies have demonstrated that nanoscale corrugation of the metal layer permits access to the TP mode from outside, thus opening exciting perspectives for many real-life applications. In this study, we show that the TP resonance obtained by capping a DBR with a nanostructured layer of silver is responsive to Escherichia coli. Our data indicate that the modification of the TP mode originates from the well-known capability of silver to interact with bacteria, within a process in which the release of Ag+ ions leaves an excess of negative charge in the metal lattice. Finally, we exploited this effect to devise a case study in which we optically differentiated between the presence of proliferative and nonproliferative bacteria using the TP resonance as a read-out. These findings make these devices promising all-optical probes for bacterial metabolic activity, including their response to external stressors

2,12-diaza[6]helicene: An efficient non-conventional stereogenic scaffold for enantioselective electrochemical interphases

The new configurationally stable, unsymmetrical 2,12-diaza[6]helicene was synthesized as a racemate and the enantiomers were separated in an enantiopure state by semi-preparative HPLC on chiral stationary phase. Under selected alkylation conditions it was possible to obtain both the enantiopure 2-N-mono- and di-N-ethyl quaternary iodides. Metathesis with bis(trifluoromethanesulfonyl)imide anion gave low-melting salts which were tested as inherently chiral additives to achiral ionic liquids for the electrochemical enantiodiscrimination of chiral organic probes in voltammetric experiments. Remarkable differences in the oxidation potentials of the enantiomers of two probes, a chiral ferrocenyl amine and an aminoacid, were achieved; the differences increase with increasing additive concentration and number of alkylated nitrogen atoms