Universal method to describe multiple localized modes in photonic crystal heterojunction

A general method is proposed to describe the energy levels of the interface states in one-dimensional photonic crystal (PC) heterojunction [Formula: see text] containing dispersive or non-dispersion materials. We found that the finite energy levels of the interface states for the finite configuration can be described totally by the dispersion relation of the PC with a periodic unit [Formula: see text]. It is further found that this method is also applicable for the case of defect modes. We believe our method can be used to guide the practical application.

Existence of Gibbs point processes with stable infinite range interaction

We provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

Intraoceanic subduction of the northwestern Neotethys and geodynamic interaction with Serbo-Macedonian foreland: Descending vs. overriding near-trench dynamic constraints (East Vardar Zone, Jastrebac Mts., Serbia)

A composite paleogeographic and plate kinematic spatiotemporal reconstruction of the exhumed Neotethyan cross-lithospheric footwall amalgamation (Jastrebac dome) incorporates the two formerly underplating oceanic entities, West Vardar- and East Vardar Zone. These ophiolite-bearing agglomerations are unroofed within the accretionary Paleogene to Miocene core-complex, beneath the Serbo-Macedonian overriding plate. The exposed Neotethyan crustal amalgamation is comprised of: an (i) folded trench assemblage of uncertain Mesozoic? Paleogeographic affinity metamorphosed under a greenschist-grade (West- vs. East Vardar Zone or Neotethyan crust- vs. its back-arc system?) sandwiched beneath the overlying (ii) late Cretaceous - Paleogene (meta)turbidites. To make matters more intricate, at the closest proximity of the dome (Mali Jastrebac Mountain) there is a similar (iii) greenschist-facies amalgamation comprised of the Neoproterozoic - Lower Paleozoic ocean-floor assembly (Supragetic basement). The interpretations of this rather controversial cross-lithospheric structure include a reassessment of the obduction sequence, and are underpinned by the restoration of the near-trench microplate motions. The study addresses the (1) local finite configuration (Serbo-Macedonian hanging wall vs. Neo - tethyan intraoceanic arc) and the (2) spatiotemporal geometry of the principal (micro)plate boundaries (Serbo-Macedonian Unit vs. Apulia/Adria). Unlike the earlier proposal of the ophiolite obduction onto the Serbo-Macedonian Unit onto the Apulia/Adria hinterland (or external segment of the ?Dacia mega-terrane?), we here propose a west-vergent obduction of the East Vardar Zone ophiolites onto the descending Neotethyan lithosphere (West Vardar ophiolites) - a similar scenario to its continuation in Greece (Peonias subzone).

Characterizing asymptotic randomization in abelian cellular automata

Abelian cellular automata (CAs) are CAs which are group endomorphisms of the full group shift when endowing the alphabet with an abelian group structure. A CA randomizes an initial probability measure if its iterated images have weak*-convergence towards the uniform Bernoulli measure (the Haar measure in this setting). We are interested in structural phenomena, i.e., randomization for a wide class of initial measures (under some mixing hypotheses). First, we prove that an abelian CA randomizes in Cesàro mean if and only if it has no soliton, i.e., a non-zero finite configuration whose time evolution remains bounded in space. This characterization generalizes previously known sufficient conditions for abelian CAs with scalar or commuting coefficients. Second, we exhibit examples of strong randomizers, i.e., abelian CAs randomizing in simple convergence; this is the first proof of this behaviour to our knowledge. We show, however, that no CA with commuting coefficients can be strongly randomizing. Finally, we show that some abelian CAs achieve partial randomization without being randomizing: the distribution of short finite words tends to the uniform distribution up to some threshold, but this convergence fails for larger words. Again this phenomenon cannot happen for abelian CAs with commuting coefficients.

Wave propagation in finite periodically ribbed structures with fluid loading

The paper studies the problem of wave transmission along a fluid-loaded plane elastic membrane supported by a finite array of equally spaced ribs. One of the ribs is driven by a time-harmonic line force and the rest have infinite impedance, so that fluid loading provides the only mechanism for the transmission of energy. Existing solutions for the infinite analogue exhibit a stop/pass band frequency structure, in which the energy is, alternately, exponentially localized around the driving force and constant along the array. However, at pass band frequencies this is inconsistent with numerical studies of finite arrays, which reveal marked amplitude fluctuations. In this paper an exact solution is given for a general finite configuration. This is used to explain and further explore the response. In particular it is shown that as the array length increases the pass band response becomes increasingly sensitive to frequency, and the solution cannot approach an asymptotic limit. The results give the forces along the array as an interference pattern, which may be thought of as propagating inwards from each end. This solution is obtained by forming a 2 x 2 matrix which relates the forces at any pair of adjacent ribs to those at the next pair. From the action of this matrix the response can be found everywhere, and the detailed properties of the solution are determined by those of the matrix. Special treatment is needed to deal with the band edges, which conform neither to stop nor pass band behaviour.

Flow Driven by a Finite, Shrouded Spinning Disk With Suction

Numerical solutions are presented for the flow driven by a spinning disk which forms an endwall of a finite, closed cylinder. The effects of imposing a uniform suction (or blowing) through the spinning disk in finite configuration are investigated. The Reynolds number is large and the cylinder aspect ratio is 0(1). Finite-difference techniques are employed to integrate the time-dependent Navier-Stokes equations. The initial state is taken to be a uniform axial motion. Integration is performed until an approximate steady state is attained. When there is no suction, the infinite disk model is shown to provide a qualitatively representative approximation to the flow in the central core region. As a suction (blowing) is imposed, the core rotation rate in the case of finite configuration becomes smaller (larger) than that for the case of no suction, which is in disagreement with the predictions of the infinite disk model. These significant discrepancies point to a fundamental difficulty of the infinite disk model to adequately describe the real flow infinite geometry when there is a mass flux across the system boundary. Plots showing the meridional stream function at various times are constructed. Details of the flow structure in the approximate steady state are analyzed. When there is a suction, a strong Ekman layer is present on the spinning disk but the Ekman layer on the stationary disk fades. When there is a blowing, a strong Ekman layer forms on the stationary disk. It is shown that the dynamic effects influencing the character of the flow are confined to these Ekman layers.