Multichip Differential Phase-Shift-Keyed Transmission Over (Non)Linear Optical Channels

The recently introduced multichip differential phase-shift keying (MC-DPSK) optical transmission format, entailing the modulation of relative phases over a moving transmission window of successive chip intervals, is analytically and numerically analyzed. The maximum-likelihood optimal MC-DPSK receiver is derived and synthesized using integrated-optic Mach-Zehnder delay interferometers, whose electrical outputs are interpreted as generalized Stokes' parameters. The MC-DPSK performance over a nonlinear fiber channel, limited by the combination of amplified spontaneous emission noise and self-phase modulation, is further derived and simulated, demonstrating that the lowest complexity three-chip binary-phase MC-DPSK receiver provides an ~1-dB Q-factor advantage over conventional DPSK.     

Magnets with random anisotropies: The random cubic model and other models with p-fold spin interactions

In this paper we investigate in detail models with random anisotropies and p-fold spin interactions. We construct the random cubic model (p = 4) and show that when N > 2 (N being the number of spin components) its properties are similar to the random uniaxial anisotropy model, since quartic interactions, characteristic of the random uniaxial model, are generated through renormalization even if they vanish to start with. Similar conclusions apply to a random p-fold interaction model of the form $\text{?D∑}{}_{\mathrm{i}}\text{(}\text{n}\text{?}\text{,}{}_{\mathrm{i}}\text{·}\text{S}{}_{\mathrm{i}}\text{)}{}^{\mathrm{p}}$, when p is even. In the case of odd p, a random field interaction is generated. Other models are also discussed.     

Melting of the nanocrystalline vortex matter in highly anisotropic high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 were performed. We introduced low concentration of columnar defects satisfying Bphi < or = B. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid, and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.     

Directed paths with random phases

Directed Feynman paths in 1 + 1 dimensions that acquire random phases are examined numerically and analytically. This problem is relevant for the behavior of the conductance in two-dimensional amorphous insulators in the variable-range-hopping regime. Large-scale numerical simulations were performed on a model with short-range correlations. For the scaling of the transverse fluctuations ( t^ν), we obtain ν = 0.68 ± 0.025; and for the r.m.s free-energy fluctuations ( t^ω), we obtain ω = 0.335 ± 0.01. Up to 100 000 random samples were used for times as large as 2000. These results seem to exclude a recent conjecture that ν = 3/4 and ω = 1/2. Two versions of a model with long-range correlations are solved and shown to yield ν = 1/2; a physical explanation is given.     

Analysis of thermal phases in calcareous Iron Age pottery using FT-IR and Raman spectroscopy

The work deals with the FT-IR and micro-Raman spectroscopy study of the pseudo-amorphous and crystalline thermal phases in the composition of calcareous Iron Age pottery from the Galilee. The application of second-derivative and curve-fitting techniques improves the identification of the thermal phases in the composition of the pottery and makes it possible to analyze the pseudo-amorphous phases which are formed during the firing of the clayey raw material to pottery. This technique makes it possible to distinguish between meta-smectite and meta-kaolinite and to estimate the firing temperature of the pottery. The Micro-Raman spectroscopy is sensitive to the structural degree of ordering of the thermal phases and enables point analysis of peculiar components in the composition of the pottery. Based on the spectroscopic study, it is concluded that the calcareous pottery contained large amounts of microcrystalline-recarbonated calcite mixed with the meta-clay. The large amount of recarbonated calcite in the pottery material and the relatively low firing temperature indicates that instead of sintering the clay, lime technology was used for the cementation of the calcareous vessels. This process took place after the firing by recarbonation of the decomposed calcite which leads to cementation of the vessels with microcrystalline calcite.     

Large q expansions for q-state gauge-matter Potts models in lagrangian form

We consider the lagrangian form of a q-state generalization of Ising gauge theories with matter fields in d = 3 and 4 dimensions. The theory is exactly soluble in the limit q → ∞ and corrections are easily calculable in power series in $\text{1}\text{q}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$. Extrapolating the series for the free energies and latent heats by the method of Padé approximants, we have constructed the phase diagrams for all values of q. Our results agree well with known results for pure spin systems and, for the case q = 2, with Ising Monte Carlo data.     

Queueing Systems with a Removable Service Station

A single-server queueing system with constant Poisson input is considered and the partial elimination of the station's idle fraction is envisaged by intermittent close-down and set-up. The rule pertaining to the dismantling and re-establishing of the service station—the management doctrine—is based on the instantaneous size of the queue, but these processes are assumed to consume time. Operating characteristics of such systems—in particular, average queue length and queueing time—are evaluated. A cost structure is superimposed on the system and optimization procedures are outlined. The close relationship with (a) priority queueing and (b) storage models is pointed out.     

Diffusion Limited Aggregation on a Cylinder

We consider the DLA process on a cylinder . It is shown that this process “grows arms”, provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most , the time it takes the cluster to reach the m ^th layer of the cylinder is at most of order . In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily small density. In addition, we provide an upper bound on the rate at which the “arms” grow. This bound is valid for a large class of base graphs G, including discrete tori of dimension at least 3. It is also shown that for any base graph G, the density of the DLA process on a G-cylinder is related to the rate at which the arms of the cluster grow. This implies that for any vertex transitive G, the density of DLA on a G-cylinder is bounded by 2/3.     

Harmonic functions of linear growth on solvable groups

We answer a question posed by Bonilla and Grosse-Erdmann by showing that the operators P(D) on the space of entire functions H(C), where D is the differentiation operator and P is a polynomial, do not possess a frequently hypercyclic subspace.     

Rehydroxyiation of clay minerals and hydration in ancient pottery from the ‘Land of Geshur’

Rehydroxylation of clay minerals and hydration in Bronze and Iron Age pottery from the Land of Geshur (east of the Sea of Galilee), were investigated by IR thermospectrometry. A weak OH band, which resembles those in smectite or illite, exists in most samples, but it is masked by the water bands at lower temperature. Two types of transformation of clay minerals occur during firing of raw materials, reversible and nonreversible dehydroxylation, taking place at a relatively low and high firing temperatures, respectively.Clay minerals rehydroxylate and reconstruct after relatively higher firing temperatures in noncalcareous raw materials than in calcareous ones. These processes take place after higher temperatures in cooking pots made from the former type of raw material as compared with storage and table-ware vessels made from the latter.The absorbed water in the pottery is mainly connected with the dominant X-ray amorphous matter formed by the firing process.

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Zusammenfassung Mittels IR-Thermospektrometrie wurde die Rehydroxylierung von Tonerdemineralien und die Hydratierung in Geschirr aus dem Bronze- und Eisenzeitalter, aus dem Land der Geshur (Osten des Galiläischen Meeres) untersucht. Eine schwache OH-Bande, die denen in Smektit oder Illit ähnelt, existiert in den meisten Proben, es wird aber bei niedrigeren Temperaturen durch Wasserbanden verdeckt. Während des Brennens von Rohmaterial finden zweierlei Umwandlungen der Tonerdemineralien statt, bei relativ niedrigen Temperaturen reversible und bei relativ hohen Temperaturen nichtreversible Dehydroxylierung.Tonerdemineralien werden in kalkfreiem Rohmaterial nach relativ höheren Brenntemperaturen rehydroxyliert und wiederaufgebaut als in kalkhaltigen. Diese Prozesse verlaufen nach höheren Temperaturen in Kochtöpfen aus ersterem Rohmaterial im Vergleich zu Vorrats- und Eßgeschirr aus letzterem Material.Das in der Töpferware adsorbierte Wasser ist in erster Linie an dem beim Brennprozeß gebildeten, röntgenmäßig amorphen Material gebunden.

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Dedicated to Prof. Dr. H. J. Seifert on the occasion of his 60^th birthday

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This research was supported by the Basic Research Foundation administered by the Israel Academy of Sciences and Humanities. This support is gratefully acknowledged.

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The pottery was excavated by the Land of Geshur Archaeological Project, the Institute of Archaeology, Tel-Aviv University, M. Kochavi, director.

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The work was carried out while the first author was a visiting scientist at the Geological Survey in Jerusalem. The author expresses his appreciation to Dr. Yaacov Nathan and Mr. Yoetz Deutsch of the Geological Survey, for the hospitality and helpful discussions.

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The authors express their appreciation to L. Vinitzky from the Institute of Archaeology, Tel-Aviv University for supplying the Intermediate Bronze pottery and useful discussions.