Shallow Ones Research Articles

Charge transfer mechanisms between some shallow-trap centres involved in the photochromism of Bi 12GeO 20

Charge transfers between traps in undoped Bi 12GeO 20 (BGO) crystals have been investigated so as to complete our previous studies concerning the mechanism of the photochromism in these crystals. Thermally stimulated current measurements as a function of both the temperature at which the crystals are photoexcited and the density of energy used to photoexcite them were carried out between 80 and 350 K. The results show that the detected electron traps, due to their behaviour, can be schematically divided into two families: the shallower ones and the deeper ones. Two of the most important traps among the latter which play the role of electron reservoirs for the fundamental state of the photochromic transitions in the visible spectral range are populated via the former. Hence, the shallower traps act as precursory levels to the filling of the deeper traps.

Source Time Function and Duration of Mexican Earthquakes

We have compiled source-time functions (STFs) of 54 Mexican earthquakes (3.0 ≤ M ≤ 8). The depth, H , of 48 of these earthquakes lies between 10 and 50 km. The STFs of 43 earthquakes were determined from local and regional strong-motion and/or broadband recordings. For the rest of the events, the STFs were taken from published analysis of teleseismic body waves, or from the University of Michigan Source-Time Function catalog. If available, the seismic moments were taken from the analysis of teleseismic body waves; if not, as was often the case for earthquakes with M ≤ 5.5, they were estimated from the local recordings themselves. From the STF of each earthquake we have measured pulse duration of each subevent (τp), total rupture duration (τt), and rise time (τr), along with their respective seismic moments. The data fit the relation \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M\_{0}{/}{\tau}\_{\mathrm{p}}^{3}{\sim}6.7{\times}10^{23}\) \end{document} dyne cm/s3. This relation is similar to that reported for deeper earthquakes (mostly in the 50 to 125 km depth range) in the Kanto district of Japan. The pulse duration of Mexican and Kanto earthquakes, scaled to a seismic moment of 1026 dyne cm, τps, is about 5 s, nearly independent of depth for 10 ≤ H ≤ 125 km. We compliment these two data sets with those for California (H ≤ 20 km) and for deep earthquakes ( H ≥ 100 km). When viewed over the entire depth range, the total rupture duration (τt) is related to M by log τt = (0.363 ± 0.008) log M - 8.58 (±0.190), and the duration, within the scatter of the data, appears to be independent of depth. When the data are examined in smaller subsets, as has been done by several authors, certain trends manifest themselves. For example, the pulse and the total duration of deep earthquakes ( H ≥ 100 km) scales as \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M_{0}^{0.16}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M_{0}^{0.25}\) \end{document}, respectively, and the moment-scaled pulse and total duration decreases by about 20% between 100 and 600 km depth. This decrease is much less than that reported previously. Furthermore, an earlier finding of fast rise times for very deep earthquakes is not substantiated by the recent data. Thus, the anomaly in the duration of the deep earthquakes, as compared to the shallow ones, appears to be smaller than previously suspected. Manuscript received 15 June 1999.

Fouling mussels (Dreissena spp.) colonize soft sediments in Lake Erie and facilitate benthic invertebrates

Summary We conducted survey and transplant studies to determine whether colonization and residency on soft sediments by introduced, fouling mussels (Dreissena polymorpha and D. bugensis) were affected by physical disturbance, and whether Dreissena presence in turn influenced the diversity and population densities of other benthic invertebrates. Surveys revealed that colony density was typically higher at moderate depths than at shallower and greater ones. However, the largest, midsummer colonies and greatest coverage of sediments by mussels occurred at deeper sites. Disturbance of transplanted colonies varied by depth and colony size, with deeper and larger colonies experiencing the lowest destruction rates. Colony destruction rate was positively correlated with current velocity adjacent to the lakebed. Absence of mussel colonies at shallow sites was not determined by recruitment or substrate limitation, as recruit density was higher and sediment characteristics more suitable for postveliger settlement at shallow than at deeper sites. Rather, seasonal storms have much stronger effects in shallow than in deep water. Mussel residency on soft sediment has profound effects on invertebrate biodiversity. Invertebrate species (taxon) richness and total abundance were positively correlated with mussel colony area. Mussel‐sediment habitat supported between 462 and 703% more taxa, and between 202 and 335% more individuals (exclusive of Dreissena) than adjacent soft‐sediment lacking mussels. Results from this study illustrate that physical disturbance directly limits the distribution of mussels on soft sediments, and the diversity and abundance of other benthic invertebrates in consequence.

Linguistic models of F0 use, physiological models of F0 control, and the issue of "mean response time".

This paper evaluates "mean response time" (MRT), a method used in previous studies to relate physiological evidence (recordings of electromyographic activity in the cricothyroid and sternohyoid) to acoustic evidence (fundamental frequency). Rather than averaging over tokens before correlating these signals, we calculated the best response time (RT) for each token, and evaluated the pattern of variability across utterances. Furthermore, rather than correlating over whole utterances, we correlated electromyographic activity (EMG) to fundamental frequency (F0) only over intervals defined in terms of linguistically significant events in the F0 trace, identified using a linguistically motivated model of English intonation. Steep changes in the F0 tended to have better correlation coefficients than shallow ones, which we relate to the physiological model by noting the complex of components contributing to both signal types. Also, the distribution of lead times was easier to interpret when the two tones delimiting the analysis domain had some tight temporal relationship specified by the intonational phonology. Finally, lead times tended to vary as a function of what preceded the target rise or fall. In short, averaging over signals before analysis obscures patterns of variation in the data which may lead to new insights and to new directions for research.

Scaling food chains in aquatic mesocosms: do the effects of depth override the effects of planktivory?

To assess the effects of physical dimension and planktivorous fish on phytoplankton standing crop, we repeated an experiment at different scales in plastic enclosures during summer 1995 in Lake Créteil, France. Enclosures were scaled for a constant surface (1.5 × 1.5 m) as depth was increased from 2.5 to 4.5 m. Even-link (zooplankton and phytoplankton) and odd-link (planktivorous fish, zooplankton and phytoplankton) food webs were established in both shallow and deep enclosures. Fish densities in the deep enclosures were scaled to allow comparisons with shallow ones for both in individuals m-2 or individuals m-3. We explicitly designed this experiment to examine the scale-dependent behavior of the top-down mechanism of algal biomass control in lakes, and in particular to test the hypothesis of stronger cascading effects of fish on lower trophic levels at reduced depth. Both fish and enclosure size had highly significant effects on phytoplankton biomass over the duration of the experiment. No depth × fish interaction effects were observed. The presence of planktivorous fish enhanced phytoplankton biomass in both shallow and deep enclosures, although the reduction in depth generally produced a stronger effect. The mean concentration of chlorophyll a in the deep odd-link systems (ca 5 mg m-3) was lower than in the shallow even-link systems (ca 17 mg m-3). Statistical interpretation did not change when data were expressed as phytoplankton biomass per unit of surface area. Light limitation and zooplankton grazing are the most probable mechanisms explaining our results in these nutrient-enriched systems. Moreover, we found that the strength of the cascading effect of fish on plankton was not a function of depth. We believe that further studies on scaling effects should be conducted in order to improve our understanding of ecological patterns and to extrapolate results from micro/mesocosms to natural ecosystems.

Trimodal Characteristics of Tropical Convection

It has long been known that trade wind cumulus and deep cumulonimbus represent primary components of the broad spectrum of cumulus clouds in the Tropics, which has led to the concept of a bimodal distribution of tropical clouds. However, recent analyses of shipboard radar data from Tropical Ocean Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment (COARE) provide evidence of abundant populations of a third cloud type, cumulus congestus. Congestus clouds constitute over half the precipitating convective clouds in COARE and contribute over one-quarter of the total convective rainfall. Global Atmospheric Research Program Atlantic Tropical Experiment studies reveal a similar midlevel peak in the distribution of radar-echo tops. These findings lead to the conclusion that shallow cumulus, congestus,and cumulonimbus are all prominent tropical cumulus cloud types. They are associated with trimodal distributions of divergence, cloud detrainment, and fractional cloudiness in the Tropics. The peaks in the distributions of radar-echo tops for these three cloud types are in close proximity to prominent stable layers that exist over the Pacific warm pool and the tropical eastern Atlantic: near 2 km (the trade stable layer), ;5 km (near 08C), and ;15‐16 km (the tropopause). These stable layers are inferred to inhibit cloud growth and promote cloud detrainment. The 08C stable layer can produce detrainment from cumulonimbi (attendant shelf clouds) and help retard the growth of precipitation-laden and strongly entraining congestus clouds. Moreover, restriction of growth of congestus clouds to just above the 08C level limits further enhancement of cloud buoyancy through glaciation. The three cloud types are found to vary significantly during COARE on the timescale of the 30‐60-day intraseasonal oscillation. The specific roles of clouds of the congestus variety in the general circulation are not yet clear, but some (the shallower ones) contribute to moistening and preconditioning the atmosphere for deep convection; others (the deeper ones) contribute an important fraction of the total tropical rainfall, and both likely produce many midlevel clouds, thereby modulating the radiative heating of the tropical atmosphere.

Tethyan subducted slabs under India

Tomographic imaging of the mantle under Tibet, India and the adjacent Indian Ocean reveals several zones of relatively high P-wave velocities at various depths. Under the Hindu Kush region in northeastern Afghanistan and southern Tajikistan, a regional northward-dipping slab is seen in the entire upper 600 km of the mantle and is apparently still attached to the lithosphere of the Indian plate. Under northern Pakistan this same slab shows a roll-over structure with the deeper portion overturned and dipping southward, as can also be seen in the distribution of earthquake hypocenters. Farther east-southeast (e.g., in the vicinity of Nepal), a well-resolved anomaly below 450 km depth is connected to the slab under the Hindu Kush, but seems to be separated from the lithosphere above 350 km. These upper-mantle anomalies are interpreted as the remnants of delaminated sub-continental lithosphere that went down when Greater India continued to converge northward with Asia after ∼45 Ma. The deeper high-velocity anomalies under the Indian sub-continent appear clearly separated from the shallower ones as well as from each other, and are inferred to represent remnants of oceanic lithospheric slabs that have sunk into the lower mantle and were subsequently overridden by the Indian plate. They occur at depths between 1000 and 2300 km and occasionally descend down to the core-mantle boundary. The anomalies form three parallel WNW-ESE striking zones. We interpret the two southern zones as remnants of oceanic lithosphere that was subducted when the Neo-Tethys Ocean closed between India and Tibet in the Cretaceous and earliest Tertiary. The northern deep-mantle zone under northern Afghanistan, the Himalayas and the Lhasa block in southern Tibet may represent the last-subducted remnant of the Paleo-Tethys Ocean, which is thought to have closed before the Hauterivian stage of the Early Cretaceous. The middle zone continues southeastward as a rather straight high-velocity zone towards Sumatra, where it becomes convex southward and parallel to the subduction zone under the Sunda arc. Comparison of this straight middle zone near India with the shallower (upper 600–1000 km) northern zone, which displays a cusp-like shape near the Yunnan (SW China) Syntaxis of the eastern Himalayas, supports the notion that the shallow northern zone represents later subduction than the deeper middle zone. The suggestion of a counterclockwise rotation (>20°) of the Indian plate during Tertiary indentation of Asia is supported by these features. The present-day latitudes of 5°–35°N of the deep slabs under India and adjacent areas correspond to the approximate paleolatitudes of the Cretaceous subduction zones. The slab remnants in the middle mantle occur therefore near the ancient locations where they started their downward journey, which implies that lateral movements in the deeper mantle were not large.

Is the Phillips Curve A Curve? Some Evidence and Implications for Australia

The Phillips curve has generally been estimated in a linear framework. This paper investigates the possibility that the Phillips curve is indeed a curve, and shows that a convex short‐run Phillips curve may be a more accurate representation of reality than the traditionally used linear specification. The paper also discusses the policy implications of convexity in the Phillips curve. These include the need for policy to be forward looking and to act pre‐emptively. Convexity provides a strong rationale for stabilization policy, and it reinforces the need for policy makers to proceed cautiously. It also implies that deep recessions may have only a marginally greater disinflationary impact than shallower ones, unless they induce large credibility bonuses.

The environmental state of freshwater resources in Greece (rivers and lakes)

The dominant factor regulating Greek riverine dissolved inorganic solid concentrations is chemical weathering, which depends on catchment climate and petrography. The majority of Greek rivers are moderately polluted and only a few of them show significant human impact and an increase in pollutant concentrations over time. Due to droughts in recent years and anthropogenic influence, the mean annual riverine dissolved solid concentrations exhibit a general interannual increase and significant long-term variations in their intra-annual hydrochemical fluctuations. The shallow Greek lakes are eutrophic, while the deep ones are oligo-mesotrophic. The majority of the lakes are monomictic and show summer thermal stratification, while the shallow ones are characterized by anoxic hypolimnetic conditions. Catchment petrography is not a dominant factor in the composition of lake waters since biochemical processes prevail. The majority of Greek lakes are also moderately polluted and are characterized by phosphorous-limited photosynthesis.

Polymer thermal protection induced by ion beam irradiation

The thermal stability of F, Ne, He, and B implanted/irradiated AZ1350-J photoresist films has been investigated via the Rutherford backscattering (RBS) technique. We find that both shallow and deep implantations raise the temperature at which the photoresist starts to decompose (from 400°C to 450°C). It is shown that radiation rather than chemical effects are responsible for the improvement in the thermal behavior of the implanted/irradiated films. In addition it is observed that the deep implantations give better results as compared with the shallow ones. In fact after a high energy Ne, B or He irradiation fluence was reached, no material loss was observed when the samples were further submitted to 450°C annealings. This is at variance with what was observed with shallow F and Ne implantations, where only partial protection was achieved.

Environmental impacts of deep opencast limestone mines in Laegerdorf, Northern Germany

Deep opencast mines for limestone of Upper Cretaceous age in the northernmost state of Germany, Sch!eswig-Holstein, greatly impact the local environment. In three pits with depths of nearly 100 m, mine pumping affects deeper aquifers and sometimes shallow ones as well. The total amount of mine water pumped ranges up to 6*106 m3/year. Due to the relief of hydraulic pressure, saline water is ascending from deeper parts of the limestone and infiltrating into the pits via the minefloor. The salt content of the deep ground water exceeds that of the sea in some places. The saline water causes process engineering problems and adversely affects the water quality of a receiving channel. Shallow aquifers are affected by dewatering due to hydraulic connections to the limestone. In places with organic soils (mostly peat of Holocene age), this is followed by ground subsidence, which damages buildings and agricultural drainage systems.

Charge Redistribution and Defect Relaxation in Heavily Damaged Silicon Studied Using Time Analyzed Transient Spectroscopy

AbstractWe have carried out electrical characterization of defects in heavily damaged silicon, where damage is created by MeV heavy ions at doses near but below amorphization threshold. Trapping kinetics over several orders of magnitude in time have been monitored using isothermal spectroscopy called Time Analyzed Transient Spectroscopy (TATS). Two distinct effects regarding the nature of changes in density of states in the gap have been demonstrated. Firstly, we show that charge redistribution among multiple traps occur such that only the occupancy of the deeper states increase at the cost of shallower ones for long time filling. Secondly, a novel defect relaxation mechanism is observed for samples with relatively lower damage. A trap is seen to exhibit progressive deepening in energy with increase in filling time, finally stabilizing for large filling times. From the athermal nature of associated TATS peaks, it is argued that the relaxation involves large entropic contribution to free energy. The necessity of using a time domain relaxation spectroscopy such as TATS in the study of different mechanisms of relaxation is demonstrated.

Facies sequences of the middle-upper jurassic carbonate platform (Amran Group) in the Sana'a region, Republic of Yemen

Rocks of the Amran Group in the Sana'a region of Yemen disconformably overlie the Kohlan Formation and unconformably underlie the Tawilah Group. Sea-level rises have produced landward migration of facies belts and the development of deeper water facies over shallow ones. The geometry of the depositional environments identified has enabled the passage of relatively short-lived transgressive-regressive cycles of sedimentation to be recognized. Three facies associations are introduced: (1) Carbonate platform facies, (2) Carbonate-marl alternation facies, and (3) Shallow water coral and stromatoporoid build-up facies. These facies are widely distributed and the whole sequence reflects deposition on a broad platform upon which shoals separated platform carbonates from basin sedimentation and an open marine environment. The repetition and interfingering of both fining- and shallowing-upward cycles within the study areas suggest that deposition occurred within the same basin with slightly different conditions in different places. The main factors controlling their deposition are sea-level changes and tectonics.

Local dynamics of laser cooling in an optical lattice

Using the basis of Wannier states, we study the local dynamics of polarization gradient cooling for an atom driven on a Jg52!Je53 transition by a one-dimensional optical lattice. This analysis allows us to formulate a physical picture of the cooling mechanism, analogous to Sisyphus cooling for a J g51/2!Je53/2 atom, which depends strongly on coherences in the Zeeman sublevels of the ground state. In addition, we are able to explain the steady-state properties of the laser-cooled atoms in a regime where the standard semiclassical analysis breaks down. @S1050-2947~97!50309-X# PACS number~s!: 32.80.Pj, 71.23.An The paradigm for sub-Doppler laser cooling is the Sisyphus effect as formulated by Dalibard and Cohen-Tannoudji @1#. The beauty of this model is that it gives a simple physical picture of the cooling mechanism. An atom driven on a Jg51/2!J e53/2 transition moves in a one-dimensional ~1D! light field formed by two counterpropagating plane waves with orthogonal linear polarizations—the 1D lin ’lin configuration. Cooling occurs as atoms are preferentially optically pumped from the peaks of the light shift potential associated with one ground state to the valleys of the other. Indeed, the simplicity of this model led to the realization of this 1D model in the laboratory, signifying a shift away from the image of atoms moving in a disordered ‘‘optical molasses’’ to that of an ordered ‘‘optical lattice’’ @2#. These experiments showed that in the steady state most of the atoms are trapped in the microscopic potential wells of the lattice, oscillating many periods before inelastic photon scattering occurs, and localized to a small fraction of the optical wavelength ~the ‘‘oscillating regime’’ !@ 3 # . Despite the considerable success of the simple Sisyphus model in explaining the basic steady-state properties of the laser-cooled atoms, there has been little detailed study of the dynamics. Recent experiments have shown some discrepancies with the dynamical model proposed in the simple Sisyphus picture @4#. The goal of this article is to develop a physical picture of the cooling mechanism applicable to the experiments: atoms with larger angular momentum trapped in the oscillating regime. Consider, for example, an atom with a ground-state angular momentum Jg52 and excited state Je53, moving in a 1D lin’lin lattice. In this more complex system there is a set of optical potentials associated with the five ground states, coupled by stimulated Raman transitions. For such an atom, two possible semiclassical pictures of the cooling mechanism arise. In one @Fig. 1~a!#, cooling occurs locally at a given lattice site as atoms preferentially climb steep potentials and descend shallow ones. Because of the difference in curvature between these two potentials, atoms expend more of their kinetic energy climbing wells than they regain on the descent, the difference being dissipated in optical pumping. Alternatively, atoms may cool when hopping between lattice sites by making nonadiabatic transitions between the coupled set of optical potentials and preferentially pumping to the potential with the largest light shift @Fig. 1~b!#. The difference between these mechanisms has implications for the diffusion of atoms within the lattice, as studied in recent experiments @5#, and theories @6#. Though fully quantum-mechanical numerical simulations for large-angular-momentum atoms in optical lattices @7,8# have yielded fantastic agreement with experiments, it is difficult to extract the local cooling mechanism. In these simulations the center-of-mass motion was expanded in a basis of free-particle plane waves or Bloch states of the periodic potential @9#, which were delocalized over the entire lattice. In order to gain physical insight into the local cooling dynamics, we reanalyze the system using the basis of Wannier states for the periodic potential. These represent a complete orthonormal set of functions localized at a particular lattice site @10#. As discussed in @2,7#, after identifying the complete set of symmetries of the Hamiltonian, the energy eigenstates are Bloch spinors,

Self-compensation in nitrogen-doped ZnSe

Nitrogen-doped and nitrogen-implanted ZnSe epitaxial layers grown by molecular-beam epitaxy are studied through photoluminescence (PL), selective PL, and PL-excitation spectroscopies. The results are compared with those obtained from samples implanted with other impurities. All N-containing samples, and only those, give rise to transitions corresponding to a dominant shallow donor with a binding energy of 29.1 meV. This donor is not a residual impurity in ZnSe but is associated with nitrogen. We propose that it involves nitrogen located on interstitial sites. In addition, the deep compensating donor is already present in lightly doped samples. Our results demonstrate that N doping of ZnSe is accompanied by the concomitant creation of N-related defects, both shallow and deep ones, from the onset of doping. An inescapable dramatic compensation of N acceptors ensues.

The Ecological Condition of Dead-End Canals of the Delaware and Maryland Coastal Bays

Manmade, dead-end canals are common in residential developments along the coastal bays of Delaware and Maryland. The close proximity of housing to the water and the concentration of boating activities enhances the potential for anthropogenic stress to living resources in these poorly flushed aquatic systems. Measurements of water quality, sediment contaminants, and benthic macroinvertebrate assemblages were taken in 25 randomly selected canals and compared to 175 non-canal sites located throughout the coastal bays. The mean bottom dissolved oxygen concentrations in canals was half that found in non-canal sites. Mean water-column and benthic chlorophyll concentrations were, respectively, two times and four times higher in the canals. Sediment contaminant concentrations were significantly higher in the canals compared to the coastal bays, and exceeded published guideline values indicating possible adverse ecological effects. The contaminants of greatest concern in the canals included arsenic, copper, polyaromatic hydrocarbons, polychlorinated biphenyls, and several banned, persistent pesticides (DDT, dieldrin, endrin, and chlordane). Benthic macroinvertebrate assemblages in canals were severely degraded; mean species richness, abundance, and biomass were 1/7, 1/10, and 1/20, respectively, of the values for the remaining coastal bays. A single pollution-tolerant polychaete species (Streblospio benedicti) comprised approximately three-fourths (70%) of the community in the canals. Deep (>1 m) and muddy canals were in poorer condition than shallow and sandy ones.

Effects of joint attributes on tunnel stability

Abstract A parametric study was carried out using the two-dimensional Discontinuous Deformation Analysis (DDA) to study the effects of joint attributes on tunnel stability. Cases were analyzed with different combinations of tunnel depth, joint orientation, joint spacing, and joint friction angle. The DDA results for 22 cases presented shed light on the effects of joint attributes on tunnel stability. DDA results show that for relatively shallow tunnels, blocks may slide on joints dipping at an angle steeper than its friction angle. Furthermore, different joint orientations may result in different block sizes and shapes even though all the joint sets have the same spacing. As a result, joint spacing may not be an adequate measure of block size. A rock block volumebased parameter may be more appropriate than joint spacing as a measure of the effects of block size on tunnel stability. In addition, DDA results show that if the intact rock is hard and the tunnel is not extremely deep, deeper tunnels are in general more stable than shallower ones due to better confinement at depth. However, higher stresses at depth may cause local failures that may not occur at shallower depths.

Plant Reproductive Traits as a Function of Local, Regional, and Global Abundance

Most ecological generalizations stem from the study of common organisms, but most species are rare. There are a number of reasons to expect that rare and common species may differ consistently in their characteristics, with possible implications for conservation. Past analyses of this issue, however, have generally considered only a single measure of rarity and have not corrected analyses for the lack of independence in the traits of related species. We compared several reproductive characteristics of Mediterranean annual crucifers as a function of their global range, regional abundance, and local population density in Israel, making use of independent contrast methods to correct for the phylogenetic relationships of the species involved. We found plants growing at low local density to be disproportionately likely to be self‐compatible. Petal length and floral depth (sepal length) were correlated with breeding system but showed significant interaction effects between breeding system and abundance. Floral longevity was inversely related to abundance and also showed significant interaction effects between breeding system and abundance. Overall, rare species tended to display more extreme values for floral traits than did common plants with the same breeding systems; they had unusually large and deep flowers if self‐incompatible and unusually small, shallow ones if self‐compatible.

Coupled-mode theory for light propagation through deep nonlinear gratings

In ordinary coupled-mode theory, the standard tool to analyze optical grating structures in both linear and nonlinear regimes, the grating is usually assumed to be shallow. Here we generalize this theory in a systematic way to include deep gratings. We do so by expanding in the exact eigenfunctions of the linear structure (the Bloch functions) rather than simply in the forward and backward propagating modes. We show that the resulting equations for deep gratings are qualitatively similar to those for shallow ones, except that the value of some of the coefficients is different and that some additional nonlinear terms arise. We also discuss solutions to these equations and point out differences from solutions of the conventional theory. \textcopyright{} 1996 The American Physical Society.

Use by tits of nest boxes of different designs in pinewoods

Two experiments tested the preferences by tits in pinewoods for different nest box designs. Great, Blue and Coal Tits preferred deep boxes (≈ 19 cm from base to entrance lip) over shallow ones (≈ 9 cm). Crested `Tits preferred boxes that had been filled with sawdust and wood-shaving which they removed before nesting. The excavation of a fresh nest cavity each year perhaps ensures that nests are free of fleas for Crested Tits.