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On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Coherent molecular solitons in Bose-Einstein condensates

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEG, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output. [S0031-9007(98)07283-4].

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].

Inference of phylogeny and taxonomy within the Didymozoidae (Digenea) from the second internal transcribed spacer (ITS2) of ribosomal DNA

DNA sequences of the second internal transcribed spacer (ITS2) of ribosomal DNA (rDNA) were determined for 11 species from four genera of Didymozoinae (Indodidymozoon, Helicodidymozoon, Rhopalotrema and Neometadidymozoon) and a species of the Lecithasteridae, Lecithaster stellatus. Sequences were used to test the validity of species recognised on morphological criteria and to infer phylogenetic relationships. Sequences of the 11 didymozoids differed by 0.5% to 19%. Our phylogenetic analyses: (i) indicate that species in the genera Helicodidymozoon and Rhopalotrema are a monophyletic group; (ii) support separation of the genus Helicodidymozoon from the genera Indodidymozoon and Neometadidymozoon; and (iii) support recognition of Rhopalotrema as a genus distinct from Neometadidymozoon. We found the gonochoristic species, I. pearsoni and I. suttiei, to be genetically similar to the hermaphroditic species in the genus Indodidymozoon and found no evidence to indicate that they belong in a separate genus.

Coupling of a Jahn-Teller pseudorotation with a hindered internal rotation in an isolated molecule: 9-hydroxytriptycene

The irregular vibronic structure in the S-1<--S-0 resonant two-photon ionization (R2PI) spectrum of supersonically cooled triptycene is a result of a classic Exe Jahn-Teller effect [A. Furlan et al., J. Chem. Phys. 96, 7306 (1992)]. This is well characterized and can be used as an effective probe of intramolecular perturbations. Here we examine the S-1<--S-0 R2PI spectrum of 9-hydroxytriptycene and the fluorescence from various excited state vibronic levels. In this system the pseudorotation of the Jahn-Teller vibration is strongly coupled to the torsional motion of the bridgehead hydroxy group. This torsional motion results in a tunneling splitting in both the ground and excited states. The population of the upper level in the ground electronic state results in additional vibronic transitions becoming symmetry allowed in the R2PI spectrum that are forbidden in the bare triptycene molecule. The assignment of the R2PI and fluorescence spectra allows the potential energy surfaces of these vibrational modes to be accurately quantified. The full C-3v vibronic point group must be used to interpret the spectra. The time scale of the internal rotation of the-OH group and the butterfly flapping of the Jahn-Teller pseudorotation are of similar magnitude. The tunneling between the nine minima on the three dimensional potential energy surface is such that the Jahn-Teller pseudorotation occurs in concert with the-OH internal rotation. The Berry phase that is acquired during this motion is discussed. The simple physical picture emerges of the angle between two of the three benzene moieties opening in three equivalent ways in the S-1 electronic state. This geometry follows the position of the hydroxy group, which preferentially orients itself to point between these two rings. (C) 1998 American Institute of Physics. [S0021-9606(98)02348-4].

Autoinhibition by an internal nuclear localization signal revealed by the crystal structure of mammalian importin alpha

Importin alpha is the nuclear import receptor that recognizes classical monopartite and bipartite nuclear localization signals (NLSs). The structure of mouse importin alpha has been determined at 2.5 Angstrom resolution. The structure shows a large C-terminal domain containing armadillo repeats, and a less structured N-terminal importin beta-binding domain containing an internal NLS bound to the NLS-binding site. The structure explains the regulatory switch between the cytoplasmic, high-affinity form, and the nuclear, low-affinity form for NLS binding of the nuclear import receptor predicted by the current models of nuclear import. Importin beta conceivably converts the low- to high-affinity form by binding to a site overlapping the autoinhibitory sequence. The structure also has implications for understanding NLS recognition, and the structures of armadillo and HEAT repeats.

Theory of modulational instability in Bragg gratings with quadratic nonlinearity

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrodinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions maybe useful in the generation of ultrafast pulse trains at relatively low intensities. [S1063-651X(99)03005-6].

Development of P2 olfactory glomeruli in P2-internal ribosome entry site-tau-lacZ transgenic mice

Primary olfactory neurons project their axons to the olfactory bulb, where they terminate in discrete loci called glomeruli. All neurons expressing the same odorant receptor appear to terminate in a few glomeruli in each olfactory bulb. In the P2-IRES-tau-LacZ line of transgenic mice, LacZ is expressed in the perikarya and axons of primary olfactory neurons that express the P2 odorant receptor. In the present study, we examined the developmental appearance of P2 neurons, the topographical targeting of P2 axons, as well as the formation of P2 glomeruli in the olfactory bulb. P2 axons were first detected in the olfactory nerve fiber layer at embryonic day 14.5 (E14.5), and by E15.5 these axons terminated in a broad locus in the presumptive glomerular layer. During the next 5 embryonic days, the elongated cluster of axons developed into discrete glomerulus-like structures. In many cases, glomeruli appeared as pairs, which were initially connected by a fascicle of P2 axons. This connection was lost by postnatal day 7.5, and double glomeruli at the same locus were observed in 85% of adult animals. During the early postnatal period, there was considerable mistargeting of P2 axons. In some cases P2 axons entered inappropriate glomeruli or continued to grow past the glomerular layer into the deeper layers of the olfactory bulb. These aberrant axons were not observed in adult animals. These results indicate that olfactory axons exhibit errors while converging onto a specific glomerulus and suggest that guidance cues may be diffusely distributed at target sites in the olfactory bulb.

Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed.

The perceptual magnet effect in Australian English vowels

Recent research (Kuhl, 1991) has suggested that the internal structure of vowel categories is graded in terms of stimulus goodness. It has been proposed that a best instance stimulus reflects a central point or prototype, which effectively renders within-category members perceptually more similar. Discrimination experiments suggest a nonlinear relationship between acoustic and perceptual space near category centers (Iverson & Kuhl, 1995b). This phenomenon has been described as the perceptual magnet effect. The present study investigated the presence of the perceptual magnet effect in five Australian vowel categories. Australian English speakers identified, rated, and discriminated between a pool of 32 vowel stimuli that varied in F1 and F2 values. The results from Experiments 1 and 2 showed that subjects were able to judge the quality and identity of each stimulus and that a general grading of stimulus quality was reported. This was not symmetrical, and the subjects' responses varied considerably. In Experiment 3, closer control of the methodology in the discrimination task and of contextual factors influencing the test materials was exercised. Despite this, evidence of the warping of perceptual space in discrimination data was not found. In general, these results do not provide support for the existence of the perceptual magnet effect, and explanations for this finding are discussed.