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.

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.

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

An atom-optical Maxwell demon

The separation, by an optical standing wave, of a beam of two-level atoms prepared in a thermal mixture of ground and excited states, is considered as an example of a Maxwell demon. By including the momentum exchanged with the cavity, it is shown how no violation of the second law is possible. A classical and quantum analysis is given which illustrates this principle in some detail.

Optical properties of metallic films for vertical-cavity optoelectronic devices

We present models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). We used two simple phenomenological models, the Lorentz-Drude (LD) and the Brendel-Bormann (BB), to interpret both the free-electron and the interband parts of the dielectric response of metals in a wide spectral range from 0.1 to 6 eV. Our results show that the BE model was needed to describe appropriately the interband absorption in noble metals, while for Al, Be, and the transition metals both models exhibit good agreement with the experimental data. A comparison with measurements on surface normal structures confirmed that the reflectance and the phase change on reflection from semiconductor-metal interfaces (including the case of metallic multilayers) can be accurately described by use of the proposed models for the optical functions of metallic films and the matrix method for multilayer calculations. (C) 1998 Optical Society of America.

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].

TFEC is a macrophage-restricted member of the microphthalmia-TFE subfamily of basic helix-loop-helix leucine zipper transcription factors

The murine homologue of the TFEC was cloned as part of an analysis of the expression of the microphthalmia-TFE (MiT) subfamily of transcription factors in macrophages. TFEC, which most likely acts as a transcriptional repressor in heterodimers with other MiT family members, was identified in cells of the mononuclear phagocyte lineage, coexpressed,vith all other known MiT subfamily members (Mitf, TFE3, TFEB), Northern blot analysis of several different cell lineages indicated that the expression of murine TFEC (mTFEC) was restricted to macrophages. A 600-bp fragment of the TATA-less putative proximal promoter of TFEC shares features with many known macrophage-specific promoters and preferentially directs luciferase expression in the RAW264.7 macrophage cell line in transient transfection assays. Five of six putative Ets motifs identified in the TFEC promoter bind the macrophage-restricted transcription factor PU,I under in vitro conditions and in transfected 3T3 fibroblasts; the minimal luciferase activity of the TFEC promoter could be induced by coexpression of PU.1 or the related transcription factor Ets-2. The functional importance of the tissue-restricted expression of TFEC and a possible role in macrophage-specific gene regulation require further investigation, but are likely to be linked to the role of the other MiT family members in this lineage.

Modeling the optical constants of GaP, InP, and InAs

An extension of the Adachi model with the adjustable broadening function, instead of the Lorentzian one, is employed to model the optical constants of GaP, InP, and InAs. Adjustable broadening is modeled by replacing the damping constant with the frequency-dependent expression. The improved flexibility of the model enables achieving an excellent agreement with the experimental data. The relative rms errors obtained for the refractive index equal 1.2% for GaP, 1.0% for InP, and 1.6% for InAs. (C) 1999 American Institute of Physics. [S0021-8979(99)05807-7].

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].

Modeling the optical constants of AlxGa1-xAs alloys

The extension of Adachi's model with a Gaussian-like broadening function, in place of Lorentzian, is used to model the optical dielectric function of the alloy AlxGa1-xAs. Gaussian-like broadening is accomplished by replacing the damping constant in the Lorentzian line shape with a frequency dependent expression. In this way, the comparative simplicity of the analytic formulas of the model is preserved, while the accuracy becomes comparable to that of more intricate models, and/or models with significantly more parameters. The employed model accurately describes the optical dielectric function in the spectral range from 1.5 to 6.0 eV within the entire alloy composition range. The relative rms error obtained for the refractive index is below 2.2% for all compositions. (C) 1999 American Institute of Physics. [S0021-8979(99)00512-5].

Structure-activity relationships of omega-conotoxins MVIIA, MVIIC and 14 loop splice hybrids at N and P/Q-type calcium channels

The omega-conotoxins are a set of structurally related, four-loop, six cysteine containing peptides, that have a range of selectivities for different subtypes of the voltage-sensitive calcium channel (VSCC). To investigate the basis of the selectivity displayed by these peptides, we have studied the binding affinities of two naturally occurring omega-conotoxins, MVIIA and MVIIC and a series of 14 MVIIA/MVIIC loop hybrids using radioligand binding assays for N and P/Q-type Ca2+ channels in rat brain tissue. A selectivity profile was developed from the ratio of relative potencies at N-type VSCCs (using [I-125]GVIA radioligand binding assays) and P/Q-type VSCCs (using [I-125]MVIIC radioligand binding assays). in these peptides, loops 2 and 4 make the greatest contribution to VSCC subtype selectivity, while the effects of loops 1 and 3 are negligible. Peptides with homogenous combinations of loop 2 and 4 display clear selectivity preferences, while those with heterogeneous combinations of loops 2 and 4 are less discriminatory. H-1 NMR spectroscopy revealed that the global folds of MVIIA, MVIIC and the 14 loop hybrid peptides were similar; however, several differences in local structure were identified. Based on the binding data and the 3D structures of MVIIA, GVIA and MVIIC, we have developed a preliminary pharmacophore based on the omega-conotoxin residues most Likely to interact with the N-type VSCC. (C) 1999 Academic Press.

Two-wave-mixing induced self-focusing in an active photorefractive oscillator

We derive a nonlinear wave equation for a signal beam which is coupled to a pump beam by two-wave-mixing in a photorefractive crystal. This equation describes self-focusing of the signal beam. We compare two-wave-mixing induced spatial self-focusing of single-pass experiments in a diffusion-type photorefractive crystal and of a photorefractive oscillator using the same crystal. We observe that the nonlinear refractive index change in the oscillator is decreased while increasing resonator losses.

The ocular morphology of the southern hemisphere lamprey Geotria australis gray with special reference to optical specialisations and the characterisation and phylogeny of photoreceptor types

This paper describes the ocular morphology of young adults of the southern hemisphere lamprey Geotria australis, the sole representative of the Geotriidae, and makes comparisons with those of holarctic lampreys (Petromyzontidae). As previously reported for the holarctic lamprey Ichthyomyzon unicuspis [Collin and Fritzsch, 1993], the lens of G. australis is non-spherical and possesses a cone-shaped posterior that may be capable of mediating variable focus. The avascular retina of G. australis is well differentiated, containing three retinal ganglion cell populations, three layers of horizontal cells and three photoreceptor types, in contrast to petromyzontids that contain only two photoreceptor types (short and long), G. australis possesses one rod-like (R1) and two cone-like (C1 and C2) photoreceptors. Although the rodlike receptor in G. australis may be homologous with the short receptors of holarctic lampreys, the two cone-like receptors have morphological characteristics that differ markedly from those of the long receptors of their holarctic counterparts. The features which distinguish the two cone-like receptors from those of the long receptor type in holarctic lampreys are the characteristics of the mitochondria and the presence of large amounts of two different types of stored secretory material in the endoplasmic reticulum of the myoid (refractile bodies). The endoplasmic reticulum of each receptor type has a different shape and staining profile and is polymorphic, each showing a continuum of distension. It is proposed that the presence of two cone-like photoreceptors with different characteristics would increase the spectral range of G. australis and thus be of value during the parasitic phase, when this lamprey lives in the surface marine waters. The irideal flap, present in G. australis but not petromyzontids, would assist in reducing intraocular flare during life in surface waters. The results of this study, which are discussed in the context of the proposed evolution of lampreys, emphasise that it is important to take into account the characteristics of the eyes of southern hemisphere lampreys when making generalizations about the eyes of lampreys as a whole.

Three-dimensional imaging with optical tweezers

We demonstrate a three-dimensional scanning probe microscope in which the extremely soft spring of an optical tweezers trap is used. Feedback control of the instrument based on backscattered light levels allows three-dimensional imaging of microscopic samples in an aqueous environment. Preliminary results with a 2-mu m-diameter spherical probe indicate that features of approximately 200 nm can be resolved, with a sensitivity of 5 nm in the height measurement. The theoretical resolution is limited by the probe dimensions. (C) 1999 Optical Society of America.