Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Helix-sheet interconversion in a synthetic pore lining peptide derived from a designed ion channel

We have designed a four-helix protein that is expected to tetramerize in the membrane to form an ion channel with a structurally well defined pore. A synthetic peptide corresponding to the channel lining helix facilitates ion transport across liposomal membranes and largely helical in membranes. Detailed circular dichroism studies of the peptide in methanol, water and methanal-water mixtures reveal that it is helical in methanol, beta-structured in 97.5% water and a combination of these two structures at intermediate compositions of methanol and water. A fluorescence resonance energy transfer study of the peptide shows that the peptide is monomeric in methanol but undergoes extensive anti-parallel aggregation in aqueous solution.

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Alamethicin, a Transmembrane Channel

Peptides possessing antibiotic activity, isolated from microbial sources, have been the subject of intensive structural and biological investigation over the past two decades.

Anisotropic gaussian beams

Anisotropic gaussian beams are obtained as exact solutions to the parabolic wave equation. These beams have a quadratic phase front whose principal radii of curvature are non-degenerate everywhere. It is shown that, for the lowest order beams, there exists a plane normal to the beam axis where the intensity distribution is rotationally symmetric about the beam axis. A possible application of these beams as normal modes of laser cavities with astigmatic mirrors is noted.

Boundary-layer convective heat transfer in a convergent channel

In this paper the numerical solution of the heat transfer problem in a convergent channel with uniform and non-uniform wall temperatures under boundary-layer approximations has been presented. Also, a semi-analytical solution for uniform wall temperature has been obtained.

Exact evaluation of Gaussian path integrals involving non-local potentials

An exact expression for the calculation of gaussian path integrals involving non-local potentials is given. Its utility is demonstrated by using it to evaluate a path integral arising in the study of an electron gas in a random potential.

Alamethicin and related membrane channel forming polypeptides

Alamethicin and several related microbial polypeptides, which contain a high proportion of agr-aminoisobutyric acid (Aib) residues, possess the ability to modify the permeability properties of phospholipid bilayer membranes. Alamethicin induces excitability phenomena in model membranes and has served as an excellent model for the study of voltage sensitive transmembrane channels. This review summarizes various aspects of the structural chemistry and membrane modifying properties of alamethicin and related Alb containing peptides. The presence of Aib residues in these sequences, constrains the polypeptides to 310 or agr-helical conformations. Functional membrane channels are formed by aggregation of cylindrical peptide helices, which span the lipid bilayer, forming a scaffolding for an aqueous column across the membrane. After consideration of the available data on the conductance characteristics of alamethicin channels, a working, hypothesis for a channel model is outlined. Channel aggregates in the lipid phase may be stabilized by intermolecular hydrogen bonding, involving a central glutamine residue and also by interactions between the macro-dipoles of proximate peptide helices. Fluctuations between different conductance states are rationalized by transitions between states of different aggregation and hence altered dimensions of the aqueous core or by changes in net dipole moment of the aggregate. Ion fluxes through the channel may also be affected by the electric field within the aqueous core.

The helical conformations of 14- and 16-residue fragments of suzukacillin, a membrane channel-forming polypeptide

The suzukacillin fragments, Boc-Ala-Aib-Aib-Gln-Aib-Leu-Aib-Gly-Leu-Aib-Pro-Val-Aib-Aib-OMe (14), Boc-Ala-Aib-Ala-Aib-Aib-Gln-Aib-Leu-Aib-Gly-Leu-Aib-Pro-Val-Aib-Aib-OMe (16G) and the completely apolar 16-residue peptide in which the glutamine residue has been replaced by alanine (16A) have been studied by 270 MHz 1H-HMR, in C2HCl3 and (C2H3)2SO solution. Intramolecularly hydrogen-bonded NH groups have been identified by temperature and solvent dependence of chemical shifts. Peptides 14 and 16A adopt folded 310 helical conformations stabilized by 11 and 13 hydrogen bonds, respectively. In peptide 16G there are 12 intramolecular hydrogen bonds, with the glycine NH being solvent-exposed, in contrast to 14 and 16A.

Invited paper Application of the least mean fourth (LMF) adaptive algorithm to signals associated with gaussian noise

This paper considers the applicability of the least mean fourth (LM F) power gradient adaptation criteria with 'advantage' for signals associated with gaussian noise, the associated noise power estimate not being known. The proposed method, as an adaptive spectral estimator, is found to provide superior performance than the least mean square (LMS) adaptation for the same (or even lower) speed of convergence for signals having sufficiently high signal-to-gaussian noise ratio. The results include comparison of the performance of the LMS-tapped delay line, LMF-tapped delay line, LMS-lattice and LMF-lattice algorithms, with the Burg's block data method as reference. The signals, like sinusoids with noise and stochastic signals like EEG, are considered in this study.

Validation-Based Sparse Gaussian Process Classifier Design

Gaussian processes (GPs) are promising Bayesian methods for classification and regression problems. Design of a GP classifier and making predictions using it is, however, computationally demanding, especially when the training set size is large. Sparse GP classifiers are known to overcome this limitation. In this letter, we propose and study a validation-based method for sparse GP classifier design. The proposed method uses a negative log predictive (NLP) loss measure, which is easy to compute for GP models. We use this measure for both basis vector selection and hyperparameter adaptation. The experimental results on several real-world benchmark data sets show better orcomparable generalization performance over existing methods.

Analysis of randomly time varying systems by gaussian closure technique

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Helical conformations of three crystalline pentapeptide fragments of suzukacillin, a membrane channel forming polypeptide

The crystal structures of three pentapeptide fragments of suzukacillin-A have been determined. Boc-Aib-Pro-Val-Aib-Val-OMe (peptide 1–5) adopts a distorted helical conformation, stabilized by three intramolecular hydrogen bonds (two 5→1, one 4→1). Boc-Ala-Aib-Ala-Aib-Aib-OMe (peptide 6–10) and Boc-Leu-Aib-Pro-Val-Aib-OMe (peptide 16–20) adopt 310 helical structures stabilized by three and two 4→1 intramolecular hydrogen bonds, respectively. These structures provide substantial support for a largely helical conformation for the suzukacillin membrane channel.