Semiflexible amphiphilic polymers: cylindrical-shaped, collagenlike, and toroidal structures

A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.     

Novel integrated paired emitter-detector diode (PEDD) as a miniaturized photometric detector in HPLC

A novel low power, low cost, highly sensitive, miniaturized light emitting diode (LED) based flow detector has been used as optical detector for the detection of sample components in high performance liquid chromatography (HPLC). This colorimetric detector employs two LEDs, one operating in normal mode as a light source and the other is reverse biased to work as a light detector. Instead of measuring the photocurrent directly, a simple timer circuit is used to measure the time taken for the photocurrent generated by the emitter LED (lambda(max) 500 nm) to discharge the detector LED (lambda(max) 621 nm) from 5 V (logic 1) to 1.7 V (logic 0) to give digital output directly without using an A/D converter. Employing a post-column reagent method, a Nucleosil 100-7 column (functionalized with iminodiacetic acid (IDA) groups) was used to separate a mixture of transition metal complexes, manganese(II) and cobalt(II) in 4-(2-pyridylazo)-resorcinol (PAR). All optical measurements were taken by using both the in-built HPLC variable wavelength detector and the proposed paired-emitter-detector-diode (PEDD) optical detector configured in-line for data comparison. The concentration range investigated using the PEDD was found to give a linear response to the Mn(II) and Co(II) PAR complexes. The effects of flow rate and emitter LED light source intensity were investigated. Under optimised conditions the PEDD detector offered a linear range of 0.9-100 microM and LOD of 0.09 microM for Mn-PAR complex. A linear range of 0.2-100 microM and LOD of 0.09 microM for Co-PAR complex was achieved.     

Internal concentration gradients of guest molecules in nanoporous host materials: measurement and microscopic analysis

Evolution of internal concentration profiles of methanol in 2-D pore structure of ferrierite crystal was measured in the pressure range of 0 to 80 mbar with the help of the recently developed interference microscopy technique. The measured profiles showed that both a surface barrier and internal diffusion controlled the kinetics of adsorption/desorption. Furthermore, they indicated that in the main part of the crystal, the z-directional 10-ring channels were not accessible to methanol and that the transport of methanol mainly occurred via 8-ring y-directional channels. The roof-like part of the crystal was almost instantaneously filled/emptied during adsorption/desorption, indicating accessible 10-ring channels in this section. The measured profiles were analyzed microscopically with the direct application of Fick's second law, and the transport diffusivity of methanol in ferrierite was determined as a function of adsorbed phase concentration. The transport diffusivity varied by more than 2 orders of magnitude over the investigated pressure range. Transport diffusivities, calculated from measured profiles from small and large pressure step changes, were all found to be consistent. Simulated concentration profiles obtained from the solution of Fick's second law with the calculated functional dependence of diffusivities on concentration compared very well with the measured concentration profiles, indicating validity and consistency of the measured data and the calculated diffusivities. The results indicate the importance of measuring the evolution of concentration profiles as this information is vital in determining (1) the direction of internal transport, (2) the presence of internal structural defects, and (3) surface/internal transport barriers. Such detailed information is available neither from common macroscopic methods since, they measure changes in macroscopic properties and use model assumptions to predict the concentration profiles inside, nor from microscopic methods, since they only provide information on average displacement of diffusing molecules.     

Basis properties of eigenfunctions of the -Laplacian

For , the eigenfunctions of the non-linear eigenvalue problem for the -Laplacian on the interval are shown to form a Riesz basis of and a Schauder basis of whenever .

     

Cascaded optical parametric oscillation with a dual-grating periodically poled lithium niobate crystal

We demonstrate continuous-wave cascaded optical parametric oscillation in which the signal field of the primary parametric oscillator internally pumps the secondary parametric oscillator. Wavelength tuning is achieved with temperature tuning and a fan-out grating structure of a dual-grating periodically poled lithium niobate crystal. Above the secondary threshold the primary signal power is clamped, and all the other output powers increase linearly with the input pump power, in accordance with theory. Cascaded parametric oscillation offers a convenient and efficient way to generate multiple tunable outputs.     

Ultracold Rb-OH collisions and prospects for sympathetic cooling

We compute ab initio cross sections for cold collisions of Rb atoms with OH radicals. We predict collision rate constants of order 10(-11) cm3/s at temperatures in the range 10-100 mK at which molecules have already been produced. However, we also find that in these collisions the molecules have a strong propensity for changing their internal state, which could make sympathetic cooling of OH in a Rb buffer gas problematic in magnetostatic or electrostatic traps.     

Inequalities for Means of Chords, with Application to Isoperimetric Problems

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr?dinger operator in with an attractive interaction supported on a closed curve Γ, formally given by −Δ−αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread Γ in , homogeneously charged but not conducting, and we ask about the (renormalized) potential-energy minimizer. Both problems reduce to purely geometric questions about inequalities for mean values of chords of Γ. We prove an isoperimetric theorem for p-means of chords of curves when p ≤ 2, which implies in particular that the global extrema for the physical problems are always attained when Γ is a circle. The letter concludes with a discussion of the p-means of chords when p > 2.     

A note on “New kink-shaped solutions and periodic wave solutions for the (2 + 1)-dimensional Sine-Gordon equation”

Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2 + 1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009) 3777-3781] are analyzed. We have observed that fourteen solutions by Li from 30 do not satisfy the equation. The other 16 exact solutions by Li can be found from the general solutions of the well-known solution of the equation for the Weierstrass elliptic function.     

Wave Operators on Quantum Algebras via Noncanonical Quantization

We suggest a method to quantize basic wave operators of Relativistic Quantum Mechanics (Laplace, Maxwell, Dirac ones) without using canonical coordinates. We define two-parameter deformations of the Minkowski space algebra and its 3-dimensional reduction via the so-called Reflection Equation Algebra and its modified version. Wave operators on these algebras are introduced by means of quantized partial derivatives described in two ways. In particular, they are given in so-called pseudospherical form which makes use of a q-deformation of the Lie algebra sl(2) and quantum versions of the Cayley-Hamilton identity.