Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

Higher Order Nonlinear Effect and Limitation of Soliton Propagation in Dispersive-Nonlinear Medium for Dispersion-Shifted Fiber

A computer simulation of the nonlinear Schrödinger equation is carried out to evaluate the impact of nonlinear susceptibility of a single mode fiber on the transmission of a soliton pulse. The third and fifth order nonlinear susceptibilities are considered in the simulation. The results show that the output soliton pulse shape strongly depends on the third order nonlinear susceptibility and gets distorted when the full width half maximum (FWHM) pulse width is of the order of 10ps or less.     

Exact maximal height distribution of fluctuating interfaces

We present an exact solution for the distribution P(h(m),L) of the maximal height h(m) (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h(m),L)=L(-1/2)f(h(m)L(-1/2)) for all L>0, where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds, but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.     

Complexes of poly(ethylene glycol)-based cationic random copolymer and calf thymus DNA: a complete biophysical characterization

Complete biophysical characterization of complexes (polyplexes) of cationic polymers and DNA is needed to understand the mechanism underlying nonviral therapeutic gene transfer. In this article, we propose a new series of synthesized random cationic polymers (RCPs) from methoxy poly(ethylene glycol) monomethacrylate (MePEGMA) and (3-(methacryloylamino)propyl)trimethylammonium chloride with different mole ratios (32:68, 11:89, and 6:94) which could be used as a model system to address and answer the basic questions relating to the mechanism of the interaction of calf thymus DNA (CT-DNA) and cationic polymers. The solubility of the complexes of CT-DNA and RCP was followed by turbidity measurements. It has been observed that complexes of RCP with 68 mol % MePEGMA precipitate near the charge neutralization point, whereas complexes of the other two polymers are water-soluble and stable at all compositions. Dnase 1 digestion experiments show that DNA is inaccessible when it forms complexes with RCP. Ethidium bromide exclusion and gel electrophoretic mobility show that both polymers are capable of binding with CT-DNA. Atomic force microscopy images in conjunction with light scattering experiments showed that the complexes are spherical in nature and 75-100 nm in diameter. Circular dichroism spectroscopy studies indicated that the secondary structure of DNA in the complexes is not perturbed due to the presence of poly(ethylene glycol) segments in the polymer. Furthermore, we used a combination of spectroscopic and calorimetric techniques to determine complete thermodynamic profiles accompanying the helix-coil transition of CT-DNA in the complexes. UV and differential scanning calorimetry melting experiments revealed that DNA in the complexes is more stable than in the free state and the extent of stability depends on the polymer composition. Isothermal titration calorimetry experiments showed that the binding of these RCPs to CT-DNA is associated with small exothermic enthalpy changes. A complete thermodynamic profile showed that the RCP/DNA complex formation is entropically favorable. Much broader opportunities to vary the architecture of the polymers studied here make these systems promising in addressing various basic and practical problems in gene delivery systems.     

4‐Iodoquinoline

Nearly planar molecules of the title compound, C₉H₆IN, are packed in inclined stacks along the short crystallographic b axis and molecules in adjacent stacks are packed to form antiparallel zigzag chains. Short intermolecular N...I contacts [3.131 (3) Å] are observed between molecules in adjacent stacks. A network of C—H...π hydrogen bonds [2.821 (5) and 3.083 (3) Å] between molecules in adjacent stacks is also present. These motif‐generating interactions, including the weak C—H...π interactions, are of relevance in crystal engineering and design.     

Physicochemical studies on the interaction of gelatin with cationic surfactants alkyltrimethylammonium Bromides (ATABs) with special focus on the behavior of the hexadecyl homologue

The interaction of a denatured interfacially active protein, gelatin (G) (at pH 9, above its isoelectric pH 4.84, and ionic strength mu=0.005), with a cationic amphiphile, hexadecyl (or cetyl) trimethylammonium bromide, CTAB, has been elaborately studied using a variety of techniques. Two types of protein-surfactant complexes at a concentration below the normal critical micellar concentration (cmc) were formed in solution. The first, G-CTAB (monomer) combined complex (GS(n)(I)) adsorbed at the air/solution interface, followed by its gradual transformation to the poor interfacially active second G-CTAB (aggregate) complex (GS(m)(B)) at a critical aggregation concentration (cac) of the interacting oppositely charged surfactant. In the higher concentration range, upon completion of GS(m)(B) formation, coacervation (association of GS(m)(B)) led to add turbidity. With increasing addition of CTAB, the coacervates became disintegrated and ultimately remained dissolved in the free micellar solution of CTAB. The above features were studied using the techniques of tensiometry, conductometry, turbidimetry, fluorimetry, and microcalorimetry. The interaction features were prominent at [G] >or= 0.05 g %, and several of these were either marginal or absent at [G]<0.05 g %. The denatured protein was found to form viscous as well as gel-forming consistencies at higher [G] and at lower temperature. A temperature variation study on the interaction of G with CTAB has revealed that enhanced interaction takes place at higher temperature. The effect of [G] on its interaction with cationic surfactants of varying chain length in the alkyltrimethylammonium bromide (ATAB) series has been also studied; a similar interactional profile as that of CTAB has been exhibited by octadecyltrimethylammonium bromide; however, the lower homologues (dodecyl- and tetradecyl-) of ATAB have offered different profiles. It has been found that the ATABs with higher alkyl chain lengths were more interactive with negatively charged G than their lower homologues. Quantification of the results in terms of different transition points, counterion binding of the protein-bound surfactant aggregates and free micelles, the enthalpy of binding interactions and energetics of ATAB micellization, and so forth have been studied. The results have been rationalized in terms of an interaction model.     

JR 400–NaAOT interaction: a detailed thermodynamic study of polymer–surfactant interaction bearing opposite charges

The present study entails interaction between the cationic polymer N,N-dimethylhydroxyethyl cellulose (JR 400) and the double-tailed anionic surfactant Na-bis-2-ethyhexylsulphosuccinate (NaAOT). This oppositely charged polymer and surfactant are expected to cause coacervation and precipitation; hence, we have observed formation of thick solution similar to diluted gel at [JR 400]?~?0.01 and 0.10 %?w/v in aqueous solution. Viscometry, conductometry, tensiometry, and microcalorimetry techniques are used to monitor the interaction process. The results are explained in the light of both intrachain and interchain linking by way of NaAOT reverse micelle formation. Adsorption of NaAOT monomers onto the charged side chains of the polymer shields interchain electrostatic repulsion, leading to the formation of hydrophobic microdomains and microscopic heterogeneity in the solution. The morphologies of the domains depend on the level of addition of NaAOT in the system. The different stages of physiochemical changes that arise in solution have been identified by the use of different techniques, and correlations of the results have been attempted in terms of pragmatic models.     

Cumulative yields of short-lived isotopes of barium in the spontaneous fission of252Cf

Cumulative yields of short-lived/barium isotopes^{139, 141, 142}Ba have been determined in the spontaneous fission of²⁵²Cf, using fast radiochemical separation and gamma-ray spectrometry.¹⁴²Ba yield is reported for the first time. The measured cumulative yields are converted to chain yields, assuming normal charge distribution systematics for comparision with the literature data.     

Stokes flow past a porous spheroid embedded in another porous medium

A study is made with an analysis of an incompressible viscous fluid flow past a slightly deformed porous sphere embedded in another porous medium. The Brinkman equations for the flow inside and outside the deformed porous sphere in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in small parameter characterizing the deformation. The flow through the porous oblate spheroid embedded in another porous medium is considered as the particular example of the deformed porous sphere embedded in another porous medium. The drag experienced by porous oblate spheroid in another porous medium is also evaluated. The dependence of drag coefficient and dimensionless shearing stress on the permeability parameter, viscosity ratio and deformation parameter for the porous oblate spheroid is presented graphically and discussed. Previous well-known results are then also deduced from the present analysis.