Ising model on self-avoiding walk chains

The phase transitions of nearest-neighbour interacting Ising models on self-avoiding walk (SAW) chains on square and triangular lattices have been studied using Monte Carlo technique. To estimate the transition temperature (T _c) bounds, the average number of nearest-neighbours (Z _eff) of spins on SAWs have been determined using the computer simulation results, and the percolation thresholds (p _c) for site dilution on SAWs have been determined using Monte Carlo methods. We find, for SAWs on square and triangular lattices respectively,Z _eff=2.330 and 3.005 (which compare very well with our previous theoretically estimated values) andp _c=0.022±0.003 and 0.045±0.005. When put in Bethe-Peierls approximations, the above values ofZ _eff givekT _c/J<1.06 and 1.65 for Ising models on SAWs on square and triangular lattices respectively, while, using the semi-empirical relation connecting the Ising modelT _c's andp _c's for the same lattices, we findkT _c/J0.57 and 0.78 for the respective models. Using the computer simulation results for the shortest connecting path lengths in SAWs on both kinds of lattices, and integrating the spin correlations on them, we find the susceptibility exponent =1.024±0.007, for the model on SAWs on two dimensional lattices.     

Quantitative estimations of ferric iron by phosphoric acid in aqueous-alcoholic medium

Summary The only method recommended for the direct estimation of ferric iron in presence of HCl is to reduce the ferric iron to ferrous iron and then to titrate against KMnO₄ solution by adding Reinhardt-Zimmermann reagent (MnSO₄ + H₂SO₄ + H₃PO₄). The solubility of the phosphato complexes of ferric chloride and phosphoric acid is much reduced by adding a nonaqueous solvent, ethyl alcohol or acetone. This property has been availed of to find out a method of estimating ferric iron directly against standard solution of phosphoric acid in aqueous-nonaqueous medium using K₄Fe(CN)₆ or cupferron as external indicators. A slight discrepancy at the end point, however, exists in the direct titration but it can be removed by applying a correction factor determined from the estimated results.     

Brownian dynamics simulation study of self-assembly of amphiphiles with large hydrophilic heads

We have studied the effect of shape of an amphiphilic molecule on micellization properties by carrying out stochastic molecular dynamics simulation on a bead-spring model of amphiphiles for several sizes of hydrophilic head group with a fixed hydrophobic tail length. Our studies show that the effect of geometry of an amphiphile on shape and cluster distribution of micelles is significant. We find the critical micelle concentration increases with the increasing size of the hydrophilic head. We demonstrate that the onset of micellization is accompanied by (i) a peak in the specific heat as found earlier in the simulation studies of lattice models, and (ii) a peak in the characteristic relaxation time of the cluster autocorrelation function. Amphiphiles with larger hydrophilic head form smaller micelles with sharper cluster distribution. Our studies are relevant to the controlled synthesis of nanostructures of desired shapes and sizes using self-assembling properties of amphiphiles.     

On the functional central limit theorem and the law of the iterated logarithm for Markov processes

Summary Let X _tt0 be an ergodic stationary Markov process on a state space S. If  is its infinitesimal generator on L ²(S, dm), where m is the invariant probability measure, then it is shown that for all f in the range of } } 0)$$ " align="middle" border="0"> converges in distribution to the Wiener measure with zero drift and variance parameter ² =–2f, g=–2Âg, g where g is some element in the domain of  such that Âg=f (Theorem 2.1). Positivity of ² is proved for nonconstant f under fairly general conditions, and the range of  is shown to be dense in 1. A functional law of the iterated logarithm is proved when the (2+)th moment of f in the range of  is finite for some >0 (Theorem 2.7(a)). Under the additional condition of convergence in norm of the transition probability p(t, x, d y) to m(dy) as t , for each x, the above results hold when the process starts away from equilibrium (Theorems 2.6, 2.7 (b)). Applications to diffusions are discussed in some detail.This research was partially supported by NSF Grants MCS 79-03004, CME 8004499     

Efficacious and sustained release of an anticancer drug mitoxantrone from new covalent organic frameworks using protein corona

Solid porous and crystalline covalent organic frameworks (COFs) are characterized by their higher specific BET surface areas and functional pore walls, which allow the adsorption of various bioactive molecules inside the porous lattices. We have introduced a perylene-based COF, PER@PDA-COF-1, which acts as an effective porous volumetric reservoir for an anticancer drug, mitoxantrone (MXT). The drug-loaded COF (MXT–PER@PDA-COF-1) exhibited zero cellular release of MXT towards cancer cells, which can be attributed to the strong intercalation between the anthracene-dione motif of the drug and the perylene-based COF backbone. Here, we have introduced a strategy involving the serum-albumin-triggered intracellular release of mitoxantrone from MXT–PER@PDA-COF-1. The serum albumin acts as an exfoliating agent and as a colloidal stabilizer in PBS medium (pH = 7.4), rapidly forming a protein corona around the exfoliated COF crystallites and inducing the sustained release of MXT from the COF into tumorigenic cells.

Solid porous and crystalline covalent organic frameworks (COFs) are characterized by their higher specific BET surface areas and functional pore walls, which allow the adsorption of various bioactive molecules inside the porous lattices.     

Tailoring a robust Al-MOF for trapping C2H6 and C2H2 towards efficient C2H4 purification from quaternary mixtures

Light hydrocarbon separation is considered one of the most industrially challenging and desired chemical separation processes and is highly essential in polymer and chemical industries. Among them, separating ethylene (C₂H₄) from C2 hydrocarbon mixtures such as ethane (C₂H₆), acetylene (C₂H₂), and other natural gas elements (CO₂, CH₄) is of paramount importance and poses significant difficulty. We demonstrate such separations using an Al-MOF synthesised earlier as a non-porous material, but herein endowed with hierarchical porosity created under microwave conditions in an equimolar water/ethanol solution. The material possessing a large surface area (793 m² g⁻¹) exhibits an excellent uptake capacity for major industrial hydrocarbons in the order of C₂H₂ > C₂H₆ > CO₂ > C₂H₄ > CH₄ under ambient conditions. It shows an outstanding dynamic breakthrough separation of ethylene (C₂H₄) not only for a binary mixture (C₂H₆/C₂H₄) but also for a quaternary combination (C₂H₄/C₂H₆/C₂H₂/CO₂ and C₂H₄/C₂H₆/C₂H₂/CH₄) of varying concentrations. The detailed separation/purification mechanism was unveiled by gas adsorption isotherms, mixed-gas adsorption calculations, selectivity estimations, advanced computer simulations such as density functional theory (DFT), grand canonical Monte Carlo (GCMC) and ab initio molecular dynamics (AIMD), and stepwise multicomponent dynamic breakthrough experiments.

Industrially important C₂H₄ purification from multi-component hydrocarbon mixtures.     

Temperature Effects on Attenuation Due to Rain for Millimeter and Centimeter Waves

Radio wave operating in millimetrewave and microwave frequency bands are adversely affected due to rain. Particularly the attenuation is of immense significance for sensitive remote measurements by satellites using frequencies greater than 10 GHz. Maintenance of an uninterrupted communication link requires a precise knowledge of the attenuation effect due to rain for commissioning right kind of transmitting sources for various purposes required in present day situation. Precise measurement of attenuation at various frequencies will enable us to choose the right frequency, polarization, incident angle and power of the source for different purposes. In this paper we have compared the results of earlier works using aR^b Olsen et al, (1) and the formulation by Moupfouma, (2) on the basis of theoretical analysis for explaining the observed results. Effect of temperature, considered in detail in this communication, has contributed the necessary correction factor of the rain attenuation for explaining the observed results. Theoretical analyses to measure the attenuation of the propagating wave due to temperature variation in the rain path have been presented. Correction factor due to temperature profile (temperature from the ground to the rain height within which the radio wave traces its path) has been incorporated in two models by using the concept of dipole energy changes. The effect of this temperature is noted to be quite significant and incorporates an error to the extent of 7–8%.     

Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces

We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.     

Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.