Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.     

Bifurcation analysis of a multidelayed HIV model in presence of immune response and understanding of in‐host viral dynamics

In this paper, we proposed a multidelayed in‐host HIV model to represent the interaction between human immunodeficiency virus and immune response. One delay was considered to incorporate the time required by the virus for various intracellular events to make a host cell productively infective, and the second delay was introduced to take into account the time required for adaptive immune system to respond against infection. We extensively analyzed this multidelayed model analytically and numerically. We show that delay may have both destabilizing and stabilizing effects even when the system contains a single immune response delay. It happens when there exists two sequences of critical values of this delay. If the system starts with stable state in absence of delay, then the smallest value of these critical delays causes instability and the next higher value causes stability. The system may also show stability switching for different values of the virus replication factor. These results demonstrate the possible reasons of intrapatients and interpatients variability of CD4⁺ T cells and virus counts in HIV‐infected patients.     

Partial Molar Volumes of Some of α-Amino Acids in Binary Aqueous Solutions of MgSO4·7H2O at 298.15 K

The apparent molar volume, V ^o _{φ, 2}, of glycine, alanine, α-amino-n-butyric acid, valine and leucine have been determined in aqueous solutions of 0.25, 0.5 and 1.0 mol⋅dm⁻³ magnesium sulfate, and the partial specific volume from density measurements at 298.15 K. These data have been used to calculate the infinite dilution apparent molar volume, V ^o _2,m , group contribution of amino acids and partial molar volume of transfer, Δ_tr V _2,m ^o, from water to aqueous magnesium sulfate solutions. The linear correlation of V _2,m ^o for a homologous series of amino acids has been utilized to calculate the contributions of charged end groups (NH₃ ⁺, COO⁻), CH₂ - groups and other alkyl chains of amino acids to V _2,m ^o. The results for Δ_tr V _2,m ^o of amino acids from water to aqueous magnesium sulfate solutions have been interpreted in terms of ion-ion, ion-polar, hydrophilic-hydrophilic and hydrophobic-hydrophobic group interactions. The values of the standard partial molar volume of transfer for the amino acids with different hydrophobic contents, from water to aqueous MgSO₄ are in general positive, indicating the predominance of the interactions of zwitterionic/hydrophilic groups of amino acids with ions of the salt. The hydration number decreases with increasing concentration of salt. The number of water molecules hydrated to amino acids decreases, further strengthening the predominance of ionic/hydrophilic interactions in this system.     

Metal-Stabilized [B8H8]2− Derivatives with Dodecahedral Structure in the Solid and Solution States: [(Cp2MBH3)2B8H6] (Cp=η5-C5H5; M=Zr (1-Zr) and Hf (1-Hf)).

Despite the synthesis and structural characterization of closo-hydroborate dianions, [B_nH_n]²⁻ (n=6–12) more than 50 years ago, some ambiguity remains about the structure of [B₈H₈]²⁻. Although the solid-state structure of [B₈H₈]²⁻ was established by single-crystal X-ray studies in 1969, fast rearrangements in solution at accessible temperatures prevented its detailed characterization. We therefore stabilized a derivative of [B₈H₈]²⁻ by using Cp₂MBH₃ and structurally characterized two new octaborane analogues, [(Cp₂MBH₃)₂B₈H₆] (Cp=η⁵-C₅H₅; M=Zr ( 1-Zr ) and Hf ( 1-Hf )), so that the dynamics of the B₈ skeleton were arrested. The solid-state structures of both 1-Zr and 1-Hf comprise a dodecahedron core protected by {Cp₂MBH₃} moieties on both sides of the cluster. Spectroscopic characterization (¹¹B NMR) validates the intactness of the B₈ dodecahedron core in solution as well. Theoretical calculations establish that the two exo-{Cp₂MBH₃} fragments provide structural and electronic structural stability to the B₈ core and its intact dodecahedral dianionic nature. Furthermore, we propose isodesmic equations for the formation of higher analogues of the B_n core (n>8) guarded by different group 4 transition metals. Our analysis suggests that, as we move to higher polyhedra (n>10), the formation becomes unfavourable irrespective of metal.     

Discretization of an eco-epidemiological model and its dynamic consistency

In this paper, we discretize a continuous-time eco-epidemiological model by non-standard finite difference (NSFD) scheme as well as standard Euler forward scheme. Dynamical properties of both the systems are explored and compared with their continuous-time model. We show that the solution of NSFD system remains positive for all positive initial values. Fixed points and their local stability properties are shown to be identical with that of the continuous model, indicating its dynamic consistency. Dynamics of the Euler model, however, depend on the step–size and therefore dynamically inconsistent. Solutions in this latter method may be negative and allows numerical instabilities, leading to chaos. Extensive numerical simulations have been performed to validate the theoretical results.     

Fe‐enriched Clay‐coated and Reduced Graphene Oxide‐modified N‐doped Polymer Nanocomposite: A Natural Recognition Element‐based Sensing Electrode for DNT

Dinitrotoluene (DNT) is a signature material of all nitro‐aromatic explosives including the lethal 2,4,6‐trinitrotoluene (TNT). A clay‐modified reduced graphene oxide (rGO)‐polymer nanocomposite was prepared as sensing electrode for the detection of (DNT) in the aquatic systems. rGO was in situ dispersed in the electro‐conductive N‐doped phenol/formaldehyde polymer and the clay ‘montmorillonite’ was coated on the nanocomposite. The clay, containing iron as one of its mineral components, served as the recognition element for DNT. Tested using electrochemical measurement techniques – cyclic voltammetry and differential pulse voltammetry, the prepared sensing electrode exhibited a low detection limit (0.0016 μM) on signal to noise ratio basis (S/N=3) and excellent linearity (R²=0.997) over 0.02–10 mg L^?1 with high sensitivity value (428 μA mM^?1 cm^?2) for DNT. The electrode showed negligible interference with the gravimetric and volumetric salts commonly present in seawater, and also, with explosive derivatives. The separate tests performed in a simulated seawater confirmed the suitability of the prepared electrode for use in field applications.     

Micellar effect on hydrolysis of 4-methyl-2-nitroaniline phosphate

The effect of anionic surfactant sodium dodecyl sulfate (SDS) on the hydrolysis of a substrate (mono-4-methyl-2-nitroaniline phosphate) by HCl was studied at 303 K. The reaction followed the first-order kinetics with respect to both HCl and the substrate. SDS effectively catalyzes this reaction, which rate increases with the concentration of SDS due to an increase of dielectric constant of the medium. The kinetic data were fitted to Menger-Portnoy, Piszkiewicz and Berezin kinetic models to explain the observed micellar effects. The various activation parameters both in the presence and absence of SDS were evaluated; a reasonable mechanism was proposed. The rate constant in micellar phase, binding constant and index of cooperativity were calculated accordingly.     

Dispersal-induced pattern-forming instabilities in host–parasitoid metapopulations

Nonlinear Dynamics - Dispersal-induced pattern formation is important from both fundamental and application points of view. Spatial pattern in an ecological system can strongly depend on exogenous...     

Mathematical Modelling of a Non‐enzymatic Amperometric Electrochemical Biosensor for Cholesterol

Thickness of the electro‐polymerized layer grown on a substrate and used as the recognition element for the analyte is critical to measuring the response of a biosensor, with high sensitivity and accuracy. However, it is difficult to control the thickness during synthesis. A mathematical model is developed in this study that considers thickness of the electro‐polymerized layer in simulating the electrochemical response of a non‐enzymatic biosensor for cholesterol in blood. The model includes transient kinetics and one‐dimensional diffusion of the analyte in the poly‐methyl orange (PMO) recognition layer electrochemically grown on the electrode. The governing partial differential equations resulting from the species conservation balances in the PMO layer are numerically solved. Time and spatial concentration profiles of the analyte in the PMO layer are determined. Model predictions are calibrated with the experimental data for different PMO thicknesses. Interestingly, model predictions show a linear response over the calibrated concentration range of cholesterol for all PMO layer thicknesses. Based on the chronoamperometry measurements, the model predictions for the cholesterol concentrations measured in the laboratory samples were also found to be remarkably accurate. This is the first mathematical model developed to understand the transport and kinetics of an analyte in the electro‐polymerized layer used as the recognition element of a non‐enzymatic biosensor.     

Pelican at Risk in Salton Sea – a Delay-Induced Eco-Epidemiological Model

Elevated salinity, accelerated eutrophication, blooms of Avian botulism and dramatic water quality fluctuation are supposed to be the key factors for massive die-off of Tilapia (prey) and Pelican (predator) in the Salton sea. We modify the model of Chattopadhyay and Bairagi [Ecological Modelling 136 (2001), pp. 103-112] with an assumption that the growth rate of susceptible fish population is very high and study the dynamics of the system by introducing a delay factor in the predator response function. It is observed that the otherwise stable system exhibit a stable limit cycle solution when the lag factor attains its critical value. It is also observed that there is a high possibility of an epidemic out break in the fish as well as in the Pelican population if the predation process is delayed by a considerable amount of time. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.