Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pK(a) Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation deprotonation reaction of the 20 canonical alpha amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metad-ynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pK(a) values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pK(a) values with a mean relative error, with respect to experimental results, of 0.2 pK(a) units.

Ab Initio MD Simulations of the Bronsted Acidity of Glutathione in Aqueous Solutions: Predicting pK(a) Shifts of the Cysteine Residue

The tripeptide glutathione (GSH) is one of the most abundant peptides and the major repository for nonprotein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thiol-disulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influence the redox couple, and hence the pK(a) value of the cysteine residue of GSH is critical to its functioning. Here we report ab initio Car-Parrinello molecular dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. We show that the free-energy landscape for the protonation-deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides shift in the dissociation constant values as compared with the isolated accurate estimates of the pK(a) and correctly predicts the cysteine amino acid.

Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations

In this paper, we present the solutions of 1-D and 2-D non-linear partial differential equations with initial conditions. We approach the solutions in time domain using two methods. We first solve the equations using Fourier spectral approximation in the spatial domain and secondly we compare the results with the approximation in the spatial domain using orthogonal functions such as Legendre or Chebyshev polynomials as their basis functions. The advantages and the applicability of the two different methods for different types of problems are brought out by considering 1-D and 2-D nonlinear partial differential equations namely the Korteweg-de-Vries and nonlinear Schrodinger equation with different potential function. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Pattern formation in thin films of polymer solutions: Theory and simulations

Self-assembly has been recognized as an efficient tool for generating a wide range of functional, chemically, or physically textured surfaces for applications in small scale devices. In this work, we investigate the stability of thin films of polymer solutions. For low concentrations of polymer in the solution, long length scale dewetting patterns are obtained with wavelength approximately few microns. Whereas, for concentrations above a critical value, bimodal dispersion curves are obtained with the dominant wavelength being up to two orders smaller than the usual dewetting length scale. We further show that the short wavelength corresponds to the phase separation in the film resulting in uniformly distributed high and low concentration regions. Interestingly, due to the solvent entropy, at very high concentration values of polymer, a re-entrant behaviour is observed with the dominant length scale now again corresponding to the dewetting wavelength. Thus, we show that the binary films of polymer solutions provide additional control parameters that can be utilized for generating functional textured surfaces for various applications. (C) 2016 AIP Publishing LLC.

Spin-glass state in nanoparticulate (La0.7Sr0.3MnO3)(1-x) (BaTiO3)(x) solid solutions: Experimental and density-functional studies

We report the transition from robust ferromagnetism to a spin- glass state in nanoparticulate La0.7Sr0.3MnO3 through solid solution with BaTiO3. The field- and temperature-dependent magnetization and the frequency-dependent ac magnetic susceptibility measurements strongly indicate the existence of a spin- glass state in the system, which is further confirmed from memory effect measurements. The breaking of long-range ordering into short-range magnetic domains is further investigated using density-functional calculations. We show that Ti ions remain magnetically inactive due to insufficient electron leakage from La0.7Sr0.3MnO3 to the otherwise unoccupied Ti-d states. This results in the absence of a Mn-Ti-Mn spin exchange interaction and hence the breaking of the long-range ordering. Total-energy calculations suggest that the segregation of nonmagnetic Ti ions leads to the formation of short-range ferromagnetic Mn domains.

Benchmark analytical solutions from beams with shared eigenpair

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.