Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.

Energy funneling and macromolecular conformational dynamics: a 2D Raman correlation study of PEG melting

Cascading energy landscapes through funneling has been postulated as a mechanistic route for achieving the lowest energy configuration of a macromolecular system (such as proteins and polymers). In particular, understanding the molecular mechanism for the melting and crystallization of polymers is a challenging fundamental question. The structural modifications that lead to the melting of poly(ethylene glycol) (PEG) are investigated here. Specific Raman bands corresponding to different configurations of the PEG chain have been identified, and the molecular structural dynamics of PEG melting have been addressed using a combination of Raman spectroscopy, 2D Raman correlation and density functional theory (DFT) calculations. The melting dynamics of PEG have been unambiguously explained along the C-O bond rotation coordinate.

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.

Experimental determination and theoretical correlation for the solubilities of dicarboxylic acid esters in supercritical carbon dioxide

The synthesis of high molecular weight esters such as bis (2-ethylhexyl) sebacate is of significance for its use as a lubricant. This ester is synthesized by the transesterification of dimethyl sebacate with 2-ethylhexanol. Therefore, the solubilities of bis (2-ethylhexyl) sebacate and dimethyl sebacate were determined at 308-328 K at pressures of 10-18 MPa in supercritical carbon dioxide. The solubility of dimethyl sebacate was always higher than bis (2-ethylhexyl) sebacate at a given temperature and pressure. The Mendez-Teja model was used to verify the self-consistency of data. Further, a new semi-empirical model with three parameters was developed using the solution theory coupled with Wilson activity coefficient. This model was used to correlate the experimental data of this work and solubilities of many high molecular weight esters reported in the literature. (C) 2015 Elsevier B.V. All rights reserved.

A thermodynamic correlation between damage and fracture as applied to concrete fatigue

Fatigue damage in concrete is characterized by the simultaneous presence of micro and macrocracks. The theory of fracture mechanics conveniently handles the propagation of macrocracks, whereas damage mechanics precisely describes the state of microcracking. This paper provides a platform to correlate fracture mechanics and damage mechanics theories through an energy equivalence within a thermodynamic framework by equating the energy dissipated according to each theory. Through this correlation, damage corresponding to a given crack length could be obtained, and alternatively a discrete crack could be transformed into an equivalent damage zone. The results are validated using available experimental data on concrete fatigue including stiffness degradation and acoustic emission. (C) 2015 Elsevier Ltd. All rights reserved.

A thermodynamic correlation between damage and fracture as applied to concrete fatigue

Fatigue damage in concrete is characterized by the simultaneous presence of micro and macrocracics. The theory of fracture mechanics conveniently handles the propagation of macrocracks, whereas damage mechanics precisely describes the state of microcracking. This paper provides a platform to correlate fracture mechanics and damage mechanics theories through an energy equivalence within a thermodynamic framework by equating the energy dissipated according to each theory. Through this correlation, damage corresponding to a given crack length could be obtained, and alternatively a discrete crack could be transformed into an equivalent damage zone. The results are validated using available experimental data on concrete fatigue including stiffness degradation and acoustic emission. (C) 2015 Elsevier Ltd. All rights reserved.

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence

Previous research has shown a strong positive correlation between short-term persistence and long-term output growth as well as between depreciation rates and long-term output growth. This evidence, therefore, contradicts the standard predictions from traditional neoclassical or AK-type growth models with exogenous depreciation. In this paper, we first confirm these findings for a larger sample of 101 countries. We then study the dynamics of growth and persistence in a model where both the depreciation rate and growth are endogenous and procyclical. We find that the model s predictions become consistent with the empirical evidence on persistence, long-term growth and depreciation rates.

Estimation of Correlation Distance of Soil Properties by Geostatistics

Random field theory has been used to model the spatial average soil properties, whereas the most widely used, geostatistics, on which also based a common basis (covariance function) has been successfully used to model and estimate natural resource since 1960s. Therefore, geostistics should in principle be an efficient way to model soil spatial variability Based on this, the paper presents an alternative approach to estimate the scale of fluctuation or correlation distance of a soil stratum by geostatistics. The procedure includes four steps calculating experimental variogram from measured data, selecting a suited theoretical variogram model, fitting the theoretical one to the experimental variogram, taking the parameters within the theoretical model obtained from optimization into a simple and finite correlation distance 6 relationship to the range a. The paper also gives eight typical expressions between a and b. Finally, a practical example was presented for showing the methodology.

Density functional theory embedding for correlated wavefunctions

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems.

First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures.

Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the effect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

We significantly improve the numerics of the algorithm by enforcing orthogonality between subsystems by introduction of a projection operator. Utilizing the projection-based embedding scheme, we rigorously analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using CWs, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We develop an algorithm which corrects this term and demonstrate the accuracy of this corrected embedding scheme.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

Theory of defects in amorphous semiconductors

We review the electronic structure of defects in aSi:H, aGaAs and aSi3N4, emphasising in aSi:H the doping mechanism, the evidence that its dangling bond defect has a small electron-lattice coupling and a positive correlation energy, and possible atomic mechanisms for the Staebler-Wronski effect. © 1985.

Theory and experiment of two-photon 'direct' interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump

Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young's double-slit experiment. In this experiment, a short focal length tens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.