Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Image reconstruction by inhomogeneous diffusion for positron emission tomography

In positron emission tomography (PET), image reconstruction is a demanding problem. Since, PET image reconstruction is an ill-posed inverse problem, new methodologies need to be developed. Although previous studies show that incorporation of spatial and median priors improves the image quality, the image artifacts such as over-smoothing and streaking are evident in the reconstructed image. In this work, we use a simple, yet powerful technique to tackle the PET image reconstruction problem. Proposed technique is based on the integration of Bayesian approach with that of finite impulse response (FIR) filter. A FIR filter is designed whose coefficients are determined based on the surface diffusion model. The resulting reconstructed image is iteratively filtered and fed back to obtain the new estimate. Experiments are performed on a simulated PET system. The results show that the proposed approach is better than recently proposed MRP algorithm in terms of image quality and normalized mean square error.

Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound-modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time-independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Determination of diffusion parameters and activation energy of diffusion in V3Si phase with A15 crystal structure

Diffusion such is the integrated diffusion coefficient of the phase, the tracer diffusion coefficient of species at different temperatures and the activation energy for diffusion, are determined in V3Si phase with A15 crystal structure. The tracer diffusion coefficient of Si Was found to be negligible compared to the tracer diffusion coefficient of V. The calculated diffusion parameters will help to validate the theoretical analysis of defect structure of the phase, which plays an important role in the superconductivity.

Spatial distribution of aerosol black carbon over India during pre-monsoon season

Aerosol black carbon (BC) mass concentrations ([BC]), measured continuously during a multi-platform field experiment, Integrated Campaign for Aerosols gases and Radiation Budget (ICARB, March-May 2006), from a network of eight observatories spread over geographically distinct environments of India, (which included five mainland stations, one highland station, and two island stations (one each ill Arabian Sea and Bay of Bengal)) are examined for their spatio-temporal characteristics. During the period of study, [BC] showed large variations across the country, with values ranging from 27 mu g m(3) over industrial/urban locations to as low as 0.065 mu g m(-3) over the Arabian Sea. For all mainland stations, [BC] remained high compared to highland as well as island stations. Among the island stations, Port Blair (PBR) had higher concentration of BC, compared to Minicoy (MCY), implying more absorbing nature of Bay of Bengal aerosols than Arabian Sea. The highland station Nainital (NTL), in the central Himalayas, showed low values of [BC], comparable or even lower than that of the island station PBR, indicating the prevalence of cleaner environment over there. An examination of the changes in the mean temporal features, as the season advances from winter (December-February) to pre-monsoon (March-May), revealed that: (a) Diurnal variations were pronounced over all the mainland stations, with all afternoon low and a nighttime high: (b) At the islands, the diurnal variations, though resembled those over the mainlands, were less pronounced; and (c) In contrast to this, highland station showed an opposite pattern with an afternoon high and a late night or early morning low. The diurnal variations at all stations are mainly caused by the dynamics of local Atmospheric Boundary Layer (ABL), At the entire mainland as well as island stations (except HYD and DEL), [BC] showed a decreasing trend from January to May, This is attributed to the increased convective mixing and to the resulting enhanced vertical dispersal of species in the ABL. In addition, large short-period modulations were observed at DEL and HYD, which appeared to be episodic, An examination of this in the light of the MODIS-derived fire count data over India along with the back-trajectory analysis revealed that advection of BC from extensive forest fires and biomass-burning regions upwind were largely responsible for this episodic enhancement in BC at HYD and DEL.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Effect of spatial dispersion of the dielectric on the binding energy of D- ion in Si and Ge

Using a multivalley effective mass theory, we obtain the binding energy of a D- ion in Si and Ge taking into account the spatial variation of the host dielectric function. We find that on comparison with experimental results the effect of spatial dispersion is important in the estimation of binding energy for the D- formed by As in Si and Ge. The effect is less significant for the case of D- formed by P and Sb donors.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Interdiffusion and Growth of the Superconductor Nb3Sn in Nb/Cu(Sn) Diffusion Couples

The confusion over the growth rate of the Nb3Sn superconductor compound following the bronze technique is addressed. Furthermore, a possible explanation for the corrugated structure of the product phase in the multifilamentary structure is discussed. Kirkendall marker experiments are conducted to study the relative mobilities of the species, which also explains the reason for finding pores in the product phase layer. The movement of the markers after interdiffusion reflects that Sn is the faster diffusing species. Furthermore, different concentrations of Sn in the bronze alloy are considered to study the effect of Sn content on the growth rate. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined.

Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.

Nanopatterning by solid-state dewetting on reconstructed ceramic surfaces

We demonstrate ordered array formation of Au nanoparticles by controlled solid-state dewetting of a metal film on stepped alumina substrates. In situ transmission electron microscopy studies reveal that the dewetting process starts with nucleation of ordered dry regions on the substrate. The chemical potential difference between concave and convex surface regions induces anisotropic metal diffusion leading to the formation of nanowires in the valleys. The nanowires fragment due to Rayleigh instability forming arrays of metal nanoparticles on the substrate. The length scale of reconstruction relative to the starting film thickness is an important parameter in controlling the spatial order of the nanoparticles.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.