Application of the statistical rate theory of interfacial transport to investigate the kinetics of divalent metal ion adsorption onto the energetically heterogeneous surfaces of oxides and activated carbons

Divalent metal cation adsorption from solution onto oxides or activated carbons can be described by the Surface Complexation Model (SCM). We assumed that the adsorbent surface is strongly energetically heterogeneous and derived the adsorption isotherm using rectangular distribution of adsorption energy and condensation approximation for the local isotherm equation. Assuming additionally that the bulk concentration of divalent metal ion is low and does not change considerably during the adsorption process and next applying the Statistical Rate Theory of Interfacial Transport (SRT) we derived the Elovich equation—the experimental formula describing adsorption kinetics.     

Fluid-fluid interaction during miscible and immiscible displacement under ultrasonic waves

This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation at the interface between immiscible (different types of oils and aqueous solutions) and miscible (different types of oil and solvent) fluids. An extensive set of Hele-Shaw type experiments were performed for several viscosity ratios, and interfacial tension. Fractal analysis techniques were applied to quantify the degree of fingering and branching. This provided a rough assessment of the degree of perturbation generated at the interface when the capillary forces along with the viscous forces are effective. Miscible Hele-Shaw experiments were also presented to isolate the effect of viscous forces. We found that ultrasound acts to stabilize the interfacial front, and that such effect is most pronounced at low viscosity ratios. An erratum to this article is available at .     

Statistical mechanics of Arakawa’s discretizations

The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization used. This is illustrated for quasi-geostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa [Arakawa, Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1 (1966) 119–143] which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.     

The combined effect of nonlinear filtration and window size on the accuracy of tissue displacement estimation using detected echo signals

In cardiac elastography, the regional strain and strain rate imaging is based on displacement estimation of tissue sections within the heart muscle carried out with various block-matching techniques (cross-correlation, sum of absolute differences, sum of squared differences, etc.). The accuracy of these techniques depends on a combination of ultrasonic imaging parameters such as ultrasonic frequency of interrogation, signal-to-noise ratio, size of a kernel used in a block-matching algorithm, type of data and speckle decorrelation. In this paper, we discuss the possibility to enhance the accuracy of the displacement estimation via nonlinear filtering of B-mode images before block-matching operation. The combined effect of a filter algorithm and a kernel size on the accuracy of the displacement estimation is analyzed using a 36-frame sequence of grayscale B-mode images of a human heart acquired by an ultrasound system operating at 1.77 MHz. It is shown that the nonlinear filtering of images enables to obtain the desired accuracy (less than one pixel) of the displacement estimation with smaller kernels than without filtering. These results are obtained for two filters--an adaptive anisotropic diffusion filter and a nonlinear Gaussian filter chain.     

A new method of spatial compounding imaging

A new method of spatial compound imaging is presented that improves image quality without the usual requirement to decrease the frame rate. The new method of imaging utilizes three transducers for data acquisition. The transducer located at the center of the transducer system is a phased array probe that acts as both transmitter and receiver. The other transducers are unfocused pistons that act only as receivers. Envelope data acquired by each transducer are combined to form a final image with improved quality (speckle contrast, target detectability and lateral resolution). It is shown that the improvement in speckle contrast depends on the correlation between individual images acquired by the transducers. The effective aperture approach is used for analytic estimation of the correlation between images in order to optimize the lateral separation between transducers. Using simulations, several compounding strategies have been performed to find the strategy that maximizes image quality. The central frequency of 2.5 MHz is used in simulations. Quantitative analysis of simulated B-mode images shows that the new method of imaging efficiently improves visibility, detectability, and lateral resolution of low contrast regions. The image frame rate is preserved because multiple scans are not required for the spatial compounding.     

Statistical analysis of queueing systems

This paper provides an overview of the literature on statistical analysis of queueing systems. Topics discussed include: model identification, estimation, hypothesis testing and other related aspects. Not all of these statistical problems are covered in books on queueing theory or stochastic processes. The bibliography is not exhaustive, but comprehensive enough to provide sources from the literature.     

On the statistical mechanics of rigid particles

In this paper, generalized functions are used in the configuration partition function for fluids composed of arbitrarily shaped, rigid particles. This leads to new expressions for the basic statistical thermodynamic functions and some equations that may be useful in developing approximate theories, such as the scaled particle theory, for such fluids. The results are applicable to a large class of arbitrarily shaped, rigid particles and reduce exactly to the usual hard-sphere expressions.     

Correlation functions of odd numbers of spins with finite separations on the Onsager-Ising lattice

A method is developed for making exact evaluations of correlation functions of odd numbers of spins on the Onsager-Ising lattice, applicable to cases in which the separations between the spins are finite. The method is based on an identity which permits the reduction of determinants of infinite-dimensional matrices to those of finite dimension. Particularly simple results are obtained when all spins are on a straight line. Numerical calculations are carried out for a few cases.     

Statistically periodic processes and toeplitz(α by β) matrices

If each element in a Toeplitz matrix is replaced by an by matrix and the original constraints preserved, the result is a doubly infinite matrix with periodic structure called a toeplitz_{( by)} matrix. Such matrices are a basic tool for describing, generating, estimating, filtering, synchronizing, and analyzing information-theoretic functions for statistically periodic processes.     

Mixture-model approach to the theory of classical fluids. III. Application to aqueous solutions of nonelectrolytes

An extension of the mixture-model approach to the theory of liquid water is developed to include aqueous solutions of nonelectrolytes. The Kirkwood-Buff theory of solution is employed to obtain a general and exact expression for the stabilization effect induced by the solute. This relation is applied, in the framework of a two-structure model, to obtain further insight into the molecular origin of some anomalous thermodynamic properties of aqueous solutions. The generalized continuous mixture-model formalism is also extended to solutions. It is demonstrated that current concepts such as structural changes in the solvent are strongly dependent on the particular classification procedure adopted to construct the mixture model.