Comparison of Perturbation Theory and Mean Spherical Approximation Based on Molecular Simulation Data

A comprehensive study on various internal energies for the dipolar hard sphere fluids, including Stockmayer fluids, the mixtures of Lennard-Jones and Stockmayer and Stockmayer fluids and the electrolyte solutions is reported based on the perturbation theory and mean spherical approximation. Compared with the results of molecular simulations, it is shown that the perturbation theory is better than the mean spherical approximation.

Performance evaluation of the simpli¯ed spherical harmonics approximation for cone-beam X-ray luminescence computed tomography imaging

As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)distribution of the probes from surface measurements.A proper photon-transportation model is critical to accuracy of XLCT.Here,we presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN).The performance of the two methods was evaluated over several main spec-trums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP_(3) could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP_(1)(which is equivalent to the difusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction perfor-mance of the SP:and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT.

BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.

APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE

In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.

Sound scattering from underwater elastic spherical shell covered with multilayered medium approximated acoustic cloak

The anechoic performance and mechanism of underwater elastic spherical shell covered with coating are studied at low frequencies.The acoustic cloak is anisotropic material,which can be designed with homogeneous isotropic materials on the basis of effective medium approximation theory.The analytic expression of scattering acoustic field from the shell covered with multilayered medium is formulated and the scattering form function,resonance mode,acoustic field distribution are computed,the scattering characteristics and mechanism of transmission are analyzed.The results show that the direction of sound transmission inside the multilayered medium is changed,the acoustic field is deflected gradually,and the acoustic energy flux is guided around the target,which reduces the scattering intensity at low frequencies,the acoustic intensity of target＇s surface is very weak.Excepting the first resonance peak in spectrum produced by the zero order partial wave,the other resonance modes of elastic spherical shell are not excitated and the multilayered medium can suppress the resonance of the spherical shell effectively.

Recent Advances in Study on Thermodynamic Models for Real Systems Including Electrolytes

A comprehensive review of recent advances in study on thermodynamic models for real electrolyte solutions is presented. The differences between primitive and non-primitive electrolyte models are demonstrated. Some new thermodynamic models for electrolyte solutions based on the mean spherical approximation and perturbation theory are introduced. An extended scaled-particle theory and modified CleggPitzer equation are presented for physical and chemical absorption processes with mixed solvents, respectively. A pseudo one-component two-Yukawa equation of state is used for the aqueous two-phase extraction process in charged colloidal systems.

Recent Advances in the Use of Statistical Mechanics to Establish Molecular Thermodynamic Models for Electrolyte Solutions

Based on statistical mechanics, a review of recent theoretical studies of real electrolyte solutions is presented from three aspects, namely, molecular simulation, mean spherical approximation (MSA), and perturbation theory. Recent advances in studies of three kinds of electrostatic potentials of mean force, three kinds of internal energies (ion-ion, ion-dipole, and dipole-dipole interactions), and three kinds of electro-lyte models (primitive, non-primitive, and solvent primitive models) are introduced. The advantages and dis-advantages between primitive and non-primitive models, and between MSA and perturbation theory are dis-cussed. Some new equations of state (EOSs) based on MSA and perturbation theory for real electrolyte so-lutions are introduced. The one-Yukawa EOS and the two-Yukawa EOS for charged colloid systems are presented.

STABLE BOUNDARY CONDITIONS AND DISCRETIZATION FOR P_(N) EQUATIONS

A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over time.In this paper,we present boundary conditions(BCs)for the spherical harmonic(P_(N))approximation,which ensure that this fundamental energy bound is satisfied by the P_(N) approximation.Our BCs are compatible with the characteristic waves of P_(N) equations and determine the incoming waves uniquely.Both,energy bound and compatibility,are shown on abstract formulations of P_(N) equations and BCs to isolate the necessary structures and properties.The BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step,which is similar to the truncation of the series expansion in the P_(N) method.We show that summation by parts(SBP)finite differences on staggered grids in space and the method of simultaneous approximation terms(SAT)allows to maintain the energy bound also on the semi-discrete level.