Computation of partial molar properties using continuous fractional component Monte Carlo

ABSTRACT

An alternative method for calculating partial molar excess enthalpies and partial molar volumes of components in Monte Carlo (MC) simulations is developed. This method combines the original idea of Frenkel, Ciccotti, and co-workers with the recent continuous fractional component Monte Carlo (CFCMC) technique. The method is tested for a system of Lennard–Jones particles at different densities. As an example of a realistic system, partial molar properties of a [NH₃, N₂, H₂] mixture at chemical equilibrium are computed at different pressures ranging from P = 10 to 80 MPa. Results obtained from MC simulations are compared to those obtained from the PC-SAFT Equation of State (EoS) and the Peng–Robinson EoS. Excellent agreement is found between the results obtained from MC simulations and PC-SAFT EoS, and significant differences were found for PR EoS modelling. We find that the reaction is much more exothermic at higher pressures.     

Validation of practical diffusion approximation for virtual near infrared spectroscopy using a digital head phantom

Light propagation in the digital head phantom for virtual near infrared spectroscopy and imaging is calculated by diffusion theory. In theory, diffusion approximation is not valid in a low-scattering cerebrospinal fluid (CSF) layer around the brain. The optical path length and spatial sensitivity profile predicted by the finite element method based upon the diffusion theory are compared with those predicted by the Monte Carlo method to validate a practical implementation of diffusion approximation to light propagation in an adult head. The transport scattering coefficient of the CSF layer is varied from 0.01 to 1.0 mm⁻¹ to evaluate the influence of that layer on the error caused by diffusion approximation. The error is practically ignored and the geometry of the brain surface such as the sulcus structure in the digital head phantom scarcely affects the error when the transport scattering coefficient of the CSF layer is greater than 0.3 mm⁻¹.     

A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor

An approximate numerical method for fast calculations of the radiation heat transfer in a solar thermochemical reactor cavity is formulated based on the separate treatment of the solar and thermal radiative exchange by the diffusion approach. The usual P₁ approximation is generalized by applying an equivalent radiation diffusion coefficient for the optically thin central part of the cavity. The resulting boundary-value problems are solved using the finite element algorithm. The accuracy of the model is assessed by comparing the results to those obtained by a pathlength-based Monte Carlo simulation. The applicability of the proposed model is demonstrated by performing calculations for an example problem, which incorporates a range of parameters typical for a solar chemical reactor and the spectral radiative properties of polydisperse zinc oxide particles.     

Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I∝L^-1-α, where L is the ring length and α>0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.     

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

We propose the P_N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P_N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.     

用双点源δ-P1近似光学模型反演生物组织的光学参量

根据空间分辨漫反射的双点源δ-P₁近似理论模型,采用非线性最小二乘法,从反射率的测量数据中反演得到了生物组织的吸收系数μ_a、有效散射系数μ' _s和二阶参量γ.研究表明,在光源与探测器之间距离大于一个输运平均自由程的情况下,双点源δ-P₁近似能较好地描述光源附近的光辐射分布,而且能够根据参量γ与μ' _s的关系得到组织的各向异性因子g.这些研究对于生物组织的光学性质测量以及漫反射光谱技术的应用具有重要意义. 关键词： 组织光学 P₁近似')" href="#">δ-P₁近似 光学参量 双点源     

Lasing and fluorescence properties of dye-doped xerogel

Dye-doped SiO₂-xerogels are prepared for application as laser active medium. An optical surface and a sealing of the samples are achieved by covering them with silicon oil and an optical glass window. All optical properties were compatible with the assumption that the active chromophores are dissolved in the liquid which fills the pores of the xerogel. A replacement of the dye molecules destroyed by the pumping radiation via diffusion was observed. For stilbene 3 a diffusion coefficient ofD = 0.35 × 10^–9 m²/s was determined. Thus a durable operation of the laser with low repetition rates is possible.Notation as in [10]     

Density-Dependent Diffusion in the Periodic Lorentz Gas

We study the deterministic diffusion coefficient of the two-dimensional periodic Lorentz gas as a function of the density of scatterers. Based on computer simulations, and by applying straightforward analytical arguments, we systematically improve the Machta–Zwanzig random walk approximation [Phys. Rev. Lett. 50:1959 (1983)] by including microscopic correlations. We furthermore, show that, on a fine scale, the diffusion coefficient is a non-trivial function of the density. On a coarse scale and for lower densities, the diffusion coefficient exhibits a Boltzmann-like behavior, whereas for very high densities it crosses over to a regime which can be understood qualitatively by the Machta–Zwanzig approximation.     

Kinetics of monolayer growth

The kinetics of a monolayer growth is studied using the two-dimensional lattice gas model by means of the path-probability method (PPM) for nonequilibrium phenomena. Kinetic equations for the combined processes of relaxation (adsorption and desorption) and diffusion are derived analytically and solved for the first time in the square approximation of the PPM. Comparison of the square approximation with the point and pair approximations along with Monte Carlo simulation shows the effect of using a larger basic cluster than in the previous studies. When the square approximation is used, the growth rate results are much improved in both cases with and without diffusion and agree well with the Monte Carlo simulations results, except for very small values of the driving forceL=/k _b T where is the chemical potential difference between the vapor and the solid phase. In the range where the agreement is good, there exists a region where the growth rateR is proportional to exp(–c/L with a constantc. This is the feature which is characteristic of two-dimensional nucleation-limited growth.     

基于delta-P1近似模型的空间分辨漫反射一阶散射参量灵敏度研究

以delta-P1近似光学模型为基础, 推导了双点源近似下空间分辨漫反射一阶散射参量μ_s'灵敏度的解析式, 并进行了数值分析和比较. 研究表明, 与混合漫射近似模型和漫射近似模型相比, delta-P1 近似模型能更好地描述强散射较强吸收情况下近光源区域生物组织漫反射光子的分布, 且在有效反照率a'>0.83时, 获得最佳优化距离ρ_opt, ρ_opt 随μ_s' 的增大而减小, 且在距光源约2.7—4个输运平均自由程处μ_s'的变化对测量吸收的影响最小. 这项研究对于优化传感器几何结构以及生物组织光学参量的测量具有重要意义.     

Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations

We report on the design, test and Monte Carlo simulations of a non-descanned (NDS) collection port that we compare to a descanned (DS) port implemented on the same confocal microscope to carry out two-photon excitation fluorescence (TPEF) imaging. Our optical concept provides compactness, a wide field of view to the NDS port and allows the usage of small-area photosensors. The collection efficiency of the NDS port was measured with respect to those of the DS port as function of the imaging depth within a tissue-like optical phantom, for two high numerical aperture objectives. A NDS-to-DS collection ratio as high as about 30 was found for an imaging depth of 500 μm, corresponding to four mean scattering paths of the collected photons within the turbid medium. Measurements were fully interpreted by Monte Carlo simulations of light scattering through the turbid medium and collection by the spatio-angular apertured DS and NDS ports. Comparison of XZ cross-sectional views of mice liver samples imaged with the two ports emphasized the advantage of our NDS device for imaging deeply inside biological samples using TPEF microscopy.     

On the influence of two coexisting species of susceptibility-producing structures on the R21 relaxation rate

PurposeTissue microstructure can influence quantitative magnetic resonance imaging such as relaxation rate measurements. Consequently, relaxation rate mapping can provide useful information on tissue microstructure. In this work, the theory on relaxation mechanisms of the change of the relaxation rate ∆R₂^⁎ in the presence of spherical susceptibility sources in a spin bearing medium is validated in simulations and phantom experiments for the coexistence of two species of susceptibility sources.MethodsThe influence of coexisting spherical perturbers with magnetic susceptibilitys of different signs was evaluated in Monte Carlo simulations including diffusion effects in the surrounding medium. Simulations were compared with relaxometry measurements at 1.5 Tesla and at 3 Tesla. The phantoms used to validate the simulations were built from agarose gel containing calcium carbonate and tungsten carbide particles of different size and concentration.ResultsThe Monte Carlo simulations showed, that the change in relaxation rate only depends on the overall amount of susceptibility producing structures in the simulation volume and no difference was found, if mixtures of positive and negative particles were simulated. Phantom measurements within the static dephasing regime showed linear additivity of the effects from positive and negative susceptibility sources that were present within the same voxel.ConclusionsIn summary, both the simulations and the phantom measurements showed that changes in the relaxation rate ΔR₂^⁎ add up linearly for spherical particles with different susceptibilities within the same voxel if the conditions for the static dephasing regime are fulfilled. If particles with different susceptibilities have both different sizes and violate the conditions of the static dephasing regime, effects on relaxation rates might no longer be linear.     

Highly Asymmetric Electrolytes in the Associative Mean-Spherical Approximation

The associate mean-spherical approximation (AMSA) is used to derive the closed-form expressions for the thermodynamic properties of an (n+m)-component mixture of sticky charged hard spheres, with m components representing polyions and n components representing counterions. The present version of the AMSA explicitly takes into account association effects due to the high asymmetry in charge and size of the ions, assuming that counterions bind to only one polyion, while the polyions can bind to an arbitrary number of counterions. Within this formalism an extension of the Ebeling–Grigo choice for the association constant is proposed. The derived equations apply to an arbitrary number of components; however, the numerical results for thermodynamic properties presented here are obtained for a system containing one counterion and one macroion (1+1 component) species only. In our calculation the ions are pictured as charged spheres of different sizes (primitive model) embedded in a dielectric continuum. Asymmetries in charge of –10:+1, –10:+2, –20:+1, and –20:+2 and asymmetries in diameter of 2:0.4nm and 3:0.4nm are studied. Monte Carlo simulations are performed for the same model solution. By comparison with new and existing computer simulations it is demonstrated that the present version of the AMSA provides semiquantitative or better predictions for the excess internal energy and osmotic coefficient in the range of parameters where the regular hypernetted chain (HNC) and improved (associative) HNC do not yield convergent solutions. The AMSA liquid–gas phase diagram in the limit of complete association (infinitely strong sticky interaction) is calculated for models with different degrees of asymmetry.     

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

ABSTRACT

Short-range ordering as the formation of couples and pairs between solutes is affected by their formation energies. This is not reflected in the standard regular solution model. Here, we present a new thermodynamic model which accounts for the dependence of the molar Gibbs energy on the concentrations of couples and pairs and their formation energies. The model treats kinetics of couples and pairs formation controlled by diffusion. This new model uses tracer diffusion coefficients of solutes and bond formation energies, which can be taken from ab initio calculations. Insofar, the current concept bridges the gap between ab initio methods and non-equilibrium thermodynamics. The reliability of the model is checked by comparison with kinetic Monte Carlo simulations. The model is applied to an Al-Mg-Si-Cu system. Finally, the configurational entropy for a binary system evaluated with the current model is compared with Bethe’s approximation, which allows estimating of applicability limits of the current model.     

Determination of optical properties of slices of turbid media by diffuse CW laser light scattering profilometry

In this work we present a method for determining the optical parameters of turbid media, namely its absorption coefficient (μ_a) and its reduced scattering coefficient . It is based on the measurement of CW transmittance profiles and analysis of the experimental data by a theoretical model based on the diffusion approximation (DA) of the radiative transfer equation (RTE). The method developed has been investigated with solid polymer probes but it could be applied for liquid materials as well. Experimental results are presented and compared to those of other authors together with a discussion about the accuracy of measurements. In addition, measurements using integrating spheres as well as Monte Carlo simulations are also presented to validate these results.     

Modeling of light propagation in turbid medium using Monte Carlo simulation technique

The aim of the current study is to simulate the laser photon through biological tissue during PDT therapy using Monte Carlo simulation technique. The model is coded using MATLAB. Interaction of laser light with turbid medium e.g. human tissue depends on the optical properties of the medium i.e. refractive index n, absorption coefficient μ _a , scattering coefficient μ _s and anisotropy factor g. Laser light transport through tissue is governed by the radiative transport equations based on absorption and scattering. Direct sampling is used for step-size generation before interaction via absorption or scattering with the transmitting medium, for deflection and azimuthal angle (θ and ϕ) when the scattering even occurs. The tissue medium considered is divided into radial, axial and angular grid elements and an infinite narrow beam with normal incidence on the tissue is considered. The laser light absorbance inside the tissue, reflectance at the top boundary of the tissue and transmittance at the bottom are estimated and these quantities are shown varying radially and angularly. Results of reflectance, transmittance and fluence are compared with the already published results to confirm the authenticity of our coding and these results are found to lie at only 3–4% error.     

Collective diffusion in a lattice gas automaton

We report on non-mean-field and ring-kinetic-theory calculations of both the momentum autocorrelation function and the collective diffusion coefficient in a diffusive lattice gas automaton. For both quantities the ring approximation is calculated exactly. A saddle point method yields a leadingt ^–2 and a subleadingt ^–5/2 long-time tail in the momentum autocorrelation function. The ring kinetic corrections to the mean field value of the diffusion coefficient are in good agreement with computer simulations.     

Structure and equilibrium optical properties of liquid CS2

Equilibrium optical properties of liquid carbon disulphide (CS₂), i.e. its refractive index, Kerr constant and depolarized light scattering intensity are calculated using two models of optical response of the fluid. The first one, the point polarizability approximation (PPA) assumes that a point dipole, proportional to the total polarizability, is induced in each molecule. The second one, the point atomic polarizability approximation (PAPA) assumes that point dipoles are induced in individual atomic sites.

The symmetry components of the intermolecular pair distribution function needed to calculate optical properties of the fluid are obtained by Monte Carlo computer simulation on a hard triatomic model of CS₂ as well as by two approximate approaches using this same model. The approximations are both based on the use of the site superposition approximation (SSA) for the intermolecular pair distribution function. In the first approach, the SSA pair distribution is obtained using the Monte Carlo site-site functions and in the second using the site-site functions calculated using the reference interaction site model (RISM) equations.

Extensive comparisons are carried out between the Monte Carlo results and the two approximations in order to examine the influence of the SSA and the RISM equations on optical properties of CS₂. We conclude that, while these approximations, especially the SSA, have a substantial effect on individual symmetry components of the pair distribution, they predict measurable optical properties with satisfactory accuracy.     

Imaging and multiple scattering through media containing optically active particles

Abstract

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Spectroscopic manifestations of phase changes in CaAr n clusters: finite size effects

The finite temperature optical spectroscopy of CaAr_n clusters in the range 6 n 146 is investigated using a Diatomics-In-Molecule (DIM) Hamiltonian and classical parallel tempering Monte Carlo simulations. The absorption spectrum is calculated in the vertical approximation at various temperatures between 2 K and 50 K. Several typical situations are reported. CaAr₆ shows a strong thermal broadening and shift of the spectral lines, possibly associated with isomerization. CaAr₁₃ only shows some broadening. CaAr₃₇ exhibits features corresponding to coexisting isomers at low temperature. Finally, the abrupt changes in the absorption spectrum in CaAr₁₄₆ at about 20 K are indicative of surface diffusion.