Inverse Monte Carlo Method Research Articles

Macroion shielding and state-dependent pair potentials in colloidal suspensions

We determine radial distribution functions for charge-stabilized colloidalsuspensions for various volume fractions. By means of two independent inversionroutines based on (i) the Ornstein–Zernike equation and (ii) the inverse MonteCarlo method, we extract effective colloid–colloid pair potentials from thedistribution functions. Working at a fixed salinity, these potentials would notdepend on the colloid density if the interactions between the colloids were purelypairwise additive. Our potentials however show a density dependence; agreementwith the Yukawa form of DLVO (Derjaguin–Landau–Verwey–Overbeek) theoryis found only at low densities, but not at high densities. Such a statedependence of pair potentials reveals the density-dependent impact ofmany-body terms in the total interaction energy of the system. We also performprimitive model calculations, with parameters simulating our experiment,and find qualitatively similar deviations of the effective pair potentialsfrom the Yukawa form, which thus confirms our experimental findings.Using results from a calculation of three-body interactions in colloidalsuspensions, we are able to trace the observed density dependence of the pairpotentials back to a shielding effect of the macroions. This interpretationis consistent with other experimental studies observing attractive partsin the pair potentials which were interpreted as ‘like-charge attraction’.Our results, however, suggest that this attraction is a many-body effect.

X-ray study of the short-range order structure in Cu–24.3 at.% Mn alloy

The diffuse X-ray scattering from a single crystal of Cu–24.3 at.% Mn aged within the fcc phase at 770 K was measured at room temperature. Diffuse peaks were found at 2 n 1+0.2, 2 n 2+0.2, 0 and equivalent positions ( n 1 and n 2 are integers) in reciprocal space. The Warren–Cowley short-range order parameters were derived from the separated short-range order scattering and used to generate the corresponding local atomic arrangements on a computer. The generated arrangements indicated that Mn atoms form clusters. A set of effective pair interaction energies obtained using an inverse Monte Carlo method showed that the interaction between the first nearest neighbors mainly affects the clustering of like atoms.

Experimental and numerical study of the colour appearance of tattoo models.

The colour of tattooed skin has been predicted by a Monte Carlo method based on the optical coefficient spectra of the skin and tattoo dyes. Slices of pig skin, a tattoo phantom and skin phantoms with different thickness were prepared, and their reflectance and transmittance spectra were measured using an integrating sphere at wavelengths varying from 400nm to 700nm. The absorption and scattering coefficient spectra of skin phantoms, pig skins and the tattoo phantom were each calculated using the inverse Monte Carlo method. The skin phantoms and pig skins were overlaid on the tattoo phantom, and the reflectance spectra of the two-layered structures were measured. The reflectance spectra of the two-layered structures were calculated from the optical coefficient spectra using the Monte Carlo method. They agreed well with the measured spectra. The colour differences between the calculated and measured spectra were also evaluated by the L*a*b* colour space distances and showed good agreement, with 3.49 for the skin phantoms and 8.27 for the pig skins.

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.

A Monte Carlo-tuned model of the flow in the NorthGRIP area

AbstractThe North Greenland Icecore Project (NorthGRIP) drill site was chosen in order to obtain a good Eemian record. At the present depth, 3001 m, the Eemian interstadial has yet to be seen. Clearly the flow in this area is poorly understood and needs further investigation. After a review of specific features of the bottom topography, it is believed that the geology changes along the flowline. In order to investigate whether this explains the observed age–depth relationship at NorthGRIP, the inverse Monte Carlo method has been applied to a simple model. the inversion reveals that the main reason no Eemian is observed is a high basal melt rate (2.7 mma–1). the melting is a consequence of a higher geothermal heat flux than the expected 51 mWm–2 of the Precambrian shield. from our analyses it is concluded that the geothermal heat flux at NorthGRIP is 98 mWm–2.The high basal melt rate also gives rise to sliding at the bed. In addition to these results, an accumulation model has been established specifically for NorthGRIP. These results are essential for further modelling of the NorthGRIP flow and depth–age relationship.

Infrared Yang–Mills theory as a spin system. A lattice approach

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants are suggested. A universality of the effective spin field action is also discussed.

Analysis of cation distribution in the octahedral sheet of dioctahedral 2:1 phyllosilicates by using inverse Monte Carlo methods

An inverse Monte Carlo (MC) method was developed to determine the distribution of octahedral cations (Al3+, Fe3+, and Mg2+) in bentonite illite–smectite (I–S) samples (dioctahedral 2:1 phyllosilicates) using FT–IR and 27Al MAS NMR spectroscopies. FT–IR allows determination of the nature and proportion of different cation pairs bound to OH groups measuring the intensities of OH-bending bands. 27Al MAS NMR data provide information about cation configuration because 27Al MAS NMR intensity depends on Fe distribution. MC calculations based on FT–IR data alone show Fe segregation by short-range ordering (Fe clusters within 9 to 15 A from a given Fe atom). Fe segregation increases with illite proportion. MC calculations based on IR and 27Al NMR simultaneously yield similar configurations in which Fe clusters are smaller. The latter calculations fail to build appropriate cation distributions for those samples with higher number of illite layers and significant Fe content, which is indicative of long-range Fe ordering that cannot be detected by FT–IR and 27Al MAS NMR. The proportion of Mg–Mg pairs is negligible in all samples, and calculations, in which the number of Mg atoms, as second neighbours, is minimised, create appropriate configurations.

Lattice instanton action from 3D SU(2) Georgi-Glashow model

3D Georgi-Glashow model is studied on the lattice in the London limit in an infrared but an intermediate region before the screening appears. Abelian and instanton dominances are observed after abelian projections in a unitary gauge and roughly in the maximally abelian gauge. Using an inverse Monte-Carlo method, we determine an effective instanton action in both gauges. When we restrict ourselves to some regions of parameters $\beta$ and $\kappa$, we obtain an almost perfect instanton action, performing a block-spin transformation on the dual lattice. It takes a form of a Coulomb gas and reproduces fairly well the string tension obtained analytically by Polyakov. The almost perfect actions in both gauges look the same in the infrared region, which suggests gauge independence.

313 皮膚下血液層ヘモグロビン量の分光学的推定に関する基礎検討(OS6-3 生体計測)(OS6 スポーツと医療福祉工学)

To estimate the condition of hemoglobin in the local blood layer under the human skin, we propose an inverse Monte Carlo method using spectral reflectances obtained from the skin surface. To investigate fundamental possibility, we employed as a sample the spectral reflectance generated by the computer simulation for a multi-layered skin tissue model. We confirmed from computational results that the concentration of hemoglobin and the oxygen saturation might be successfully estimated in the near infrared range.

Aerosol properties from spectral extinction and backscatter estimated by an inverse Monte Carlo method

The feasibility of using a generalized stochastic inversion methodology to estimate aerosol size distributions accurately by use of spectral extinction, backscatter data, or both is examined. The stochastic method used, inverse Monte Carlo (IMC), is verified with both simulated and experimental data from aerosols composed of spherical dielectrics with a known refractive index. Various levels of noise are superimposed on the data such that the effect of noise on the stability and results of inversion can be determined. Computational results show that the application of the IMC technique to inversion of spectral extinction or backscatter data or both can produce good estimates of aerosol size distributions. Specifically, for inversions for which both spectral extinction and backscatter data are used, the IMC technique was extremely accurate in determining particle size distributions well outside the wavelength range. Also, the IMC inversion results proved to be stable and accurate even when the data had significant noise, with a signal-to-noise ratio of 3.

Determination of effective pair potentials from ab initio simulations: application to liquid water

We present a novel approach to construct pairwise site–site intermolecular interaction potentials from the results of ab initio quantum-mechanical modeling to be used in classical molecular simulations. In the present application, as a first step, we have carried out ab initio Car–Parrinello molecular dynamics (MD) simulations of liquid water to calculate the radial distribution functions (RDF) between all the pairs of nuclei. A second step involves use of the inverse Monte Carlo method, recently developed by us [Phys. Rev. E 52 (1995) 3730], to construct a full set of site–site interaction potentials from the ab initio RDFs. The resulting three-site SPC-like water model, which reproduces the liquid structure obtained in the Car–Parrinello MD simulations, can be used as a potential function in classical molecular simulations. We have also found that there exist no pair potential for a rigid three-site water model which exactly satisfy the experimental water RDFs.

A new seismic velocity model for the Moon from a Monte Carlo inversion of the Apollo lunar seismic data

A reanalysis of the Apollo lunar seismic data and the subsequent application of an inverse Monte Carlo method to P and S‐wave arrival times has resulted in a more detailed lunar velocity structure than previously obtainable. The velocity is seen to increase from the surface down to the base of the crust at 45±5 km depth. The results furthermore indicate a constant velocity upper mantle extending to 560±15 km km depth, separated from a more complex high velocity middle mantle by an increase in velocity of 1.0 km/s. In addition, the moonquake locations have been improved. The shallow moonquakes are found to be located in the depth range 50–220 km. The majority of deep moonquakes are concentrated in the depth range 850–1000 km with an apparently rather sharp lower boundary.

Effective potentials for ion–DNA interactions

Effective, solvent-mediated interaction potentials between alkali metal ions (Li+, Na+, K+, and Cs+) and selected sites on the DNA surface are derived from molecular dynamics simulations data. The effective potentials reproduce the corresponding ion–ion and ion–DNA radial distribution functions, obtained in the detailed full-atomistic molecular dynamics simulations. In this work, we have first calculated the ion–DNA and ion–ion radial distribution functions from molecular dynamics simulations of a periodic fragment of double-helix DNA in ionic aqueous solution. Thereafter we applied the inverse Monte Carlo method, previously suggested by us [Phys. Rev. E 52, 3730 (1995)], to derive the effective interaction potentials. Finally, a considerably larger DNA fragment was constructed together with its surrounding solvent environment and Monte Carlo simulations were performed to calculate the ion distributions and the relative binding affinities of different alkali ions to DNA. The results agree well with available experimental data.

Inversion of particle-size distribution from angular light-scattering data with genetic algorithms

A stochastic inverse technique based on a genetic algorithm (GA) to invert particle-size distribution from angular light-scattering data is developed. This inverse technique is independent of any given a priori information of particle-size distribution. Numerical tests show that this technique can be successfully applied to inverse problems with high stability in the presence of random noise and low susceptibility to the shape of distributions. It has also been shown that the GA-based inverse technique is more efficient in use of computing time than the inverse Monte Carlo method recently developed by Ligon et al. [Appl. Opt. 35, 4297 (1996)].

The type of order in Cu–10 at.% Au—evidence from the diffuse scattering of X-rays

In a recent publication, Kuhlmann et al. ( Acta mater., 1997, 45, 3319) claimed Cu–10 at.% Au to be long-range ordered at temperatures above 473 K and as high as 723 K. This is in contrast to the generally accepted phase diagram where this region is attributed to the range of solid solutions. To clarify this problem, a three-dimensional diffuse X-ray scattering experiment was performed at room temperature on a Cu–10 at.% Au single crystal aged at 573 K. The Warren–Cowley short-range order parameters derived from this experiment show conclusively that only short-range order is present. Effective pair interaction parameters determined by the inverse Monte-Carlo method are somewhat different from those obtained for Cu–25 at.% Au in the short-range ordered state.

High-Resolution Structural Study of an Electrical Double Layer by Neutron Diffraction

We present the first high-resolution study of the aqueous structure developed in the electrical double layer region of a colloidal clay system. Our samples were highly oriented vermiculite gels containing isotopically labelled propylammonium counterions: C3H7NH3+ and C3D7NH3+. The gels were prepared with a clay layer spacing of 43.6 Å. Time-of-flight neutron diffraction was used to measure the scattering intensity normal to the clay surfaces, from which the neutron scattering density was refined by an inverse Monte Carlo method. Diffraction data from two isotopically distinct samples were fitted simultaneously, thereby allowing us to locate the labelled propyl groups unambiguously. Our results show that the counterions in our vermiculite gels are separated from the clay surfaces by two layers of partially ordered water molecules. In fact, the counterion density reaches a maximum at the center of the interlayer region. The measured structure is therefore at odds with traditional primitive models of the electrical double layer. Such models place the maximum of the counterion density adjacent to the vermiculite clay surfaces, in the so-called Stern layer.

Studies of epitaxial Fe0.5Pd0.5 thin films by x-ray diffraction and polarized fluorescence absorption spectroscopy

The long range order as well as the short range order of magnetic Fe0.5Pd0.5 epitaxial thin films was studied. These alloys were elaborated by five methods: codeposition at room temperature, codeposition at room temperature followed by a 700 K annealing, codeposition at 600 K, and alternating deposit of pure Fe and pure Pd atomic layers at room temperature controlled either by the deposition time or by the reflection high energy electron diffraction oscillations. These samples were studied by x-ray diffraction (XRD) and polarized fluorescence extended x-ray absorption fine structure (EXAFS). These (001) oriented thin films have a face-centered tetragonal structure flattened along the growth direction. For each sample, a simulation program based on an inverse Monte Carlo method was used to build an atomic configuration satisfying both the long range order obtained by the XRD study and the directional short range order obtained by the EXAFS study. The best ordered sample (both on a long range and a short range scale) is the one codeposited at 600 K.

Collective Dynamics in Quasibidimensional Colloidal Suspensions

We report the direct measurement by video microscopy of the Van Hove function of quasi-two-dimensional colloidal suspensions. Under these conditions of confinement, the effective interparticlepotential exhibits an intermediate range attractive component. This is obtained by deconvolutingthe measured pair correlation function using an inverse Monte Carlo method. The experimentaldynamic behavior is well represented by a Brownian dynamics simulation, performed using theexperimental pair potential and an effective quasi-two-dimensional short-time diffusion coefficient.[S0031-9007(98)06595-8]

Determination of aerosol parameters from light-scattering data using an inverse Monte Carlo technique

An inverse, Monte Carlo (IMC) technique is developed to solve the electromagnetic inverse-scattering problem from generally complex distributions of dielectric particles. One can verify the technique using simulated scattering data from aerosols composed of spherical dielectrics. The IMC method is found to give accurate inversion results even when the data have a signal-to-noise ratio to as low as 3:1.