Self-diffusion in submonolayer colloidal fluids near a wall

Theoretical expressions are developed to describe self-diffusion in submonolayer colloidal fluids that require only equilibrium structural information as input. Submonolayer colloidal fluids are defined for the purpose of this work to occur when gravity confines colloids near a planar wall surface so that they behave thermodynamically as two dimensional fluids. Expressions for self-diffusion are generalized to consider different colloid and surface interaction potentials and interfacial concentrations from infinite dilution to near fluid-solid coexistence. The accuracy of these expressions is demonstrated by comparing self-diffusion coefficients predicted from Monte Carlo simulated equilibrium particle configurations with standard measures of self-diffusion evaluated from Stokesian Dynamics simulated particle trajectories. It is shown that diffusivities predicted for simulated equilibrium fluid structures via multibody hydrodynamic resistance tensors and particle distribution functions display excellent agreement with values computed from mean squared displacements and autocorrelation functions of simulated tracer particles. Results are obtained for short and long time self-diffusion both parallel and normal to underlying planar wall surfaces in fluids composed of particles having either repulsive electrostatic or attractive van der Waals interactions. The demonstrated accuracy of these expressions for self-diffusion should allow their direct application to experiments involving submonolayer colloidal fluids having a range of interaction potentials and interfacial concentrations.     

Gamma distribution model to provide a direct assessment of the overall quality of quantum Monte Carlo-generated electron distributions

Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.     

Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.     

Brownian diffusion of aerosol particles in slit-like channel with moving gas for uniform, point, and segment sources positioned at channel inlet

Analytical solutions to the equations of Brownian diffusion were derived to depict the outlet distributions of local concentrations of particles penetrating through a slit-like channel for both the spatially uniform and non-uniform sources of particles at the channel inlet. The “point” and “segment” sources positioned at the inlet form the non-uniform entering concentrations. The sources could emit particles in either the single-pulse or pulse-periodic (steady-state) operating mode. The solutions were obtained for both the laminar gas stream with parabolic-velocity profile (the Poiseuille flow) and the stream with plane profile (the slug flow). The physical and mathematical features of the Brownian diffusion were considered with respect to the pulse and the pulse-periodic (steady-state) point and segment emissions of particles in the Poiseuille flow. The Monte Carlo simulation of the Brownian motion of particles was performed to compare the analytical and the simulated distributions of particles for the point source.     

Behavior of rodlike polyelectrolytes near an oppositely charged surface

The behavior of highly charged short rodlike polyelectrolytes near oppositely charged planar surfaces is investigated by means of Monte Carlo simulations. A detailed microstructural study, including monomer and fluid charge distributions and chain orientation, is provided. The influence of chain length, substrate's surface-charge density, and image forces is considered. Due to the lower chain entropy (compared to flexible chains), our simulation data show that rodlike polyelectrolytes can, in general, better adsorb than flexible ones do. Nonetheless, at low substrate-dielectric constant, it is found that repulsive image forces tend to significantly reduce this discrepancy.     

The density distributions of the counterions and the coions confined in two similarly charged plates

By using the field-theoretic method, we established a unified systematic formulation of a model of counterions and coions confined in two similarly charged plates, and calculated the density distributions of counterions and coions with various coupling parameters by the two methods: Poisson-Boltzmann (PB) approach and the strong coupling (SC) theory, respectively. We also performed Monte Carlo simulations, and obtained the density distributions of counterions and coions with several different coupling parameters. Comparing our theoretical results with those from Monte Carlo simulation, we find that the PB approach is valid when the coupling parameter Xi is smaller than 1, but, as Xi > or = 1, the results by the PB approach deviate from the corresponding Monte Carlo simulation data, and the deviation gets larger with the coupling parameter increasing. This shows that the PB approach is completely invalid when the coupling parameter is equal to 1 or larger than 1. For the latter case, the development trend of the distribution curve calculated by SC theory agrees with that from Monte Carlo simulation as the coupling parameter increases. This demonstrates that the SC theory can give a qualitative available explanation on the density distribution of the counterions in the system in which the coupling parameters are strictly confined.     

Statistical mechanics of bilayer membrane with a fixed projected area

The equilibrium and fluctuation methods for determining the surface tension, sigma, and bending modulus, kappa, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation method the elastic coefficients sigma and kappa are measured from the amplitude of thermal fluctuations of the planar membrane, while in the equilibrium method the free energy required to deform the membrane is considered. The latter approach is used to derive new expressions for sigma and kappa (as well as for the saddle-splay modulus), which relate them to the pair-interactions between the amphiphiles forming the membrane. We use linear response theory to argue that the two routes lead to similar values for sigma and kappa. This argument is confirmed by Monte Carlo simulations of a model membrane whose elastic coefficients are calculated using both methods.     

Boundary conditions in local electrostatics algorithms

We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We first show how to implement constant-potential, Dirichlet boundary conditions by introducing extra Monte Carlo moves to the algorithm. Second, we show the interest of the algorithm for studying systems which require anisotropic electrostatic boundary conditions for simulating planar geometries such as membranes.     

Evaluating changes of writhe in computer simulations of supercoiled DNA

We compute changes in the writhe of a polygonal space curve when one of the vertices is displaced. The resulting expressions can be used in simulations of supercoiled DNA. For Brownian dynamics simulations, the expressions can be used to eliminate the explicit twisting degree of freedom. For Monte Carlo simulations, they can be used in fast local moves. Preliminary Monte Carlo simulations using only such fast local moves show that these can be used to efficiently simulate small DNA supercoils.     

Distribution functions for filaments under tension

We develop a biased Monte Carlo simulation technique to measure the distribution functions of the extension and the end-to-end distance of fluctuating filaments stretched by external force. The method is applicable for arbitrary ratio of the persistence length to the contour length and for arbitrary forces, and also for the case of steric constraints, such as an external wall. The fundamental idea underlying the algorithm is to account explicitly for the length-scale dependence of the effective elastic moduli. We find that orientational fluctuations and wall effects produce non-Gaussian distributions for nearly rigid filaments in the small to intermediate force regime. The simulation results are tested against analytic expressions for the force-extension curves, both in the semiflexible and nearly stiff limits.     

Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.     

单链DNA在受限环境中伸展的Monte Carlo模拟

Stretching and relaxation of a single DNA molecule tethered in a specially designed thin slit were studied using Monte Carlo simulation combined with bond fluctuation method. It was found that the extension and relaxation of the single DNA molecule are greatly affected by the confined environment. If the extent of the confined environment is increased by decreasing the distance between the two planar surfaces of the slit, the extension of the single DNA molecule increases, due to the screening of the hydrodynamic interaction of DNA segments by the planar surfaces of the slit. The relaxation of the single DNA molecule in different confined environments verifies this assumption completely. The correlation between the end-to-end separation and flow velocity obtained by Monte Carlo simulation is in good agreement with either the experimental results or theoretical consideration reported previously.     

An atlas of selected beta-ray spectra and depth-dose distributions in lithium fluoride and soft tissue generated by a fast Monte Carlo-based sampling method

A method to generate depth-dose distributions due to beta radiation in LiF and soft tissue is proposed. In this method, the EGS4 Monte Carlo radiation transport code is initially used to generate a library of monoenergetic electron depth-dose distributions in the material for electron energies in the range of 10 keV to 5 MeV in 10 keV increments. A polynomial least-squares fit is applied to each distribution. In addition, a theoretical model is developed to generate beta-ray energy spectra of selected radionuclides. A standard Monte Carlo random sampling technique is then employed to sample the spectra and generate the depth-dose distributions in LiF and soft tissue. The proposed method has an advantage over more traditional methods in that the actual radiation transport in the media is performed only once for a set of monoenergetic cases and the beta depth-dose distributions are easily generated by sampling this previously-acquired database in a matter of minutes. This method therefore reduces the demand on computer resources and time. The method can be used to calculate depth-dose distribution due to any beta-emitting nuclide or combination of nuclides with up to ten beta components.     

A variational principle in Wigner phase-space with applications to statistical mechanics

We consider the Dirac-Frenkel variational principle in Wigner phase-space and apply it to the Wigner-Liouville equation for both imaginary and real time dynamical problems. The variational principle allows us to deduce the optimal time-evolution of the parameter-dependent Wigner distribution. It is shown that the variational principle can be formulated alternatively as a "principle of least action." Several low-dimensional problems are considered. In imaginary time, high-temperature classical distributions are "cooled" to arrive at low-temperature quantum Wigner distributions whereas in real time, the coherent dynamics of a particle in a double well is considered. Especially appealing is the relative ease at which Feynman's path integral centroid variable can be incorporated as a variational parameter. This is done by splitting the high-temperature Boltzmann distribution into exact local centroid constrained distributions, which are thereafter cooled using the variational principle. The local distributions are sampled by Metropolis Monte Carlo by performing a random walk in the centroid variable. The combination of a Monte Carlo and a variational procedure enables the study of quantum effects in low-temperature many-body systems, via a method that can be systematically improved.     

Super-Monte Carlo: A photon/electron dose calculation algorithm for radiotherapy

Super-Monte Carlo (SMC) is a method of dose calculation for radiotherapy which combines both analytical calculations and Monte Carlo electron transport. Analytical calculations are used where possible, such as the determination of photon interaction density, to decrease computation time. A Monte Carlo method is used for the electron transport in order to obtain high accuracy of results. To further speed computation, Monte Carlo is used once only, to form an electron track kernel (etk). The etk is a dataset containing the lengths and energy deposition of each step of a number of electron tracks. The etk is transported from each incident particle interaction site, from which the dose is calculated. Dose distributions calculated in heterogeneous media show SMC results similar to those of Monte Carlo. For the same statistical uncertainty, SMC takes an order of magnitude less computation time than a full Monte Carlo simulation. SMC has only been implemented for photons and electrons, however the same basic method could be used for the transport of other particles. Current development includes the optimisation of the etks and the code in order to decrease computation time, and also the inclusion of SMC onto a clinical planning system.     

The behavior of the form factor in two dimensions for linear polymers in different regimes

Off-lattice Monte Carlo simulations employing the PIVOT algorithm are used to generate ideal and excluded volume linear polymers in two dimensions. The form factor at small and large wave vectors is calculated from the resulting configurations and compared to the exact equation for ideal chains and to both scaling and renormalization group predictions for excluded volume chains. It is found that using the des Cloizeaux form for the distance distribution function in an analytic calculation of the form factor leads to close agreement with the Monte Carlo data and that simple expressions for both the small and large wave vector expansions reproduce the essential features of the form factor.     

Molecular weight distribution of A_2-B_2 type condensation polymers in the presence of capping monomer C

The molecular weight distribution of A2-B2 type condensation polymers in the presence of capping monomer C has been derived with statistical calculation and Monte Carlo simulation methods. The Monte Carlo simulation result agrees with that of statistical calculation. The number distribution function and weight distribution function of seven types of molecules existing in A2-B2-C system have been obtained. The effect of reactivity of capping monomer C on these distributions are discussed.     

Monte Carlo Simulations on Nanoparticles in Elastomers. Effects of the Particles on the Dimensions of the Polymer Chains and the Mechanical Properties of the Networks

Summary: Reinforcement of elastomers is modeled using Monte Carlo simulations on rotational isomeric state chains, to characterize their spatial configurations in the vicinity of filler particles. The resulting filler-perturbed distributions of the chain end-to-end distances are in agreement with experimental results gotten by neutron scattering. The use of these distributions in a standard molecular theory of rubberlike elasticity produces stress-strain isotherms for elongation that are consistent with available experimental results.     

Radionuclide ratios of90Sr/137Cs and239(240)Pu/137Cs in contaminated surface air after the Chernobyl accident in Asutria

Energy straggling in pulse height distributions of plastic scintillation counters of 4 and 10 cm in thickness was measured for 1 GeV/c pions and studied by Monte Carlo simulations. Calculated energy loss distributions are in good agreement with the experimental data and also with the prediction by the Landau straggling function.