Computation, Volume 3, Issue 4 (December 2015) – 12 articles , Pages 509-713

A key parameter in population genetics is the scaled mutation rate θ = 4 N μ , where N is the effective haploid population size and μ is the mutation rate per haplotype per generation. While exact likelihood inference is notoriously difficult in population genetics, we propose a novel approach to compute a first order accurate likelihood of θ that is based on dynamic programming under the infinite sites model without recombination. The parameter θ may be either constant, i.e., time-independent, or time-dependent, which allows for changes of demography and deviations from neutral equilibrium. For time-independent θ, the performance is compared to the approach in Griffiths and Tavaré’s work “Simulating Probability Distributions in the Coalescent” (Theor. Popul. Biol. 1994, 46, 131–159) that is based on importance sampling and implemented in the “genetree” program. Roughly, the proposed method is computationally fast when n × θ < 100 , where n is the sample size. For time-dependent θ ( t ) , we analyze a simple demographic model with a single change in θ ( t ) . In this case, the ancestral and current θ need to be estimated, as well as the time of change. To our knowledge, this is the first accurate computation of a likelihood in the infinite sites model with non-equilibrium demography. Full article

The present work aims to study the adsorption behavior and dynamical properties of CH₄ in clay slit pore with or without cation exchange structures at sizes of 1.0 nm–4.0 nm using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) methods. The adsorption isotherms of CH₄ have been investigated by GCMC simulations at different temperatures and various pore sizes. In the montmorillonite (MMT) clays without a cation exchange structure, from the density profile, we find the molecules preferentially adsorb onto the surface, and only an obvious single layer was observed. The general trend within slit pores is that with increasing pore width, the adsorbed amount will increase. However, the larger pores exhibit lower excess density and the smaller pores exhibit higher excess density. The preloaded water will reduce CH₄ sorption. The in plane self-diffusion coefficient of CH₄ which is investigated by MD simulations combined with Einstein fluid equation increases rapidly with the pore size increasing at low pressure. Under these given conditions, the effect of temperature has little influence on the in-plane self-diffusion coefficient. In the MMT clays with cation exchange structure, cation exchange has little effect on CH₄ adsorption and self-diffusion. Full article

In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation. Full article

The real and imaginary parts of the complex refractive index of Si_xN_yH_z have been calculated from first principles. Optical spectra for reflectivity, absorption coefficient, energy-loss function (ELF), and refractive index were obtained. The results for Si₃N₄ are in agreement with the available theoretical and experimental results. To understand the electron energy loss mechanism in Si-rich silicon nitride, the influence of the Si/N ratio, the positions of the access Si atoms, and H in and on the surface of the ELF have been investigated. It has been found that all defects, such as dangling bonds in the bulk and surfaces, increase the intensity of the ELF in the low energy range (below 10 eV). H in the bulk and on the surface has a healing effect, which can reduce the intensity of the loss peaks by saturating the dangling bonds. Electronic structure analysis has confirmed the origin of the changes in the ELF. It has demonstrated that the changes in ELF are not only affected by the composition but also by the microstructures of the materials. The results can be used to tailor the optical properties, in this case the ELF of Si-rich Si₃N₄, which is essential for secondary electron emission applications. Full article

Ionization potentials (IPs) and electron affinities (EAs) are important quantities input into most models for calculating the open-circuit voltage (V_oc) of organic solar cells. We assess the semi-empirical density-functional tight-binding (DFTB) method with the third-order self-consistent charge (SCC) correction and the 3ob parameter set (the third-order DFTB (DFTB3) organic and biochemistry parameter set) against experiments (for smaller molecules) and against first-principles GW (Green’s function, G, times the screened potential, W) calculations (for larger molecules of interest in organic electronics) for the calculation of IPs and EAs. Since GW calculations are relatively new for molecules of this size, we have also taken care to validate these calculations against experiments. As expected, DFTB is found to behave very much like density-functional theory (DFT), but with some loss of accuracy in predicting IPs and EAs. For small molecules, the best results were found with ΔSCF (Δ self-consistent field) SCC-DFTB calculations for first IPs (good to ± 0.649 eV). When considering several IPs of the same molecule, it is convenient to use the negative of the orbital energies (which we refer to as Koopmans’ theorem (KT) IPs) as an indication of trends. Linear regression analysis shows that KT SCC-DFTB IPs are nearly as accurate as ΔSCF SCC-DFTB eigenvalues (± 0.852 eV for first IPs, but ± 0.706 eV for all of the IPs considered here) for small molecules. For larger molecules, SCC-DFTB was also the ideal choice with IP/EA errors of ± 0.489/0.740 eV from ΔSCF calculations and of ± 0.326/0.458 eV from (KT) orbital energies. Interestingly, the linear least squares fit for the KT IPs of the larger molecules also proves to have good predictive value for the lower energy KT IPs of smaller molecules, with significant deviations appearing only for IPs of 15–20 eV or larger. We believe that this quantitative analysis of errors in SCC-DFTB IPs and EAs may be of interest to other researchers interested in DFTB investigation of large and complex problems, such as those encountered in organic electronics. Full article

Two-dimensional (2D) pore-scale models have successfully simulated microfluidic experiments of aqueous-phase flow with mixing-controlled reactions in devices with small aperture. A standard 2D model is not generally appropriate when the presence of mineral precipitate or biomass creates complex and irregular three-dimensional (3D) pore geometries. We modify the 2D lattice Boltzmann method (LBM) to incorporate viscous drag from the top and bottom microfluidic device (micromodel) surfaces, typically excluded in a 2D model. Viscous drag from these surfaces can be approximated by uniformly scaling a steady-state 2D velocity field at low Reynolds number. We demonstrate increased accuracy by approximating the viscous drag with an analytically-derived body force which assumes a local parabolic velocity profile across the micromodel depth. Accuracy of the generated 2D velocity field and simulation permeability have not been evaluated in geometries with variable aperture. We obtain permeabilities within approximately 10% error and accurate streamlines from the proposed 2D method relative to results obtained from 3D simulations. In addition, the proposed method requires a CPU run time approximately 40 times less than a standard 3D method, representing a significant computational benefit for permeability calculations. Full article

Game theory and its quantum extension apply in numerous fields that affect people’s social, political, and economical life. Physical limits imposed by the current technology used in computing architectures (e.g., circuit size) give rise to the need for novel mechanisms, such as quantum inspired computation. Elements from quantum computation and mechanics combined with game-theoretic aspects of computing could open new pathways towards the future technological era. This paper associates dominant strategies of repeated quantum games with quantum automata that recognize infinite periodic inputs. As a reference, we used the PQ-PENNY quantum game where the quantum strategy outplays the choice of pure or mixed strategy with probability 1 and therefore the associated quantum automaton accepts with probability 1. We also propose a novel game played on the evolution of an automaton, where players’ actions and strategies are also associated with periodic quantum automata. Full article

We present a comparative dispersion-corrected Density Functional Theory (DFT) and Density Functional Tight Binding (DFTB-D) study of several phases of nitrogen, including the well-known alpha, beta, and gamma phases as well as recently discovered highly energetic phases: covalently bound cubic gauche (cg) nitrogen and molecular (vdW-bound) N₈ crystals. Among several tested parametrizations of N–N interactions for DFTB, we identify only one that is suitable for modeling of all these phases. This work therefore establishes the applicability of DFTB-D to studies of phases, including highly metastable phases, of nitrogen, which will be of great use for modelling of dynamics of reactions involving these phases, which may not be practical with DFT due to large required space and time scales. We also derive a dispersion-corrected DFT (DFT-D) setup (atom-centered basis parameters and Grimme dispersion parameters) tuned for accurate description simultaneously of several nitrogen allotropes including covalently and vdW-bound crystals and including high-energy phases. Full article

Effective thermal conductivity is an important thermophysical property in the design of metal-organic framework-5 (MOF-5)-based hydrogen storage tanks. A modified thermal conductivity model is built by coupling a theoretical model with the grand canonical Monte Carlo simulation (GCMC) to predict the effect of the H₂ adsorption process on the effective thermal conductivity of a MOF-5 powder bed at pressures ranging from 0.01 MPa to 50 MPa and temperatures ranging from 273.15 K to 368.15 K. Results show that the mean pore diameter of the MOF-5 crystal decreases with an increase in pressure and increases with an increase in temperature. The thermal conductivity of the adsorbed H₂ increases with an increased amount of H₂ adsorption. The effective thermal conductivity of the MOF-5 crystal is significantly enhanced by the H₂ adsorption at high pressure and low temperature. The effective thermal conductivity of the MOF-5 powder bed increases with an increase in pressure and remains nearly unchanged with an increase in temperature. The thermal conductivity of the MOF-5 powder bed increases linearly with the decreased porosity and increased thermal conductivity of the skeleton of the MOF-5 crystal. The variation in the effective thermal conductivities of the MOF-5 crystals and bed mainly results from the thermal conductivities of the gaseous and adsorption phases. Full article

Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM) is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM) is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media. Full article

The irregular distribution of prime numbers amongst the integers has found multiple uses, from engineering applications of cryptography to quantum theory. The degree to which this distribution can be predicted thus has become a subject of current interest. Here, we present a computational analysis of the deviations between the actual positions of the prime numbers and their predicted positions from Riemann’s counting formula, focused on the variance function of these deviations from sequential enumerative bins. We show empirically that these deviations can be described by a class of probabilistic models known as the Tweedie exponential dispersion models that are characterized by a power law relationship between the variance and the mean, known by biologists as Taylor’s power law and by engineers as fluctuation scaling. This power law behavior of the prime number deviations is remarkable in that the same behavior has been found within the distribution of genes and single nucleotide polymorphisms (SNPs) within the human genome, the distribution of animals and plants within their habitats, as well as within many other biological and physical processes. We explain the common features of this behavior through a statistical convergence effect related to the central limit theorem that also generates 1/f noise. Full article

A detailed Computational Fluid Dynamics (CFD) and experimental investigation into characterizing the fluid flow and thermal profiles in a wind tunnel was carried out, highlighting the effect of progressive heating on the non-uniformity flow profile of air. Using controllable electrical heating elements, the operating temperatures in the test-section were gradually increased in order to determine its influence on the subsequent velocity and thermal profiles found inside the test-section. The numerical study was carried out using CFD FLUENT code, alongside validating the experimental results. Good correlation was observed as the comparison yielded a mean error of 6.4% for the air velocity parameter and 2.3% for the air temperature parameter between the two techniques. The good correlation established between the numerically predicted and experimentally tested results identified broad scope for using the advanced computational capabilities of CFD applicable to the thermal modeling of wind tunnels. For a constant temperature process, the non-uniformity and turbulence intensity in the test section was 0.9% and 0.5%, which is under the recommended guidelines for wind tunnels. The findings revealed that the increase in temperature from 20 °C to 50 °C reduced the velocity by 15.2% inside the test section. Full article