Standard Homogeneous Model Research Articles

Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment

Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.

An Assessment of Computational Fluid Dynamics Cavitation Models Using Bubble Growth Theory and Bubble Transport Modeling

This effort investigates advancing cavitation modeling relevant to computational fluid dynamics (CFD) through two strategies. The first aims to reformulate the cavitation models and the second explores adding liquid–vapor slippage effects. The first aspect of the paper revisits cavitation model formulations with respect to the Rayleigh–Plesset equation (RPE). The present approach reformulates the cavitation model using analytic solutions to the RPE. The benefit of this reformulation is displayed by maintaining model sensitivities similar to RPE, whereas the standard models fail these tests. In addition, the model approach is extended beyond standard homogeneous models, to a two-fluid modeling framework that explicitly models the slippage between cavitation bubbles and the liquid. The results indicate a significant impact of slip on the predicted cavitation solution, suggesting that the inclusion of such modeling can potentially improve CFD cavitation models. Overall, the results of this effort point to various aspects that may be considered in future CFD-modeling efforts with the goal of improving the model accuracy and reducing computational time.

Influence of heterogeneities introduced into the modelling of a ring compression test

This paper analyses the influence of heterogeneities introduced into the constitutive model of Aluminium alloy 6060. Two types of modelling are hereby presented: a standard phenomenological homogeneous model and a compartmentalized hybrid model, the formulation of which is based on the physical phenomena underlying plasticity. The mechanical parameters needed to establish such models are determined by two different experimental tests: a uniaxial tensile test and a ring compression test. The ability of such models to simulate a forming operation that differs from the operation used to determine their parameters will then be discussed.

Modelling Population Dynamics in Realistic Landscapes with Linear Elements: A Mechanistic-Statistical Reaction-Diffusion Approach.

We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid “2D/1D model”, i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.

The galaxy luminosity function and the Local Hole

Whitbourn & Shanks (2014) have reported evidence for a local void underdense by ~15% extending to 150-300h-1Mpc around our position in the Southern Galactic Cap (SGC). Assuming a local luminosity function they modelled K- and r-limited number counts and redshift distributions in the 6dFGS/2MASS and SDSS redshift surveys and derived normalised n(z) ratios relative to the standard homogeneous cosmological model. Here we test further these results using maximum likelihood techniques that solve for the galaxy density distributions and the galaxy luminosity function simultaneously. We confirm the results from the previous analysis in terms of the number density distributions, indicating that our detection of the 'Local Hole' in the SGC is robust to the assumption of either our previous, or newly estimated, luminosity functions. However, there are discrepancies with previously published K and r band luminosity functions. In particular the r-band luminosity function has a steeper faint end slope than the r0.1 results of Blanton et al. (2003) but is consistent with the r0.1 results of Montero-Dorta & Prada (2009); Loveday et al. (2012).

Modeling and Experimental Validation of Pt Loading and Electrode Composition Effects in PEM Fuel Cells

A low platinum loading model, considering both the platinum loading and platinum particle distribution on carbon support, is developed. This model takes into account the interfacial transport resistances at ionomer, water film and Pt particle surfaces in order to capture the effects of Pt loading and electrode composition on fuel cell performance. After coupling this electrode model into a comprehensive PEM fuel cell model, i.e. M2 model, experimental validation is performed for a wide range of Pt loading from 0.2 to 0.025 mg/cm2 for two electrode compositions with and without carbon dilution. Good agreement between the predicted and measured polarization curves is achieved under wide-ranging operating conditions. The agglomerate size effect is also examined and it is shown that the agglomerates have virtually no effect on cell performance for agglomerate radius smaller than 150 nm. Since in realistic fuel cell catalyst layers, agglomerates may not exist, or may only exist with sizes no larger than 150 nm based on SEM observations, the present work suggests that the standard homogeneous electrode model is suitable and sufficient for analyses of transport losses in PEM fuel cell electrodes where interfacial transport resistances exist.

Genomic support for a moa-tinamou clade and adaptive morphological convergence in flightless ratites.

One of the most startling discoveries in avian molecular phylogenetics is that the volant tinamous are embedded in the flightless ratites, but this topology remains controversial because recent morphological phylogenies place tinamous as the closest relative of a monophyletic ratite clade. Here, we integrate new phylogenomic sequences from 1,448 nuclear DNA loci totaling almost 1 million bp from the extinct little bush moa, Chilean tinamou, and emu with available sequences from ostrich, elegant crested tinamou, four neognaths, and the green anole. Phylogenetic analysis using standard homogeneous models and heterogeneous models robust to common topological artifacts recovered compelling support for ratite paraphyly with the little bush moa closest to tinamous within ratites. Ratite paraphyly was further corroborated by eight independent CR1 retroposon insertions. Analysis of morphological characters reinterpreted on a 27-gene paleognath topology indicates that many characters are convergent in the ratites, probably as the result of adaptation to a cursorial life style.

A Sign of Superspreading in Tuberculosis

Molecular typing is a valuable tool for gaining insight into spread of Mycobacterium tuberculosis. Typing allows for clustering of cases whose isolates share an identical genotype, revealing epidemiologic relatedness. Observed distributions of genotypic cluster sizes of tuberculosis (TB) are highly skewed. A possible explanation for this skewness is the concept of "superspreading": a high heterogeneity in the number of secondary cases caused per infectious individual. Superspreading has been previously found for diseases such as severe acute respiratory syndrome and smallpox, where the entire transmission tree is known. So far, no method exists to relate superspreading to the distribution of genotypic cluster sizes. We quantified heterogeneity in secondary infections per infectious individual by describing this number as a negative binomial distribution. The dispersion parameter k is a measure of superspreading; standard (homogeneous) models use values of k ≥ 1, whereas small values of k imply superspreading. We estimated this negative binomial dispersion parameter for TB in the Netherlands, using the genotypic cluster size distribution for all 8330 cases of culture confirmed, pulmonary TB diagnosed between 1993 and 2007 in the Netherlands. The dispersion parameter k was estimated at 0.10 (95% confidence interval = 0.09-0.12), well in the range of values consistent with superspreading. Simulation studies showed the method reliably estimates the dispersion parameter across a range of scenarios and parameter values. Heterogeneity in the number of secondary cases caused per infectious individual is a plausible explanation for the observed skewness in genotypic cluster size distribution of TB.

In vivospatial frequency domain spectroscopy of two layer media

Monitoring of tissue blood volume and local oxygen saturation can inform the assessment of tissue health, healing, and dysfunction. These quantities can be estimated from the contribution of oxyhemoglobin and deoxyhemoglobin to the absorption spectrum of the dermis. However, estimation of blood related absorption in skin can be confounded by the strong absorption of melanin in the epidermis and epidermal thickness and pigmentation varies with anatomic location, race, gender, and degree of disease progression. Therefore, a method is desired that decouples the effect of melanin absorption in the epidermis from blood absorption in the dermis for a large range of skin types and thicknesses. A previously developed inverse method based on a neural network forward model was applied to simulated spatial frequency domain reflectance of skin for multiple wavelengths in the near infrared. It is demonstrated that the optical thickness of the epidermis and absorption and reduced scattering coefficients of the dermis can be determined independently and with minimal coupling. Then, the same inverse method was applied to reflectance measurements from a tissue simulating phantom and in vivo human skin. Oxygen saturation and total hemoglobin concentrations were estimated from the volar forearms of weakly and strongly pigmented subjects using a standard homogeneous model and the present two layer model.

Competing conventions

This paper introduces a new coordination problem for a large but finite population – The Language Game. The population is partitioned into two groups of identical agents. Each player shares a common two-action strategy set and interacts pairwise with everyone else. Both symmetric profiles are Pareto-efficient strict equilibria, but the groups rank them differently. The profile where successful coordination occurs only within-group, with each group adopting their most preferred equilibrium action, is also an equilibrium provided the smaller groupʼs preferences are sufficiently strong. In all dynamically stable long-run outcomes, players in the same group adopt the same action. Three properties, that do not matter for equilibrium selection in standard homogeneous agent models, do matter in the Language Game. These are: group size, strength of group preferences, and rates of group adaptiveness (“group dynamism”). A relative increase in group size and group dynamism is always weakly beneficial.

Heat capacity in the glass transition range modeled on the basis of heterogeneous dynamics

A heterogeneous version of the Tool-Narayanaswamy-Moynihan (TNM) model is proposed, in which enthalpy relaxation is heterogeneous in the sense that the overall nonexponential relaxation originates from the superposition of independently and exponentially relaxing domains with individual time constants. Analogous to rate exchange at a constant temperature, there is only a single fictive temperature that controls the rate at which all time constants can change considerably during a temperature scan. The model is shown to be consistent with differential scanning calorimetry (DSC) data taken across the glass transition of polystyrene, propylene carbonate, and glycerol. In contrast to the standard homogeneous TNM model, the heterogeneous counterpart fits DSC up-scans for As(2)Se(3) for cooling rates of 0.31, 2.5, and 20 K∕min with a common set of parameters.

Evaluation of the models handling heterotachy in phylogenetic inference

BackgroundThe evolutionary rate at a given homologous position varies across time. When sufficiently pronounced, this phenomenon – called heterotachy – may produce artefactual phylogenetic reconstructions under the commonly used models of sequence evolution. These observations have motivated the development of models that explicitly recognize heterotachy, with research directions proposed along two main axes: 1) the covarion approach, where sites switch from variable to invariable states; and 2) the mixture of branch lengths (MBL) approach, where alignment patterns are assumed to arise from one of several sets of branch lengths, under a given phylogeny.ResultsHere, we report the first statistical comparisons contrasting the performance of covarion and MBL modeling strategies. Using simulations under heterotachous conditions, we explore the properties of three model comparison methods: the Akaike information criterion, the Bayesian information criterion, and cross validation. Although more time consuming, cross validation appears more reliable than AIC and BIC as it directly measures the predictive power of a model on 'future' data. We also analyze three large datasets (nuclear proteins of animals, mitochondrial proteins of mammals, and plastid proteins of plants), and find the optimal number of components of the MBL model to be two for all datasets, indicating that this model is preferred over the standard homogeneous model. However, the covarion model is always favored over the optimal MBL model.ConclusionWe demonstrated, using three large datasets, that the covarion model is more efficient at handling heterotachy than the MBL model. This is probably due to the fact that the MBL model requires a serious increase in the number of parameters, as compared to two supplementary parameters of the covarion approach. Further improvements of the both the mixture and the covarion approaches might be obtained by modeling heterogeneous behavior both along time and across sites.

The Abundance and Emission of H[TINF]2[/TINF]O and O[TINF]2[/TINF] in Clumpy Molecular Clouds

Recent observations with the Submillimeter Wave Astronomy Satellite (SWAS) indicate abundances of gaseous H2O and O2 in dense molecular clouds that are significantly lower than those found in standard homogeneous chemistry models. We present here results for the thermal and chemical balance of inhomogeneous molecular clouds exposed to ultraviolet radiation in which the abundances of H2O and O2 are computed for various density distributions, radiation field strengths, and geometries. It is found that an inhomogeneous density distribution lowers the column densities of H2O and O2 compared with the homogeneous case by more than an order of magnitude at the same AV. O2 is particularly sensitive to the penetrating ultraviolet radiation, more so than H2O. The S140 and ρ Ophiuchi clouds are studied as relevant test cases of star-forming and quiescent regions. The SWAS results of S140 can be accommodated naturally in a clumpy model with a mean density of 2 × 103 cm-3 and an enhancement of IUV = 140 compared with the average interstellar radiation field, in agreement with observations of [C I] and 13CO of this cloud. Additional radiative transfer computations suggest that this diffuse H2O component is warm, ~60-90 K, and can account for the bulk of the 110-101 line emission observed by SWAS. The ρ Oph model yields consistent O2 abundances but too much H2O, even for [C]/[O] = 0.94, if IUV < 10 (respectively <40) for a mean density of 103 (respectively 104 cm-3). It is concluded that enhanced photodissociation in clumpy regions can explain the low H2O and O2 abundances and emissivities found in the large SWAS beam for extended molecular clouds but that additional freezeout of oxygen onto grains is needed in dense cold cores.

Deuterium to hydrogen towards QSO 1009+2956 from a mesoturbulent model

Abstract We present a new analysis of the deuterium absorption at z = 2.504 towards the quasar Q1009+2956 using the mesoturbulent model which accounts for possible correlations in the large-scale velocity field. We obtain a slightly higher deuterium-to-hydrogen ratio D/H ≈ (3.5–5.0) × 10−5 as compared with the recent measurement D/H ≈ (3.3–4.5) × 10−5 (68% C.L.) performed by Burles and Tytler (1998b) using the usual microturbulent approximation which assumes that the velocity field is uncorrelated. Other mesoturbulent calculations of the D-abundances at z = 3.572 towards Q1937–1009 and at z = 0.701 towards Q1718+4807 (the systems showing ‘low’ and possibly ‘high’ D/H values, respectively, in the microturbulent approaches) agree with the present one with the errors of measurements. Thus, the mesoturbulent analysis does not reveal any spatial variations of D/H and supports the standard homogeneous model of big bang nucleosynthesis.

Elastodynamical properties of nuclear matter from the observed activity of neutron stars

The results of studies devoted to describing the large-scale motions of the nuclear matter of neutron stars are reviewed. The approach is based on the idea that stellar nuclear matter is an elastic Fermi continuum possessing the properties of a compensated magneto-active plasma. The fundamental dynamical equations of motion of self-gravitating nuclear matter are taken to be the equations of nuclear elastodynamics, formulated in the macroscopic theory of nuclear collective processes. A variational method is presented for calculating the frequencies of gravitational-elastic spheroidal ( s -mode) and torsional ( t -mode) vibrations of a neutron star, and the star’s stability with respect to linear deformations is studied. The effectiveness of the elastodynamical method is illustrated by calculations of the periods of global gravitational elastic vibrations within the standard homogeneous model, and also for a family of realistic models of neutron stars, constructed on the basis of the relativistic equation of gravitational equilibrium and the nuclear-matter equations of state taking into account the heterophase nature of the nuclear statistical equilibrium. The motions of the magnetized Ae phase of the neutron-star matter are described using the magneto-hydrodynamical approach, which is used to calculate the frequencies of toroidal and poloidal Alfven oscillations. It is emphasized that magneto-plasma vibrations can significantly affect the electromagnetic activity of pulsars.

Novel spectralevolution with electron doping in d 0 transition metal oxides

We discuss high-energy spectroscopic results for systems representing electron doping near the d 0 configuration and establish that the spectral evolution with doping is inconsistent with expectations based on the Hubbard model. We argue that this failure arises due to the neglect of disorder in the real system. We present a new theoretical approach which takes into account the inhomogeneity of real systems; this approach provides results which are qualitatively different from the standard homogeneous models, but are in agreement with the experimental observations.

Inhomogeneous Primordial Nucleosynthesis and New Abundance Constraints on Omega BH 2

view Abstract Citations (25) References (70) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Inhomogeneous Primordial Nucleosynthesis and New Abundance Constraints on Omega BH 2 Mathews, G. J. ; Kajino, T. ; Orito, M. Abstract We discuss the upper limit to the baryonic contribution to the closure density. We consider effects of new observational and theoretical uncertainties in the primordial light-element abundances and the effects of fluctuation geometry on the inhomogeneous nucleosynthesis yields. We also consider implications of the possible detection of a high D/H abundance in a Lyman-α absorption cloud at high redshift and the implied chemical evolution effects of a high deuterium abundance. We show that there exists a region of the parameter space for inhomogeneous models in which a somewhat higher baryonic contribution to the closure density is possible than that allowed in standard homogeneous models. This result is contrary to some other recent studies and is due to both geometry and recently revised uncertainties in primordial light-element abundances, particularly 7Li. We find that the presently adopted abundance constraints are consistent with a contribution of baryons to the closure density as high as Ωbh250 ≤ 0.11 (n ≤ 7 × 10-10). This corresponds to a 20% increase over the limit from standard homogeneous models (Ωbh250 ≤ 0.08, η ≤ 5.8 × 10-10). With a high deuterium abundance the upper limits for the inhomogeneous and homogeneous models would be Ωbh250 ≤ 0.04 and 0.03 (η ≤ 2.6 × 10-10 and 1.9 × 10-10), respectively. Even higher limits could be obtained by further relaxing the presently accepted primordial lithium abundance constraint as some have proposed. Publication: The Astrophysical Journal Pub Date: January 1996 DOI: 10.1086/176630 Bibcode: 1996ApJ...456...98M Keywords: COSMOLOGY: THEORY; COSMOLOGY: DARK MATTER; COSMOLOGY: EARLY UNIVERSE; NUCLEAR REACTIONS; NUCLEOSYNTHESIS; ABUNDANCES full text sources ADS |

Large-Scale Baryon Isocurvature Inhomogeneities

Big bang nucleosynthesis constraints on baryon isocurvature perturbations are determined. A simple model ignoring the effects of the scale of the perturbations is first reviewed. This model is then extended to address the claim that large amplitude perturbations will collapse, preventing their baryons from contributing to the observed baryon density. It is found that baryon isocurvature perturbations are constrained to provide only a slight increase in the density of baryons in the universe over the standard homogeneous model. In particular, it is found that models which rely on power laws and the random phase approximation for the power spectrum are incompatible with big bang nucleosynthesis unless an ad hoc, small-scale cutoff is included. {copyright} {ital 1995 The American Astronomical Society.}

Inhomogeneous big-bang model, revived, and evolution of the light elements in cosmic rays

Abstract Inhomogeneous big-bang model for primordial nucleosynthesis allows higher universal mass density parameter of baryons than the standard homogeneous model does, which is marginally consistent with recent astronomical suggestion that some kind of dark matter is made of baryons. Observation of the enhanced heavy elements in metal weak dwarfs is proposed to test the inhomogeneous model. The studies of radioactive nuclear reactions help predict the theoretical abundances more precisely.

Primordial nucleosynthesis and the abundances of beryllium and boron

The ability to now make measurements of Be and B as well as put constraints on \lisix abundances in metal-poor stars has led to a detailed reexamination of Big Bang Nucleosynthesis in the $A\groughly6$ regime. The nuclear reaction network has been significantly expanded with many new rates added. It is demonstrated that although a number of $A>7$ reaction rates are poorly determined, even with extreme values chosen, the standard homogeneous model is unable to produce significant yields (Be/H and B/H $ 7$. However models that fit the $A\le7$ abundances still seem to have difficulty in obtaining significant $A>7$ yields.