Stochastic Heterogeneity Research Articles

Optics of vegetation: implications for the radiation balance and photosynthetic performance

This paper considers light propagation in vegetation stands using an analysis of transmitted, absorbed and reflected visible and near-infrared radiation, light gradients and photosynthetic performance. Optical theories of different complexity, including the most sophisticated novel extension of the radiative transfer theory to fluctuating media, have been compared. Whereas for the global radiation balance even the simple models are acceptable, calculation of absorption of the light and light spectra necessary for the analysis of the photosynthetic performance requires more advanced radiation transfer theories. It was shown that the stochastic heterogeneity of a canopy caused by clustering and clumping of the phytoelements affects absorption and photosynthesis. In particular, heterogeneous canopies can absorb up to 15% less radiation and can have up to 15% higher efficiency of photosynthesis than a macrohomogeneous canopy with the same biomass. The state of the phytochrome, the main pigment for the developmental control of light, has been calculated at different depths in the canopy. The calculated phytochrome profile is distorted when simple radiation transfer models are used. This profile is also strongly affected by the degree of stochastic heterogeneity.

Effect of stochastic heterogeneity on lung impedance during acute bronchoconstriction: a model analysis.

In a previous study (J. H. T. Bates, A. M. Lauzon, G. S. Dechman, G. N. Makaym, and T. F. Schuessler. J. Appl. Physiol. 76: 616-626, 1994), we investigated the acute changes in isovolume lung mechanics immediately after a bolus injection of histamine. We found that dynamic resistance and elastance increased progressively in the 80-s period after injection, whereas the estimated tissue hysteresivity reached a stable plateau after approximately 25 s. In the present study, we developed a computer model of the lung to investigate the mechanisms responsible for these observations. The model conforms to Horsfield's morphometry, with the addition of compliant airways and structural damping tissue units. Using this model, we simulated the time course of acute bronchoconstriction after intravenous administration of a bolus of bronchial agonist. Heterogeneity was induced by randomly varying the values of the maximal airway smooth muscle contraction and the tissue response to the agonist. Our results demonstrate that much of the increase in lung impedance observed in our previous study can be produced purely by the effects of airway heterogeneity. However, we were only able to reproduce the plateauing of hysteresivity by assigning a minimum radius to each airway, beyond which it would immediately snap completely shut. We propose that airway closure played an important role in our experimental observations.

Influence of time-dependent stochastic heterogeneity on the radiation response of a cell population

A solid tumor is a cell population with extensive cellular heterogeneity, which severely complicates tumor treatment by therapeutic agents such as ionizing radiation. We model the response to ionizing radiation of a multicellular population whose cells have time-dependent stochastic radiosensitivity. A reaction-diffusion equation, obtained by assuming a random process with the radiation response of a cell partly determined by competition between repair and binary misrepair of DNA double-strand breaks, is used. By a suitable transformation, the equation is reduced to that of an Ornstein–Uhlenbeck process so explicit analytic solutions are available. Three consequences of the model's assumptions are that (1) response diversity within a population increases resistance to radiation, that is, the population surviving is greater than that anticipated from considering an average cell; (2) resistant cell subpopulations preferentially spared by the first part of a prolonged radiation protocol are driven biologically into more radiosensitive states as time increases, that is, resensitization occurs; (3) an inverse dose-rate effect, that is, an increase in cell killing as overall irradiation time is increased, occurs in those situations where resensitization dominates effects due to binary misrepair of repairable damage. The results are consistent with the classic results of Elkind and coworkers on extra cell killing attributed to cell-cycle redistribution and are in agreement with some recent results on in vitro and in vivo population radiosensitivity. They also generalize the therapeutic paradigm that low dose rate or fractionated radiation can help overcome hypoxic radioresistance in tumors.

Stochastic flow unit modelling of a North Sea coastal-deltaic reservoir

A procedure, based on a conceptual sedimentological model founded on sequence stratigraphy principles, for the stochastic heterogeneity modelling of coastaldeltaic reservoirs is outlined. The procedure has been tested using data from the Middle Jurassic Tarbert Formation of the Gullfaks Field, Norwegian North Sea. A chronostratigraphic rather than a lithostratigraphic correlation approach is used to define simulation grids for both reservoir description and fluid flow models. This ensures that important internal heterogeneities are aligned parallel to the simulation grids and establishes an efficient coupling between heterogeneity and flow simulation models.

Dynamic (S, s) Economies

In this paper we provide a framework to study the aggregate dynamic behavior of an economy where individual units follow (S,s) policies. We characterize structural and stochastic heterogeneities that ensure convergence of the economy's aggregate to that of its frictionless counterpart, determine the speed at which convergence takes place, and describe the transitional dynamics of this economy. In particular, we consider a dynamic economy where agents differ in their initial positions within their bands and face both stochastic and structural heterogeneity; where the former refers to the presence of (unit specific) idiosyncratic shocks, and the latter to differences in the widths of units' (S,s) bands and their response to aggregate shocks. We study the evolution of the economy's aggregate and the evolution of the difference between this aggregate and that of an economy without macroeconomic friction, where the latter pertains to a situation where individual units adjust with no delay to all shocks. We also examine the sensitivity of this difference to common shocks. For example, in the retail inventory problem the aggregate deviation and sensitivity to common shocks correspond to the aggregate inventory level and its sensitivity to aggregate demand shocks, respectively.

Guided wave attenuation in laterally varying media

SUMMARY Coupled mode techniques for guided wave propagation are extended to 2-D stochastic heterogeneity superimposed on a stratified medium. This approach requires the variations to be smoothly varying and of modest size (less than ±2 per cent). By averaging over an ensemble of statistically similar models, coupled equations for the modal energy transport can be generated. The intermode coupling depends on the horizontal correlation functions for the heterogeneity in the crust and mantle, and the integrated effect of the vertical variations in velocity and the modal eigenfunctions. For a particular stochastic model, the attenuation of a single mode as a function of distance can be calculated as a superposition of intrinsic attenuation and scattering loss by energy transfer to other modes of propagation. These statistical estimates of attenuation can be compared with observations of regional phases travelling over a variety of paths in a single region. For Lg and Sn phases, intermode scattering may represent up to 30 per cent of the apparent loss.

Balanced-budget redistribution as the outcome of political competition

This paper models balanced-budget redistribution between socio-economic groups as the outcome of electoral competition between two political parties. Equilibrium is unique in the present model, and a sufficient condition for existence is given, requiring that there be enough ‘stochastic heterogeneity’ with respect to party preferences in the electorate. The validity of Hotelling's ‘principle of minimum differentiation’, and of ‘Director's Law’, are examined under alternative hypotheses concerning administrative costs of redistributions, and voter's possibilities both of abstaining from voting and of becoming campaign activists for one of the parties. The policy strategy of expected-plurality maximization is contrasted with the strategy of maximizing the probability of gaining a plurality. Incomes are fixed and known, so lump-sum taxation is feasible. However, constraints on tax/transfer differentiation between individuals are permitted in the analysis.

Asymptotic Approximations of the Assignment Model with Stochastic Heterogeneity in the Matching Utilities

A large-scale linear assignment problem is considered under the assumption that the coefficients of the objective function are imperfectly known but have a probability distribution. Asymptotic approximations are derived by using the statistical theory of extremes. It is shown how the resulting approximate problem has an easily computable form, provides a closed-form solution which has the structure of a logit model, and is embedded by a mathematical program whose objective function is related to entropy.

Field heterogeneity: Some basic issues

Present‐day soil‐water physics enables useful quantitative predictions in the laboratory and in simple field situations. Difficulties, however, frequently arise for areas of appreciable size in the field. Known and unknown heterogeneities, on many scales, may vitiate predictions based on theory for homogeneous, or very simple heterogeneous, systems. Two types of heterogeneity are distinguished, deterministic and stochastic. The first often demands an extension of established analyses and may involve important phenomena absent from the analogous homogeneous problem. Stochastic heterogeneity may involve many scales and is imperfectly known. The statistical properties may be stationary, but in more complicated cases, randomness may be embedded in (either known or unknown) systematic trends. Some aspects of unsaturated and generally unsteady flow in heterogeneous systems are reviewed: the mathematical nature of the flow equation; the concept of scale‐heterogeneity; analytical and quasi‐analytical solutions. The enormity of the total problem of unsaturated unsteady flows in stochastic heterogeneous systems is illustrated through a dialectic of eight successive stages of simplification. The concept of the autocorrelation function governing λ, the internal characteristic length, is introduced; and the problem posed in terms involving the distribution and autocorrelation functions of λ, the reduced potential and conductivity functions, and the initial and boundary conditions as the data, from which it is required to establish distribution functions of various descriptors of the flow. The solution to a grossly simplified example of horizontal absorption is presented. Mean apparent sorptivity decreases rapidly to about one fifth of the mean (and about half the minimum) sorptivity of the component soils. Variation about the mean is very great but decreases as absorption proceeds. The example epitomizes the failure of additivity of properties in stochastic heterogeneous media, which arises because spatial textural changes in either sense tend to reduce unsaturated flow rates.

Contribution of compliance of airways to frequency-dependent behavior of lungs.

Contribution of compliance of airways to frequency-dependent behavior of lungs.

Mechanical factors in distribution of pulmonary ventilation.

Mechanical factors in distribution of pulmonary ventilation.