scholarly journals Dispersal Distances for Airborne Spores Based on Deposition Rates and Stochastic Modeling

2007 ◽  
Vol 97 (10) ◽  
pp. 1325-1330 ◽  
Author(s):  
Anders Stockmarr ◽  
Viggo Andreasen ◽  
Hanne Østergård
Keyword(s):  
Fungal Spores ◽  
Two Dimensional ◽  
Airborne Spores ◽  
Modeling Framework ◽  
Deposition Rates ◽  
Spore Release ◽  
Special Cases ◽  
Release Height ◽  
Dispersal Distances ◽  
Parameter Values

A new modeling framework for particle dispersal is explored in the context of the particles being fungal spores dispersed within a field. The model gives rise to both exponentially decreasing and polynomially decreasing two-dimensional densities of deposited fungal spores. We reformulate the model in terms of time to deposition, and show how this concept is equivalent to the deposition rate for fungal spores. Special cases where parameter values for wind and gravitation lead to exponentially or polynomially decreasing densities are discussed, and formulas for one- and two-dimensional densities of deposited spores are given explicitly in terms of parameters for diffusion, wind, gravitation, and spore release height.

scholarly journals Marine boundary layer cloud regimes and POC formation in a CRM coupled to a bulk aerosol scheme

2013 ◽  
Vol 13 (24) ◽  
pp. 12549-12572 ◽  
Author(s):  
A. H. Berner ◽  
C. S. Bretherton ◽  
R. Wood ◽  
A. Muhlbauer
Keyword(s):  
Boundary Layer ◽  
Marine Boundary Layer ◽  
Three Dimensional ◽  
Two Dimensional ◽  
State Variables ◽  
Liquid Water Path ◽  
Modeling Framework ◽  
Boundary Layer Cloud ◽  
Cloud Regimes ◽  
Layer Cloud

Abstract. A cloud-resolving model (CRM) coupled to a new intermediate-complexity bulk aerosol scheme is used to study aerosol–boundary-layer–cloud–precipitation interactions and the development of pockets of open cells (POCs) in subtropical stratocumulus cloud layers. The aerosol scheme prognoses mass and number concentration of a single lognormal accumulation mode with surface and entrainment sources, evolving subject to processing of activated aerosol and scavenging of dry aerosol by clouds and rain. The CRM with the aerosol scheme is applied to a range of steadily forced cases idealized from a well-observed POC. The long-term system evolution is explored with extended two-dimensional (2-D) simulations of up to 20 days, mostly with diurnally averaged insolation and 24 km wide domains, and one 10 day three-dimensional (3-D) simulation. Both 2-D and 3-D simulations support the Baker–Charlson hypothesis of two distinct aerosol–cloud "regimes" (deep/high-aerosol/non-drizzling and shallow/low-aerosol/drizzling) that persist for days; transitions between these regimes, driven by either precipitation scavenging or aerosol entrainment from the free-troposphere (FT), occur on a timescale of ten hours. The system is analyzed using a two-dimensional phase plane with inversion height and boundary layer average aerosol concentrations as state variables; depending on the specified subsidence rate and availability of FT aerosol, these regimes are either stable equilibria or distinct legs of a slow limit cycle. The same steadily forced modeling framework is applied to the coupled development and evolution of a POC and the surrounding overcast boundary layer in a larger 192 km wide domain. An initial 50% aerosol reduction is applied to half of the model domain. This has little effect until the stratocumulus thickens enough to drizzle, at which time the low-aerosol portion transitions into open-cell convection, forming a POC. Reduced entrainment in the POC induces a negative feedback between the areal fraction covered by the POC and boundary layer depth changes. This stabilizes the system by controlling liquid water path and precipitation sinks of aerosol number in the overcast region, while also preventing boundary layer collapse within the POC, allowing the POC and overcast to coexist indefinitely in a quasi-steady equilibrium.

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Masataka Fukunaga
Keyword(s):  
Critical Point ◽  
Fractional Order ◽  
Time Derivative ◽  
Turing Instability ◽  
Reaction Diffusion Equations ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Linearized Equations ◽  
Special Cases ◽  
Fractional Reaction

There are two types of time-fractional reaction-subdiffusion equations for two species. One of them generalizes the time derivative of species to fractional order, while in the other type, the diffusion term is differentiated with respect to time of fractional order. In the latter equation, the Turing instability appears as oscillation of concentration of species. In this paper, it is shown by the mode analysis that the critical point for the Turing instability is the standing oscillation of the concentrations of the species that does neither decays nor increases with time. In special cases in which the fractional order is a rational number, the critical point is derived analytically by mode analysis of linearized equations. However, in most cases, the critical point is derived numerically by the linearized equations and two-dimensional (2D) simulations. As a by-product of mode analysis, a method of checking the accuracy of numerical fractional reaction-subdiffusion equation is found. The solutions of the linearized equation at the critical points are used to check accuracy of discretized model of one-dimensional (1D) and 2D fractional reaction–diffusion equations.

scholarly journals Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

2018 ◽  
Vol 51 (1) ◽  
pp. 198-210 ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Ulam Stability ◽  
Step Size ◽  
First Order ◽  
Linear Dynamic ◽  
Discrete Step ◽  
Special Cases ◽  
Parameter Values ◽  
Homogeneous Linear

Abstract We establish theHyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.

scholarly journals Aerosol measurement methods to quantify spore emissions from fungi and cryptogamic covers in the Amazon

2020 ◽  
Vol 13 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Nina Löbs ◽  
Cybelli G. G. Barbosa ◽  
Sebastian Brill ◽  
David Walter ◽  
Florian Ditas ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Amazon Basin ◽  
Large Fraction ◽  
Fungal Spores ◽  
Measurement Data ◽  
Minor Role ◽  
Model Species ◽  
Natural Conditions ◽  
Experimental Conditions ◽  
Spore Release

Abstract. Bioaerosols are considered to play a relevant role in atmospheric processes, but their sources, properties, and spatiotemporal distribution in the atmosphere are not yet well characterized. In the Amazon Basin, primary biological aerosol particles (PBAPs) account for a large fraction of coarse particulate matter, and fungal spores are among the most abundant PBAPs in this area as well as in other vegetated continental regions. Furthermore, PBAPs could also be important ice nuclei in Amazonia. Measurement data on the release of fungal spores under natural conditions, however, are sparse. Here we present an experimental approach to analyze and quantify the spore release from fungi and other spore-producing organisms under natural and laboratory conditions. For measurements under natural conditions, the samples were kept in their natural environment and a setup was developed to estimate the spore release numbers and sizes as well as the microclimatic factors temperature and air humidity in parallel to the mesoclimatic parameters net radiation, rain, and fog occurrence. For experiments in the laboratory, we developed a cuvette to assess the particle size and number of newly released fungal spores under controlled conditions, simultaneously measuring temperature and relative humidity inside the cuvette. Both approaches were combined with bioaerosol sampling techniques to characterize the released particles using microscopic methods. For fruiting bodies of the basidiomycetous species, Rigidoporus microporus, the model species for which these techniques were tested, the highest frequency of spore release occurred in the range from 62 % to 96 % relative humidity. The results obtained for this model species reveal characteristic spore release patterns linked to environmental or experimental conditions, indicating that the moisture status of the sample may be a regulating factor, whereas temperature and light seem to play a minor role for this species. The presented approach enables systematic studies aimed at the quantification and validation of spore emission rates and inventories, which can be applied to a regional mapping of cryptogamic organisms under given environmental conditions.

scholarly journals Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

2018 ◽  
Vol 23 (4) ◽  
pp. 65 ◽  
Author(s):  
Kaijun Peng ◽  
Jieqing Tan ◽  
Zhiming Li ◽  
Li Zhang
Keyword(s):  
Singular Point ◽  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Subdivision Scheme ◽  
Fractal Curve ◽  
Rational Scheme ◽  
Special Cases ◽  
Necessary And Sufficient ◽  
Parameter Values ◽  
Selection Of

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

Two-dimensional quasi-stationary flows in gas dynamics

1968 ◽  
Vol 64 (4) ◽  
pp. 1099-1108 ◽  
Author(s):  
A. G. Mackie
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Exact Solutions ◽  
Gas Dynamics ◽  
Two Dimensional ◽  
Independent Variables ◽  
Stationary Flows ◽  
First Case ◽  
Special Cases ◽  
Flow Round

In this paper we are concerned with the two-dimensional, unsteady flow of an inviscid, polytropic gas whose adiabatic index γ lies between 1 and 3. We recall that comparatively early in the study of gas dynamics we encounter two exact solutions of gas dynamic problems. One, in one-dimensional unsteady flow, is the expansion of a semi-infinite column of gas which is initially at rest behind a piston which, at time t = 0, begins to move with constant speed away from the gas. The second, in two-dimensional, steady, supersonic flow, is the Prandtl–Meyer flow round a sharp convex corner. Both of those flows may be regarded as special cases of more general exact solutions which are obtained by the method of characteristics (see, for example, Courant and Friedrichs(1)). On the other hand, each may be obtained directly from the appropriate equations by making use of the fact that, in so far as neither problem contains any characteristic length parameter in its formulation, the principle of dynamic similarity can be used to reduce the system of partial differential equations to one of ordinary differential equations. In the first case the independent variables x and t occur only in the combination x/t and in the second the independent variables x and y occur only in the combination x/y. Interesting and instructive as the derivation of these solutions from such principles may be, it is an unfortunate fact that they are the only non-trivial solutions of the respective equations. This is not altogether surprising as the equations are ordinary with (in this case) a limited number of non-trivially distinct solutions.

scholarly journals Normal Distribution on the Rotation Group So(3)

1997 ◽  
Vol 29 (3-4) ◽  
pp. 201-233 ◽  
Author(s):  
Dmitry I. Nikolayev ◽  
Tatjana I. Savyolov
Keyword(s):  
Normal Distribution ◽  
Orientation Distribution ◽  
Rotation Group ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Normal Distributions ◽  
The Central Limit Theorem ◽  
Special Cases ◽  
Wrapped Normal ◽  
Circular Normal Distribution

We study the normal distribution on the rotation group SO(3). If we take as the normal distribution on the rotation group the distribution defined by the central limit theorem in Parthasarathy (1964) rather than the distribution with density analogous to the normal distribution in Eucledian space, then its density will be different from the usual (1/2πσ) exp⁡(−(x−m)2/2σ2) one. Nevertheless, many properties of this distribution will be analogous to the normal distribution in the Eucledian space. It is possible to obtain explicit expressions for density of normal distribution only for special cases. One of these cases is the circular normal distribution.The connection of the circular normal distribution SO(3) group with the fundamental solution of the corresponding diffusion equation is shown. It is proved that convolution of two circular normal distributions is again a distribution of the same type. Some projections of the normal distribution are obtained. These projections coincide with a wrapped normal distribution on the unit circle and with the Perrin distribution on the two-dimensional sphere. In the general case, the normal distribution on SO(3) can be found numerically. Some algorithms for numerical computations are given. These investigations were motivated by the orientation distribution function reproduction problem described in the Appendix.

scholarly journals Complex potentials in two-dimensional elasticity

1945 ◽  
Vol 184 (997) ◽  
pp. 129-179 ◽  
Keyword(s):  
Complex Variable ◽  
Body Force ◽  
Displacement Function ◽  
The Body ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Two Dimensional ◽  
Special Cases ◽  
Airy’S Stress Function

This paper gives an approach to two-dimensional isotropic elastic theory (plane strain and generalized plane stress) by means of the complex variable resulting in a very marked economy of effort in the investigation of such problems as contrasted with the usual method by means of Airy’s stress function and the allied displacement function. This is effected (i) by considering especially the transformation of two-dimensional stress; it emerges that the combinations xx + yy , xx — yy + 2 ixy are all-important in the treatment in terms of complex variables; (ii) by the introduction of two complex potentials Ω( z ), ω( z ) each a function of a single complex variable in terms of . which the displacements and stresses can be very simply expressed. Transformation of the cartesian combinations u + iv , xx + yy , xx — yy + 2 ixy to the orthogonal curvilinear combinations u ξ + iu n , ξξ + ηη, ξξ - ηη + 2iξη is simple and speedy. The nature of "the complex potentials is discussed, and the conditions that the solution for the displacements shall be physically admissible, i.e. single-valued or at most of the possible dislocational types, is found to relate the cyclic functions of the complex potentials. Formulae are found for the force and couple resultants at the origin z = 0 equivalent to the stresses round a closed circuit in the elastic material, and these also are found to relate the cyclic functions of the complex potentials. The body force has bhen supposed derivable from a particular body force potential which includes as special cases (i) the usual gravitational body force, (ii) the reversed mass accelerations or so-called ‘centrifugal’ body forces of steady rotation. The power of the complex variable method is exhibited by finding the appropriate complex potentials for a very wide variety of problems, and whilst the main object of the present paper has been to extend the wellknown usefulness of the complex variable method in non-viscous hydrodynamical theory to two-dimensional elasticity, solutions have been given to a number of new problems and corrections made to certain other previous solutions.

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