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A method for calculating the Poisson cdf (cumulative distribution function) is presented. The method avoids computer underflow and overflow during the process. The computer program uses this technique to calculate the Poisson cdf for arbitrary inputs. An algorithm that determines the Poisson parameter required to yield a specified value of the cdf is presented.
Laboratory-based bidirectional reflectance distribution functions of radiometric tarp samples used in the vicarious calibration of Earth remote sensing satellite instruments are presented in this paper. The results illustrate the BRDF dependence on the orientation of the tarps weft and warp threads. The study was performed using the GSFC scatterometer at incident zenith angles of 0 deg, 10 deg, and 30 deg; scatter zenith angles from 0 deg. to 60 deg.; and scatter azimuth angles of 0 deg., 45 deg., 90 deg., 135 deg. and 180 deg. The wavelengths were 485nm, 550nm, 633nm and 800nm. The tarp's weft and warp dependence on BRDF is well defined at all measurement geometries and wavelengths. The BRDF difference can be as high as 8% at 0o incident angle and 12% at 30 deg. incident angle. The fitted BRDF data shows a very small discrepancy from the measured ones. New data on the forward and backscatter properties of radiometric tarps are reported. The backward scatter is well pronounced for the white samples. The black sample has well pronounced forward scatter. The provided BRDF characterization of radiometric tarps is an excellent reference for anyone interested in using tarps for radiometric calibrations. The results are NIST traceable.
Lorentz gas approximation to Boltzmann collision operator generalized for heavy molecule nonMaxwellian gas distribution function, obtaining equilibrium distribution applicable to ionized gas
Solution of Boltzmann and rate equations for electron distribution function and state populations in nonequilibrium MHD plasmas
A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.
The bulk parameters (number density and thermal energy density) of cometary water-group ions in the region surrounding Comet Giacobini-Zinner have been derived using data from the EPAS instrument on the ICE spacecraft. The derivation is based on the assumption that the pick-up ion distribution function is isotropic in the frame of the bulk flow, an approximation which has previously been shown to be reasonable within about 400,000 km of the comet nucleus along the spacecraft trajectory. The transition between the pick-up and mass-loaded regions occurs at the cometary shock, which was traversed at a cometocentric distance of about 100,000 km along the spacecraft track. Examination of the ion distribution functions in this region, transformed to the bulk flow frame, indicates the occurrence of a flattened distribution in the vicinity of the local pick-up speed, and a steeply falling tail at speeds above, which may be approximated as an exponential in ion speed.
A kinetic theory for the velocity distribution of solar wind electrons which illustrates the global and local properties of the solar wind expansion is proposed. By means of the Boltzmann equation with the Krook collision operator accounting for Coulomb collisions, it is found that Coulomb collisions determine the population and shape of the electron distribution function in both the thermal and suprathermal energy regimes. For suprathermal electrons, the cumulative effects of Coulomb interactions are shown to take place on the scale of the heliosphere itself, whereas the Coulomb interactions of thermal electrons occur on a local scale near the point of observation (1 AU). The bifurcation of the electron distribution between thermal and suprathermal electrons is localized to the deep solar corona (1 to 10 solar radii).
We evaluate the pion and kaon transverse momentum dependent parton distribution functions in the instanton liquid model, a model of the QCD vacuum at low resolution. The relevant transverse momentum distributions (TMDs) are factored into a constituent quark distribution times a rapidity dependent soft factor from staple-shaped Wilson lines, for fixed parton longitudinal momentum and transverse separation. The results are evolved to higher rapidities using the Collins-Soper kernel and higher resolution using renormalization group evolution. The comparison to existing extractions of pion TMDs from Drell-Yan data is briefly discussed.
High density form of molecular pair distribution function for rigid spheres system, using cell- cluster technique
Solution of Boltzmann and rate equations for electron distribution function and state populations in nonequilibrium MHD plasmas
Comparison of monte carlo, percus-yevick integral equations and convolution-hypernetted-chain methods for computing radial distribution functions of gaussian model
Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuna and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time . Results for ToF estimation using Acuna's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition. Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.
Effect of ionization and recombination on the electron distribution function of a slightly ionized gas in the presence of an external magnetic and electric field
Our present understanding of the distribution functions of the solar wind ion and electron thermal/suprathermal populations will be reviewed covering selected theoretical and observational topics. Roughly half the review will be devoted to recent discoveries (since Solar Wind 7). Among recent results are those of the Ulysses mission. The SWICS experiment observed pick-up protons and alpha particles, and acceleration of these particles at interplanetary shocks. Positive ion phenomena observed by SWOOPS include enhanced proton-alpha particle differential streaming both: (1) at high latitudes; and (2) in the ecliptic beyond 1 AU in the vicinity of shocks. The SWOOPS positive ion observations also demonstrate relative constancy of the entropy per proton at high latitudes beyond about 2.5 AU. Double beaming in both protons and alphas is observed by SWOOPS on either side of the current sheet, but not within; a possible explanation is reconnection at the edge of the current sheet. SWOOPS observed bi-directional streaming of electrons beyond 2 AU not only within Coronal Mass Ejections, but also upstream of corotating interplanetary shocks. Latitudinal and radial gradients of Ulysses electron core and halo temperatures will be discussed, as will work in progress on the three dimensional (in velocity space) properties of ion distributions.
Electron distribution function for steady homogeneous plasma of arbitrary ionization degree under strong electric fields, discussing kinetic equations for elastic and nonelastic encounters
Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.
Results of an extensive investigation of probability distribution functions (pdf's) for Rayleigh-Benard convection, in the hard turbulence regime, are presented. It is seen that the pdf's exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to universality is presented.
Our present understanding of the distribution functions of the solar wind ion and electron thermal/suprathermal populations are reviewed, covering selected theoretical and observational topics (half of material new since Solar Wind 7).