Assessment of influence of urban aerosol vertical profile on clear-sky diffuse radiance pattern

Aerosol particles spread in the atmosphere play an important role in solar light scattering and thus co-determine the sky radiance/luminance pattern as well as diffuse irradiances/illuminances at the ground. The particular influence is given by their optical properties and by their distribution in the atmosphere. The dependence of the aerosol extinction coefficient on altitude is usually described by the exponential law, which results from averaging of a large amount of aerosol realizations. This is also frequently the case of simulating of the solar diffuse radiance/luminance distribution over the sky, when it is based on solving the radiative transfer problem. However, the aerosol vertical profile can sometimes be significantly different from the exponential one. Mainly in the urban environment, the aerosol is often well-mixed within the atmospheric boundary layer, so its volume extinction coefficient is almost constant there. This work investigates how such different profiles affect the clear sky radiance pattern and consequently also the ground-based horizontal diffuse irradiance. The numerical simulations reveal that the discrepancies are negligible in practice. So it appears that the aerosol vertical distribution does not play any important role in sky radiance calculations and the standard exponential law is general enough to cover also various specific aerosol conditions.

Efficiency Analysis of OLAP-data Hypercube Decomposition for Exponential Computational Complexity Methods

The paper studies problems of reduction (decomposition) of OLAP-hypercube multidimensional data models. When decomposing large hyper-cubes of multidimensional data into sub-cube components the goal is to increase the computational performance of analytical OLAP systems, which is related to decreasing computational complexity of reduction methods for solving OLAP-data analysis problems with respect to the computational complexity of non-reduction methods, applied to data directly all over the hypercube. The paper formalizes the concepts of reduction and non-reduction methods and gives a definition of the upper bound for the change in the computational complexity of reduction methods in the decomposition of the problem of analyzing multidimensional OLAP-data in comparison with non-reduction methods in the class of exponential degree of computational complexity.The exact values of the upper bound for changing computational complexity are obtained for the hypercube decomposition into two sub-cubes on sets consisting of an even and an odd number of sub-cube structures, and its main properties are given, which are used to determine the decomposition efficiency. A formula for the efficiency of decomposition into two sub-cube structures for reduction of OLAP data analysis problems is obtained, and it is shown that with an increase in the dimension “n” of the lattice specifying the number of sub-cubes in the hypercube data structure, the efficiency of such a decomposition obeys an exponential law with an exponent “n/2”, regardless of the parity “n”. The examples show the possibility to use the values (found) of the upper bound for the change in computational complexity to establish the effectiveness criteria for reduction methods and the expediency of decomposition in specific cases.The paper results can be used in processing and analysis of information arrays of hypercube structures of analytical OLAP systems belonging to the Big-Data or super-large computer systems of multidimensional data.

An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data

In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.

Mathematical modeling and optimization of traffic flows

The article presents a mathematical model for optimizing traffic flows in an urban environment based on a stochastic approach. It allows to optimize traffic flows using a genetic algorithm by changing the phases of traffic lights operation. An exponential law of distribution of the generation of cars at the input points of the transport network has been established. The relationship between the intensity of servicing the traffic flow and the time of the green signal of the traffic light is revealed. Practical calculations have confirmed the applicability of the optimization model in traffic management.

Time-Rescaling Regression Method for Exponential Decay Time Series Predictions

The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

Similarity solutions for cylindrical shock wave in rotating non-ideal gas using Lie group theoretic method

In this paper, the propagation of cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition using Lie group of transformation method is investigated. The density is assumed to be constant and azimuthal fluid velocity is assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations bring about two different cases of solutions i.e. with a power-law and exponential-law shock paths. Numerical solutions are obtained for both the cases. Distribution of gasdynamical quantities is illustrated through figures. It is obtained that the reduced flow variables pressure and azimuthal fluid velocity decrease in general, whereas density and radial fluid velocity increase in case of power-law shock path. The reduced azimuthal fluid velocity decreases, whereas reduced density, pressure and radial fluid velocity increase in case of exponential-law shock path. Also, it is obtained that shock strength decreases with increase in value of adiabatic exponent or gas non-idealness parameter, whereas it increases due to increase in ambient azimuthal fluid velocity exponent.

Kinetic Description of Nonequilibrium Transfer Processes

The paper uses the example of the Brownian motion to kinetically describe the process of entropy increment in a nonequilibrium medium. The study shows that depending on the degree of nonequilibrium, the convergence to an equilibrium state occurs according to different laws. In the case of a strongly nonequilibrium medium, the entropy increment is described mathematically by the weakest logarithmic law, and in the case of a close-to-equilibrium medium, the entropy seeks a maximum value according to the strongest mathematical law --- the exponential law. The obtained expressions describing the Brownian motion can be extended to all other nonequilibrium processes. Mathematical modeling made it possible to calculate the process of entropy increment for an arbitrary degree of nonequilibrium and establish the parameters at which the transition from logarithmic to exponential law of entropy increment occurs when the thermodynamic system seeks an equilibrium state

In-Depth Analysis of the Effect of Fragmentation on the Crystallization-Driven Self-Assembly Growth Kinetics of 1D Micelles Studied by Seed Trapping

Studying the growth of 1D structures formed by the self-assembly of crystalline-coil block copolymers in solution at elevated temperatures is a challenging task. Like most 1D fibril structures, they fragment and dissolve when the solution is heated, creating a mixture of surviving crystallites and free polymer chains. However, unlike protein fibrils, no new nuclei are formed upon cooling and only the surviving crystallites regrow. Here, we report how trapping these crystallites at elevated temperatures allowed us to study their growth kinetics at different annealing times and for different amounts of unimer added. We developed a model describing the growth kinetics of these crystallites that accounts for fragmentation accompanying the 1D growth process. We show that the growth kinetics follow a stretched exponential law that may be due to polymer fractionation. In addition, by evaluating the micelle growth rate as a function of the concentration of unimer present in solution, we could conclude that the micelle growth occurred in the mononucleation regime.

Scaling Conjecture Regarding the Number of Unknots among Polygons of N≫1 Edges

The conjecture is made based on a plausible, but not rigorous argument, suggesting that the unknot probability for a randomly generated self-avoiding polygon of N≫1 edges has only logarithmic, and not power law corrections to the known leading exponential law: Punknot(N)∼exp−N/N0+o(lnN) with N0 being referred to as the random knotting length. This conjecture is consistent with the numerical result of 2010 by Baiesi, Orlandini, and Stella.

Revisiting the Planet Mass and Stellar Metallicity Relation for Low-Mass Exoplanets Orbiting GKM Class Stars

The growing database of exoplanets has shown us the statistical characteristics of various exoplanet populations, providing insight towards their origins. Observational evidence suggests that the process by which gas giants are conceived in the stellar disk may be disparate from that of smaller planets. Using NASA’s Exoplanet Archive, we analyzed the relationships between planet mass and stellar metallicity, as well as planet mass and stellar mass for low-mass exoplanets (MP < 0.13 MJ) orbiting spectral class G, K, and M stars. We performed further uncertainty analysis to confirm that the exponential law relationships found between the planet mass, stellar mass, and the stellar metallicity cannot be fully explained by observation biases alone.