This paper introduces a novel non-classical probability distribution, termed the Logistic Map distribution, which is constructed by transforming a polynomial function derived from the second iteration of the logistic map. The logistic map a well-known discrete-time dynamical system has been extensively employed in diverse scientific domains, including population dynamics (to model bounded growth under environmental constraints), physics (to study nonlinear dynamics and deterministic chaos), and economics (to represent complex, nonlinear patterns in financial and economic time series). The proposed distribution is fully characterized by two parameters: a scale parameter and a shape parameter, with the constraint ensuring the non-negativity and integrability of the density. Within this valid parameter space, we rigorously derive and establish a comprehensive suite of statistical properties. These include the probability density function, cumulative distribution function, reliability (survival) function, and hazard (failure rate) function. Furthermore, we obtain analytical expressions for key descriptive measures such as the mode and median, as well as for higher-order characteristics including the moment generating function, factorial moment generating function, and characteristic function. The proposed distribution most closely application field in materials science specifically, the statistical modeling of particle or grain size distributions in industrial powder processing, metallurgy, and pharmaceutical manufacturing. The primary objective of this study is to formalize a new family of probability distributions grounded in the mathematical framework of dynamical systems, specifically leveraging the logistic function commonly encountered in differential and difference equations. By doing so, we bridge concepts from nonlinear dynamics and classical statistical theory. The secondary aim is to conduct a thorough investigation of the distribution’s mathematical structure and statistical behavior, thereby establishing its potential utility for modeling bounded, non-negative random phenomena in applied fields such as reliability engineering, survival analysis, and environmental statistics.
Titanium-dioxide (TiO2) nanoparticles suspended in water, and ethanol based fluids have been prepared using one step method and characterized by scanning electron microscopy (SEM), and UV–visible spectrophotometer. The TiO2 nanoparticles were added to base fluids with different volume concentrations from 0.1% to1.5% by dispersing the synthesized nanoparticles in deionized water and ethanol solutions. The effective thermal conductivity, viscosity and pH of prepared nanofluids at different temperatures from 15 to 30 oC were carried out and investigated. It was observed that the thermal conductivity, pH, and viscosity of nanofluids increases with the increase in TiO2 nanoparticle volume fraction
... Show MoreThis research aims at studying each of the cold and hot thermal wavelengths affecting
Iraq for a minimum climatic course of 11 years beginning from 1992 till 2002. Three stations
were selected including the parts of Iraq surface: Mosul, Baghdad and Basrah.
The wave days were also connected with the related climatic elements represented by
the wind direction and speeds and the relative humidity. It was shown that Iraq is affected by
the rates of hot thermal wave lengths greatly compared to the rates of cold wavelengths. The
results suggested that the highest rate of hot and cold wavelengths recorded over Basra station
was (3.5) days for the cold and (5) days for the hot. While the lowest rates was at Mosul
station
In this study, SnS thin films were deposited onto glass substrate by thermal evaporation technique at 300K temperature. The SnS films have been prepared with different thicknesses (100,200 &300) nm. The crystallographic analysis, film thickness, electrical conductivity, carrier concentration, and carrier mobility were characterized. Measurements showed that depending on film thickness. The D.C. conductivity increased with increase in film thickness from 3.720x10-5 (Ω.cm)-1 for 100 nm thickness to 9.442x10-4 (Ω.cm)-1 for 300 nm thicknesses, and the behavior of activation energies, hall mobility, and carrier concentration were also studied.
This contribution investigates the effect of the addition of the Hubbard U parameter on the electronic structural and mechanical properties of cubic (C-type) lanthanide sesquioxides (Ln2O3). Calculated Bader's charges confirm the ionic character of Lnsingle bondO bonds in the C-type Ln2O3. Estimated structural parameters (i.e., lattice constants) coincide with analogous experimental values. The calculated band gaps energies at the Ueff of 5 eV for these compounds exhibit a non-metallic character and Ueff of 6.5 eV reproduces the analogous experimental band gap of cerium sesquioxide Ce2O3. We have thoroughly investigated the effect of the O/Ce ratios and the effect of hafnium (Hf) and zirconium (Zr) dopants on the reduction energies of C
... Show MoreInterest has largely centered on the use of plant fibers to reinforce plastics, because these fibers are abundant and cheap. Carrot fibers (Curran) have been extracted from carrot, left over from carrot juice manufacture. The fibers of two sizes fine (50<µm) and coarse (100-150 µm) have been mixed with epoxy in four levels of loading (10, 20, 30, 40 wt %) respectively. Impact test, shore d hardness test and three point bending test of epoxy and carrot fiber-epoxy composites samples have been determined. The impact strength values of samples prepared with fine and coarse fibers increased as compared with pure epoxy sample. Hardness values increased, and the Young’s modulus values decreased with fiber content of both sizes.
Nanotechnology has shown a lot of promise in the oil and gas sectors, including nanoparticle-based drilling fluids. This paper aims to explore and assess the influence of various nanoparticles on the performance of drilling fluids to make the drilling operation smooth, cost effective and efficient. In order to achieve this aim, we exam the effect of Multi Wall Carbon Nanotube and Silicon Oxide Nanoparticles as Nanomaterial to prepare drilling fluids samples.
Anew method for mixing of drilling fluids samples using Ultra sonic path principle will be explained. Our result was drilling fluids with nano materials have high degree of stability.
The results of using Multiwall Carbon Nanotube and Silicon Oxide show t
... Show MoreOptical detector was manufactured Bashaddam thermal evaporation technique at room temperature under pressure rays studied characteristics of reactive Scout efficiency quantitative ratio of the signal and the ability equivalent to noise