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.
The refractive indices, nD densities 𝜌, and viscosities of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity ∆nD, excess molar viscosity E and excess molar Gibbs free energy of activation of viscous flow G *E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative ∆nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol sulfolane , nD was positive over the whole mole fraction rang , while VE , E and G *E show a negative deviation. The
... Show MoreThis research is focusing on finding more effective polymers that leads to enhance the rheological properties of Water Base Muds. The experiments are done for different types of mud for all substances which are Polyacrylamide, Xanthan gum, CMC (Carboxyl Methyl Cellulose). This study shows the effect of add polymer to red bentonite mud, effect of add polymer to Iraqi bentonite mud, the effect of add bentonite to polymer mud. The mud properties of Iraqi bentonite blank are enhanced after adding the polymers to the blank mix, CMC gives the highest value of plastic viscosity and Gel strength than others; X-anthan gives the highest value of yield point and gel strength than others. For the red bentonite mud, Polyacrylamide ha
... Show MoreTransparent thin films of CdO:Ce has been deposited on to glass and silicon substrates by spray pyrolysis technique for various concentrations of cerium (2, 4, and 6 Vol.%). CdO:Ce films were characterized using different techniques such as X-ray diffraction (XRD), atomic force microscopy(AFM) and optical properties. XRD analysis show that CdO films exhibit cubic crystal structure with (1 1 1) preferred orientation and the intensity of the peak increases with increasing's of Ce contain when deposited films on glass substrate, while for silicon substrate, the intensity of peaks decreases, the results reveal that the grain size of the prepared thin film is approximately (73.75-109.88) nm various with increased of cerium content. With a sur
... Show MoreThe performance of asphalt pavements is crucial due to heavy traffic loads from civil and industrial developments. Various additives and modifiers are used in flexible roads to improve their resistance to deterioration caused by climatic changes. From this context, modifying the asphalt binder with polymers is popular in asphalt pavement construction. The present research investigates the effect of Polyethylene (PE) polymers in powder form on the characteristics of asphalt mixtures since these polymers are composed of hydrocarbons. It is similar to asphalt binders, making them very effective in enhancing the performance of neat asphalt produced from the oil refinery. To confirm this, two types of PE, High-Density PE (HDPE) and Low-Density P
... Show MoreOilwell cementing operations are crucial for drilling and completion, preserving the well's productive life. However, weak and permeable formations pose a high risk of cement slurry loss, leading to failure. Lightweight cement, like foamed cement, is used to avoid these difficulties. This study is focused on creating a range of foamed slurry densities and examining the effect of gas concentration on their rheological properties. The foaming agent and foam stabilizer are tested, and the optimal concentration is determined to be 2% and 0.12%, respectively, by the weight of the cement.
Furthermore, the construction of samples of foam cement with different densities (0.8, 1.0, 1.2, 1.4, and 1.6) g/cc is performed to f
... Show MoreIn this study, the physical, and mechanical properties of low-cost and biocomposites were evaluated. The walnut shell and date palm frond fibers were thermally treated in an oven at a temperature of 70°C and then chemically treated with NaOH and distilled water solution, after these treatments, the biocomposite materials will be thermally treated again at 50°C. This procedure was performed for three types of biocomposite; Walnut shell Fiber Reinforced Polymer (WFRP), Date palm Fiber Reinforced Polymer (DFRP), and Hybrid Fiber Reinforced Polymer (HFRP), whereas the biocomposite sheets consisting of 30% biofibers and 70% unsaturated polyester, the mechanical test specimens were cut by a CNC machine according to ASTM standards. The e
... Show MoreIntroduction: This study was performed to compare the effect of Fractional CO2 laser or Q switched Nd:YAG laser of surface treatment on the shear bond strength of zirconia-porcelain interface. Methods: Fractional CO2 laser at 30 W, 2 ms, time interval 1 ms, distance between spots 0.3 mm, and number of scans is (4) or Q switched Nd:YAG laser at 30 J/mm2 and 10 Hz were used to assess the shear bond strength of zirconia to porcelain. Pre-sintered zirconia specimens were divided into three groups (n = 10) according to the surface treatment technique used: (a) untreated (Control) group; (b) CO2 group; (c) Nd:YAG group. All samples were then sintered and veneered with porcelain according to the manufacturer’s instructions. Surface morph
... Show MoreThis study aims to know the degree of importance and the availability of the enhancing specifications of the educational process, and the way its objectives are achieved. Such a step involves using educational techniques, laying the selection foundations, knowing the methods of their employment and tracking the obstacles that limit this employment in teaching Arabic to non-native speakers. To achieve these objectives, the study followed a descriptive approach, and collected the necessary data through an integrated questionnaire prepared for the purpose of describing the phenomenon or topic. This approach was adopted, as it is characterized by being comprehensive, focuses on collecting data related and necessary to the topic under study.
... Show MoreIn this study, polymeric composites were prepared from unsaturated polyester as a base material with glass powder (fluorescent) in different weight ratios (4, 6, 8, 10,and 11%) as a support material and after comparison before and after reinforcement of the prepared composites, an increase was found. In the values of mechanical properties (hardness, compressive strength), the shock resistance values decreased, but an increase in temperature leads to an increase in the values of shock resistance, as well as the values of compressive strength And it reduces the hardness value.