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.
Fiber reinforced polymer composite is an important material for structural application. The diversified application of FRP composite has taken center of attraction for interdisciplinary research. However, improvements on mechanical properties of this class of materials are still under research for different applications. In this paper we have modified the epoxy matrix by Al2O3, SiO2 and TiO2 nano particles in glass fiber/epoxy composite to improve the mechanical and physical properties. The composites are fabricated by hand lay-up method. It is observed that mechanical properties like flexural strength, hardness are more in case of SiO2 modified epoxy composite compare to other nano
... Show MoreCdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.77- 1.84) eV and from
... Show MoreThis work concerns the thermal and sound insulation as well as the mechanical properties of polymer matrix composite reinforced with glass fibers. These fibers may have dangerous effect during handling, for example the glass fibers might cause some damage to the eyes, lungs and even skin. For this reason the present work, investigates the behavior of polymer composite reinforced with natural fibers (Plant fibers) as replacement to glass fibers. Unsaturated Polyester resin was used as matrix material reinforced with two types of fibers, one of them is artificial (Glass fibers) and the other type is natural (Jute, Fronds Palm and Reed Fibers) by hand lay-up technique. All fibers are untreated with any chemical solvent. The Percentage of mi
... Show MoreThe physical, the thermal and the mechanical properties of Nano-composites, that consisted of Polyprime EP epoxy that reinforced by multi-walled carbon nanotubes (MWCNTs), have been studied. Various loading ratios, 0.1, 0.5, and 1 wt. %of MWCNT shave been infused into epoxy by a magnetic stirrer and then the hardener mixed with the mthat supplied with the epoxy. All sample shave been cutting using CNC machine. Tensile test, three-point bending, hardness tests, lee's disk, differential scanning calorimetry, water absorption and dielectric and electrical conductivity test were utilized on unfilled, MWCNT-filled epoxy to identify the loading effect on the properties of materials. Scanning electron microscopy (SEM) was used to determine the
... Show MoreIn this research, damping properties for composite materials were evaluated using logarithmic decrement method to study the effect of reinforcements on the damping ratio of the epoxy matrix. Three stages of composites were prepared in this research. The first stage included preparing binary blends of epoxy (EP) and different weight percentages of polysulfide rubber (PSR) (0%, 2.5%, 5%, 7.5% and 10%). It was found that the weight percentage 5% of polysulfide was the best percentage, which gives the best mechanical properties for the blend matrix. The advantage of this blend matrix is that; it mediates between the brittle properties of epoxy and the flexible properties of a blend matrix with the highest percentage of PSR. The second stage
... Show MoreThe paper include studies the effect of solvent of dye doped in polymeric laser sample which manufactured in primo press way, which is used as an active (R6G) tunable dye lasers. The remarks show that, when the viscosity of the solvent (from Pure Water to Ethanol), for the same concentration and thickness of the performance polymeric sample is increased, the absorption spectrum is shifts towards the long wave length (red shift), & towards short wave length (blue shift) for fluorescence spectrum, also increased the quantum fluorescence yield. The best result we obtained for the quantum fluorescence yield is (0.882) with thickness (0.25mm) in Ethanol solvent in concentration (2*10-3mole/liter), while when we used the Pure Water as a solvent,
... Show MoreCarbides or nitrides thin films present materials with good mechanical properties for industrial applications as they can be coatings at low temperatures serve temperature sensitive surfaces. In this work the effect of the C percentage on the mechanical properties represented by the Young modulus (E) of combinatorial magnetron sputtered TiCx (34%x˂65%) has been studied. The structure of the produced films is TiC independent on the C concentration. The mechanical properties are increased with increasing the C concentration up to 50%, and then decreasing with further C % increasing. These results can be explained by considering the resultant residual stresses.
Applications of superconductor compounds were considered as modern and important topics, especially these which are exposures to one of the nuclear radiation kinds. So, we gone to investigate the influence of fast neutrons irradiation on electrical and structural characteristics of HgxSb1-xBa2Ca2Cu3O8+δ superconducting compound at (x = 0.7) in ratio. The superconducting specimens were synthesized using solid state technique. Specimens were exposure to the nuclear radiation using fast neutrons with doses (0, 9.06 x1010, 15.3 x 1010 and 18.17 x 1010) n/cm2 respectively. Electrical and X-ray diffraction properties of superconductor specimens before and after irradiation were investigated under standard conditions. Results of X-ray diffraction
... Show MoreBackground: Impression materials, impression trays, and poured stone cast have been said to be the main source of cross infection between patients and dentists. However, it was observed that disinfection of the impression is not performed systematically in routine dental practice. Disinfection of alginates either by immersion or spray technique was found to cause dimensional inaccuracies, although with proper disinfection of alginates there were small dimensional changes. A variety of fluoride releasing products designed for topical use is currently available. Following their use, varied amount of fluoride is systemically absorbed depending on the fluoride concentration and the manner of its use. The objective of this study was to evaluate
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