Numerical solution of a Gamma - integral equation using a higher order composite Newton-Cotes formulas

The paper aims at solving a complex equation with Gamma - integral. The solution is the infected size (p) at equilibrium. The approaches are both numerical and analytical methods. As a numerical method, the higher-order composite Newton-Cotes formula is developed and implemented. The results show that the infected size (p) increases along with the shape parameter (k). But the increase has two phases: an increasing rate phase and a decreasing rate phase; both phases can be explained by the instantaneous death rate characteristics of the Gamma distribution hazard function. As an analytical method, the Extreme Value Theory consolidates the numerical solutions of the infected size (p) when k ≥ 1 and provides a solution limit ( p = 1 − 1 2 R ) as k goes to +∞.

Influence of Natural and Climatic Factors on Water Horizons Protection Degree in Site Evaluation for Radioactive Waste Disposal

In this paper, natural (geological and hydrological) and climatic impact conditions on the influence zone for two different sites of radioactive waste disposals have been studied. Probabilistic approach to assessment of the groundwater vulnerability from radionuclide contamination during disposal of radioactive waste is developed. As to climatic conditions, an effective numerical and analytical methods for annual precipitation rates assessment of rare recurrence have been proposed which allow to take into account uncertainties of rare events as well.

Prediction and measurement of acoustic transmission loss of acoustic window with composite sandwich structure

Underwater acoustic detection sensors are mounted on the outside of the submarine; the acoustic window for protecting these sensors must be structurally robust while also minimizing any deterioration of sensor's sound detection performance. These two conditions are typically satisfied simultaneously by using composite materials with acoustic window materials. However, since such composite material is manufactured by laminating fibers, there is the probability that delamination occurs, in which an air layer is formed inside, due to manufacturing process errors. Delamination inside the acoustic window degrades the sensor's acoustic performance and results in a failure of military operations. In the case of composites composed of sandwich structures located in the central part, the possibility of internal delamination is higher than in a single composite material. Therefore, it is very important to discriminate the presence or absence of internal delamination after producing an acoustic window. This article uses numerical and analytical methods to determine the internal delamination of the acoustic window fabricated with a sandwich structure. In addition, the results were analyzed and compared through ultrasonic measurement and acoustic transmission loss test.

Magnetic anisotropic colloids in nematic liquid crystals: Fluctuating dynamics simulated by multi-particle collision dynamics

Elongated colloids with a permanent magnetic moment and immersed in a nematic liquid crystal are studied numerically using a mesoscopic scheme that supports fluctuations, hydrodynamics, and topological defects. Colloids are accompanied by disclinations curves and subjected to an effective torque caused by the nematic environment and to a magnetic torque due to an external magnetic field. The case is analyzed where these torques compete to bring colloids to two different mutually perpendicular equilibrium states. The fluctuating dynamics of the colloid-defect pair is studied in terms of orientational correlation functions. Analytical expressions for these correlations are derived on the basis of an approximated planar lineal model. A good agreement is found between the numerical and analytical methods when magnetic torques are much larger than nematic torques, while for smaller magnetic torques nonlinear effects are demonstrated to be important. As conclusion, the numerical technique could be considered a reliable approach to the rotational motion of polar nanoparticles in liquid crystals.

Investigation of Effective Mechanical Characteristics of Nanomodified Carbon-Epoxide Composite by Numerical and Analytical Methods

In this work, the mechanical properties of composite samples prepared using a conventional and nanomodified matrix were studied. The thickness of the monolayers in the samples was 0,2 μm. It was found in experiments, that the addition of fullerene soot as a nanomodifierled to an increase in the mechanical properties of the samples along the direction of reinforcement. At the same time, an improvement in the quality of the contact of the matrix with the fibers in the samples with the nanomodifier was observed: on the fracture surface, the nanomodified matrix envelops the fibers, while the usual matrix completely exfoliates. The obtained effects of changing the strength of composites can be associated, among other things, with a change in the level of residual stresses arising in composites during nanomodification. Analytical and numerical modeling methods are used to explain these effects.

Barrier effect of underground structures on aquifers

Impervious structures below the water table modify the natural groundwater flow in aquifers. They act as barriers, causing heads to rise upgradient and to fall downgradient. We define the barrier effect as the increase in head loss across the barrier with respect to the natural conditions prior to construction. We distinguish between regional (the minimum head loss observed at long distances) and local (the maximum head loss observed close to the structure) barrier effects. We use numerical and analytical methods to derive semi-empirical equations to quantify the two barrier effects for semi-permeable, partially penetrating (or fully penetrating but finite in length), and barriers with a by-pass in confined aquifers. The resulting equations depend on the barrier geometry and on the natural head gradient in the aquifer and they are easy to apply. We test their validity at two construction sites, obtaining excellent agreement between the computed and observed barrier effects.