Current Issue : January-March Volume : 2025 Issue Number : 1 Articles : 5 Articles
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as 2 , a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x- , y- , and z- axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma....
This paper introduces fractional Brownian motion into the study of Maxwell nanofluids over a stretching surface. Nonlinear coupled spatial fractional-order energy and mass equations are established and solved numerically by the finite difference method with Newton’s iterative technique. The quantities of physical interest are graphically presented and discussed in detail. It is found that the modified model with fractional Brownian motion is more capable of explaining the thermal conductivity enhancement. The results indicate that a reduction in the fractional parameter leads to thinner thermal and concentration boundary layers, accompanied by higher local Nusselt and Sherwood numbers. Consequently, the introduction of a fractional Brownian model not only enriches our comprehension of the thermal conductivity enhancement phenomenon but also amplifies the efficacy of heat and mass transfer within Maxwell nanofluids. This achievement demonstrates practical application potential in optimizing the efficiency of fluid heating and cooling processes, underscoring its importance in the realm of thermal management and energy conservation....
Data has attributes, and synchronous changes between data and attributes are the basic characteristics of a type of data: under the condition of supplementing (deleting) some attributes, some data elements are deleted (supplemented) from data. The attributes of data elements follow the conjunctive normal form. Based on the dynamic mathematical model P-sets, firstly, the conception and generation criteria of embedded data are proposed, and the inference theory of embedded data are studied. Secondly, intelligent retrieval and retrieval theorems for embedded data are proposed. Then, intelligent retrieval and secure acquisition algorithms for embedded data are designed. Finally, an application example is presented....
This study presents a numerical simulation methodology for investigating blood flow in veins and arteries using a computational approach. The simulation is based on the Navier-Stokes equations, discretization techniques, and finite difference methods. The aim of this research is to provide insights into the behavior of blood flow under simplified conditions, enabling a better understanding of the underlying fluid dynamics. The methodology incorporates steady-state flow assumptions and a 2D geometry, making it suitable for initial explorations of blood flow patterns in a controlled environment. However, it is important to note that the model’s assumptions limit its applicability to realworld scenarios, and additional considerations such as pulsatile flow, arterial compliance, and non-Newtonian viscosity should be incorporated for more accurate simulations....
From 1948 until around 1965, Louis de Broglie, awarded the Nobel Prize for Physics in 1929 for his fundamental contributions to quantum theory, pursued a systematic study of the formal analogies between wave mechanics and the thermomechanics of Boltzmann and Helmholtz. As part of this line of research, he produced several interesting observations, which were, however, published only in French, and, therefore, had a very limited diffusion. Here, we reconsider, in particular, a result of his relating to the analogy between the internal clock (de Broglie phase) of a free particle and a cyclic isothermal process in a thermomechanical system. We show that the fundamental equivalence obtained by him can be derived under more convenient hypotheses than the original ones, essentially tied to the quantization of the action exchanged by the particle with a suitable thermostat. In this emended formulation, the relations proposed by de Broglie describe the emergence of the particle proper time from a thermal background. They also suggest a specific physical meaning of theWick rotation, often used in quantum mechanical calculations, and the thermal time that appears in it....
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