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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
π Molecular Orbitals of 1,3-Butadiene01:24

π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...
Vector Algebra: Method of Components01:08

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
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Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...

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Solucionador de modo vectorial completo basado en el método de perturbación adiabática no hermetiana.

Junhe Zhou, Yuekai Zhang, Chengwen Huang

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    PubMed
    Resumen

    Este estudio introduce un eficiente solucionador de modo de guía de onda óptica utilizando la teoría de perturbaciones adiabáticas no hermetianas. El método reduce significativamente el tiempo de computación al tiempo que mantiene una alta precisión para varias estructuras de guía de onda.

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    Área de la Ciencia:

    • Fotónica e ingeniería de guías de onda.
    • La electromagnetismo computacional es el campo de la electromagnetismo.

    Sus antecedentes:

    • El cálculo de los modos de guía de onda óptica requiere recursos computacionales significativos.
    • Los métodos existentes para resolver el modo vectorial completo son computacionalmente intensivos.

    Objetivo del estudio:

    • Desarrollar un solucionador de modo vectorial completo computacionalmente eficiente y preciso para guías de onda ópticas.
    • Aprovechar la teoría de perturbaciones adiabáticas no hermetianas para el análisis de modos.

    Principales métodos:

    • Un nuevo solucionador de modo vectorial completo que integra un solucionador de modo escalar con la teoría de perturbaciones adiabáticas no hermetianas.
    • El método incorpora gradientes de índice de guía de onda y no ortogonalidad modal durante la conversión de modo.

    Principales resultados:

    • El solucionador propuesto reduce el tiempo computacional en aproximadamente un 75% en comparación con los métodos convencionales.
    • Se demostró una alta precisión a través de guías de onda de bajo / alto índice de contraste y guías de onda de sección grande / pequeña.
    • Las discrepancias del índice efectivo fueron mínimas, por debajo de 4e-9 para las guías de onda de guía débil y 0,17 para las guías de onda de guía fuerte.

    Conclusiones:

    • El método de perturbación adiabática no hermetiana ofrece una aceleración significativa para el análisis de guías de onda ópticas.
    • El método es preciso y versátil para diversos diseños de guías de onda.
    • Las aplicaciones potenciales se extienden a otros problemas de modos propios no herméticos.