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The Tidyverse is a collection of R packages designed for data science that share an underlying design philosophy, grammar, and data structures. Developed by Hadley Wickham and others, it provides a consistent and powerful toolkit for data import, tidying, transformation, visualization, and modeling. Key packages include `ggplot2`, `dplyr`, `tidyr`, and `readr`, which compose together using…
Photosynthesis is a process used by plants, algae, and some bacteria to convert light energy into chemical energy. Sunlight provides the energy to convert carbon dioxide and water into glucose (a sugar for energy storage) and oxygen as a byproduct. The overall simplified chemical equation is 6CO_2 + 6H_2O + text{Light Energy} rightarrow C_6H_{12}O_6 +…
The Hampson-Linde cycle liquefies gases like air using the Joule-Thomson effect combined with regenerative cooling. High-pressure gas is cooled in a counter-flow heat exchanger by the cold, low-pressure gas returning from the expansion valve. This progressively lowers the temperature at the valve until it drops below the critical point and liquefaction begins, forming the basis…
Fraunhofer lines are a set of dark absorption lines in the optical spectrum of the Sun. They are the result of specific wavelengths of light from the Sun’s hot interior being absorbed by cooler atoms and ions in its photosphere. Each line corresponds to a particular electron transition in a specific element, allowing for the…
A hierarchical classification system for organizing scientific and technological research.[/caption] The “UNESCO Nomenclature for Fields of Science and Technology” is a hierarchical classification system developed by the United Nations Educational, Scientific and Cultural Organization to categorize research papers and doctoral dissertations. Initially proposed in the early 1970s, this system provides a standardized method for organizing…
The Kelvin relations are two equations that thermodynamically link the three thermoelectric coefficients: the first relation connects the Peltier coefficient (Pi[/latex]) to the Seebeck coefficient (S[/latex]) via absolute temperature (T[/latex]): Pi = S cdot T[/latex]. The second relates the Thomson coefficient (mathcal{K}[/latex]) to the temperature derivative of the Seebeck coefficient: mathcal{K} = T frac{dS}{dT}[/latex].
The natural CRISPR-Cas9 system was repurposed into a revolutionary gene-editing technology. By fusing the two essential RNA components (crRNA and tracrRNA) into a synthetic single-guide RNA (sgRNA), scientists created a simple two-component system. This sgRNA directs the Cas9 nuclease to any desired DNA location to create a precise double-strand break, which can then be repaired…
Dynamic pressure, denoted by q[/latex] or Q[/latex], is the kinetic energy per unit volume of a fluid. It is defined by the formula q = frac{1}{2} rho u^2[/latex], where rho[/latex] is the local fluid density and u[/latex] is the fluid velocity. This quantity is fundamental in fluid dynamics for quantifying the pressure arising from fluid…
Ohm’s law states that the electric current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This fundamental relationship in DC circuits is expressed by the equation I = frac{V}{R}[/latex], where I is the current in amperes, V is the potential difference in volts, and R…
A key theorem in non-equilibrium thermodynamics, these relations express the equality of certain cross-coefficients between coupled flows of energy and matter. They state that in the absence of a magnetic field, the matrix of transport coefficients is symmetric: L_{alphabeta} = L_{betaalpha}[/latex]. This links seemingly unrelated transport phenomena, such as the Seebeck and Peltier effects in…
