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Topic Review
Fractional Calculus in Electromagnetic Theory
Fractional calculus (FC) was introduced more than 300 years ago as a generalization of classical derivative and integral definitions. It is receiving increasing attention for a growing number of applications in different sciences such as physics, biology, chemistry, engineering, finance, mechanics, optics and, in particular, for modeling physical phenomena related to non-Markovian processes, signal and image processing, dielectric relaxation, viscoelasticity, electromagnetism, control theory, pharmacokinetics, fluids, heat transfer, and so on.
  • 831
  • 27 May 2022
Topic Review
Fractional Schrödinger Equation
The fractional Schrödinger equation is a fundamental equation of fractional quantum mechanics. It was discovered by Nick Laskin (1999) as a result of extending the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical paths. The term fractional Schrödinger equation was coined by Nick Laskin.
  • 1.0K
  • 24 Oct 2022
Topic Review
Framework for Building Resilient Water and Infrastructure Systems
Planning and developing resilient socio-technical and natural systems to cope with and respond to unprecedented changes has been one of the top goals of government bodies, researchers, and practitioners worldwide. 
  • 556
  • 24 Apr 2022
Topic Review
Free Entropy
A thermodynamic free entropy is an entropic thermodynamic potential analogous to the free energy. Also known as a Massieu, Planck, or Massieu–Planck potentials (or functions), or (rarely) free information. In statistical mechanics, free entropies frequently appear as the logarithm of a partition function. The Onsager reciprocal relations in particular, are developed in terms of entropic potentials. In mathematics, free entropy means something quite different: it is a generalization of entropy defined in the subject of free probability. A free entropy is generated by a Legendre transformation of the entropy. The different potentials correspond to different constraints to which the system may be subjected.
  • 478
  • 04 Nov 2022
Topic Review
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute (2 hertz), its period, T, — the time interval between beats—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.
  • 4.2K
  • 16 Nov 2022
Topic Review
Fresnel Imager
A Fresnel imager is a proposed ultra-lightweight design for a space telescope that uses a Fresnel array as primary optics instead of a typical lens. It focuses light with a thin opaque foil sheet punched with specially shaped holes, thus focusing light on a certain point by using the phenomenon of diffraction. Such patterned sheets, called Fresnel zone plates, have long been used for focusing laser beams, but have so far not been used for astronomy. No optical material is involved in the focusing process as in traditional telescopes. Rather, the light collected by the Fresnel array is concentrated on smaller classical optics (e.g. 1/20th of the array size), to form a final image. The long focal lengths of the Fresnel imager (a few kilometers) require operation by two-vessel formation flying in space at the L2 Sun-Earth Lagrangian point. In this two spacecraft formation-flying instrument, one spacecraft holds the focussing element: the Fresnel interferometric array; the other spacecraft holds the field optics, focal instrumentation, and detectors.
  • 275
  • 01 Nov 2022
Topic Review
Friction Force Microscope
In materials science, chemical force microscopy (CFM) is a variation of atomic force microscopy (AFM) which has become a versatile tool for characterization of materials surfaces. With AFM, structural morphology is probed using simple tapping or contact modes that utilize van der Waals interactions between tip and sample to maintain a constant probe deflection amplitude (constant force mode) or maintain height while measuring tip deflection (constant height mode). CFM, on the other hand, uses chemical interactions between functionalized probe tip and sample. Choice chemistry is typically gold-coated tip and surface with R–SH thiols attached, R being the functional groups of interest. CFM enables the ability to determine the chemical nature of surfaces, irrespective of their specific morphology, and facilitates studies of basic chemical bonding enthalpy and surface energy. Typically, CFM is limited by thermal vibrations within the cantilever holding the probe. This limits force measurement resolution to ~1 pN which is still very suitable considering weak COOH/CH3 interactions are ~20 pN per pair. Hydrophobicity is used as the primary example throughout this consideration of CFM, but certainly any type of bonding can be probed with this method.
  • 269
  • 17 Nov 2022
Topic Review
Frost Diagram
A Frost diagram or Frost–Ebsworth diagram is a type of graph used by inorganic chemists in electrochemistry to illustrate the relative stability of a number of different oxidation states of a particular substance. The graph illustrates the free energy vs oxidation state of a chemical species. This effect is dependent on pH, so this parameter also must be included. The free energy is determined by the oxidation–reduction half-reactions. The Frost diagram allows easier comprehension of these reduction potentials than the earlier-designed Latimer diagram, because the “lack of additivity of potentials” was confusing. The free energy ΔG° is related to reduction potential E in the graph by given formula: ΔG° = −nFE° or nE° = −ΔG°/F, where n is the number of transferred electrons, and F is Faraday constant (F = 96,485 J/(V·mol)). The Frost diagram is named after Arthur Atwater Frost (de), who originally created it as a way to "show both free energy and oxidation potential data conveniently" in a 1951 paper.
  • 3.3K
  • 01 Dec 2022
Topic Review
FTIR for Vehicle Exhaust Emissions
In a Fourier Transform InfraRed (FTIR) spectrometer, some of the infrared (IR) radiation is absorbed by the sample, and some of it is passed through (transmitted). The resulting molecular absorption and transmission response can be used to identify the components of the sample and their concentration.
  • 1.7K
  • 20 Aug 2021
Topic Review
Fully Integrated Photoacoustic NO2 Sensor
A fully integrated photoacoustic nitrogen dioxide (NO2) sensor is developed and demonstrated. In this sensor, an embedded photoacoustic cell was manufactured by using an up-to-date 3D printing technique. A blue laser diode was used as a light source for excitation of photoacoustic wave in the photoacoustic cell. The photoacoustic wave is detected by a sensitive microelectromechanical system (MEMS) microphone. Homemade circuits are integrated into the sensor for laser diode driving and signal processing. The sensor was calibrated by using a chemiluminescence NO–NO2–NOX gas analyzer. And the performance of this sensor was evaluated. The linear relationship between photoacoustic signals and NO2 concentrations was verified in a range of below 202 ppb. The limit of detection was determined to 0.86 ppb with an integration time of 1 s. The corresponding normalized noise equivalent absorption was 2.0 × 10−8 cm−1∙W∙Hz−1/2. The stability and the optimal integration time were evaluated with an Allan deviation analysis, from which a detection limit of 0.25 ppb at the optimal integration time of 240 s was obtained. The sensor was used to measure outdoor air and the results agree with that obtained from the NO–NO2–NOX gas analyzer. The low-cost and portable photoacoustic NO2 sensor has a potential application for atmospheric NO2 monitoring.
  • 993
  • 01 Nov 2020
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