In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in common use: D4σ, 10/90 or 20/80 knife-edge, 1/e2, FWHM, and D86. The beam width can be measured in units of length at a particular plane perpendicular to the beam axis, but it can also refer to the angular width, which is the angle subtended by the beam at the source. The angular width is also called the beam divergence.
An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. Aerosols can be natural or anthropogenic. Examples of natural aerosols are fog or mist, dust, forest exudates, and geyser steam. Examples of anthropogenic aerosols include particulate air pollutants, mist from the discharge at hydroelectric dams, irrigation mist, perfume from atomizers, smoke, dust, steam from a kettle, sprayed pesticides, and medical treatments for respiratory illnesses. When a person inhales the contents of a vape pen or e-cigarette, they are inhaling an anthropogenic aerosol.
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering. As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays and X-rays was observed and discussed. With the discovery of subatomic particles and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.
In physics, mean free path is the average distance over which a moving particle travels before substantially changing its direction or energy, typically as a result of one or more successive collisions with other particles.
A synchrotron light source is a source of electromagnetic radiation (EM) usually produced by a storage ring, for scientific and technical purposes. First observed in synchrotrons, synchrotron light is now produced by storage rings and other specialized particle accelerators, typically accelerating electrons. Once the high-energy electron beam has been generated, it is directed into auxiliary components such as bending magnets and insertion devices in storage rings and free electron lasers. These supply the strong magnetic fields perpendicular to the beam that are needed to convert high energy electrons into photons.
The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Soil texture is a classification instrument used both in the field and laboratory to determine soil classes based on their physical texture. Soil texture can be determined using qualitative methods such as texture by feel, and quantitative methods such as the hydrometer method based on Stokes' law. Soil texture has agricultural applications such as determining crop suitability and to predict the response of the soil to environmental and management conditions such as drought or calcium (lime) requirements. Soil texture focuses on the particles that are less than two millimeters in diameter which include sand, silt, and clay. The USDA soil taxonomy and WRB soil classification systems use 12 textural classes whereas the UK-ADAS system uses 11. These classifications are based on the percentages of sand, silt, and clay in the soil.
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function. Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation.
The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation.
In granulometry, the particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Significant energy is usually required to disintegrate soil, etc. particles into the PSD that is then called a grain size distribution.
Particle size is a notion introduced for comparing dimensions of solid particles, liquid particles (droplets), or gaseous particles (bubbles). The notion of particle size applies to particles in colloids, in ecology, in granular material, and to particles that form a granular material.
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers — ultraviolet, visible, infrared, continuous wave, pulsed, high-power, low-power — there is an assortment of instrumentation for measuring laser beam profiles. No single laser beam profiler can handle every power level, pulse duration, repetition rate, wavelength, and beam size.
Particle size analysis, particle size measurement, or simply particle sizing, is the collective name of the technical procedures, or laboratory techniques which determines the size range, and/or the average, or mean size of the particles in a powder or liquid sample.
In probability theory and statistics, the index of dispersion, dispersion index,coefficient of dispersion,relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer. It is used in the determination of size of crystals in the form of powder.
The vapor–liquid–solid method (VLS) is a mechanism for the growth of one-dimensional structures, such as nanowires, from chemical vapor deposition. The growth of a crystal through direct adsorption of a gas phase on to a solid surface is generally very slow. The VLS mechanism circumvents this by introducing a catalytic liquid alloy phase which can rapidly adsorb a vapor to supersaturation levels, and from which crystal growth can subsequently occur from nucleated seeds at the liquid–solid interface. The physical characteristics of nanowires grown in this manner depend, in a controllable way, upon the size and physical properties of the liquid alloy.
Laser diffraction analysis, also known as laser diffraction spectroscopy, is a technology that utilizes diffraction patterns of a laser beam passed through any object ranging from nanometers to millimeters in size to quickly measure geometrical dimensions of a particle. This particle size analysis process does not depend on volumetric flow rate, the amount of particles that passes through a surface over time.
Grain size is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders.
A spray is a dynamic collection of drops dispersed in a gas. The process of forming a spray is known as atomization. A spray nozzle is the device used to generate a spray. The two main uses of sprays are to distribute material over a cross-section and to generate liquid surface area. There are thousands of applications in which sprays allow material to be used most efficiently. The spray characteristics required must be understood in order to select the most appropriate technology, optimal device and size.
