Scientific model in the context of "Particles"

Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.

In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.

The term particle is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun particulate is most frequently used to refer to pollutants in the Earth's atmosphere, which are a suspension of unconnected particles, rather than a connected particle aggregation.

Peripatric speciation is a mode of speciation in which a new species is formed from an isolated peripheral population. Since peripatric speciation resembles allopatric speciation, in that populations are isolated and prevented from exchanging genes, it can often be difficult to distinguish between them, and peripatric speciation may be considered one type or model of allopatric speciation. The primary distinguishing characteristic of peripatric speciation is that one of the populations is much smaller than the other, as opposed to (other types of) allopatric speciation, in which similarly-sized populations become separated. The terms peripatric and peripatry are often used in biogeography, referring to organisms whose ranges are closely adjacent but do not overlap, being separated where these organisms do not occur—for example on an oceanic island compared to the mainland. Such organisms are usually closely related (e.g. sister species); their distribution being the result of peripatric speciation.

The concept of peripatric speciation was first outlined by the evolutionary biologist Ernst Mayr in 1954. Since then, other alternative models have been developed such as centrifugal speciation, that posits that a species' population experiences periods of geographic range expansion followed by shrinking periods, leaving behind small isolated populations on the periphery of the main population. Other models have involved the effects of sexual selection on limited population sizes. Other related models of peripherally isolated populations based on chromosomal rearrangements have been developed such as budding speciation and quantum speciation.

In fluid dynamics, the wave method (WM), or wave characteristic method (WCM), is a model describing unsteady flow of fluids in conduits (pipes).

DNA condensation refers to the process of compacting DNA molecules in vitro or in vivo. Mechanistic details of DNA packing are essential for its functioning in the process of gene regulation in living systems. Condensed DNA often has surprising properties, which one would not predict from classical concepts of dilute solutions. Therefore, DNA condensation in vitro serves as a model system for many processes of physics, biochemistry and biology. In addition, DNA condensation has many potential applications in medicine and biotechnology.

DNA diameter is about 2 nm, while the length of a stretched single molecule may be up to several dozens of centimetres depending on the organism. Many features of the DNA double helix contribute to its large stiffness, including the mechanical properties of the sugar-phosphate backbone, electrostatic repulsion between phosphates (DNA bears on average one elementary negative charge per each 0.17 nm of the double helix), stacking interactions between the bases of each individual strand, and strand-strand interactions. DNA is one of the stiffest natural polymers, yet it is also one of the longest molecules. The persistence length of double-stranded DNA (dsDNA) is a measure of its stiffness or flexibility, which depends on the DNA sequence and the surrounding environment, including factors like salt concentration, pH, and temperature. Under physiological conditions (e.g., near-neutral pH and physiological salt concentrations), the persistence length of dsDNA is generally around 50 nm, which corresponds to approximately 150 base pairs. This means that at large distances DNA can be considered as a flexible rope, and on a short scale as a stiff rod. Like a garden hose, unpacked DNA would randomly occupy a much larger volume than when it is orderly packed. Mathematically, for a non-interacting flexible chain randomly diffusing in 3D, the end-to-end distance would scale as a square root of the polymer length. For real polymers such as DNA, this gives only a very rough estimate; what is important, is that the space available for the DNA in vivo is much smaller than the space that it would occupy in the case of a free diffusion in the solution. To cope with volume constraints, DNA can pack itself in the appropriate solution conditions with the help of ions and other molecules. Usually, DNA condensation is defined as "the collapse of extended DNA chains into compact, orderly particles containing only one or a few molecules". This definition applies to many situations in vitro and is also close to the definition of DNA condensation in bacteria as "adoption of relatively concentrated, compact state occupying a fraction of the volume available". In eukaryotes, the DNA size and the number of other participating players are much larger, and a DNA molecule forms millions of ordered nucleoprotein particles, the nucleosomes, which is just the first of many levels of DNA packing.

A biological rule or biological law is a generalized law, principle, or rule of thumb formulated to describe patterns observed in living organisms. Biological rules and laws are often developed as succinct, broadly applicable ways to explain complex phenomena or salient observations about the ecology and biogeographical distributions of plant and animal species around the world, though they have been proposed for or extended to all types of organisms. Many of these regularities of ecology and biogeography are named after the biologists who first described them.

From the birth of their science, biologists have sought to explain apparent regularities in observational data. In his biology, Aristotle inferred rules governing differences between live-bearing tetrapods (in modern terms, terrestrial placental mammals). Among his rules were that brood size decreases with adult body mass, while lifespan increases with gestation period and with body mass, and fecundity decreases with lifespan. Thus, for example, elephants have smaller and fewer broods than mice, but longer lifespan and gestation. Rules like these concisely organized the sum of knowledge obtained by early scientific measurements of the natural world, and could be used as models to predict future observations. Among the earliest biological rules in modern times are those of Karl Ernst von Baer (from 1828 onwards) on embryonic development (see von Baer's laws), and of Constantin Wilhelm Lambert Gloger on animal pigmentation, in 1833 (see Gloger's rule).There is some scepticism among biogeographers about the usefulness of general rules. For example, J.C. Briggs, in his 1987 book Biogeography and Plate Tectonics, comments that while Willi Hennig's rules on cladistics "have generally been helpful", his progression rule is "suspect".