Homogeneity and heterogeneity
Encyclopedia
Homogeneity and heterogeneity are concepts relating to the uniformity or lack thereof in a substance. A material that is homogeneous is uniform in composition or character; one that is heterogeneous lacks uniformity in one of these qualities.
The concepts are applicable to every level of complexity, from atom
s to population
s of animal
s or people
, to galaxies
. Hence, a substance may be homogeneous on a larger scale, compared to being heterogeneous on a smaller scale within the same substance. This is known as an effective medium
approach, or effective medium approximations.
Various disciplines understand heterogeneity, or being heterogeneous, in different ways. For example:
.
, homogeneous may refer to:
of two or more compounds
. Examples are: mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a salad, trail mix, and concrete (not cement). During the sampling
of heterogeneous mixtures of particles, the variance of the sampling error
is generally non-zero. Gy's sampling theory
quantitatively defines the heterogeneity of a particle as:
where
, 
, 
, 
, and 
are respectively: the heterogeneity of the 
th particle of the population, the mass concentration of the property of interest in the 
th particle of the population, the mass concentration of the property of interest in the population, the mass of the 
th particle in the population, and the average mass of a particle in the population.
Homogenization is the process of causing a heterogeneous mixture to become homogeneous, as is done with the making of homogenized milk.
s in which the reactants are in the same phase
, while heterogeneous reactions have reactants in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous. A reaction between two gases, two liquids or two solids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous.
A mixture can be determined to be homogeneous when everything is settled and equal, and the liquid, gas, object is one color or the same form. Various models have been proposed to model the concentrations in different phases. The phenomena to be considered are mass rates and reaction rates. Surface area affects the reaction rate of heterogeneous reactions but not homogeneous reactions.
refers to multiple origins causing the same disorder in different individuals. Heterogeneity of ion channel
s means diversity of different types of channels serving a specific kind of current, e.g. by channels with different constitutive subunits
.
because it may cause statistical bias in estimated coefficients. It complicates the theoretical analysis of economic models, since the model must be enlarged with more equations or variables to take into account the effects of the differences across units.
The concepts are applicable to every level of complexity, from atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s to population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...
s of animal
Animal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
s or people
Human
Humans are the only living species in the Homo genus...
, to galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
. Hence, a substance may be homogeneous on a larger scale, compared to being heterogeneous on a smaller scale within the same substance. This is known as an effective medium
Effective Medium Approximations
Effective medium approximations or effective medium theory are physical models that describe the macroscopic properties of a medium based on the properties and the relative fractions of its components...
approach, or effective medium approximations.
Heterogeneity
Heterogeneity is the state of being heterogeneous. It is the nature of opposition, or contrariety of qualities. Pertaining to the sciences, it is a substance that is diverse in kind or nature; composed of diverse parts. In other words, it is composed of dissimilar parts, hence the constituents are of a different kind. The parts (or constituents) are connected, and of a conglomerate mass, and viewed in respect to the parts of which it is made up.Various disciplines understand heterogeneity, or being heterogeneous, in different ways. For example:
- In physicsPhysicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, it is understood as having more than one phasePhase (matter)In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
(solid, liquid, gas) present in a system or process. - In chemistryChemistryChemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, a heterogeneous material consists of either or both of a) multiple states of matter or b) hydrophilic and hydrophobic substances in one mixture; an example of the latter would be a mixture of water, octaneOctaneOctane is a hydrocarbon and an alkane with the chemical formula C8H18, and the condensed structural formula CH36CH3. Octane has many structural isomers that differ by the amount and location of branching in the carbon chain...
, and silicone grease. - With information technologyInformation technologyInformation technology is the acquisition, processing, storage and dissemination of vocal, pictorial, textual and numerical information by a microelectronics-based combination of computing and telecommunications...
(see:Heterogeneous computingHeterogeneous computingHeterogeneous computing systems refer to electronic systems that use a variety of different types of computational units. A computational unit could be a general-purpose processor , a special-purpose processor Heterogeneous computing systems refer to electronic systems that use a variety of...
) it means a networkNetwork scienceNetwork science is a new and emerging scientific discipline that examines the interconnections among diverse physical or engineered networks, information networks, biological networks, cognitive and semantic networks, and social networks. This field of science seeks to discover common principles,...
comprising different types of computers, potentially with vastly differing memoryComputer memoryIn computing, memory refers to the physical devices used to store programs or data on a temporary or permanent basis for use in a computer or other digital electronic device. The term primary memory is used for the information in physical systems which are fast In computing, memory refers to the...
sizes, processing power and even basic underlying architecture. Alternatively, a data resource with multiple types of formats. - In sociologySociologySociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...
it may refer to a society or group that includes individuals of differing ethnicities, cultural backgrounds, sexes, or ages. - Rocks (geology) are inherently heterogeneous, usually occurring at the micro-scale and mini-scale.
Homogeneity
Homogeneity is the state of being homogeneous. Pertaining to the sciences, it is a substance where all the constituents are of the same nature; consisting of similar parts, or of elements of the like nature. For example, homogeneous particles, homogeneous elements, homogeneous principles, or homogeneous bodies; or (algebra) possessing the same number of factors of a given kind as with a homogeneous polynomialHomogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose monomials with nonzero coefficients all have thesame total degree. For example, x^5 + 2 x^3 y^2 + 9 x y^4 is a homogeneous polynomial...
.
Mathematics
In mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, homogeneous may refer to:
- Homogeneous differential equationHomogeneous differential equationThe term homogeneous differential equation has several distinct meanings.One meaning is that a first-order ordinary differential equation is homogeneous if it has the formwhere F is a homogeneous function of degree zero; that is to say, that F = F.In a related, but distinct, usage, the term linear...
- Homogeneous distribution
- Homogeneous functionHomogeneous functionIn mathematics, a homogeneous function is a function with multiplicative scaling behaviour: if the argument is multiplied by a factor, then the result is multiplied by some power of this factor. More precisely, if is a function between two vector spaces over a field F, and k is an integer, then...
- Homogeneous polynomialHomogeneous polynomialIn mathematics, a homogeneous polynomial is a polynomial whose monomials with nonzero coefficients all have thesame total degree. For example, x^5 + 2 x^3 y^2 + 9 x y^4 is a homogeneous polynomial...
- Homogeneous spaceHomogeneous spaceIn mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group,...
Chemistry
A heterogeneous mixture is a mixtureMixture
In chemistry, a mixture is a material system made up by two or more different substances which are mixed together but are not combined chemically...
of two or more compounds
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...
. Examples are: mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a salad, trail mix, and concrete (not cement). During the sampling
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
of heterogeneous mixtures of particles, the variance of the sampling error
Sampling error
-Random sampling:In statistics, sampling error or estimation error is the error caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic...
is generally non-zero. Gy's sampling theory
Gy's sampling theory
Gy's sampling theory is a theory about the sampling of materials, developed by Pierre Gy from the 1950s to beginning 2000s in articles and books including:* Sampling nomogram* Sampling of particulate materials; theory and practice...
quantitatively defines the heterogeneity of a particle as:
where
, , , , and are respectively: the heterogeneity of the th particle of the population, the mass concentration of the property of interest in the th particle of the population, the mass concentration of the property of interest in the population, the mass of the th particle in the population, and the average mass of a particle in the population.Homogenization is the process of causing a heterogeneous mixture to become homogeneous, as is done with the making of homogenized milk.
Homogeneous and heterogeneous reactions
Homogeneous reactions are chemical reactionChemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
s in which the reactants are in the same phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
, while heterogeneous reactions have reactants in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous. A reaction between two gases, two liquids or two solids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous.
A mixture can be determined to be homogeneous when everything is settled and equal, and the liquid, gas, object is one color or the same form. Various models have been proposed to model the concentrations in different phases. The phenomena to be considered are mass rates and reaction rates. Surface area affects the reaction rate of heterogeneous reactions but not homogeneous reactions.
Biology
Genetic heterogeneityGenetic heterogeneity
Genetic Heterogeneity is a phenomenon in which a single phenotype or genetic disorder may be caused by any one of a multiple number of alleles or non-allele mutations. This is in contrast to pleiotropy, where a single gene may cause multiple phenotypic expressions or disorders...
refers to multiple origins causing the same disorder in different individuals. Heterogeneity of ion channel
Ion channel
Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...
s means diversity of different types of channels serving a specific kind of current, e.g. by channels with different constitutive subunits
Protein subunit
In structural biology, a protein subunit or subunit protein is a single protein molecule that assembles with other protein molecules to form a protein complex: a multimeric or oligomeric protein. Many naturally occurring proteins and enzymes are multimeric...
.
Economics
Heterogeneity of the units under study (consumers, firms, products, etcetera) causes complications in economic analysis. Unobserved heterogeneity complicates econometricsEconometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
because it may cause statistical bias in estimated coefficients. It complicates the theoretical analysis of economic models, since the model must be enlarged with more equations or variables to take into account the effects of the differences across units.
See also
- Complete spatial randomnessComplete spatial randomnessComplete spatial randomness describes a point process whereby point events occur within a given study area in a completely random fashion. Such a process is often modeled using only one parameter, i.e. the density of points, \rho within the defined area...
- Spatial analysisSpatial analysisSpatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties...
- EpidemiologyEpidemiologyEpidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
- Statistical hypothesis testingStatistical hypothesis testingA statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
External link
- The following cited pages in this book cover the meaning of "homogeneity" across disciplines .