Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Photoelectrochemical cellA "photoelectrochemical cell" is one of two distinct classes of device. The first produces electrical energy similarly to a dye-sensitized photovoltaic cell, which meets the standard definition of a photovoltaic cell. The second is a photoelectrolytic cell, that is, a device which uses light incident on a photosensitizer, semiconductor, or aqueous metal immersed in an electrolytic solution to directly cause a chemical reaction, for example to produce hydrogen via the electrolysis of water.
Water splittingWater splitting is the chemical reaction in which water is broken down into oxygen and hydrogen: 2 H2O → 2 H2 + O2 Efficient and economical water splitting would be a technological breakthrough that could underpin a hydrogen economy, based on green hydrogen. A version of water splitting occurs in photosynthesis, but hydrogen is not produced. The reverse of water splitting is the basis of the hydrogen fuel cell. Electrolysis of water Electrolysis of water is the decomposition of water (H2O) into oxygen (O2) and hydrogen (H2) due to an electric current being passed through the water.
Electrolysis of waterElectrolysis of water is using electricity to split water into oxygen (O2) and hydrogen (H2) gas by electrolysis. Hydrogen gas released in this way can be used as hydrogen fuel, but must be kept apart from the oxygen as the mixture would be extremely explosive. Separately pressurised into convenient 'tanks' or 'gas bottles', hydrogen can be used for oxyhydrogen welding and other applications, as the hydrogen / oxygen flame can reach circa 2,800°C. Water electrolysis requires a minimum potential difference of 1.
Continuum mechanicsContinuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. A continuum model assumes that the substance of the object completely fills the space it occupies. This ignores the fact that matter is made of atoms, however provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances.
Photocatalytic water splittingPhotocatalytic water splitting is a process that uses photocatalysis for the dissociation of water (H2O) into hydrogen (H2) and oxygen (O2). Only light energy (photons), water, and a catalyst(s) are needed, since this is what naturally occurs in natural photosynthetic oxygen production and CO2 fixation. Photocatalytic water splitting is done by dispersing photocatalyst particles in water or depositing them on a substrate, unlike Photoelectrochemical cell, which are assembled into a cell with a photoelectrode.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Photoelectrolysis of waterPhotoelectrolysis of water, also known as photoelectrochemical water splitting, occurs in a photoelectrochemical cell when light is used as the energy source for the electrolysis of water, producing dihydrogen which can be used as a fuel. This process is one route to a "hydrogen economy", in which hydrogen fuel is produced efficiently and inexpensively from natural sources without using fossil fuels. In contrast, steam reforming usually or always uses a fossil fuel to obtain hydrogen.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Introduced speciesAn introduced species, alien species, exotic species, adventive species, immigrant species, foreign species, non-indigenous species, or non-native species is a species living outside its native distributional range, but which has arrived there by human activity, directly or indirectly, and either deliberately or accidentally. Non-native species can have various effects on the local ecosystem. Introduced species that become established and spread beyond the place of introduction are considered naturalized.
Invasive speciesAn invasive or alien species is an introduced species to an environment that becomes overpopulated and harms its new environment. Invasive species adversely affect habitats and bioregions, causing ecological, environmental, and/or economic damage. The term can also be used for native species that become harmful to their native environment after human alterations to its food web - for example, the purple sea urchin (Strongylocentrotus purpuratus) which has decimated kelp forests along the northern California coast due to overharvesting of its natural predator, the California sea otter (Enhydra lutris).
Solar energySolar energy is radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy (including solar water heating), and solar architecture. It is an essential source of renewable energy, and its technologies are broadly characterized as either passive solar or active solar depending on how they capture and distribute solar energy or convert it into solar power.
Species distributionSpecies distribution, or species dispersion, is the manner in which a biological taxon is spatially arranged. The geographic limits of a particular taxon's distribution is its range, often represented as shaded areas on a map. Patterns of distribution change depending on the scale at which they are viewed, from the arrangement of individuals within a small family unit, to patterns within a population, or the distribution of the entire species as a whole (range).
Modeling languageA modeling language is any artificial language that can be used to express data, information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure Programing language. A modeling language can be graphical or textual. Graphical modeling languages use a diagram technique with named symbols that represent concepts and lines that connect the symbols and represent relationships and various other graphical notation to represent constraints.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Agent-based modelAn agent-based model (ABM) is a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and what governs its outcomes. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. Monte Carlo methods are used to understand the stochasticity of these models.
Native speciesIn biogeography, a native species is indigenous to a given region or ecosystem if its presence in that region is the result of only local natural evolution (though often popularised as "with no human intervention") during history. The term is equivalent to the concept of indigenous or autochthonous species. A wild organism (as opposed to a domesticated organism) is known as an introduced species within the regions where it was anthropogenically introduced.
