Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Travelling salesman problemThe travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Equilibrium thermodynamicsEquilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction.
Flowering plantFlowering plants are plants that bear flowers and fruits, and form the clade Angiospermae (ˌændʒiəˈspərmi:), commonly called angiosperms. They include all forbs (flowering plants without a woody stem), grasses and grass-like plants, a vast majority of broad-leaved trees, shrubs and vines, and most aquatic plants. The term "angiosperm" is derived from the Greek words ἀγγεῖον /angeion ('container, vessel') and σπέρμα / sperma ('seed'), meaning that the seeds are enclosed within a fruit.
Quantum thermodynamicsQuantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905, Albert Einstein argued that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized obtaining the relation . This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules.
Parasitic plantA parasitic plant is a plant that derives some or all of its nutritional requirements from another living plant. They make up about 1% of angiosperms and are found in almost every biome. All parasitic plants develop a specialized organ called the haustorium, which penetrates the host plant, connecting them to the host vasculature – either the xylem, phloem, or both. For example, plants like Striga or Rhinanthus connect only to the xylem, via xylem bridges (xylem-feeding).
Meshfree methodsIn the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.
Aquatic plantAquatic plants are plants that have adapted to living in aquatic environments (saltwater or freshwater). They are also referred to as hydrophytes or macrophytes to distinguish them from algae and other microphytes. A macrophyte is a plant that grows in or near water and is either emergent, submergent, or floating. In lakes and rivers macrophytes provide cover for fish, substrate for aquatic invertebrates, produce oxygen, and act as food for some fish and wildlife.
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.
