Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
Stochastic simulationA stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values. These steps are repeated until a sufficient amount of data is gathered. In the end, the distribution of the outputs shows the most probable estimates as well as a frame of expectations regarding what ranges of values the variables are more or less likely to fall in.
Training simulationIn business, training simulation is a virtual medium through which various types of skills can be acquired. Training simulations can be used in a variety of genres; however they are most commonly used in corporate situations to improve business awareness and management skills. They are also common in academic environments as an integrated part of a business or management course. The word simulation implies an imitation of a real-life process, usually via a computer or other technological device, in order to provide a lifelike experience.
Mechanical engineeringMechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the engineering branches. Mechanical engineering requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science, design, structural analysis, and electricity.
Section (fiber bundle)In the mathematical field of topology, a section (or cross section) of a fiber bundle is a continuous right inverse of the projection function . In other words, if is a fiber bundle over a base space, : then a section of that fiber bundle is a continuous map, such that for all . A section is an abstract characterization of what it means to be a graph. The graph of a function can be identified with a function taking its values in the Cartesian product , of and : Let be the projection onto the first factor: .
Critical point (thermodynamics)In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature Tc and a critical pressure pc, phase boundaries vanish.
Critical exponentCritical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.
Spinodal decompositionSpinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no thermodynamic barrier to phase separation. As a result, phase separation via decomposition does not require the nucleation events resulting from thermodynamic fluctuations, which normally trigger phase separation. Spinodal decomposition is observed when mixtures of metals or polymers separate into two co-existing phases, each rich in one species and poor in the other.
Strength of materialsThe field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.
Heat treatingHeat treating (or heat treatment) is a group of industrial, thermal and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve the desired result such as hardening or softening of a material.
