Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
In computer engineering, a hardware description language (HDL) is a specialized computer language used to describe the structure and behavior of electronic circuits, and most commonly, digital logic circuits.
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards. The tools work together in a design flow that chip designers use to design and analyze entire semiconductor chips. Since a modern semiconductor chip can have billions of components, EDA tools are essential for their design.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system. Since they allow to check the reliability of chosen mathematical models, computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics, astrophysics, climatology, chemistry, biology and manufacturing, human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.
Mathematical and theoretical biology 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. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
Computational science is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core it involves the development of models and simulations to understand natural systems.
MIMIC, known in capitalized form only, is a former simulation computer language developed 1964 by H. E. Petersen, F. J. Sansom and L. M. Warshawsky of Systems Engineering Group within the Air Force Materiel Command at the Wright-Patterson AFB in Dayton, Ohio, United States. It is an expression-oriented continuous block simulation language, but capable of incorporating blocks of FORTRAN-like algebra.
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.
Not to be confused with computer engineering.
Dynamic simulation is the use of a computer program to model the time varying behavior of a system. The systems are typically described by ordinary differential equations or partial differential equations. As mathematical models incorporate real-world constraints, like gear backlash and rebound from a hard stop, equations become nonlinear. This requires numerical methods to solve the equations. A numerical simulation is done by stepping through a time interval and calculating the integral of the derivatives by approximating the area under the derivative curves. Some methods use a fixed step through the interval, and others use an adaptive step that can shrink or grow automatically to maintain an acceptable error tolerance. Some methods can use different time steps in different parts of the simulation model. Industrial uses of dynamic simulation are many and range from nuclear power, steam turbines, 6 degree of freedom vehicle modeling, electric motors, econometric models, biological systems, robot arms, mass spring dampers, hydraulic systems, and drug dose migration through the human body to name a few. These models can often be run in real time to give a virtual response close to the actual system. This is useful in process control and mechatronic systems for tuning the automatic control systems before they are connected to the real system, or for human training before they control the real system. Simulation is also used in computer games and animation and can be accelerated by using a physics engine, the technology used in many powerful computer graphics software programs, like 3ds Max, Maya, Lightwave, and many others to simulate physical characteristics. In computer animation, things like hair, cloth, liquid, fire, and particles can be easily modeled, while the human animator animates simpler objects. Computer-based dynamic animation was first used at a very simple level in the 1989 Pixar short film Knick Knack to move the fake snow in the snowglobe and pebbles in a fish tank.
Advanced process monitor (APMonitor) is a modeling language for differential algebraic (DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
CSMP III, or Continuous System Modelling Program IlI is an early scientific computer software designed for modelling and solving differential equations numerically. This enables real-world systems to be simulated and tested with a computer.
Continuous Simulation refers to a computer model of a physical system that continuously tracks system response according to a set of equations typically involving differential equations.
DYNAMO is a historically important simulation language and accompanying graphical notation developed within the system dynamics analytical framework. It was originally for industrial dynamics but was soon extended to other applications, including population and resource studies and urban planning.
MLDesigner is an integrated modeling and simulation tool for the design and analysis of complex embedded and networked systems. MLDesigner speeds up modeling, simulation and analysis of discrete event, discrete time and continuous time systems concerning architecture, function and performance. The tools is based on ideas of the "Ptolemy Project", done at the University if California Berkeley. MLDesigner is developed by MLDesign Technologies Inc. Palo Alto, CA, USA in collaboration with Mission Level Design GmbH, Ilmenau, Germany.
