An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, 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".
Integration may refer to:
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
A vertical take-off and landing (VTOL) aircraft is one that can hover, take off and land vertically without relying on a runway. This classification can include a variety of types of aircraft including helicopters as well as thrust-vectoring fixed-wing aircraft and other hybrid aircraft with powered rotors such as cyclogyros/cyclocopters and gyrodynes.
System analysis in the field of electrical engineering that characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio speakers; electrical engineers often use it because of its direct relevance to many areas of their discipline, most notably signal processing, communication systems and control systems.
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.
The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables.
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable."
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally. The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels. A simple gear ratio of 1:2 then enables multiplication by two, so addition are achieved. Multiplication is just a special case of integration, namely integrating a constant function.
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Hybrid computers are computers that exhibit features of analog computers and digital computers. The digital component normally serves as the controller and provides logical and numerical operations, while the analog component often serves as a solver of differential equations and other mathematically complex equations. The first desktop hybrid computing system was the Hycomp 250, released by Packard Bell in 1961. Another early example was the HYDAC 2400, an integrated hybrid computer released by EAI in 1963. In the 1980s, Marconi Space and Defense Systems Limited developed their "Starglow Hybrid Computer", which consisted of three EAI 8812 analog computers linked to an EAI 8100 digital computer, the latter also being linked to an SEL 3200 digital computer. Late in the 20th century, hybrids dwindled with the increasing capabilities of digital computers including digital signal processors.
Finite-difference time-domain (FDTD) or Yee's method is a numerical analysis technique used for modeling computational electrodynamics. Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way.
In automata theory, a hybrid automaton is a mathematical model for precisely describing systems in which digital computational processes interact with analog physical processes. A hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed.
HRS-100, ХРС-100, GVS-100 or ГВС-100, was a third generation hybrid computer developed by Mihajlo Pupin Institute and engineers from USSR in the period from 1968 to 1971. Three systems HRS-100 were deployed in Academy of Sciences of USSR in Moscow and Novosibirsk (Akademgorodok) in 1971 and 1978. More production was contemplated for use in Czechoslovakia and German Democratic Republic (DDR), but that was not realised.
The Dornier Do 31 is an experimental vertical take-off and landing (VTOL) jet-propelled transport designed and produced by West German aircraft manufacturer Dornier.
A computer is a digital electronic machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a "complete" computer that includes the hardware, operating system, and peripheral equipment needed and used for "full" operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster.
Differential equations, in particular Euler equations, rose in prominence during World War II in calculating the accurate trajectory of ballistics, both rocket-propelled and gun or cannon type projectiles. Originally, mathematicians used the simpler calculus of earlier centuries to determine velocity, thrust, elevation, curve, distance, and other parameters.
SICONOS is an Open Source scientific software primarily targeted at modeling and simulating non-smooth dynamical systems (NSDS):
The General Purpose Analog Computer (GPAC) is a mathematical model of analog computers first introduced in 1941 by Claude Shannon. This model consists of circuits where several basic units are interconnected in order to compute some function. The GPAC can be implemented in practice through the use of mechanical devices or analog electronics. Although analog computers have fallen almost into oblivion due to emergence of the digital computer, the GPAC has recently been studied as a way to provide evidence for the physical Church–Turing thesis. This is because the GPAC is also known to model a large class of dynamical systems defined with ordinary differential equations, which appear frequently in the context of physics. In particular it was shown in 2007 that the GPAC is equivalent, in computability terms, to Turing machines, thereby proving the physical Church–Turing thesis for the class of systems modelled by the GPAC. This was recently strengthened to polynomial time equivalence.
