Transmission lineIn electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency).
History of computing hardwareThe history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers. The first aids to computation were purely mechanical devices which required the operator to set up the initial values of an elementary arithmetic operation, then manipulate the device to obtain the result. Later, computers represented numbers in a continuous form (e.g. distance along a scale, rotation of a shaft, or a voltage). Numbers could also be represented in the form of digits, automatically manipulated by a mechanism.
Legendre polynomialsIn mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.
Computer hardwareComputer hardware includes the physical parts of a computer, such as the case, central processing unit (CPU), random access memory (RAM), monitor, mouse, keyboard, computer data storage, graphics card, sound card, speakers and motherboard. By contrast, software is the set of instructions that can be stored and run by hardware. Hardware is so-termed because it is "hard" or rigid with respect to changes, whereas software is "soft" because it is easy to change. Hardware is typically directed by the software to execute any command or instruction.
Telegrapher's equationsThe telegrapher's equations (or just telegraph equations) are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. The equations and their solutions are applicable from 0 Hz to frequencies at which the transmission line structure can support higher order non-TEM modes. The equations can be expressed in both the time domain and the frequency domain.
Negative resistanceIn electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordinary resistor in which an increase of applied voltage causes a proportional increase in current due to Ohm's law, resulting in a positive resistance. While a positive resistance consumes power from current passing through it, a negative resistance produces power.
ComputerA computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic 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 nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
AcousticsAcoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.
Time–frequency analysisIn signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.
Chebyshev polynomialsThe Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as and . They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind are defined by Similarly, the Chebyshev polynomials of the second kind are defined by That these expressions define polynomials in may not be obvious at first sight, but follows by rewriting and using de Moivre's formula or by using the angle sum formulas for and repeatedly.
Computer experimentA computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines. Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used.
