Nanoelectromechanical systemsNanoelectromechanical systems (NEMS) are a class of devices integrating electrical and mechanical functionality on the nanoscale. NEMS form the next logical miniaturization step from so-called microelectromechanical systems, or MEMS devices. NEMS typically integrate transistor-like nanoelectronics with mechanical actuators, pumps, or motors, and may thereby form physical, biological, and chemical sensors.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Terahertz radiationTerahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequencies from 0.3 to 3 terahertz (THz), although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz. One terahertz is 1012 Hz or 1000 GHz. Wavelengths of radiation in the terahertz band correspondingly range from 1 mm to 0.1 mm = 100 μm.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
SiliceneSilicene is a two-dimensional allotrope of silicon, with a hexagonal honeycomb structure similar to that of graphene. Contrary to graphene, silicene is not flat, but has a periodically buckled topology; the coupling between layers in silicene is much stronger than in multilayered graphene; and the oxidized form of silicene, 2D silica, has a very different chemical structure from graphene oxide. Although theorists had speculated about the existence and possible properties of free-standing silicene, researchers first observed silicon structures that were suggestive of silicene in 2010.
Cavalieri's quadrature formulaIn calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral and generalizations thereof. This is the definite integral form; the indefinite integral form is: There are additional forms, listed below. Together with the linearity of the integral, this formula allows one to compute the integrals of all polynomials. The term "quadrature" is a traditional term for area; the integral is geometrically interpreted as the area under the curve y = xn.
BiosensorA biosensor is an analytical device, used for the detection of a chemical substance, that combines a biological component with a physicochemical detector. The sensitive biological element, e.g. tissue, microorganisms, organelles, cell receptors, enzymes, antibodies, nucleic acids, etc., is a biologically derived material or biomimetic component that interacts with, binds with, or recognizes the analyte under study. The biologically sensitive elements can also be created by biological engineering.
Graphene oxide paperGraphene oxide paper or graphite oxide paper is a material fabricated from graphite oxide. Micrometer thick films of graphene oxide paper are also named as graphite oxide membranes (in the 1960s) or (more recently) graphene oxide membranes. The membranes are typically obtained by slow evaporation of graphene oxide solution or by the filtration method. The material has exceptional stiffness and strength, due to the intrinsic strength of the two-dimensional graphene backbone and to its interwoven layer structure which distributes loads.
Terahertz time-domain spectroscopyIn physics, terahertz time-domain spectroscopy (THz-TDS) is a spectroscopic technique in which the properties of matter are probed with short pulses of terahertz radiation. The generation and detection scheme is sensitive to the sample's effect on both the amplitude and the phase of the terahertz radiation. Typically, an ultrashort pulsed laser is used in the terahertz pulse generation process. In the use of low-temperature grown GaAs as an antenna, the ultrashort pulse creates charge carriers that are accelerated to create the terahertz pulse.
