Scanning tunneling microscopeA scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated.
CobotA cobot, or collaborative robot, is a robot intended for direct human-robot interaction within a shared space, or where humans and robots are in close proximity. Cobot applications contrast with traditional industrial robot applications in which robots are isolated from human contact. Cobot safety may rely on lightweight construction materials, rounded edges, and inherent limitation of speed and force, or on sensors and software that ensure safe behavior.
Measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
Lift (force)A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it is defined to act perpendicular to the flow and therefore can act in any direction. If the surrounding fluid is air, the force is called an aerodynamic force.
Contact forceA contact force is any force that occurs as a result of two objects making contact with each other. Contact forces are ubiquitous and are responsible for most visible interactions between macroscopic collections of matter. Pushing a car or kicking a ball are some of the everyday examples where contact forces are at work. In the first case the force is continuously applied to the car by a person, while in the second case the force is delivered in a short impulse.
Surface (topology)In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Atomic force microscopyAtomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. Atomic force microscopy (AFM) is a type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit.
Differentiable manifoldIn mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.
Contact geometryIn mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution may be given (at least locally) as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions are opposite to two equivalent conditions for 'complete integrability' of a hyperplane distribution, i.
Eötvös experimentThe Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with the same accuracy. The earliest experiments were done by Isaac Newton (1642–1727) and improved upon by Friedrich Wilhelm Bessel (1784–1846). A much more accurate experiment using a torsion balance was carried out by Loránd Eötvös starting around 1885, with further improvements in a lengthy run between 1906 and 1909.
