Ground motionGround motion is the movement of the earth's surface from earthquakes or explosions. Ground motion is produced by seismic waves that are generated by sudden slip on a fault or sudden pressure at the explosive source and travel through the earth and along its surface. This can be due to natural events, such as earthquakes and volcanic eruptions, or human activities, such as the detonation of nuclear weapons. There are two main types of seismic waves: body waves and surface waves.
Peak ground accelerationPeak ground acceleration (PGA) is equal to the maximum ground acceleration that occurred during earthquake shaking at a location. PGA is equal to the amplitude of the largest absolute acceleration recorded on an accelerogram at a site during a particular earthquake. Earthquake shaking generally occurs in all three directions. Therefore, PGA is often split into the horizontal and vertical components. Horizontal PGAs are generally larger than those in the vertical direction but this is not always true, especially close to large earthquakes.
Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Connection (mathematics)In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve.
Cruiser tankThe cruiser tank (sometimes called cavalry tank or fast tank) was a British tank concept of the interwar period for tanks designed as modernised armoured and mechanised cavalry, as distinguished from infantry tanks. Cruiser tanks were developed after medium tank designs of the 1930s failed to satisfy the Royal Armoured Corps. The cruiser tank concept was conceived by Giffard Le Quesne Martel, who preferred many small light tanks to swarm an opponent, instead of a few expensive and unsatisfactory medium tanks.
Tanks in World War IITanks were an important weapons system in World War II. Even though tanks in the inter-war years were the subject of widespread research, production was limited to relatively small numbers in a few countries. However, during World War II, most armies employed tanks, and production levels reached thousands each month. Tank usage, doctrine and production varied widely among the combatant nations. By war's end, a consensus was emerging regarding tank doctrine and design.
Connection (vector bundle)In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport must be linear. A linear connection is equivalently specified by a covariant derivative, an operator that differentiates sections of the bundle along tangent directions in the base manifold, in such a way that parallel sections have derivative zero.
Main battle tankA main battle tank (MBT), also known as a battle tank or universal tank, is a tank that fills the role of armor-protected direct fire and maneuver in many modern armies. Cold War-era development of more powerful engines, better suspension systems and lighter composite armor allowed for the design of a tank that had the firepower of a super-heavy tank, the armor protection of a heavy tank, and the mobility of a light tank, in a package with the weight of a medium tank.
Tanks in the German ArmyThis article deals with the tanks (Panzer) serving in the German Army (Deutsches Heer) throughout history, such as the World War I tanks of the Imperial German Army, the interwar and World War II tanks of the Nazi German Wehrmacht, the Cold War tanks of the West German and East German Armies, all the way to the present day tanks of the Bundeswehr. The development of tanks in World War I began as an attempt to break the stalemate which trench warfare had brought to the Western Front.
Levi-Civita connectionIn Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection.
