History.

The German name "Boyceneburg" was first documented in 1158. The written form changed to "Boiceneburg" (1171) and then "Boizeneburg" (1195). The old Low German name for the town and river (Boize) likely stems from the Slavic "boj" for war ("boj"-burg = war-castle).  Boizenburg suffered during the Thirty Years' War and its old castle was burnt down by Swedish troops in 1628. In 1709 the church and 160 or more medieval dwellings were incinerated by a fire. The Town Hall was rebuilt in 1712 and the layout of the town was redesigned by Prussian architects sent from Schwerin. They focused on incorporating efficiency of movement with fire-resistance, better sanitation and public space.  During the Napoleonic Wars French troops were quartered in Boizenburg in 1807. A battle was fought with the retreating French army near Boizenburg in 1813.  From 1815 to 1918, Boizenburg was part of the Grand Duchy of Mecklenburg-Schwerin. In 1826 a highway was built, connecting Hamburg, Berlin and subsequently Boizenburg (Highway "B5"). In 1846 the railway between Berlin and Hamburg was constructed. Boizenburg was included with its own train station along this important route.  The shipbuilding yard "Lemmsche" founded in 1793 became highly industrialized in 1852 and produced many wooden and steel ships. The shipbuilders "Thomsen & Co" supported the German war effort during World War II. In 1973 the SED reactivated the shipbuilding facilities for the production of smaller inland ships for the USSR. After being privatized in 1989, the yard was declared bankrupt in 1997. Today smaller independent companies are active in the old ship yard.  The Boizenburg Tile Factory established by Hans Duensing in 1903, became Europe's largest tile manufacturer by 1937. After being re-established in 1991, it remains one of the town's main employers. Artistic impressions of the tile work produced in Boizenburg—particularly in the Art Nouveau style - can be found at the "Erstes Deutsches Fliesen Museum".  During the communist East German era, residents of Boizenburg were kept under close scrutiny by the Stasi. Many deemed 'politically untrustworthy' had their property confiscated during a state-sponsored terror campaign code-named Operation Vermin ().

Sightseeing.

One of the advantages of Boizenburg's isolation during the Cold War, is the pristine natural landscape of the Elbe Valley region stretching to the North, South and East. Much of the architecture and infrastructure in the old city remained 'perfectly untouched' during the DDR regime. In addition to significant restoration projects, new installations such as the modern redesign of the harbor and the addition of a topiary garden have greatly added to the Old Town's charm.  Some noteworthy buildings and structures in Ludwigslust-Parchim:

Miscellaneous.

Until April 30, 1945 a Nazi concentration camp was established in Boizenburg. The camp was a subcamp to the Neuengamme concentration camp.  On March 12, 1953 a RAF Avro Lincoln heading to Berlin was shot down over Boizenburg by two VVS MiG-15.

Transport.

The town lies on the Berlin-Hamburg railway.

Boizenburg is a municipality in the Ludwigslust-Parchim district in Mecklenburg-Western Pomerania, Germany. It is situated on the right bank of the Elbe, 53 km west of Ludwigslust, 25 km northeast of Lüneburg and 50 km east of Hamburg. It is part of the Hamburg Metropolitan Region. Boizenburg's historical old town stretches along the Elbe, has a harbour and offers heritage baroque timberframe and brick buildings.

Boizenburg/Elbe [] ist die westlichste Stadt Mecklenburgs, gelegen am Dreiländereck mit Niedersachsen und Schleswig-Holstein und im UNESCO-Biosphärenreservat Flusslandschaft Elbe-Mecklenburg-Vorpommern im Landkreis Ludwigslust-Parchim in Mecklenburg-Vorpommern (Deutschland). Die Stadt ist Verwaltungssitz des Amtes Boizenburg-Land, dem elf Gemeinden angehören, ist selbst aber amtsfrei.


History.

The first commercial two-stroke engine involving in-cylinder compression is attributed to Scottish engineer Dugald Clerk, who patented his design in 1881. However, unlike most later two-stroke engines, his had a separate charging cylinder. The crankcase-scavenged engine, employing the area below the piston as a charging pump, is generally credited to Englishman Joseph Day. On 31 December 1879, German inventor Karl Benz produced a two-stroke gas engine, for which he received a patent in 1880 in Germany. The first truly practical two-stroke engine is attributed to Yorkshireman Alfred Angas Scott, who started producing twin cylinder water cooled motorcycles in 1908.  Gasoline (spark ignition) versions are particularly useful in lightweight or portable applications such as chainsaws and motorcycles. However, when weight and size are not an issue, the cycle's potential for high thermodynamic efficiency makes it ideal for diesel compression ignition engines operating in large, weight-insensitive applications, such as marine propulsion, railway locomotives and electricity generation. In a two-stroke engine, the exhaust gases transfer less heat to the cooling system than a four-stroke, which means more energy to drive the piston and, if present, a turbocharger.

Emissions.

Crankcase-compression two-stroke engines, such as common small gasoline-powered engines, are lubricated by a petroil mixture in a total-loss system. Oil is mixed in with their petrol fuel beforehand, in a ratio of around 1:50. This oil then forms emissions, either by being burned in the engine or as droplets in the exhaust, resulting in more exhaust emissions, particularly hydrocarbons, than four-stroke engines of comparable power output. The combined opening time of the intake and exhaust ports in some 2-stroke designs can also allow some amount of unburned fuel vapors to exit in the exhaust stream. The high combustion temperatures of small air-cooled engines may also produce NO emissions.

Applications.

Two-stroke petrol engines are preferred when mechanical simplicity, light weight, and high power-to-weight ratio are design priorities. With the traditional lubrication technique of mixing oil into the fuel, they also have the advantage of working in any orientation, as there is no oil reservoir dependent on gravity; this is an essential property for hand-held power tools such as chainsaws.  A number of mainstream automobile manufacturers have used two-stroke engines in the past, including the Swedish Saab and German manufacturers DKW, Auto-Union, VEB Sachsenring Automobilwerke Zwickau, VEB Automobilwerk Eisenach and. The Japanese manufacturers Suzuki and Subaru did the same in the 1970s. Production of two-stroke cars ended in the 1980s in the West, due to increasingly stringent regulation of air pollution. Eastern Bloc countries continued until around 1991, with the Trabant and Wartburg in East Germany. Two-stroke engines are still found in a variety of small propulsion applications, such as outboard motors, high-performance, small-capacity motorcycles, mopeds, and dirt bikes, underbones, scooters, tuk-tuks, snowmobiles, karts, ultralight airplanes, and model airplanes and other model vehicles. They are also common in power tools used outdoors, such as lawn mowers, chainsaws, and weed-wackers.  With direct fuel injection and a sump-based lubrication system, a two-stroke engine produces air pollution no worse than a four-stroke, and it can achieve higher thermodynamic efficiency. Therefore, the cycle has historically also been used in large diesel engines, mostly large industrial and marine engines, as well as some trucks and heavy machinery. There are several experimental designs intended for automobile use: for instance, Lotus of Norfolk, UK, had in 2008 a prototype direct-injection two-stroke engine intended for alcohol fuels called the Omnivore which it is demonstrating in a version of the Exige.

Different two-stroke design types.

Although the principles remain the same, the mechanical details of various two-stroke engines differ depending on the type. The design types vary according to the method of introducing the charge to the cylinder, the method of scavenging the cylinder (exchanging burnt exhaust for fresh mixture) and the method of exhausting the cylinder.

Piston-controlled inlet port.

Piston port is the simplest of the designs and the most common in small two-stroke engines. All functions are controlled solely by the piston covering and uncovering the ports as it moves up and down in the cylinder. In the 1970s, Yamaha worked out some basic principles for this system. They found that, in general, widening an exhaust port increases the power by the same amount as raising the port, but the power band does not narrow as it does when the port is raised. However, there is a mechanical limit to the width of a single exhaust port, at about 62% of the bore diameter for reasonable ring life. Beyond this, the rings will bulge into the exhaust port and wear quickly. A maximum 70% of bore width is possible in racing engines, where rings are changed every few races. Intake duration is between 120 and 160 degrees. Transfer port time is set at a minimum of 26 degrees. The strong low pressure pulse of a racing two-stroke expansion chamber can drop the pressure to -7 PSI when the piston is at bottom dead center, and the transfer ports nearly wide open. One of the reasons for high fuel consumption in two-strokes is that some of the incoming pressurized fuel-air mixture is forced across the top of the piston, where it has a cooling action, and straight out the exhaust pipe. An expansion chamber with a strong reverse pulse will stop this out-going flow. A fundamental difference from typical four-stroke engines is that the two-stroke's crankcase is sealed and forms part of the induction process in gasoline and hot bulb engines. Diesel two-strokes often add a Roots blower or piston pump for scavenging.

Reed inlet valve.

The reed valve is a simple but highly effective form of check valve commonly fitted in the intake tract of the piston-controlled port. It allows asymmetric intake of the fuel charge, improving power and economy, while widening the power band. Such valves are widely used in motorcycle, ATV, and marine outboard engines.

Rotary inlet valve.

The intake pathway is opened and closed by a rotating member. A familiar type sometimes seen on small motorcycles is a slotted disk attached to the crankshaft which covers and uncovers an opening in the end of the crankcase, allowing charge to enter during one portion of the cycle (aka disc valve).  Another form of rotary inlet valve used on two-stroke engines employs two cylindrical members with suitable cutouts arranged to rotate one within the other - the inlet pipe having passage to the crankcase only when the two cutouts coincide. The crankshaft itself may form one of the members, as in most glow plug model engines. In another embodiment, the crank disc is arranged to be a close-clearance fit in the crankcase, and is provided with a cutout which lines up with an inlet passage in the crankcase wall at the appropriate time, as in Vespa motor scooters.  The advantage of a rotary valve is that it enables the two-stroke engine's intake timing to be asymmetrical, which is not possible with piston-port type engines. The piston-port type engine's intake timing opens and closes before and after top dead center at the same crank angle, making it symmetrical, whereas the rotary valve allows the opening to begin and close earlier.  Rotary valve engines can be tailored to deliver power over a wider speed range or higher power over a narrower speed range than either piston port or reed valve engine. Where a portion of the rotary valve is a portion of the crankcase itself, it is particularly important that no wear is allowed to take place.

Cross-flow-scavenged.

In a cross-flow engine, the transfer and exhaust ports are on opposite sides of the cylinder, and a deflector on the top of the piston directs the fresh intake charge into the upper part of the cylinder, pushing the residual exhaust gas down the other side of the deflector and out the exhaust port. The deflector increases the piston's weight and exposed surface area, affecting piston cooling and also making it difficult to achieve an efficient combustion chamber shape. This design has been superseded since the 1960s by the loop scavenging method (below), especially for motorbikes, although for smaller or slower engines, such as lawn mowers, the cross-flow-scavenged design can be an acceptable approach.

Loop-scavenged.

This method of scavenging uses carefully shaped and positioned transfer ports to direct the flow of fresh mixture toward the combustion chamber as it enters the cylinder. The fuel/air mixture strikes the cylinder head, then follows the curvature of the combustion chamber, and then is deflected downward.  This not only prevents the fuel/air mixture from traveling directly out the exhaust port, but also creates a swirling turbulence which improves combustion efficiency, power and economy. Usually, a piston deflector is not required, so this approach has a distinct advantage over the cross-flow scheme (above).  Often referred to as "Schnuerle" (or "Schnürle") loop scavenging after Adolf Schnürle, the German inventor of an early form in the mid-1920s, it became widely adopted in that country during the 1930s and spread further afield after World War II.  Loop scavenging is the most common type of fuel/air mixture transfer used on modern two-stroke engines. Suzuki was one of the first manufacturers outside of Europe to adopt loop-scavenged two-stroke engines. This operational feature was used in conjunction with the expansion chamber exhaust developed by German motorcycle manufacturer, MZ and Walter Kaaden.  Loop scavenging, disc valves and expansion chambers worked in a highly coordinated way to significantly increase the power output of two-stroke engines, particularly from the Japanese manufacturers Suzuki, Yamaha and Kawasaki. Suzuki and Yamaha enjoyed success in grand Prix motorcycle racing in the 1960s due in no small way to the increased power afforded by loop scavenging.  An additional benefit of loop scavenging was the piston could be made nearly flat or slightly dome shaped, which allowed the piston to be appreciably lighter and stronger, and consequently to tolerate higher engine speeds. The "flat top" piston also has better thermal properties and is less prone to uneven heating, expansion, piston seizures, dimensional changes and compression losses.  SAAB built 750 and 850 cc 3-cylinder engines based on a DKW design that proved reasonably successful employing loop charging. The original SAAB 92 had a two-cylinder engine of comparatively low efficiency. At cruising speed, reflected wave exhaust port blocking occurred at too low a frequency. Using the asymmetric three-port exhaust manifold employed in the identical DKW engine improved fuel economy.  The 750 cc standard engine produced 36 to 42 hp, depending on the model year. The Monte Carlo Rally variant, 750 cc (with a filled crankshaft for higher base compression), generated 65 hp. An 850 cc version was available in the 1966 SAAB Sport (a standard trim model in comparison to the deluxe trim of the Monte Carlo). Base compression comprises a portion of the overall compression ratio of a two-stroke engine. Work published at SAE in 2012 points that loop scavenging is under every circumstance more efficient than cross-flow scavenging.

Uniflow-scavenged.

In a uniflow engine, the mixture, or "charge air" in the case of a diesel, enters at one end of the cylinder controlled by the piston and the exhaust exits at the other end controlled by an exhaust valve or piston. The scavenging gas-flow is therefore in one direction only, hence the name uniflow. The valved arrangement is common in on-road, off-road and stationary two-stroke engines (Detroit Diesel), certain small marine two-stroke engines (Gray Marine), certain railroad two-stroke diesel locomotives (Electro-Motive Diesel) and large marine two-stroke main propulsion engines (Wärtsilä). Ported types are represented by the opposed piston design in which there are two pistons in each cylinder, working in opposite directions such as the Junkers Jumo 205 and Napier Deltic. The once-popular split-single design falls into this class, being effectively a folded uniflow. With advanced angle exhaust timing, uniflow engines can be supercharged with a crankshaft-driven (piston or Roots) blower.

Stepped piston engine.

The piston of this engine is "top-hat" shaped; the upper section forms the regular cylinder, and the lower section performs a scavenging function. The units run in pairs, with the lower half of one piston charging an adjacent combustion chamber.  This system is still partially dependent on total loss lubrication (for the upper part of the piston), the other parts being sump lubricated with cleanliness and reliability benefits. The piston weight is only about 20% heavier than a loop-scavenged piston because skirt thicknesses can be less. Bernard Hooper Engineering Ltd. (BHE) is one of the more recent engine developers using this approach.

Power valve systems.

Many modern two-stroke engines employ a power valve system. The valves are normally in or around the exhaust ports. They work in one of two ways: either they alter the exhaust port by closing off the top part of the port, which alters port timing, such as Rotax R.A.V.E, Yamaha YPVS, Honda RC-Valve, Kawasaki K.I.P.S., Cagiva C.T.S. or Suzuki AETC systems, or by altering the volume of the exhaust, which changes the resonant frequency of the expansion chamber, such as the Suzuki SAEC and Honda V-TACS system. The result is an engine with better low-speed power without sacrificing high-speed power. However, as power valves are in the hot gas flow they need regular maintenance to perform well.

Direct injection.

Direct injection has considerable advantages in two-stroke engines, eliminating some of the waste and pollution caused by carbureted two-strokes where a proportion of the fuel/air mixture entering the cylinder goes directly out, unburned, through the exhaust port. Two systems are in use, low-pressure air-assisted injection, and high pressure injection.  Since the fuel does not pass through the crankcase, a separate source of lubrication is needed.

Diesel.

Diesel engines rely solely on the heat of compression for ignition. In the case of Schnuerle ported and loop-scavenged engines, intake and exhaust happens via piston-controlled ports. A uniflow diesel engine takes in air via scavenge ports, and exhaust gases exit through an overhead poppet valve. Two-stroke diesels are all scavenged by forced induction. Some designs use a mechanically driven Roots blower, whilst marine diesel engines normally use exhaust-driven turbochargers, with electrically driven auxiliary blowers for low-speed operation when exhaust turbochargers are unable to deliver enough air.  Marine two-stroke diesel engines directly coupled to the propeller are able to start and run in either direction as required. The fuel injection and valve timing is mechanically readjusted by using a different set of cams on the camshaft. Thus, the engine can be run in reverse to move the vessel backwards.

Lubrication.

Most small petrol two-stroke engines cannot be lubricated by oil contained in their crankcase and sump, since the crankcase is being used to pump fuel-air mixture into the cylinder. Over a short period, the constant stream of fuel-air mixture would carry away the lubricating oil into the combustion chamber while thinning the remainder with condensing petrol. Traditionally, the moving parts (both rotating crankshaft and sliding piston) were instead lubricated by a premixed fuel-oil mixture (at a ratio between 16:1 and 100:1). As late as the 1970s, petrol stations in the US would often have a separate pump to deliver such a premix fuel to motorcycles. Even then, in many cases, the rider would carry a bottle of their own two-stroke oil.  Two-stroke oils which became available worldwide in the 1970s are specifically designed to mix with petrol and be burnt in the combustion chamber without leaving undue unburnt oil or ash. This led to a marked reduction in spark plug fouling, which had previously been a factor in two-stroke engines.  More recent two-stroke engines might pump lubrication from a separate tank of two-stroke oil. The supply of this oil is controlled by the throttle position and engine speed. Examples are found in Yamaha's PW80 (Pee-wee), a small, 80cc two-stroke dirt bike designed for young children, and many two-stroke snowmobiles. The technology is referred to as auto-lube. This is still a total-loss system with the oil being burnt the same as in the pre-mix system; however, given that the oil is not properly mixed with the fuel when burned in the combustion chamber, it translates into a slightly more efficient lubrication. This lubrication method also pays dividends in terms of user friendliness by eliminating the user's need to mix the gasoline at every refill, makes the motor much less susceptible to atmospheric conditions (Ambient temperature, elevation) and ensures proper engine lubrication, with less oil at light loads (such as idle) and more oil at high loads (such as full throttle). Some companies, such as Bombardier, had some oil pump designs have no oil injected at idle to reduce smoke levels, as the loading on the engine parts was light enough to not require additional lubrication beyond the low levels that the fuel provides. Ultimately oil injection is still the same as premixed gasoline in that the oil is burnt in the combustion chamber (albeit not as completely as pre-mix) and the gas is still mixed with the oil, although not as thoroughly as in pre-mix. In addition, this method requires extra mechanical parts to pump the oil from the separate tank, to the carburetor or throttle body. In applications where performance, simplicity and/or dry weight are significant considerations, the pre-mix lubrication method is almost always used. For example, a two-stroke engine in a motocross bike pays major consideration to performance, simplicity and weight. Chainsaws and brush cutters must be as light as possible to reduce user fatigue and hazard, especially when used in a professional work environment.  All two-stroke engines running on a petrol/oil mix will suffer oil starvation if forced to rotate at speed with the throttle closed, e.g. motorcycles descending long hills and perhaps when decelerating gradually from high speed by changing down through the gears. Two-stroke cars (such as those that were popular in Eastern Europe in the mid-20th century) were in particular danger and were usually fitted with freewheel mechanisms in the powertrain, allowing the engine to idle when the throttle was closed, requiring the use of the brakes in all slowing situations.  Large two-stroke engines, including diesels, normally use a sump lubrication system similar to four-stroke engines. The cylinder must still be pressurized, but this is not done from the crankcase, but by an ancillary Roots-type blower or a specialized turbocharger (usually a turbo-compressor system) which has a "locked" compressor for starting (and during which it is powered by the engine's crankshaft), but which is "unlocked" for running (and during which it is powered by the engine's exhaust gases flowing through the turbine).

Two-stroke reversibility.

For the purpose of this discussion, it is convenient to think in motorcycle terms, where the exhaust pipe faces into the cooling air stream, and the crankshaft commonly spins in the same axis and direction as do the wheels i.e. "forward". Some of the considerations discussed here apply to four-stroke engines (which cannot reverse their direction of rotation without considerable modification), almost all of which spin forward, too.  Regular gasoline two-stroke engines will run backward for short periods and under light load with little problem, and this has been used to provide a reversing facility in microcars, such as the Messerschmitt KR200, that lacked reverse gearing. Where the vehicle has electric starting, the motor will be turned off and restarted backward by turning the key in the opposite direction. Two-stroke golf carts have used a similar kind of system. Traditional flywheel magnetos (using contact-breaker points, but no external coil) worked equally well in reverse because the cam controlling the points is symmetrical, breaking contact before top dead center (TDC) equally well whether running forward or backward. Reed-valve engines will run backward just as well as piston-controlled porting, though rotary valve engines have asymmetrical inlet timing and will not run very well.  There are serious disadvantages to running many engines backward under load for any length of time, and some of these reasons are general, applying equally to both two-stroke and four-stroke engines. This disadvantage is accepted in most cases where cost, weight and size are major considerations. The problem comes about because in "forward" running the major thrust face of the piston is on the back face of the cylinder which, in a two-stroke particularly, is the coolest and best-lubricated part. The forward face of the piston in a trunk engine is less well-suited to be the major thrust face since it covers and uncovers the exhaust port in the cylinder, the hottest part of the engine, where piston lubrication is at its most marginal. The front face of the piston is also more vulnerable since the exhaust port, the largest in the engine, is in the front wall of the cylinder. Piston skirts and rings risk being extruded into this port, so it is always better to have them pressing hardest on the opposite wall (where there are only the transfer ports in a crossflow engine) and there is good support. In some engines, the small end is offset to reduce thrust in the intended rotational direction and the forward face of the piston has been made thinner and lighter to compensate; but when running backward, this weaker forward face suffers increased mechanical stress it was not designed to resist. This can be avoided by the use of crossheads and also using thrust bearings to isolate the engine from end loads.  Large two-stroke ship diesels are sometimes made to be reversible. Like four-stroke ship engines (some of which are also reversible) they use mechanically operated valves, so require additional camshaft mechanisms. These engines use crossheads to eliminate sidethrust on the piston and isolate the under-piston space from the crankcase.  On top of other considerations, the oil-pump of a modern two-stroke may not work in reverse, in which case the engine will suffer oil starvation within a short time. Running a motorcycle engine backward is relatively easy to initiate, and in rare cases, can be triggered by a back-fire. It is not advisable.  Model airplane engines with reed-valves can be mounted in either tractor or pusher configuration without needing to change the propeller. These motors are compression ignition, so there are no ignition timing issues and little difference between running forward and running backward.

A two-stroke (or two-cycle) engine is a type of internal combustion engine which completes a power cycle with two strokes (up and down movements) of the piston during only one crankshaft revolution. This is in contrast to a "four-stroke engine", which requires four strokes of the piston to complete a power cycle during two crankshaft revolutions. In a two-stroke engine, the end of the combustion stroke and the beginning of the compression stroke happen simultaneously, with the intake and exhaust (or scavenging) functions occurring at the same time.

Ein Zweitaktmotor ist ein Hubkolbenmotor, der aus der Verbrennung von Kraftstoff mechanische Leistung erzielt. Zwei Takte ergeben einen Kreisprozess-Umlauf (360° Kurbelwellenumdrehung). Wie ein Viertaktmotor kann er nach dem Otto- oder dem Diesel-Kreisprozess arbeiten. Umgangssprachlich bezeichnet der Begriff „Zweitakter“ einen ventillosen Ottomotor mit Gemischschmierung und Zündkerze, der einfach, kostengünstig und leicht ist. Frühe Anwendungen des Zweitaktmotors waren Motorräder, Mopeds, Motorroller und die Mehrzahl der Karts. In Personenkraftwagen gab es Zweitakter unter anderem bei DKW, Aero, Saab, IFA (Trabant, Wartburg, Barkas), Lloyd, Subaru, Suzuki, Mitsubishi und Rollermobilen. Es gab und gibt jedoch auch große Zweitakt-Dieselmotoren für Diesellokomotiven, Lastkraftwagen (zum Beispiel Krupp Titan), Flugzeuge (zum Beispiel Junkers Jumo 223), Schiffe („Schiffsdiesel“) und Boote. Die Zweitakt-Großdieselmotoren als Schiffsmotor oder als Antrieb für Generatoren zählen zu den Wärmekraftmaschinen mit dem höchsten Wirkungsgrad (zum Beispiel Wärtsilä RT-flex96C).


Classification.

There are many criteria by which superconductors are classified. The most common are:

Response to a magnetic field.

A superconductor can be "Type I", meaning it has a single critical field, above which all superconductivity is lost and below which the magnetic field is completely expelled from the superconductor; or "Type II", meaning it has two critical fields, between which it allows partial penetration of the magnetic field through isolated points. These points are called vortices. Furthermore, in multicomponent superconductors it is possible to have a combination of the two behaviours. In that case the superconductor is of Type-1.5.

By theory of operation.

It is "conventional" if it can be explained by the BCS theory or its derivatives, or "unconventional", otherwise.

By critical temperature.

A superconductor is generally considered "high-temperature" if it reaches a superconducting state above a temperature of 30 K (-243.15 °C); as in the initial discovery by Georg Bednorz and K. Alex Müller. It may also reference materials that transition to superconductivity when cooled using liquid nitrogen – that is, at only "T" > 77 K, although this is generally used only to emphasize that liquid nitrogen coolant is sufficient. Low temperature superconductors refer to materials with a critical temperature below 30 K. One exception to this rule is the iron pnictide group of superconductors which display behaviour and properties typical of high temperature superconductors, yet some of the group have critical temperatures below 30K.

By material.

Superconductor material classes include chemical elements (e.g. mercury or lead), alloys (such as niobium–titanium, germanium–niobium, and niobium nitride), ceramics (YBCO and magnesium diboride), superconducting pnictides (like fluorine-doped LaOFeAs) or organic superconductors (fullerenes and carbon nanotubes; though perhaps these examples should be included among the chemical elements, as they are composed entirely of carbon).

Elementary properties of superconductors.

Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, and critical current density at which superconductivity is destroyed.  On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have "exactly" zero resistivity to low applied currents when there is no magnetic field present or if the applied field does not exceed a critical value. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possesses certain distinguishing properties which are largely independent of microscopic details.

Zero electrical DC resistance.

The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source "I" and measure the resulting voltage "V" across the sample. The resistance of the sample is given by Ohm's law as "R = V / I". If the voltage is zero, this means that the resistance is zero.  Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature. In practice, currents injected in superconducting coils have persisted for more than 23 years (as in August 2018) in superconducting gravimeters. In such instruments, the measurement principle is based on the monitoring of the levitation of a superconducting niobium sphere with a mass of 4 grams.  In a normal conductor, an electric current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions. As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance and Joule heating.  The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound "pairs" of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an "energy gap", meaning there is a minimum amount of energy Δ"E" that must be supplied in order to excite the fluid. Therefore, if Δ"E" is larger than the thermal energy of the lattice, given by "kT", where "k" is Boltzmann's constant and "T" is the temperature, the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation.  In a class of superconductors known as type II superconductors, including all known high-temperature superconductors, an extremely low but nonzero resistivity appears at temperatures not too far below the nominal superconducting transition when an electric current is applied in conjunction with a strong magnetic field, which may be caused by the electric current. This is due to the motion of magnetic vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.

Phase transition.

In superconducting materials, the characteristics of superconductivity appear when the temperature "T" is lowered below a critical temperature "T". The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2015, the highest critical temperature found for a conventional superconductor is 203K for HS, although high pressures of approximately 90 gigapascals were required. Cuprate superconductors can have much higher critical temperatures: YBaCuO, one of the first cuprate superconductors to be discovered, has a critical temperature above 90 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The basic physical mechanism responsible for the high critical temperature is not yet clear. However, it is clear that a two-electron pairing is involved, although the nature of the pairing (formula_1 wave vs. formula_2 wave) remains controversial.  Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the "critical magnetic field". This is because the Gibbs free energy of the superconducting phase increases quadratically with the magnetic field while the free energy of the normal phase is roughly independent of the magnetic field. If the material superconducts in the absence of a field, then the superconducting phase free energy is lower than that of the normal phase and so for some finite value of the magnetic field (proportional to the square root of the difference of the free energies at zero magnetic field) the two free energies will be equal and a phase transition to the normal phase will occur. More generally, a higher temperature and a stronger magnetic field lead to a smaller fraction of electrons that are superconducting and consequently to a longer London penetration depth of external magnetic fields and currents. The penetration depth becomes infinite at the phase transition.  The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as "e" for some constant, α. This exponential behavior is one of the pieces of evidence for the existence of the energy gap.  The order of the superconducting phase transition was long a matter of debate. Experiments indicate that the transition is second-order, meaning there is no latent heat. However, in the presence of an external magnetic field there is latent heat, because the superconducting phase has a lower entropy below the critical temperature than the normal phase. It has been experimentally demonstrated that, as a consequence, when the magnetic field is increased beyond the critical field, the resulting phase transition leads to a decrease in the temperature of the superconducting material.  Calculations in the 1970s suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field. In the 1980s it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order (i.e., latent heat) within the type I regime, and that the two regions are separated by a tricritical point. The results were strongly supported by Monte Carlo computer simulations.

Meissner effect.

When a superconductor is placed in a weak external magnetic field H, and cooled below its transition temperature, the magnetic field is ejected. The Meissner effect does not cause the field to be completely ejected but instead the field penetrates the superconductor but only to a very small distance, characterized by a parameter "λ", called the London penetration depth, decaying exponentially to zero within the bulk of the material. The Meissner effect is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100 nm.  The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a "changing" magnetic field is applied to a conductor, it will induce an electric current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.  The Meissner effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.  The Meissner effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided  where H is the magnetic field and λ is the London penetration depth.  This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.  A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value "H". Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value "H" leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength "H", superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors, except niobium and carbon nanotubes, are Type I, while almost all impure and compound superconductors are Type II.

London moment.

Conversely, a spinning superconductor generates a magnetic field, precisely aligned with the spin axis. The effect, the London moment, was put to good use in Gravity Probe B. This experiment measured the magnetic fields of four superconducting gyroscopes to determine their spin axes. This was critical to the experiment since it is one of the few ways to accurately determine the spin axis of an otherwise featureless sphere.

History of superconductivity.

Superconductivity was discovered on April 8, 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently produced liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared. In the same experiment, he also observed the superfluid transition of helium at 2.2 K, without recognizing its significance. The precise date and circumstances of the discovery were only reconstructed a century later, when Onnes's notebook was found. In subsequent decades, superconductivity was observed in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.  Great efforts have been devoted to finding out how and why superconductivity works; the important step occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, Fritz and Heinz London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.

London constitutive equations.

The theoretical model that was first conceived in human history for superconductivity was completely classical: it is summarized by London constitutive equations. It was put forward by the brothers Fritz and Heinz London in 1935, shortly after the discovery that magnetic fields are expelled from superconductors. A major triumph of the equations of this theory is their ability to explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold. By using the London equation, one can obtain the dependence of the magnetic field inside the superconductor on the distance to the surface.  The two constitutive equations for a superconductor by London are: The first equation follows from Newton's second law for superconducting electrons.

Conventional theories (1950s).

During the 1950s, theoretical condensed matter physicists arrived at an understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg–Landau theory (1950) and the microscopic BCS theory (1957).  In 1950, the phenomenological Ginzburg–Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg–Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had received the 1962 Nobel Prize for other work, and died in 1968). The four-dimensional extension of the Ginzburg–Landau theory, the Coleman-Weinberg model, is important in quantum field theory and cosmology.  Also in 1950, Maxwell and Reynolds "et al." found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.  The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper and Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972.  The BCS theory was set on a firmer footing in 1958, when N. N. Bogolyubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg–Landau theory close to the critical temperature.  Generalizations of BCS theory for conventional superconductors form the basis for understanding of the phenomenon of superfluidity, because they fall into the lambda transition universality class. The extent to which such generalizations can be applied to unconventional superconductors is still controversial.

Further history.

The first practical application of superconductivity was developed in 1954 with Dudley Allen Buck's invention of the cryotron. Two superconductors with greatly different values of critical magnetic field are combined to produce a fast, simple switch for computer elements.  Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, G. B. Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that, at 4.2 kelvin niobium–tin, a compound consisting of three parts niobium and one part tin, was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 tesla. Despite being brittle and difficult to fabricate, niobium–tin has since proved extremely useful in supermagnets generating magnetic fields as high as 20 tesla. In 1962 T. G. Berlincourt and R. R. Hake discovered that more ductile alloys of niobium and titanium are suitable for applications up to 10 tesla. Promptly thereafter, commercial production of niobium–titanium supermagnet wire commenced at Westinghouse Electric Corporation and at Wah Chang Corporation. Although niobium–titanium boasts less-impressive superconducting properties than those of niobium–tin, niobium–titanium has, nevertheless, become the most widely used "workhorse" supermagnet material, in large measure a consequence of its very high ductility and ease of fabrication. However, both niobium–tin and niobium–titanium find wide application in MRI medical imagers, bending and focusing magnets for enormous high-energy-particle accelerators, and a host of other applications. Conectus, a European superconductivity consortium, estimated that in 2014, global economic activity for which superconductivity was indispensable amounted to about five billion euros, with MRI systems accounting for about 80% of that total.  In 1962, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum "Φ" = "h"/(2"e"), where "h" is the Planck constant. Coupled with the quantum Hall resistivity, this leads to a precise measurement of the Planck constant. Josephson was awarded the Nobel Prize for this work in 1973.  In 2008, it was proposed that the same mechanism that produces superconductivity could produce a superinsulator state in some materials, with almost infinite electrical resistance.

High-temperature superconductivity.

Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in lanthanum barium copper oxide (LBCO), a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was soon found that replacing the lanthanum with yttrium (i.e., making YBCO) raised the critical temperature above 90 K.  This temperature jump is particularly significant, since it allows liquid nitrogen as a refrigerant, replacing liquid helium. This can be important commercially because liquid nitrogen can be produced relatively cheaply, even on-site. Also, the higher temperatures help avoid some of the problems that arise at liquid helium temperatures, such as the formation of plugs of frozen air that can block cryogenic lines and cause unanticipated and potentially hazardous pressure buildup.  Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics. There are currently two main hypotheses – the resonating-valence-bond theory, and spin fluctuation which has the most support in the research community. The second hypothesis proposed that electron pairing in high-temperature superconductors is mediated by short-range spin waves known as paramagnons.  In 2008, holographic superconductivity, which uses holographic duality or AdS/CFT correspondence theory, was proposed by Gubser, Hartnoll, Herzog, and Horowitz, as a possible explanation of high-temperature superconductivity in certain materials.  Since about 1993, the highest-temperature superconductor has been a ceramic material consisting of mercury, barium, calcium, copper and oxygen (HgBaCaCuO) with "T" = 133–138 K. The latter experiment (138 K) still awaits experimental confirmation, however.  In February 2008, an iron-based family of high-temperature superconductors was discovered. Hideo Hosono, of the Tokyo Institute of Technology, and colleagues found lanthanum oxygen fluorine iron arsenide (LaOFFeAs), an oxypnictide that superconducts below 26 K. Replacing the lanthanum in LaOFFeAs with samarium leads to superconductors that work at 55 K.  In 2014 and 2015, hydrogen sulfide () at extremely high pressures (around 150 gigapascals) was first predicted and then confimed to be a high-temperature superconductor with a transition temperature of 80 K. Additionally, in 2019 it was discovered that lanthanum hydride () becomes a superconductor at 250K under a pressure of 170 gigapascals. This is currently the highest temperature at which any material has shown superconductivity.  In 2018, a research team from the Department of Physics, Massachusetts Institute of Technology, discovered superconductivity in bilayer graphene with one layer twisted at an angle of approximately 1.1 degrees with cooling and applying a small electric charge. Even if the experiments were not carried out in a high-temperature environment, the results are correlated less to classical but high temperature superconductors, given that no foreign atoms need to be introduced.

Applications.

Superconducting magnets are some of the most powerful electromagnets known. They are used in MRI/NMR machines, mass spectrometers, the beam-steering magnets used in particle accelerators and plasma confining magnets in some tokamaks. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries. They can also be used in large wind turbines to overcome the restrictions imposed by high electrical currents, with an industrial grade 3.6 megawatt superconducting windmill generator having been tested successfully in Denmark.  In the 1950s and 1960s, superconductors were used to build experimental digital computers using cryotron switches. More recently, superconductors have been used to make digital circuits based on rapid single flux quantum technology and RF and microwave filters for mobile phone base stations.  Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. SQUIDs are used in scanning SQUID microscopes and magnetoencephalography. Series of Josephson devices are used to realize the SI volt. Depending on the particular mode of operation, a superconductor–insulator–superconductor Josephson junction can be used as a photon detector or as a mixer. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter photon detectors. The same effect is used in ultrasensitive bolometers made from superconducting materials.  Other early markets are arising where the relative efficiency, size and weight advantages of devices based on high-temperature superconductivity outweigh the additional costs involved. For example, in wind turbines the lower weight and volume of superconducting generators could lead to savings in construction and tower costs, offsetting the higher costs for the generator and lowering the total levelized cost of electricity (LCOE).  Promising future applications include high-performance smart grid, electric power transmission, transformers, power storage devices, electric motors (e.g. for vehicle propulsion, as in vactrains or maglev trains), magnetic levitation devices, fault current limiters, enhancing spintronic devices with superconducting materials, and superconducting magnetic refrigeration. However, superconductivity is sensitive to moving magnetic fields so applications that use alternating current (e.g. transformers) will be more difficult to develop than those that rely upon direct current. Compared to traditional power lines superconducting transmission lines are more efficient and require only a fraction of the space, which would not only lead to a better environmental performance but could also improve public acceptance for expansion of the electric grid.

Superconductivity is the set of physical properties observed in certain materials, wherein electrical resistance vanishes and from which magnetic flux fields are expelled. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

Supraleiter sind Materialien, deren elektrischer Widerstand beim Unterschreiten der sogenannten Sprungtemperatur (abrupt) gegen null strebt (unmessbar klein wird, kleiner als 1 ⋅ 10 Ω). Die Supraleitung wurde 1911 von Heike Kamerlingh Onnes, einem Pionier der Tieftemperaturphysik, entdeckt. Sie ist ein makroskopischer Quantenzustand.


Location.

The Wiehen Hills lie within the districts of Osnabrück, Minden-Lübbecke and Herford. Their northern section runs in an east-west direction roughly from the territory of Bramsche (northwest of Osnabrück) via Ostercappeln, Bad Essen, Preußisch Oldendorf and Rödinghausen, Lübbecke, Hüllhorst and Bad Oeynhausen as far as the towns of Minden and Porta Westfalica on the Porta Westfalica gorge and River Weser. They also graze Bohmte and Hille to the north. South of the Wiehen Hills lie Osnabrück, Bissendorf, Melle, Kirchlengern, Bünde, Löhne and Bad Oeynhausen. The Wiehen Hills form the northwestern boundary of the Lower Saxon Hills to which they belong geographically, together with the Westphalian part of the ridge. Whilst the eastern end of the hill chain is clearly defined by the Porta Westfalica gorge and the hill of Wittekindsberg, this is not so simple for its western extremity. To the west the Wiehen descends gradually, transitioning from a hilly ridge into a chain of hillocks and then descending almost imperceptibly into the plain. South of Bramsche the ridge rises again at the "Penter Egge" to a height of 99 metre, but 2.5 km further west it reaches the level of the surrounding countryside. The waterways of the Mittelland Canal and Osnabrück Canal running away to the south appear to mark the end of the hill range, but west of these canals is the 82-metre-high "Larberger Egge" which forms the westernmost cornerstone of the Wiehen Hills, rising just 2 km northeast of the boundary with the province of Münster. Contrary to popular assumption, Ibbenbüren is no longer considered to be situated by the Wiehen Hills and the Ibbenbüren Plateau ("Ibbenbürener Bergplatte" comprising the Schafberg, etc.) is no longer part of the Wiehen. Geological reasons, according to current research, do not support such an assumption.  To the north, the Wiehen descends to the North German Plain into a region known as the Lübbecke Loessland. On the banks of the Weser, opposite Porta Westfalica, lies the Wesergebirge, which is the eastern continuation of the Wiehen Hills. This ridge is of similar geological construction and runs as far as the area of Hessisch Oldendorf to the Süntel hills. Southeast of the Wiehen Hills are the Lippe Uplands, to the south the Ravensberg Hills, to the southwest in the area of the Tecklenburg Land are the northern foothills of the Teutoburg Forest, and to the northwest are the hills of the Gehn and the Ankum Heights, the Damme Hills and the Stemweder Berg. North of the northwestern tip of the Wiehen liest the great bog of the Großes Moor.

Hills.

The hills of the Wiehen range from west to east are:

Northernmost German uplands.

According to folklore, regionally conscious residents around the hills usually admit grudgingly that the Wiehen Hills are not particularly high. In the same breath, they may assert, often with a raised index finger and an odd emphasis on the word "gebirge" ("hill/mountain range"), that they are the northernmost hill range in Germany and the one closest to the sea. Whether this assertion is true is in fact a matter of definition. It clearly ignores the morainic ridges further north and closer to the sea, as well as other true uplands such as the Stemweder Berg or the Rehburg Hills. Of course, these hills are much lower and do not reach the 200-metre contour line. Of the higher, say up to uplands, the northern foothills of Deister and Bückeberge extend farther north than the eastern Wiehen range. However, it is also true that the highest part of the Wiehen Hills at Lübbecke has the most northerly hill over 300 metres in Germany. The Heidbrink, at almost 320 metres high, is also the northernmost "three-hundred" on the European continent between the central Ural Mountains and the Atlantic, i.e. excluding the British Isles and Fennoscandinavia.

The Wiehen Hills (, also locally, just "Wiehen") are a hill range in North Rhine-Westphalia and Lower Saxony in Germany. The hills run from west to east like a long finger away from the main upland area of the Lower Saxon Hills, beginning at the Weser River near Minden and terminating in the vicinity of Osnabrück. It is the northernmost of the German Central Upland ranges extending into the Northern Lowlands. Their highest hill is the Heidbrink near Lübbecke with an altitude of.

Das Wiehengebirge ist ein bis hohes Mittelgebirge im Südwesten Niedersachsens und Nordosten Nordrhein-Westfalens. Das zu den Nordausläufern der deutschen Mittelgebirge zählende Gebirge wird zum Weserbergland und im weiteren Sinne zum Weser-Leine-Bergland gerechnet. Es liegt am Südrand des Norddeutschen Tieflands, beginnt bei Bramsche im Westen und zieht sich bis zur rund 95 km entfernten Porta Westfalica im Osten. Das Kammgebirge bildet mit dem östlich anschließenden Wesergebirge eine geologische Einheit.


Plot.

Los Angeles.

As evening falls, tomboy cabby Corky (Winona Ryder) picks up Hollywood executive Victoria Snelling (Gena Rowlands) from the airport, and as Corky drives, Victoria tries to conduct business on her phone. Despite their extreme differences socially, the two develop a certain connection. When Victoria suggests that cab driving is not much a career, Corky counters that her dream in fact is to become a mechanic. During the ride Victoria, who is a casting agent, comes to realise that Corky would be ideal for a part in a movie she is casting, but Corky rejects the offer because she intends to be a mechanic. The taxi is a 1985 Chevrolet Caprice Classic Wagon.

New York.

Helmut (Armin Mueller-Stahl), an immigrant from East Germany who was a clown in his home country, has found work as a taxi driver. After dark, he picks up a passenger named YoYo (Giancarlo Esposito), a streetwise young man who wants to go to Brooklyn. Increasingly alarmed at Helmut's inability to handle an automatic transmission, ignorance of New York geography and feeble command of the English language, YoYo takes over the wheel. During the drive, YoYo sees his sister-in-law Angela (Rosie Perez) on the street and forces her into the cab to take her back home. Helmut is clearly amused by the vituperation between the two. After Angela and Yoyo depart, Helmut struggles to drive back to Manhattan, muttering "New York...New York." The taxi is a 1983 Ford LTD Crown Victoria.

Paris.

At night, a cab picks up two drunk African diplomats, who mock the lowly driver (Isaach De Bankolé) and find it hilarious that he is from the Ivory Coast. In French, when he says he is "ivoirien", they say "il voit rien" (he can't see a thing). Sick of their insults, he throws them out without making them pay. Next he picks up an attractive young woman (Béatrice Dalle), who is blind. As she cannot see the colour of his skin, he asks her where she thinks he is from. After a moment's thought, she says "the Ivory Coast". Prickly and sexually provocative, she rejects most of his efforts to be friendly, regarding him as beneath her, but he is genuinely fascinated by her and her predicament. So much so that, after dropping her off, he watches her walk beside a canal in the dark and drives into another car, whose driver angrily accuses him of being blind. The taxi is a 1980 Peugeot 504.

Rome.

In the early morning hours, an eccentric cabbie (Roberto Benigni) picks up a priest (Paolo Bonacelli). As he drives, he starts to confess his sins. Much to the priest's discomfort, he goes into great detail about how he discovered his sexuality, first with a pumpkin and then with a sheep, then details a love affair he had with his brother's wife, miming the actions and mouthing the cries. Already ailing, overwhelmed by the barrage of unwanted information, the priest has a fatal heart attack. Unable to revive him, the cabbie leaves him on a bench to be found once it is light. The taxi is a 1976 Fiat 128.

Helsinki.

After an evening spent drinking heavily, three workers (Kari Väänänen, Sakari Kuosmanen, and Tomi Salmela), one of whom has just been fired from his job and has passed out, climb into a cab to return home. On the way, the two conscious workers talk about the terrible situation their unconscious friend is in, being out of work and having to face a divorce and a pregnant daughter. The driver, Mika (Matti Pellonpää), then tells them all the saddest story they have ever heard. The workers are terribly moved and depressed by the story, and even become unsympathetic toward their drunken, laid-off companion. Leaving him in the cab, they stagger off to their homes. Mika wakes him, takes payment and leaves. Worker sits on the ground, passing neighbours greet him and he replies back. The taxi is a 1973 Volvo 144.

Reception.

Review aggregator website Rotten Tomatoes retrospectively gave the film an approval rating of 75%, based on 24 reviews, and an average rating of 6.3/10.

Night on Earth is a 1991 art comedy-drama film written and directed by Jim Jarmusch. It is a collection of five vignettes, taking place during the same night, concerning the temporary bond formed between taxi driver and passenger in five cities: Los Angeles, New York, Paris, Rome, and Helsinki. Jarmusch wrote the screenplay in about eight days, and the choice of certain cities was largely based on the actors with whom he wanted to work. The soundtrack of the same name is by Tom Waits.

Night on Earth ist ein US-amerikanischer Episodenfilm von Jim Jarmusch, in dem fünf Geschichten erzählt werden. Alle Episoden spielen in einem Taxi, zeitgleich in derselben Nacht, jedoch in fünf unterschiedlichen Städten: Los Angeles, New York, Paris, Rom und Helsinki. Der jeweilige Taxifahrer bzw. die Fahrerin greift in das Schicksal der Fahrgäste ein oder die Kunden beeinflussen das Schicksal der Fahrer. Die Episoden wurden in den jeweiligen Landessprachen gedreht und dauern etwa 25 Minuten. "Night On Earth" wurde auch nicht synchronisiert, sondern untertitelt, um die landesspezifischen Stimmungen besser wiederzugeben.


History.

The idea of out-of-hours cash distribution developed from bankers' needs in Japan, Sweden, the United Kingdom, and the United States. A Japanese device called the "Computer Loan Machine" supplied cash as a three-month loan at 5% p.a. after inserting a credit card. The device was operational in 1966. However, little is known about the device.  Adrian Ashfield invented the basic idea of a card combining the key and user's identity in February 1962. This was granted UK Patent 959,713 for "Access Controller" in June 1964 and assigned to W. S. Atkins & Partners who employed Ashfield. He was paid ten shillings for this, the standard sum for all patents. It was originally intended to dispense petrol but the patent covered all uses.  In the US patent record, Luther George Simjian has been credited with developing a "prior art device". Specifically his 132nd patent (US3079603), which was first filed on 30 June 1960 (and granted 26 February 1963). The roll-out of this machine, called Bankograph, was delayed by a couple of years, due in part to Simjian's Reflectone Electronics Inc. being acquired by Universal Match Corporation. An experimental Bankograph was installed in New York City in 1961 by the City Bank of New York, but removed after six months due to the lack of customer acceptance. The Bankograph was an automated envelope deposit machine (accepting coins, cash and cheques) and did not have cash dispensing features.  A cash machine was put into use by Barclays Bank in its Enfield Town branch in North London, United Kingdom, on 27 June 1967. This machine was inaugurated by English comedy actor Reg Varney. This instance of the invention is credited to the engineering team led by John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year Honours. Transactions were initiated by inserting paper cheques issued by a teller or cashier, marked with carbon-14 for machine readability and security, which in a later model were matched with a six-digit personal identification number (PIN). Shepherd-Barron stated "It struck me there must be a way I could get my own money, anywhere in the world or the UK. I hit upon the idea of a chocolate bar dispenser, but replacing chocolate with cash."  The Barclays–De La Rue machine (called De La Rue Automatic Cash System or DACS) beat the Swedish saving banks' and a company called Metior's machine (a device called Bankomat) by a mere nine days and Westminster Bank's–Smith Industries–Chubb system (called Chubb MD2) by a month. The online version of the Swedish machine is listed to have been operational on 6 May 1968, while claiming to be the first online ATM in the world, ahead of similar claims by IBM and Lloyds Bank in 1971, and Oki in 1970. The collaboration of a small start-up called Speytec and Midland Bank developed a fourth machine which was marketed after 1969 in Europe and the US by the Burroughs Corporation. The patent for this device (GB1329964) was filed in September 1969 (and granted in 1973) by John David Edwards, Leonard Perkins, John Henry Donald, Peter Lee Chappell, Sean Benjamin Newcombe, and Malcom David Roe.  Both the DACS and MD2 accepted only a single-use token or voucher which was retained by the machine, while the Speytec worked with a card with a magnetic stripe at the back. They used principles including Carbon-14 and low-coercivity magnetism in order to make fraud more difficult.  The idea of a PIN stored on the card was developed by a group of engineers working at Smiths Group on the Chubb MD2 in 1965 and which has been credited to James Goodfellow (patent GB1197183 filed on 2 May 1966 with Anthony Davies). The essence of this system was that it enabled the verification of the customer with the debited account without human intervention. This patent is also the earliest instance of a complete "currency dispenser system" in the patent record. This patent was filed on 5 March 1968 in the US (US 3543904) and granted on 1 December 1970. It had a profound influence on the industry as a whole. Not only did future entrants into the cash dispenser market such as NCR Corporation and IBM licence Goodfellow's PIN system, but a number of later patents reference this patent as "Prior Art Device".

Location.

ATMs can be placed at any location but are most often placed near or inside banks, shopping centers/malls, airports, railway stations, metro stations, grocery stores, petrol/gas stations, restaurants, and other locations. ATMs are also found on cruise ships and on some US Navy ships, where sailors can draw out their pay.  ATMs may be on- and off-premises. On-premises ATMs are typically more advanced, multi-function machines that complement a bank branch's capabilities, and are

Financial networks.

Most ATMs are connected to interbank networks, enabling people to withdraw and deposit money from machines not belonging to the bank where they have their accounts or in the countries where their accounts are held (enabling cash withdrawals in local currency). Some examples of interbank networks include NYCE, PULSE, PLUS, Cirrus, AFFN, Interac, Interswitch, STAR, LINK, MegaLink, and BancNet.  ATMs rely on authorization of a financial transaction by the card issuer or other authorizing institution on a communications network. This is often performed through an ISO 8583 messaging system.  Many banks charge ATM usage fees. In some cases, these fees are charged solely to users who are not customers of the bank that operates the ATM; in other cases, they apply to all users.  In order to allow a more diverse range

Global use.

There are no hard international or government-compiled numbers totaling the complete number of ATMs in use worldwide. Estimates developed by ATMIA place the number of ATMs currently in use at 3 million units, or approximately 1 ATM per 3,000 people in the world.  To simplify the analysis of ATM usage around the world, financial

Hardware.

An ATM is typically made up of the following devices:  Due to heavier computing demands and the falling price of personal computer–like architectures, ATMs have moved away from custom hardware architectures using microcontrollers or application-specific integrated circuits and have adopted the hardware architecture of a personal computer, such as USB connections for peripherals, Ethernet and IP communications, and use personal computer operating systems.  Business owners often lease ATMs from service providers. However, based on the economies of scale, the price of equipment has dropped to the point where many business owners are simply paying for ATMs using a credit card.  New ADA voice and text-to-speech guidelines imposed in 2010, but required

Software.

With the migration to commodity Personal Computer hardware, standard commercial "off-the-shelf" operating systems and programming environments can be used inside of ATMs. Typical platforms previously used in ATM development include RMX or OS/2.  Today, the vast majority of ATMs worldwide use a Microsoft Windows operating system, primarily Windows XP Professional or Windows XP Embedded. In early 2014, 95% of ATMs were running Windows XP. A small number of deployments may still be running older versions of the Windows OS, such as Windows NT, Windows CE, or Windows 2000, even though Microsoft still supports only Windows 8 and Windows 10.  There is a computer industry security view that general public desktop operating systems(os) have greater risks as operating systems for cash dispensing machines than other types of operating systems like (secure) real-time operating systems (RTOS). RISKS Digest has many articles about ATM operating system vulnerabilities.  Linux is also finding some reception in the ATM marketplace. An example of this is Banrisul, the largest bank in the south of Brazil, which has replaced the MS-DOS operating systems in its ATMs with Linux. Banco do Brasil is also migrating ATMs to Linux. Indian-based Vortex Engineering is manufacturing ATMs which operate only with Linux. Common application layer transaction protocols, such as Diebold 91x (911 or

Impact on labor.

The number of human bank tellers in the United States increased from approximately 300,000 in 1970 to approximately 600,000 in 2010. Counter-intuitively, a contributing factor may be the introduction

Security.

Security, as it relates to ATMs, has several dimensions. ATMs also provide a practical demonstration of a number of security systems and concepts operating together and how various security concerns are addressed.

Physical.

Early ATM security focused on making the terminals invulnerable to physical attack; they were effectively safes with dispenser mechanisms. A number of attacks resulted, with thieves attempting to steal entire machines by ram-raiding. Since the late 1990s, criminal groups operating in Japan improved ram-raiding by stealing and using a truck loaded with heavy construction machinery to effectively demolish or uproot an entire ATM and any housing to steal its cash.  Another attack method, "plofkraak", is to seal all openings of the ATM with silicone and fill the vault with a combustible gas or to place an explosive inside, attached, or near the machine. This gas or explosive is ignited and the vault is opened or distorted by the force of the resulting explosion and

Transactional secrecy and integrity.

The security of ATM transactions relies mostly on the integrity of the secure cryptoprocessor: the ATM often uses general commodity components that sometimes are not considered to be "trusted systems".  Encryption of personal information, required by law in many jurisdictions, is used to prevent fraud. Sensitive

Customer identity integrity.

There have also been a number of incidents of fraud by Man-in-the-middle attacks, where criminals have attached fake keypads or card readers to existing machines. These have then been used to record customers' PINs and bank card information in order to gain unauthorised access to their accounts. Various ATM manufacturers have put

Device operation integrity.

Openings on the customer side of ATMs are often covered by mechanical shutters to prevent tampering with the mechanisms when they are not in use. Alarm sensors are placed inside ATMs and their servicing areas to alert their operators when doors have been opened by unauthorised personnel.  To protect against hackers, ATMs have a built-in firewall. Once the firewall has detected malicious attempts to break into the machine remotely, the firewall locks

Customer security.

In some countries, multiple security cameras and security guards are a common feature. In the United States, The New York State Comptroller's Office has advised the New York State Department of Banking to have more thorough safety inspections of ATMs in high crime areas.  Consultants of ATM operators assert that the issue of customer security should have more focus by the banking industry; it has been suggested that efforts are now more concentrated on the preventive measure of deterrent legislation than on the problem of ongoing forced withdrawals.  At least as far back as July 30, 1986, consultants of the industry have advised for the adoption of an emergency PIN system for ATMs, where the user is able to send a silent alarm in response to a threat. Legislative efforts to require an emergency PIN system have appeared in Illinois, Kansas and Georgia, but none have succeeded yet. In January 2009, Senate Bill 1355 was proposed in the Illinois Senate that revisits the

Jackpotting.

The term is used to describe one method criminals utilize to steal money from an ATM. The thieves gain physical access through a small hole drilled in the machine. They disconnect

Encryption.

In recent years, many ATMs also encrypt the hard disk. This means

Uses.

ATMs were originally developed as cash dispensers, and have evolved to provide many other bank-related functions: In some countries, especially those which benefit from a fully integrated cross-bank network (e.g.: Multibanco in Portugal), ATMs include many functions that are not directly related to the management of one's own bank account, such as:  Increasingly, banks are seeking to use the ATM as a sales device to deliver pre approved loans

Reliability.

Before an ATM is placed in a public place, it typically has undergone extensive testing with both test money and the backend computer systems that allow it to perform transactions. Banking customers also have come to expect high reliability in their ATMs, which provides incentives to ATM providers to minimise machine and network failures. Financial consequences of incorrect machine operation also provide high degrees of incentive to minimise malfunctions.  ATMs and the supporting electronic financial networks are generally very reliable, with industry benchmarks typically producing 98.25% customer availability for ATMs and up to 99.999% availability for host systems that manage the networks of ATMs. If ATM networks do go out of service, customers could be left without the ability to make transactions until the beginning of their bank's next time of opening hours.  This said, not all errors are to the detriment of customers; there have been cases of machines giving out money without debiting the account, or giving out higher value notes as a result of incorrect denomination of banknote being loaded in the money cassettes. The result of receiving too much money may be influenced by the card holder agreement in place between the customer and

Fraud.

As with any device containing objects of value, ATMs and the systems they depend on to function are the targets of fraud. Fraud against ATMs and people's attempts to use them takes several forms.  The first known instance of a fake ATM was installed at a shopping mall in Manchester, Connecticut in 1993. By modifying the inner workings of a Fujitsu model 7020 ATM, a criminal gang known as the Bucklands Boys stole information from cards inserted into the machine by customers.  WAVY-TV reported an incident in Virginia Beach in September 2006 where a hacker, who had probably obtained a factory-default administrator password for a filling station's white-label ATM, caused the unit to assume it was loaded with US$5 bills instead of $20s, enabling himself—and many subsequent customers—to walk away with four times the money withdrawn from their accounts. This type of scam was featured on the TV series "The Real Hustle".  ATM behaviour can change during what is called "stand-in" time, where the bank's cash dispensing network is unable to access databases that contain account information (possibly for database maintenance). In order to give customers access to cash, customers may be allowed to withdraw cash up to a certain amount that may be less than their usual daily withdrawal limit, but may still exceed the amount of available money in their accounts, which could result in fraud if the customers intentionally withdraw more money than they had in their accounts.

Card fraud.

In an attempt to prevent criminals from shoulder surfing the customer's personal identification number (PIN), some banks draw privacy areas on the floor.  For a low-tech form of fraud, the easiest is to simply steal a customer's card along with its PIN. A later variant of this approach is to trap the card inside of the ATM's card reader with a device often referred to as a Lebanese loop. When the customer gets frustrated by not getting the card back and walks away from the machine, the criminal is able to remove the card and withdraw cash from the customer's account, using the card and

Related devices.

A talking ATM is a type of ATM that provides audible instructions so that people who cannot read a screen can independently use the machine, therefore effectively eliminating the need for assistance from an external, potentially malevolent source. All audible information is delivered privately through a standard headphone jack on the face of the machine. Alternatively, some banks such as the Nordea and Swedbank use a built-in external speaker which may be invoked by pressing the talk button on the keypad. Information is delivered to the customer either through pre-recorded sound files or via text-to-speech speech synthesis.  A postal interactive kiosk may share many components of an ATM (including a vault), but it only dispenses items related to postage.  A scrip cash dispenser may have many components in common with an ATM, but it lacks the ability to dispense physical cash and consequently requires no vault. Instead, the customer requests a withdrawal transaction from the machine, which prints a receipt or scrip. The customer then takes this receipt to a nearby sales clerk, who then exchanges it for cash from the till.  A teller assist unit (TAU) is distinct in that it is designed to be operated solely by trained personnel and not by the general public, does integrate directly into interbank networks, and usually is controlled by a computer that is not directly integrated into the overall construction of the unit.  A Web ATM is an online interface for ATM card banking that uses a smart card reader. All the usual ATM functions are available, except for withdrawing cash. Most banks in Taiwan provide these online services.

An automated teller machine (ATM) is an electronic telecommunications device that enables customers of financial institutions to perform financial transactions, such as cash withdrawals, deposits, funds transfers, or account information inquiries, at any time and without the need for direct interaction with bank staff.

Ein Geldautomat, Geldausgabeautomat (GAA), Bankautomat, Bankomat, Bancomat oder wie im Englischen ATM (Automated Teller Machine) ist ein technisches Gerät zur Bargeldabhebung in Selbstbedienung bei Geld- und Kreditinstituten vom eigenen Giro- oder Kreditkartenkonto (siehe auch Electronic Cash). Mittlerweile kann bei vielen Automaten auch eingezahlt werden, und bei einigen ist das in Fremdwährungen möglich. Der Geldausgabeautomat war – noch vor dem PC – das erste Computerterminal, das breiten Bevölkerungsschichten weltweit zugänglich war.


Informal description.

A finite-state machine just looks at the input signal and the current state: it has no stack to work with. It chooses a new state, the result of following the transition. A pushdown automaton (PDA) differs from a finite state machine in two ways:  A pushdown automaton reads a given input string from left to right. In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition. The manipulation can be to push a particular symbol to the top of the stack, or to pop off the top of the stack. The automaton can alternatively ignore the stack, and leave it as it is.  Put together: Given an input symbol, current state, and stack symbol, the automaton can follow a transition to another state, and optionally manipulate (push or pop) the stack.  If, in every situation, at most one such transition action is possible, then the automaton is called a deterministic pushdown automaton (DPDA). In general, if several actions are possible, then the automaton is called a general, or nondeterministic, PDA. A given input string may drive a nondeterministic pushdown automaton to one of several configuration sequences; if one of them leads to an accepting configuration after reading the complete input string, the latter is said to belong to the "language accepted by the automaton".

Formal definition.

We use standard formal language notation: formula_1 denotes the set of finite-length strings over alphabet formula_2 and formula_3 denotes the empty string.  A PDA is formally defined as a 7-tuple:  formula_4 where  An element formula_13 is a transition of formula_14. It has the intended meaning that formula_14, in state formula_16, on the input formula_17 and with formula_18 as topmost stack symbol, may read formula_19, change the state to formula_20, pop formula_21, replacing it by pushing formula_22. The formula_23 component of the transition relation is used to formalize that the PDA can either read a letter from the input, or proceed leaving the input untouched. In many texts the transition relation is replaced by an (equivalent) formalization, where  Here formula_27 contains all possible actions in state formula_28 with formula_21 on the stack, while reading formula_19 on the input. One writes for example formula_31 precisely when formula_32 because formula_33. Note that "finite" in this definition is essential.  In order to formalize the semantics of the pushdown automaton a description of the current situation is introduced. Any 3-tuple formula_34 is called an instantaneous description (ID) of formula_14, which includes the current state, the part of the input tape that has not been read, and the contents of the stack (topmost symbol written first). The transition relation formula_8 defines the step-relation formula_37 of formula_14 on instantaneous descriptions. For instruction formula_13 there exists a step formula_40, for every formula_41 and every formula_42.  In general pushdown automata are nondeterministic meaning that in a given instantaneous description formula_43 there may be several possible steps. Any of these steps can be chosen in a computation. With the above definition in each step always a single symbol (top of the stack) is popped, replacing it with as many symbols as necessary. As a consequence no step is defined when the stack is empty.  Computations of the pushdown automaton are sequences of steps. The computation starts in the initial state formula_44 with the initial stack symbol formula_45 on the stack, and a string formula_46 on the input tape, thus with initial description formula_47. There are two modes of accepting. The pushdown automaton either accepts by final state, which means after reading its input the automaton reaches an accepting state (in formula_48), or it accepts by empty stack (formula_3), which means after reading its input the automaton empties its stack. The first acceptance mode uses the internal memory (state), the second the external memory (stack).  Formally one defines  Here formula_55 represents the reflexive and transitive closure of the step relation formula_56 meaning any number of consecutive steps (zero, one or more).  For each single pushdown automaton these two languages need to have no relation: they may be equal but usually this is not the case. A specification of the automaton should also include the intended mode of acceptance. Taken over all pushdown automata both acceptance conditions define the same family of languages.  Theorem. For each pushdown automaton formula_14 one may construct a pushdown automaton formula_58 such that formula_59, and vice versa, for each pushdown automaton formula_14 one may construct a pushdown automaton formula_58 such that formula_62

Example.

The following is the formal description of the PDA which recognizes the language formula_63 by final state: formula_64, where  The transition relation formula_8 consists of the following six instructions:  In words, the first two instructions say that in state any time the symbol is read, one is pushed onto the stack. Pushing symbol on top of another is formalized as replacing top by (and similarly for pushing symbol on top of a ).  The third and fourth instructions say that, at any moment the automaton may move from state to state.  The fifth instruction says that in state, for each symbol read, one is popped.  Finally, the sixth instruction says that the machine may move from state to accepting state only when the stack consists of a single.  There seems to be no generally used representation for PDA. Here we have depicted the instruction formula_77 by an edge from state to state labelled by formula_78 (read ; replace by formula_79).

Understanding the computation process.

The following illustrates how the above PDA computes on different input strings. The subscript from the step symbol formula_80 is here omitted.

PDA and context-free languages.

Every context-free grammar can be transformed into an equivalent nondeterministic pushdown automaton. The derivation process of the grammar is simulated in a leftmost way. Where the grammar rewrites a nonterminal, the PDA takes the topmost nonterminal from its stack and replaces it by the right-hand part of a grammatical rule ("expand"). Where the grammar generates a terminal symbol, the PDA reads a symbol from input when it is the topmost symbol on the stack ("match"). In a sense the stack of the PDA contains the unprocessed data of the grammar, corresponding to a pre-order traversal of a derivation tree.  Technically, given a context-free grammar, the PDA has a single state, 1, and its transition relation is constructed as follows.  The PDA accepts by empty stack. Its initial stack symbol is the grammar's start symbol.  For a context-free grammar in Greibach normal form, defining (1,γ) ∈ δ(1,"a","A") for each grammar rule "A" → "a"γ also yields an equivalent nondeterministic pushdown automaton.  The converse, finding a grammar for a given PDA, is not that easy. The trick is to code two states of the PDA into the nonterminals of the grammar.  Theorem. For each pushdown automaton formula_14 one may construct a context-free grammar formula_86 such that formula_87.  The language of strings accepted by a deterministic pushdown automaton is called a deterministic context-free language. Not all context-free languages are deterministic. As a consequence, the DPDA is a strictly weaker variant of the PDA  A finite automaton with access to two stacks is a more powerful device, equivalent in power to a Turing machine. A linear bounded automaton is a device which is more powerful than a pushdown automaton but less so than a Turing machine.

Generalized pushdown automaton (GPDA).

A GPDA is a PDA which writes an entire string of some known length to the stack or removes an entire string from the stack in one step.  A GPDA is formally defined as a 6-tuple: where formula_89, and are defined the same way as a PDA. is the transition function.  Computation rules for a GPDA are the same as a PDA except that the formula_92's and formula_93's are now strings instead of symbols.  GPDA's and PDA's are equivalent in that if a language is recognized by a PDA, it is also recognized by a GPDA and vice versa.  One can formulate an analytic proof for the equivalence of GPDA's and PDA's using the following simulation:  Let formula_94 be a transition of the GPDA  where formula_95.  Construct the following transitions for the PDA:

Stack automaton.

As a generalization of pushdown automata, Ginsburg, Greibach, and Harrison (1967) investigated stack automata, which may additionally step left or right in the input string (surrounded by special endmarker symbols to prevent slipping out), and step up or down in the stack in read-only mode. A stack automaton is called "nonerasing" if it never pops from the stack. The class of languages accepted by nondeterministic, nonerasing stack automata is "NSPACE"("n"), which is a superset of the context-sensitive languages. The class of languages accepted by deterministic, nonerasing stack automata is "DSPACE"("n"⋅log("n")).

Alternating pushdown automata.

An alternating pushdown automaton (APDA) is a pushdown automaton with a state set  States in formula_99 and formula_100 are called "existential" resp. "universal". In an existential state an APDA nondeterministically chooses the next state and accepts if "at least one" of the resulting computations accepts. In a universal state APDA moves to all next states and accepts if "all" the resulting computations accept.  The model was introduced by Chandra, Kozen and Stockmeyer. Ladner, Lipton and Stockmeyer proved that this model is equivalent to EXPTIME i.e. a language is accepted by some APDA if, and only if, it can be decided by an exponential-time algorithm.  Aizikowitz and Kaminski introduced "synchronized alternating pushdown automata" (SAPDA) that are equivalent to conjunctive grammars in the same way as nondeterministic PDA are equivalent to context-free grammars.

In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.

Ein Kellerautomat (KA, auch "PDA" für englisch "pushdown automaton"; auch "Stackmaschine") ist ein Automat im Sinne der theoretischen Informatik, ein Konstrukt, das verwendet wird, um gewisse Eigenschaften von Problemen und Algorithmen zu analysieren und zu beweisen.