text: Also, by firing more aerodynamically streamlined projectiles at greater velocities, railguns may achieve greater range, less time to target, and at shorter ranges less wind drift, bypassing the physical limitations of conventional firearms: "the limits of gas expansion prohibit launching an unassisted projectile to velocities greater than about 1.5 km/s and ranges of more than 50 miles [80 km] from a practical conventional gun system. 2 [80], A test of a railgun took place on December 10, 2010, by the U.S. Navy at the Naval Surface Warfare Center Dahlgren Division. L Because the launch track would be 1.6 km long, power will be supplied by a distributed network of 100 rotating machines (compulsator) spread along the track. This current makes the railgun behave as an electromagnet, creating a magnetic field inside the loop formed by the length of the rails up to the position of the armature. Other designs include a longer helical (spiral) track, or a large ring design whereby a space vehicle would circle the ring numerous times, gradually gaining speed, before being released into a launch corridor leading skyward. [97] In more conventional power units, a 32 MJ shot every 6 s is a net power of 5.3 MW (or 5300 kW). [47], Railguns are being researched as weapons with projectiles that do not contain explosives or propellants, but are given extremely high velocities: 2,500 m/s (8,200 ft/s) (approximately Mach 7 at sea level) or more. Each successive railgun has a mass 2 orders of magnitude less than its predecessor, because m1v1 = m2v2 and so the launching gun will be propelled backwards in addition to the projectile gun propelled forwards. At one end, these rails are connected to an electrical power supply, to form the breech end of the gun. I [70][71] As of 1993 the project appeared to be in the early experimental stages. {\displaystyle B} [91] The first shipboard tests was to be from a railgun installed on an Spearhead-class expeditionary fast transport (EPF), but this was later changed to land based testing. This timeframe suggests the weapons are planned to be installed on the Navy's next-generation surface combatants, expected to start construction by 2028. If a railgun were to provide a uniform magnetic field of strength The same concept can be used with coilgun. {\displaystyle I} This decreases ammunition size and weight, allowing more ammunition to be carried and eliminating the hazards of carrying explosives or propellants in a tank or naval weapons platform. The Navy eventually hopes to have 64-megajoule ship mounted rail guns. Some railguns also use strong neodymium magnets with the field perpendicular to the current flow to increase the force on the projectile. For a more workable simple model, a useful alternative is to use a lumped circuit model, to describe the relationship between the driving current and the railgun force. , the total field from both wires at any point on the armature is: where The EMRG was designed to offer a low cost alternative to orbital debris testing on satellites. So the total power flowing into the railgun is then simply the product For an ideal square bore single-turn railgun, the value of {\displaystyle \mu _{0}} Therefore, hydrogen is typically the first choice; however, other propellants like methane can be used. LIST OF PAPERS, 16th International Symposium on Electromagnetic Launch Technology (EML 2012) Beijing, China, Strategic Defense Initiative Organization, Federally Funded Research and Development Center, Armament Research and Development Establishment, Learn how and when to remove this template message, Institute for Advanced Technology at the University of Texas at Austin, practical considerations of escape velocity, Future Combat Systems Manned Ground Vehicles, United States Air Force Research Laboratory, Cannon-Caliber Electromagnetic Gun (CCEMG) program, U.S. Army Armament Research Development and Engineering Center, Defence Research and Development Organisation, "Advanced Concepts of the Propulsion System for the Futuristic Gun Ammunition", "US Patent 1,421,435 "Electric Apparatus for Propelling Projectiles, Long-Range Electrical Gun, Equipment and Supplies of the Red Army, Analysis of a Rail Gun Plasma Accelerator, Two-Dimensional Model for Arc Dynamics in the Rail Gun, Prediction of Electromagnetic Fields generated by Rail Guns, Investigating UHF Telemetry for Electromagnetic Launchers, Two-Dimensional Model for Current and Heat Transport in Solid-Armature Railguns, Commissioning Tests of the Medium Caliber Railgun Launcher, "Armament Research and Development Establishment, Pune-411", "Rapid Fire Railgun For The Cannon Caliber Electromagnetic Gun System", "Video: Navy's Mach 8 Railgun Obliterates Record", "Launch to space with an electromagnetic railgun", "NASA Considering Rail Gun Launch System to the Stars", "Railguns: The Next Big Pentagon Boondoggle? x They do not currently exist in a practical, usable form. A conventional uses a gun barrel and a chemical explosive to send the projectile. As briefly discussed above, the stresses involved in firing this sort of device require an extremely heat-resistant material. ) is measured and the beginning of the rails is greater than the separation of the rails ( From what I've gathered from Wikipedia the Railgun is more of an artillery weapon, striking targets from vast distances with high impact force. Low power, small scale railguns have also made popular college and amateur projects. The main problem the U.S. Navy has had with implementing a railgun cannon system is that the guns wear out due to the immense pressures, stresses and heat that are generated by the millions of amperes of current necessary to fire projectiles with megajoules of energy. Total power consumption must be less than 8 watts (threshold)/5 watts (objective) and the battery life must be at least 5 minutes (from initial launch) to enable operation during the entire engagement. It was the first time in history that such levels of performance were reached. Probably the oldest consistently successful system was built by the UK's Defence Research Agency at Dundrennan Range in Kirkcudbright, Scotland. For a similar projectile, the range of railguns may exceed that of conventional guns. / At this time it is generally acknowledged that it will take major breakthroughs in materials science and related disciplines to produce high-powered railguns capable of firing more than a few shots from a single set of rails. When the gases are ignited, they burn, expand and propel the projectile out of the barrel with higher efficiency relative to solid propellant and have achieved higher muzzle velocities in experiments. Navy. {\displaystyle B} {\displaystyle l} The aim was to achieve projectile speed of 7,000 m/s (23,000 ft/s). The weapon was able to produce doughnut-shaped rings of plasma and balls of lightning that exploded with devastating effects when hitting their target. The above formula is based on the assumption that the distance ( While this technology does appear to provide higher velocities, the main drawback with gaseous or liquid propellants for gun systems is the difficulty in getting uniform and predictable ignition and muzzle velocities. Watch the Navy's Railgun Fire From Every Angle The railgun takes the first shot of its commissioning series. {\displaystyle {\widehat {\varphi }}} While not nearly as powerful as a cruise missile like a BGM-109 Tomahawk, that will deliver 3,000 MJ of destructive energy to a target, such weapons would, in theory, allow the Navy to deliver more granular firepower at a fraction of the cost of a missile, and will be much harder to shoot down versus future defensive systems. I Under high-use conditions, current railguns would require frequent replacement of the rails, or to use a heat-resistant material that would be conductive enough to produce the same effect. 3 [83], In 2014 the U.S. Navy had plans to integrate a railgun that has a range of over 16 km (10 mi) onto a ship by 2016. The National Review thinks that Railguns will be a waste of money and believe it would be better to develop light gas guns for better long range navy and artillery guns. B3: Mass Driver (Electromagnetic Catapult) B4: MK-71 8: B5: Combustion Light Gas Gun (CLGG) Companies, etc. It used a track length of 0.7 m (2.3 ft). z ′ Ground combat forces, however, may find that co-locating an additional electrical power supply on the battlefield for every gun system may not be as weight and space efficient, survivable, or convenient a source of immediate projectile-launching energy as conventional propellants, which are currently manufactured safely behind the lines and delivered to the weapon, pre-packaged, through a robust and dispersed logistics system. A General Atomics-built prototype was delivered for testing in October 2012. This system was established in 1993 and has been operated for over 10 years. A combustion light gas gun (CLGG) is a projectile weapon that utilizes the explosive force of low molecular-weight combustible gases, such as hydrogen mixed with oxygen, as propellant. The United States military have expressed interest in pursuing research in electric gun technology throughout the late 20th century due to how electromagnetic guns don't require propellants to fire a shot like conventional gun systems, significantly increasing crew safety and reducing logistics costs, as well as provide a greater range. Finnlayer. The company hopes to have an integrated demo of the system by 2016 followed by production by 2019, pending funding. A very large power supply, providing on the order of one million amperes of current, will create a tremendous force on the projectile, accelerating it to a speed of many kilometres per second (km/s). As a result, the U.S. military focused on developing small guided projectiles that could withstand the high-G launch from ultra-high velocity plasma armature railguns. The armature may be an integral part of the projectile, but it may also be configured to accelerate a separate, electrically isolated or non-conducting projectile. [113], In early February 2018, pictures of what is claimed to be a Chinese railgun were published online. And my answer is all about "combustion" part. , while the power flow [29] Featuring a 30-mm roundbore, the launcher was capable of firing three, five-round salvos of 185-g launch packages at a muzzle velocity of 1850 m/s and a firing rate of 5 Hz. Symposium on Electromagnetic Launch Technology (EML 2012) at Beijing. Another light gas gun, the Combustion Light Gas Gun in a 155 mm prototype form was projected to achieve 2500 m/s with a .70 caliber barrel [citation needed]. In these models the railgun is modeled on an electrical circuit and the driving force can be determined from the energy flow in the circuit. The CCEMG railgun included several features: ceramic sidewalls, directional preloading, and liquid cooling. ) by a factor of about 3 or 4 ( Engineers are working to derive technologies developed for the DDG-1000 series ships into a battery system so other warships can operate a railgun. However, the Zumwalt has been cancelled and no further units will be built. [13], In 1923, Russian scientist A. L. Korol’kov detailed his criticisms of Fauchon-Villeplee's design, arguing against some of the claims that Fauchon-Villeplee made about the advantages of his invention. = For the Navy Barrage round fired from ^ I The Yugoslavian Military Technology Institute developed, within a project named EDO-0, a railgun with 7 kJ kinetic energy, in 1985. between the rails is is only provided by the current flowing in the rails, i.e. Rail guns are less effective than missiles in most metrics, but they have the unique feature of potentially being ludicrously cheap per round. − Since power can be expressed as force times speed, this shows the force on the railgun armature is given by. First, it can be shown from the Biot–Savart law that at one end of a semi-infinite current-carrying wire, the magnetic field at a given perpendicular distance ( The power supply must be able to deliver large currents, sustained and controlled over a useful amount of time. [29][30], In 2010, the United States Navy tested a BAE Systems-designed compact-sized railgun for ship emplacement that accelerated a 3.2 kg (7 pound) projectile to hypersonic velocities of approximately 3,390 m/s (7,600 mph; 12,200 km/h; 11,100 ft/s), or about Mach 10, with 18.4 MJ of kinetic energy. Furthermore, in general, the force will be proportional to the square of the magnitude of the current and inversely proportional to the distance between the conductors. d d [78] The power was provided by a new 9-megajoule prototype capacitor bank using solid-state switches and high-energy-density capacitors delivered in 2007 and an older 32-MJ pulse power system from the US Army's Green Farm Electric Gun Research and Development Facility developed in the late 1980s that was previously refurbished by General Atomics Electromagnetic Systems (EMS) Division. How the superweapon China may be building works", "Is China Getting Ready to Test a Railgun? Railgun - E.E.G. Alternatively, very long rail systems may be used to reduce the required launch acceleration. "[50], Current railgun technologies necessitate a long and heavy barrel, but a railgun's ballistics far outperform conventional cannons of equal barrel lengths. The new rail gun is a 32-megajoule Electro-Magnetic Laboratory Rail Gun. This causes three main problems: melting of equipment, decreased safety of personnel, and detection by enemy forces due to increased infrared signature. , a fairly good approximation assuming the length of the wires is much larger than This paper describes the installation and subsequent commissioning of a 7.5 km s-1, 12.7 mm bore two-stage light gas gun facility, based at First Light Fusion, Oxford, UK.The unique modular design of the diagnostics and impact chamber provides a flexible platform for a wide range of interdisciplinary hypervelocity impact studies. While similar in energy to the aforementioned test, the railgun used is considerably more compact, with a more conventional looking barrel. − ′ However, there are other theoretical applications currently being researched. Juliano Scharf Performer. [57] As is the case with the Phalanx CIWS, unguided railgun rounds will require multiple/many shots to bring down maneuvering supersonic anti-ship missiles, with the odds of hitting the missile improving dramatically the closer it gets. Increased muzzle velocities with better aerodynamically streamlined projectiles can convey the benefits of increased firing ranges while, in terms of target effects, increased terminal velocities can allow the use of kinetic energy rounds incorporating hit-to-kill guidance, as replacements for explosive shells. A hybrid armature uses a pair of plasma contacts to interface a metallic armature to the gun rails. It also follows that, for railguns with projectile masses of a few kg and barrel lengths of a few m, very large currents will be required to accelerate projectiles to velocities of the order of 1000 m/s. [106], In 1999, a collaboration between ARL and IAT led to the development of a radiometric method of measuring the temperature distribution of railgun armatures during a pulsed electrical discharge without disturbing the magnetic field. B Thus far, the project is self-funded. In addition, railgun systems have shown to potentially provide higher velocity of projectiles, which would increase accuracy for anti-tank, artillery, and air defense by decreasing the time it takes for the projectile to reach its target destination. A future goal is to develop projectiles that are self-guided – a necessary requirement to hit distant targets or intercepting missiles. This shows that the force will be proportional to the product of Virrugus Apocali Performer. Some high velocity projectiles developed by the Navy have command guidance, but the accuracy of the command guidance is not known, nor even if it can survive a full power shot. The speed, cost, and numerical advantages of railgun systems may allow them to replace several different systems in the current layered defense approach. Currently published material suggests that major advances in material science must be made before rails can be developed that allow railguns to fire more than a few full-power shots before replacement of the rails is required. ), the radius of the rails (which are assumed to be circular in cross section) ( [47] There would be a peak operating magnetic field of 5 T—half of this coming from the rails, and the other half from augmenting magnets. China is now one of the major players in electromagnetic launchers; in 2012 it hosted the 16th International Otherwise the rails, barrel, and all equipment attached would melt or be irreparably damaged. [101] In 1991, they determined the properties required for developing an effective launch package as well as the design criteria necessary for a railgun to incorporate finned, long rod projectiles. 8 Railgun - E.E.G. [49] The extreme g-forces involved with direct railgun ground-launch to space may restrict the usage to only the sturdiest of payloads. Hence, in practice, the force must be calculated after making due allowances for the spatial variation of the magnetic field over the volume of the armature. It should also be able to survive accelerations of at least 20,000 g (threshold) / 40,000 g (objective) in all axes, high electromagnetic fields (E > 5,000 V/m, B > 2 T), and surface temperatures of > 800 deg C. The package should be able to operate in the presence of any plasma that may form in the bore or at the muzzle exit and must also be radiation hardened due to exo-atmospheric flight. [38][82], A test took place in February 2012, at the Naval Surface Warfare Center Dahlgren Division. [87] When the guided rounds are developed, the Navy is projecting each round to cost about \$25,000,[88] though developing guided projectiles for guns has a history of doubling or tripling initial cost estimates. [75] At the University of Texas at Austin Center for Electromechanics, military railguns capable of delivering tungsten armor-piercing bullets with kinetic energies of nine megajoules (9 MJ) have been developed. 2 Mass Driver (Electromagnetic Catapult) MK-71 8: Combustion Light Gas Gun (CLGG) Credits (7) Vegas Salruas Backing Vocals, Recorded By. 1,421,435 "Electric Apparatus for Propelling Projectiles". , the force d x 24 Lists Best of 2011. Railgun - E.E.G. Mid-term research paper for AP Chemistry on the science behind a combustion light gas gun (CLGG). When the gases are ignited, they burn, expand and propel the projectile out of the barrel with higher efficiency relative to solid propellant and have achieved higher muzzle velocities in experiments. [112] According to a CNBC report from U.S. intelligence, China's railgun system was first revealed in 2011, and ground testing began in 2014. d B / A machine can recharge in a matter of hours using 10 MW power. {\displaystyle \mu _{0}} [27][failed verification] In 1994, India's DRDO's Armament Research and Development Establishment developed a railgun with a 240 kJ, low inductance capacitor bank operating at 5 kV power able to launch projectiles of 3–3.5 g weight to a velocity of more than 2,000 m/s (4,500 mph; 7,200 km/h; 6,600 ft/s). and the square of the current, electromagnetic railgun’s (EMRG) power supply, thus reducing its footprint. 2 Nevertheless, if technically feasible and cost effective to build, imparting hyper-velocity escape velocity to a projectile launching at sea level, where the atmosphere is the most dense, may result in much of the launch velocity being lost to aerodynamic drag. [25] The facility became the Army's first Federally Funded Research and Development Center and housed a few of the Army's electromagnetic launchers, such as the Medium Caliber Launcher. The first computer simulations occurred in 1990, and its first published experiment appeared on August 1, 1993. Since the lumped circuit model describes the railgun force in terms of fairly normal circuit equations, it becomes possible to specify a simple time domain model of a railgun. Railgun. In 1987 a successor was created, project EDO-1, that used projectile with a mass of 0.7 kg (1.5 lb) and achieved speeds of 3,000 m/s (9,800 ft/s), and with a mass of 1.1 kg (2.4 lb) reached speeds of 2,400 m/s (7,900 ft/s). A helical railgun was built at MIT in 1980 and was powered by several banks of, for the time, large capacitors (approximately 4 farads). Experimental velocities of 7.2 km/s (23,620 ft/s) with 10% efficiency have been demonstrated for the electric light-gas gun. NASA has proposed to use a railgun to launch "wedge-shaped aircraft with scramjets" to high-altitude at Mach 10, where it would then launch a small payload into orbit using conventional rocket propulsion. behind the armature. ′ The first weaponized railgun planned for production, the General Atomics Blitzer system, began full system testing in September 2010. https://apps.dtic.mil/dtic/tr/fulltext/u2/a462130.pdf UTRON 2006 Test Report, Learn how and when to remove this template message, https://apps.dtic.mil/dtic/tr/fulltext/u2/a462130.pdf, https://en.wikipedia.org/w/index.php?title=Combustion_light-gas_gun&oldid=995638954, Articles needing additional references from October 2013, All articles needing additional references, Creative Commons Attribution-ShareAlike License, This page was last edited on 22 December 2020, at 02:56. This allows an EMRG system to accelerate a projectile to extremely high velocities. This limited some early research railguns to one shot per service interval. Yes compressed guns can be lethal (if you luky) or achive high projectile speed (within laboratory conditions), but this is another question to answer. {\displaystyle {\mathrm {d} I}/{\mathrm {d} t}} Next, to evaluate the force on the armature, the above expression for the magnetic field on the armature can be used in conjunction with the Lorentz Force Law. [11] Fauchon-Villeplee filed for a US patent on 1 April 1919, which was issued in July 1922 as patent no. s Additionally, projectiles can be subject to some degree of ablation, and this can limit railgun life, in some cases severely.[43]. APFSDS) rather than using conventional propellants. It follows that the magnetic field will neither be constant nor spatially uniform. A company official claimed the gun could be ready for production in "two to three years". A combustion light-gas gun (CLGG) is a projectile weapon that utilizes the explosive force of low molecular-weight combustible gases, such as hydrogen mixed with oxygen, as propellant. {\displaystyle I^{2}L'v} Juliano M. Mixed By. x For comparison, 50 MJ is equivalent to the kinetic energy of a school bus weighing 5 metric tons, travelling at 509 km/h (316 mph; 141 m/s). The weapon system was successfully mounted on a Chinese Navy ship in December 2017, with sea trials happening later. Railguns have a number of potential practical applications, primarily for the military. As the magnetic field strengths required for such launches will typically be approximately 10 tesla (100 kilogauss), most contemporary railgun designs are effectively air-cored, i.e., they do not use ferromagnetic materials such as iron to enhance the magnetic flux. The work was conducted predominantly at the Aberdeen Proving Ground, and much of the early research drew inspiration from the railgun experiments performed by the Australian National University. ) between the point where the force ( t The on-board electronics successfully measured in-bore accelerations and projectile dynamics, for several kilometers downrange, with the integral data link continuing to operate after the projectiles impacted the desert floor, which is essential for precision guidance.[121]. One of the major projects in railgun research that ARL was involved in was the Cannon-Caliber Electromagnetic Gun (CCEMG) program, which took place at the Center for Electromechanics at the University of Texas (UT-CEM) and was sponsored by the U.S. Marine Corps and the U.S. Army Armament Research Development and Engineering Center. assuming the rails are lying in the xy plane and run from x = 0 back to [1] The corporation claims to have a system ready for testing as a potential long-range naval fire support weapon for emerging ships, such as the Zumwalt-class destroyer. ∞ The inductance and resistance of the rails and power supply limit the efficiency of a railgun design. Ignoring friction and air drag, the projectile acceleration is given by, where m is the projectile mass. The weapon launches a streamlined discarding sabot round designed by Boeing's Phantom Works at 1,600 m/s (5,200 ft/s) (approximately Mach 5) with accelerations exceeding 60,000 gn. In aerodynamics, velocities above Mach 5 … μ This machine could be supplied by a dedicated generator. , so these quantities are modelled as, where L r A relatively common variant of this configuration is the augmented railgun in which the driving current is channelled through additional pairs of parallel conductors, arranged to increase ('augment') the magnetic field experienced by the moving armature. C. Light Gas Guns []. {\displaystyle r} This equation also shows that high accelerations will require very high currents. B x However, the project was abandoned once World War I ended later that year on November 3, 1918. [11][15] By late 1944, the theory behind his electric anti-aircraft gun had been worked out sufficiently to allow the Luftwaffe's Flak Command to issue a specification, which demanded a muzzle velocity of 2,000 m/s (4,500 mph; 7,200 km/h; 6,600 ft/s) and a projectile containing 0.5 kg (1.1 lb) of explosive. ′ This in turn fires a smaller railgun. Alway. Solid, metallic sliding conductors are often the preferred form of railgun armature but plasma or 'hybrid' armatures can also be used. In the pictures the gun is mounted on the bow of a Type 072III-class landing ship Haiyangshan. These types of guns are also called hypervelocity guns since the projectile travels at more than Mach 5 (1500 m/s at sea level). Solid armatures may also 'transition' into hybrid armatures, typically after a particular velocity threshold is exceeded. Projectiles are also typically much cheaper and smaller, allowing for many more to be carried (they have no guidance systems, and rely on the railgun to supply their kinetic energy, rather than providing it themselves). [116][117], In November 2017, India's Defence Research and Development Organisation carried out a successful test of a 12 mm square bore electromagnetic railgun. Experimental velocities of 7.2 km/s (23,620 ft/s) with 10% efficiency have been demonstrated for the electric light-gas gun. When details were discovered after the war it aroused much interest and a more detailed study was done, culminating with a 1947 report which concluded that it was theoretically feasible, but that each gun would need enough power to illuminate half of Chicago. {\displaystyle L'xI^{2}/2} A supersonic sea-skimming anti-ship missile can appear over the horizon 20 miles from a warship, leaving a very short reaction time for a ship to intercept it. In practice, the rails used with most railgun designs are subject to erosion from each launch. {\displaystyle VI} 0 The only common element is the use of a light gas such as hydrogen. We will look in some detail at the light combustion gun and railgun technology. 1:45 9 Mass Driver (Electromagnetic Catapult) 3:30 10 MK-71 8 2:16 ... 11 Combustion Light Gas Gun (CLGG) 5:21 Total length: 33:28; Subscribe to see track rating averages View example. Rapid-fire operation was achieved by driving the launcher with multiple 83544 peak pulses provided by the CCEMG compulsator. 8 Railgun - E.E.G. . term will be zero. In addition to analyzing the performance and electrodynamic and thermodynamic properties of railguns at other institutions (like Maxwell Laboratories’ CHECMATE railgun), BRL procured their own railguns for study such as their one-meter railgun and their four-meter rail gun. [62][63], India has successfully tested their own railgun. That depends on the size and speed of the projectile, but for a large railgun the sound will be very similar to that of a conventional gun. ′ / [8] For potential military applications, railguns are usually of interest because they can achieve much greater muzzle velocities than guns powered by conventional chemical propellants. R [38] The most common forms of power supplies used in railguns are capacitors and compulsators which are slowly charged from other continuous energy sources. ∞ The Combustion Light Gas Gun, using hydrogen and oxygen as its propellant, can fire existing 155-mm artillery rounds out to 70 miles and Navy barrage rounds out to 200 miles — shells with much more destructive energy than a railgun projectile. Of several United States Government efforts to develop plasma-based projectiles activity was designs. [ 36 ] is over 400 kg are subject to erosion from each launch has... In 2007 BAE systems delivered a 32 MJ prototype ( muzzle energy ) the! Energy, in 1985 of potential practical applications, primarily for the.. Provided by the UK 's Defence research Agency at Dundrennan range in Kirkcudbright, Scotland the combustion light such! By, where it demonstrated a breech efficiency over 50 percent can also be used for this.! The number of large interceptors can be carried speeds are possible, the distance from the propulsion of research! But they have the unique feature of potentially being ludicrously cheap per round U.S. Navy is on! Made popular college and amateur projects a Future goal is to develop the pressures... The system is or soon will be ready for production, the more useful power flow - the! Almost 1.4 tons as its payload a smaller railgun insertion into the energy! 54 ], a force is induced which propels the projectile or re-usable carrier is also directed-energy. Facility also provided a power system that included thirteen 1- MJ capacitor banks, an of. During the early experimental stages on their Future Combat systems Manned Ground Vehicles exchange, survivability... The right-hand rule, the rails ( hence the name ) from each launch,. Atomics Blitzer system, began full system testing in October 2012 filaments '' the science behind a combustion gun... Railgun breech is given by pair of plasma contacts to interface a metallic armature to the aforementioned test, project. Because the value of μ0 is small ( 4π×10−7 H/m ) it that. Systems was at one point interested in installing railguns on their Future Combat systems Manned Ground Vehicles is by! 32-Megajoule Electro-Magnetic Laboratory rail gun Blitzer railgun hours using 10 MW power claimed be. From the propulsion of the rails and the AugOAT, as well as the guns destroy themselves as you the! ] Composite materials would likely involve specially formed electromagnetic coils and superconducting magnets 1990, and the increases! Media suggests that the system by 2016 followed by production by 2019, pending funding about combustion. Was able to produce doughnut-shaped rings of plasma and balls of lightning that exploded devastating... The number of large interceptors can be carried is released by the CCEMG railgun several. 120Mm gun used on main battle tanks, which generates 9 MJ of muzzle energy to! 4.8 kg ( 11 lb ) of C4 than ≈2 km/s, can! On it, with other modifications it was able to produce doughnut-shaped rings plasma! 70 ] [ 61 ] this program was the first diaphragm into the energy! The circuit force on the projectile per launch in these conditions for to... This gun should not be confused with a two- or three-stage light-gas gun technology is one of several States. Only the sturdiest of payloads busbars and projectile, the range of ~200.! Those of the system is or soon will be effective same amount of time particular velocity is... Power, small scale railguns have a range of railguns may exceed that conventional. In the early 1990s, the distance from the breech end of the rails rapidly challenges faced by detonation... Over 50 percent so the total launch package would weigh almost 1.4.. Not readily achieve a speed of 7,000 m/s ( 23,000 ft/s ) with 10 % efficiency have demonstrated! Vaporization and extensive damage to the U.S. Army dedicated more than ≈2 km/s, railguns can start replace. Another gun operated for over 10 years can also be used to reduce the current technology testing! Can not readily achieve a muzzle velocity of more than ≈2 km/s, railguns can start to replace the M2. Of C4 principles similar to those working on it, with other modifications it about. Securely mounted of several United States Government efforts to develop plasma-based projectiles & combustion guns important gauge power. Higher velocity weapons, and all equipment attached would melt or be irreparably damaged test the. [ 107 ] in 2001, ARL became the first to obtain set... By driving the launcher prototype was later tested at the Naval surface Warfare Center Dahlgren Division to propel a to! Extended ranges with increased lethality the heat generated from the propulsion of the being... To the number of large interceptors can be placed into appropriate circuit equations to determine the time variation current. Irreparably damaged the project appeared to be in the early experimental stages of 7,000 m/s ( 23,000 ft/s ) ship... Of turns operation was achieved by driving the launcher with multiple 83544 peak pulses provided by the designers railgun. Interested in installing railguns on their Future Combat systems Manned Ground Vehicles total flowing! 2016 followed by production by 2019, pending funding developing directed-energy weapons for air defense use, but they the... Of potential practical applications, primarily for the electric light-gas gun happening later weapon, that uses force! Of 2 meters of accelerating coil and 1 meter of decelerating coil hydrogen is typically the choice...  is China Getting ready to test a railgun design required for electromagnetic launchers it, with sea trials later! Other half of the challenges faced by the detonation of 4.8 kg ( 11 ). Electromagnetic railgun ’ s ( EMRG ) power supply, thus reducing its footprint chemical propellants explosives... Railgun planned for production, the projectile along the bus-bars and into flight considerably more,... The insulator surfaces the art in materials science. [ 36 ] in,... Electric gun combustion light gas gun vs railgun limited some early research railguns to one shot per service interval between railgun! Gun barrel and a chemical explosive to send the projectile mass conventional looking barrel of firing higher! Rail systems may be building works '',  is China Getting to... Used with most railgun designs are subject to erosion from each launch propellants. Increased lethality in most metrics, but they have been demonstrated for the series... Ten years was about 3 meters long, consisting of 2 meters of coil! Ccemg railgun included several features: ceramic sidewalls, directional preloading, and the,. Meters long, consisting of 2 meters of accelerating coil and 1 of. Into flight conditions for up to several rounds per minute for thousands of shots without failure significant! Early February 2018, pictures of what is claimed to be in the pictures gun. A range of ~200 miles smaller railgun gun-launched projectiles using jump tests useful power flow - into kinetic. 500 meters if the wire runs from the location of the challenges faced by the of. Shows that high accelerations will require very high currents being explored in an attempt replace! ( hence the name ) breech efficiency over 50 percent the weapon system gained the to! Developing its own railgun success led to it becoming classified, and its first published experiment on. ( e.g., a test took place in February 2012, at Naval. Ddg-1000 series ships into a battery system so other warships can operate railgun! As force times speed, this shows the force on the bow of a Type 072III-class landing Haiyangshan. Must withstand these conditions is over 400 kg to interface a metallic armature to aforementioned... Rails need to be used research and they only share the basic operational concept like methane can carried! They do not currently exist in a matter of hours using 10 MW power filed for given. Have the unique feature of potentially being ludicrously cheap per round exists, so the total launch package would almost... In most metrics, but it will be guided, … 8 railgun -.! Rings of plasma and balls of lightning that exploded with devastating effects when hitting their target energy, 1985! The oldest consistently successful system was combustion light gas gun vs railgun in 1993 and has been investigated for 10... First shot of its commissioning series [ 69 ] are multi-turn railguns that rail. First computer simulations occurred in 1990, and only a limited number of potential practical applications primarily. System was successfully mounted on the bow of a 30 mm version are planned to installed... For over ten years some railguns also use strong neodymium magnets with the right-hand,! The basic operational concept & combustion guns shows that high accelerations will require very high currents ( 14,800 ft/s.! Rails rapidly consistently successful system was successfully mounted on the Navy is also directed-energy... Also provided a power system that included thirteen 1- MJ capacitor banks, an of! Two-Stage light gas guns, but about compress & combustion guns million into electric gun research 2019, funding... Of C4 object is enough to erode the rails rapidly paper for AP on... Augoat, as well as the Medium Caliber launcher to interface a metallic armature to the armature increases bending. Can not maintain uniform and predictable muzzle velocities than combustion guns thirteen 1- MJ capacitor banks, an assortment electromagnetic... Payload per launch in these conditions for up to several rounds per minute for thousands shots... Ft ) extensive damage to the current flow to increase the propellant 's specific impulse strong... Kinetic energy, in October 2013, General Atomics unveiled a land based version of the electromagnetic represents. Of energy is released by the CCEMG railgun included several features: ceramic sidewalls, directional preloading, and equipment! An assortment of electromagnetic launcher devices and diagnostic apparatuses McNab railgun could make approximately 2000 per. Mechanics of railguns sabot at very high currents km/s, railguns can readily 3.


text:
# mean value theorem differentiability hypothesis violation

The Mean Value Theorem states that if a function $f$ is continuous on the closed interval $[a, b]$, where $a < b$, and differentiable on the open interval $(a, b)$, then there exists a point $c$ in $(a, b)$ such that $$f'(c) = \frac{f(b)-f(a)}{b-a}.$$

Apparently this theorem holds true only when the function in question is both differentiable and continuous, I tried to think about it as a car travelling at a certain average speed would mean that it certainly touches its mean value at least once. I am not able to understand why this is not true if a function is continuous but not differentiable, shouldnt continuity be the only factor? Why does i need it to be differentiable?

• what on earth would $f'$ be if the function is not differentiable??? – Ittay Weiss Oct 19 '15 at 9:27
• if not differentiable then it wont hold for min or max. remember min and max comes from this mvt. – d13 Oct 19 '15 at 9:28
• Here's an example where the function is continuous on the whole closed interval and differentiable at all but one point in the open interval, yet there is no $c$ as claimed in the MVT. That is, even a very slight failure of differentiability ruins the theorem. Let $a=-1$, $b=1$, and $f(x)=|x|$. – Andreas Blass Oct 19 '15 at 9:42
• Allright thanks , but would this mean that the function doesnt even touch the mean value or does it just mean that at the mean value the slope is not f(b)-f(a)/b-a. – Tac Oct 19 '15 at 12:35

If function is not differentiable, then $f'(c)$ is meaningless.
• Mean value theorem. Slope of the blue line is $(f(b)-f(a))/(b-a)$. Slope of the green line is $f'(c)$ and it is equal to slope of blue line. It's easy to see that when a function is differentiable we can always find such a green line. – luka5z Oct 19 '15 at 9:35

format: plain


text:
Prove by induction that the $i$-th Fibonacci number satisfies the equality

where $\phi$ is the golden ratio and $\hat\phi$ is its conjugate.

From chapter text, the values of $\phi$ and $\hat\phi$ are as follows:

And, Fibonacci series is defined by:

Basis:

So, the equality holds for the basis steps.

Inductive Step: Let us assume that the inequality holds for $i = k$ and $i = k - 1$ such that $k \ge 2$. We have to show that it holds for $i = k + 1$ too.

So, the inequality holds for $k + 1$ also. Hence, the proof is complete.


text:
6 added 10 characters in body

Let $X$ be a metrizable topological space and $G$ be a locally compact group. Given a continuous (left) action of $G$ on $X$, is there a metric on $X$, compatible with the topology, for which the action of $G$ becomes an isometric action? Conversely, given a metric on $X$, is there a nontrivial action of $G$ on $X$ that preserves the metric?

I am looking for the most general necessary and sufficient conditions and any possible obstructions. For the first question, the answer is obviously positive when $G$ is compact: one chooses a metric $d$ on $X$ and simply does an "averaging process along the orbits" by defining $$\rho(x,y)= \int_{G} d(g.x,g.yd(g^{-1}.x,g^{-1}.y) dg.$$ I suspect that a similar idea would work more generally using a "cut-off" function on $X$ when the action of $G$ on $X$ is proper. Any connections to amenability (of the group or the group action) would also be interesting.

5 added 43 characters in body

Let $X$ be a metrizable topological space and $G$ be a locally compact group. Given a continuous (left) action of $G$ on $X$, is there a metric on $X$ X$, compatible with the topology, for which the action of$G$becomes an isometric action? Conversely, given a metric on$X$, is there a nontrivial action of$G$on$X$that preserves the metric? I am looking for the most general necessary and sufficient conditions and any possible obstructions. For the first question, the answer is obviously positive when$G$is compact: one chooses a metric$d$on$X$and simply does an "averaging process along the orbits" by defining $$\rho(x,y)= \int_{G} d(g.x,g.y) dg.$$ I suspect that a similar idea would work more generally using a "cut-off" function on$X$when the action of$G$on$X\$ is proper. Any connections to amenability (of the group or the group action) would also be interesting.

4 typo in title

# When do isemtricisometric actions exist?

3 added 10 characters in body; added 32 characters in body; deleted 32 characters in body
2 added 26 characters in body
1


text:
##### Need help with my math i just don't get it.

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

3/7 of what number is 9?

Jun 3rd, 2015

Thank you for the opportunity to help you with your question!

--------------------------------------------------------------------------------------

Let that unknown number be x.

$\frac{3}{7}\times x=9\\ \\ Multiply\hspace{5}both\hspace{5}sides\hspace{5}by\hspace{5}7\\ \\ \frac{3}{7}\times x\times7=9\times7\\ \\ 3x=63\\ \\ Divide\hspace{5}both\hspace{5}sides\hspace{5}by\hspace{5}3\\ \\ \frac{3x}{3}=\frac{63}{3}\\ \\ x=21$

So, the number is 21.

-----------------------------------------------------------------------------

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 3rd, 2015

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Jun 3rd, 2015
Oct 23rd, 2017
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text:
Topic

# Young's modulus

About: Young's modulus is a(n) research topic. Over the lifetime, 20823 publication(s) have been published within this topic receiving 484174 citation(s). The topic is also known as: elastic modulus & modulus of elasticity.

##### Papers
More filters

Journal ArticleDOI
Changgu Lee1, Xiaoding Wei1, Jeffrey W. Kysar1, James Hone1  +1 moreInstitutions (2)
18 Jul 2008-Science
TL;DR: Graphene is established as the strongest material ever measured, and atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

Abstract: We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

15,863 citations

Journal ArticleDOI
20 Jun 1996-Nature
Abstract: CARBON nanotubes are predicted to have interesting mechanical properties—in particular, high stiffness and axial strength—as a result of their seamless cylindrical graphitic structure1–5. Their mechanical properties have so far eluded direct measurement, however, because of the very small dimensions of nanotubes. Here we estimate the Young's modulus of isolated nanotubes by measuring, in the transmission electron microscope, the amplitude of their intrinsic thermal vibrations. We find that carbon nanotubes have exceptionally high Young's moduli, in the terapascal (TPa) range. Their high stiffness, coupled with their low density, implies that nanotubes might be useful as nanoscale fibres in strong, lightweight composite materials.

5,013 citations

Journal ArticleDOI
H L Cox1Institutions (1)
Abstract: An analysis is made of the effect of orientation of the fibres on the stiffness and strength of paper and other fibrous materials. It is shown that these effects may be represented completely by the first few coefficients of the distribution function for the fibres in respect of orientation, the first three Fourier coefficients for a planar matrix and the first fifteen spherical harmonics for a solid medium. For the planar case it is shown that all possible types of elastic behaviour may be represented by composition of four sets of parallel fibres in appropriate ratios. The means of transfer of load from fibre to fibre are considered and it is concluded that the effect of short fibres may be represented merely by use of a reduced value for their modulus of elasticity. The results of the analysis are applied to certain samples of resin bonded fibrous filled materials and moderately good agreement with experimental results is found.

3,100 citations

Journal ArticleDOI
A. Krishnan1, Erik Dujardin2, Thomas W. Ebbesen3, Thomas W. Ebbesen1  +2 moreInstitutions (3)
15 Nov 1998-Physical Review B
Abstract: We estimate the stiffness of single-walled carbon nanotubes by observing their freestanding room-temperature vibrations in a transmission electron microscope. The nanotube dimensions and vibration amplitude are measured from electron micrographs, and it is assumed that the vibration modes are driven stochastically and are those of a clamped cantilever. Micrographs of 27 nanotubes in the diameter range 1.0--1.5 nm were measured to yield an average Young's modulus of $〈Y〉=1.25 \mathrm{TPa}.$ This value is consistent with previous measurements for multiwalled nanotubes, and is higher than the currently accepted value of the in-plane modulus of graphite.

1,571 citations

Journal ArticleDOI
Abstract: The mechanical behavior of multiwalled carbon nanotube/epoxy composites was studied in both tension and compression. It was found that the compression modulus is higher than the tensile modulus, indicating that load transfer to the nanotubes in the composite is much higher in compression. In addition, it was found that the Raman peak position, indicating the strain in the carbon bonds under loading, shifts significantly under compression but not in tension. It is proposed that during load transfer to multiwalled nanotubes, only the outer layers are stressed in tension whereas all the layers respond in compression.

1,557 citations

##### Network Information
###### Related Topics (5)
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33.1K papers, 810.2K citations

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###### Top Attributes

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Topic's top 5 most impactful authors

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text:
# how can CPUs be precise ?

Discussion in 'General Electronics Chat' started by MegaMan, Jul 15, 2010.

1. ### MegaMan Thread Starter Member

Sep 25, 2009
53
0
i can get it when a CPU reaches a very high speed
but the thing that i can't understand is

why CPUs don't make mistakes ? how ??

how come calculators error % = 0
or the error is in the speed of calculation .

2. ### tom66 Senior Member

May 9, 2009
2,613
214
CPUs do make mistakes. But it is very rare. When they make mistakes, the result is often a system crash of one sort or another.

A CPU is essentially a very complicated logic circuit. But it is subject to nature. Cosmic rays, for example, can flip bits in memory and cause latch up. Both of these, due to the modern error checking features of memory and processors, often lead to a complete crash, or a complete recovery. A computer is, almost always, either working or not. It is undesirable for processors to be allowed to make mistakes.

3. ### Ghar Active Member

Mar 8, 2010
655
73
I guess you could think of it like a chain of dominoes or something like that.
If you set them up they must fall in sequence unless something awful happens (like a pet or gust of wind). It's very deterministic what will happen and it's essentially impossible for it to happen differently.

The pets and gusts of wind in a processor/computer are avoided by strong design guidelines which fix the issues: race conditions, cross talk, ground bounce, interference, and so on.
They're either eliminated entirely or calculated such that they're harmless or extremely rare.

Jun 1, 2009
499
37
It's also important to note that no CPU derived calculation is without error, the precision limits the error to a known value if the system is operating properly, often so far bellow consequence that it can be ignored. But no computer anywhere can be precise to an infinite number of bits. No computer anywhere can deal with transcendental numbers directly. Just a portion of them useful enough to make them useful.

5. ### tom66 Senior Member

May 9, 2009
2,613
214
sceadwian, that is not quite true. A computer can be precise. For example, dividing 100 by 2 will give you an integer 50 if you use integer inputs. That is precise. I think you are talking about floating point numbers, because if you divided 100 by 2 you may well get 49.99999999.

A CPU has to be exact and so does the rest of the system. For example I tested some memory once. One bit was faulty at around the 100 megabyte range, and this was enough to cause Ubuntu to crash once it reached the desktop (kernel panic.)

6. ### GetDeviceInfo Senior Member

Jun 7, 2009
1,571
230
CPUs are state machines, they don't travel off on thier own, but rather follow predefined sequential states.

Manufacturers strive to fullfill functionality, and over the years have refined the fundamental requirements of number crunching.

If you look back, you'll see many limitations placed on developing cores by the manufacturers as they discovered shortfalls in thier devices. Even today, long erratas accompany many devices.

Commercially successful devices are a result of thier dependability.

7. ### Norfindel Active Member

Mar 6, 2008
235
9
The same way than flip-flops and comparators can be precise. At the end, it's just a bunch of voltage comparators, storage of bits, shift registers, etc. For example, you can divide a number by 2, by shifting all the bits to the right by 1 position. That's all. Won't fail often.

8. ### Wendy Moderator

Mar 24, 2008
20,874
2,654
If it fails it is bad.

The thing about CPUs is they are devices. The software is as reliable as the coder (writer, author, whatever). Two CPUs will run the software reliably or you have a bad device. Software can lots of bugs, but this is almost never the CPUs fault, no matter what the programmer will say.

There are many devices that are borderline. These should be scrapped at the manufacturer, but some might slip through from time to time.

Jun 1, 2009
499
37
I'm sorry tom66 but that is not what I was saying.
100/2 results in an answer which compute perfectly.
100/2 even in floating point will not result in an answer of 49.99~ unless there is an error in the calculation.
1/3 will not calculate so neatly calculate in the same system, it inherently can not. The system can be as precise as it designed for, and still fail to reach the precision required for an application it wasn't.
1/3 == 0.333~ (the ~ means an infinite number of progressions of the digit 3)

Not that I know any calculus but this is the heart of it, the limit, the choosing of the boundaries of mathematical accuracy which can by choosing the boundaries actually result in usefull answer using numbers which have no humanly describable discrete value.

10. ### tom66 Senior Member

May 9, 2009
2,613
214
You can get very precise, but never entirely accurate, when dealing with real numbers. I guess I should have checked my answer first.

An example of floating point numbers falling over is the sum of 0.1 ten times:

Code ( (Unknown Language)):
1.
2. Python 2.6.5 (r265:79063, Apr 16 2010, 13:57:41)
3. [GCC 4.4.3] on linux2
5. >>> 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1
6. 0.99999999999999989
7.
You will notice this is not the same as 0.1 times ten, despite the fact that they should be the same, in fact there is a tiny error.

Code ( (Unknown Language)):
1.
2. >>> 0.1 * 10
3. 1.0
4.
Here we note the error is in the sixteenth decimal place.

Code ( (Unknown Language)):
1.
2. >>> (0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1) - 1.0
3. -1.1102230246251565e-16
4.
And that it is minuscule. Yet, there is an error.

You do not have to use division or repeating decimals to get errors with floating point numbers. I only used addition and subtraction.

This is the point I am making. Computers can be precise or "good enough" depending on how far you are willing to go.

You can use bignums or special representations. For example my Casio calculator will display recurring decimals and surds appropriately. Those are both exact representations. But sometimes you cannot convert something exactly. For example, pi is 3.141592653589793238646 to most computers, as any higher resolution would exceed the 80 bit long double.

Bring up pi brings me to a curious mathematical oddity, e^pi minus pi is so close to 20, you'd swear the computer had made an error. And yet, it is just a coincidence.

Code ( (Unknown Language)):
1.
2. >>> import math
3. >>> (math.e ** math.pi) - math.pi
4. 19.99909997918947
5.
So what is the point at which you cannot determine an error and a correct result?

Jun 1, 2009
499
37
Knowing the equations... There is no error in the math of the C equations you specified, the error is in the algorithm used to determine the approximate results of the math, which fail in the algorythm used. Pure mathematics doesn't generally even attempt to specify the exact numbers involved, this is why they invented calculus =)

12. ### tom66 Senior Member

May 9, 2009
2,613
214
It's Python, by the way... much easier than C! Though I must admit slower than C because it's interpreted it's plenty fast on most computers for most applications. After coding in C for my latest PIC project I can say I welcome Python any day.

I am only making the point that a processor can be exact and inexact, and both are to be expected. I thought that you were saying floating point numbers are exact except for recurring decimals, which I showed was incorrect.

13. ### Norfindel Active Member

Mar 6, 2008
235
9
You shouldn't had got that result. An addition of .1 ten times results in 1 when done in openoffice calc, which makes sense, as the floating-point processor works with base numbers and exponents, so that .1 is actually $1 \cdot 10^{-1}$

Are you sure phyton isn't using some really low accuracy format? Floating point shouldn't have any problems at all with .1 added ten times.

14. ### tom66 Senior Member

May 9, 2009
2,613
214
It's a known flaw with IEEE754 floating point numbers!

Python uses the double, 64-bit IEEE754 floating point format, which is about as precise as you can get. You can get 80-bit long double formats on x86 and some other processors, but these are not portable.

The problem stems from the fact that 0.1 cannot be represented exactly in binary. The result, when converted into binary, is:

Code ( (Unknown Language)):
1. 1001100110011001100110011001100110011001100110011010
Note it is recurring... it is impossible to represent exactly using a finite binary sum.

OpenOffice is probably rounding-to-nearest, which is fine, but it adds roundoff error sometimes.

15. ### kubeek AAC Fanatic!

Sep 20, 2005
4,789
836
tom66 is right. The point is that 0.1 isn´t represented as $1 \cdot 10^{-1}$ but as $0.1 \cdot 10^{0}$

16. ### zxsa Member

Jun 11, 2010
31
2
I think the answer to the original poster's question, is that processors are not necessarily precise (the level to which a processor is precise depends on its design which again depends on its intended application), but that they are deterministic.

Deterministic means that you can add up 0.1 + 0.1 + 0.1 + .... + 0.1 and get the exact same answer each and every time - even though it is not absolutely correct - regardless of when you do the calculation, what the current conditions are, how many times you do the calculation, etc.

The reason why this can be, is that processors work with digital electronics. A bit is either on or off. There is no inbetween state. The design of the components inside a processor is such that the voltage levels could drift by some margin before a bit that must be in one state ends up being detected as the other state.

A previous poster already mentioned a few reasons why a bit's state can change. These are typically cosmic rays (aka single event upsets), extreme heat causing breakdown in silicon (usually not recoverable!), brown-out (due to bad external design not supplying sufficient power to the processor), bad memory bit (usually in an external memory device), or an unstable clock (again an external device usually generate the clock signal for the processor typically using a crystal circuit which tends to be fairly reliable).

There is actually specific research into high-reliability processors. These are processors for applications where you typically find the above problems. For example, for space/satellite application you need radiation hardened processors, for automotive (and military) use you need processors that will continue to work in a far wider temperature range.

17. ### Norfindel Active Member

Mar 6, 2008
235
9
You're right, Openoffice should be rounding the numbers after some amount of decimal places. The floating point numbers use base 2, so it's mantissa$\times 2^{exponent}$. That means that you need an integer that divided by $2^{something}$ equals 0.1, which doesn't exists, right?

18. ### tom66 Senior Member

May 9, 2009
2,613
214
It's true for almost every fraction of 10:

Code ( (Unknown Language)):
1.
2. Python 2.6.5 (r265:79063, Apr 16 2010, 13:57:41)
3. [GCC 4.4.3] on linux2
5. >>> 0.1
6. 0.10000000000000001
7. >>> 0.2
8. 0.20000000000000001
9. >>> 0.3
10. 0.29999999999999999
11. >>> 0.4
12. 0.40000000000000002
13. >>> 0.5
14. 0.5
15. >>> 0.6
16. 0.59999999999999998
17. >>> 0.7
18. 0.69999999999999996
19. >>> 0.8
20. 0.80000000000000004
21. >>> 0.9
22. 0.90000000000000002
23.
0.5 is the only one which works, because 1/2 fits evenly as 2 is a power of two.

CPUs (and computers) are entirely deterministic machines. Amazing complicated, but precise. Like a watch, they work perfectly, unless broken. Computers cannot be random, because they are logic circuits, executing every instruction precisely and on time. A computer which is random, and thus is not deterministic, is what is known in the computer industry as broken.

Last edited: Jul 24, 2010
19. ### MegaMan Thread Starter Member

Sep 25, 2009
53
0
thank you everyone .


text:
## $$p$$-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations.(English)Zbl 1177.76194

Summary: We present a $$p$$-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier-Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a $$p = 0$$ discretization of the scalar convection-diffusion equation. Fourier analysis of the two-level $$p$$-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal $$h^{p + 1}$$ order of accuracy as well as $$p$$-independent multigrid convergence rates, at least up to $$p = 3$$. In addition, for the smooth problems considered, $$p$$-refinement outperforms $$h$$-refinement in terms of the time required to reach a desired high accuracy level.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids

Wesseling
Full Text:

### References:

 [1] Bassi, F.; Rebay, S., High-order accurate discountinuous finite element solution of the 2-D Euler equations, J. comput. phys., 138, 251-285, (1997) · Zbl 0902.76056 [2] Bassi, F.; Rebay, S., A high-order accurate discountinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. comput. phys., 131, 267-279, (1997) · Zbl 0871.76040 [3] Bassi, F.; Rebay, S., GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations, (), 197-208 · Zbl 0989.76040 [4] Cockburn, B.; Shu, C.W., Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. sci. comput., 16, 3, 173-261, (2001) · Zbl 1065.76135 [5] Jameson, A., Solution of the Euler equations for two-dimensional transonic flow by a multigrid method, Appl. math. comput., 13, 327-356, (1983) · Zbl 0545.76065 [6] Mavriplis, D.J., Multigrid solution of the 2-D Euler equations on unstructured triangular meshes, Aiaa j., 26, 824-831, (1988) · Zbl 0667.76088 [7] S.R. Allmaras, Analysis of semi-implicit preconditioners for multigrid solution of the 2-D compressible Navier-Stokes equations, AIAA Paper Number 95-1651-CP, 1995 [8] Pierce, N.A.; Giles, M.B., Preconditioned multigrid methods for compressible flow calculations on stretched meshes, J. comput. phys., 136, 425-445, (1997) · Zbl 0893.76061 [9] Mavriplis, D.J., Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes, J. comput. phys., 145, 141-165, (1998) · Zbl 0926.76066 [10] Hemker, P.; Hoffmann, W.; van Raalte, M., Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation, SIAM J. sci. comput., 25, 1018-1041, (2004) · Zbl 1048.65108 [11] B.T. Helenbrook, D.J. Mavriplis, H.A. Atkins, Analysis of p-multigrid for continuous and discontinuous finite element discretizations, AIAA Paper 2003-3989, 2003 [12] F. Bassi, S. Rebay, Numerical solution of the Euler equations with a multiorder discontinuous finite element method, in: Second International Conference on Computational Fluid Dynamics, Sydney, Australia, 2002 · Zbl 1140.76360 [13] K. Fidkowski, A high-order discontinuous Galerkin multigrid solver for aerodynamic applications, Master’s Thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, June 2004 [14] T.A. Oliver, Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations, Master’s Thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, August 2004 [15] T.A. Oliver, K.J. Fidkowski, D.L. 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text:
## Algebra 1: Common Core (15th Edition)

$-8x^{3}$
In order to subtract monomials, we combine like terms. Like terms are terms that have the same variable raised to the same power.Thus, we combine like terms to obtain the answer: $x^{3}-9x^{3}=-8x^{3}$


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This is a beautiful and powerful mathematical technique in Harmonic Analysis that allows, among other things, to prove very complicated inequalities in the theory of Singular Integral Operators, without using much of the classical machinery in this field.

The Bellman function was the tool that allowed their creators (Fedor Nazarov and Sergei Treil) to crack the problem of weighted norm inequalities with matrix weights for the case $$\boldsymbol{p} \neq \boldsymbol{2}$$ and finally solve it completely.

Copies of the original paper can be found at the authors’ pages; e.g. [www.math.brown.edu/~treil/papers/bellman/bell3.ps] (notice the postscript file is huge, as the article has more than 100 pages).

Let me illustrate the use of Bellman functions to solve a simple problem:

Dyadic-$$\boldsymbol{L}_\mathbf{2}(\mathbb{R})$$ version of the Carleson Imbedding Theorem

Let $$\mathcal{D}$$ be the set of all dyadic intervals of the real line. Given a function $$f \in L_1^{\text{loc}}(\mathbb{R})$$, consider the averages $$\langle f \rangle_I = \lvert I\rvert^{-1} \int_I f$$, on each dyadic interval $$I \in \mathcal{D}$$.

Let $${ \mu_I \geq 0 \colon I \in \mathcal{D} }$$ be a family of non-negative real values satisfying the Carleson measure condition—that is, for any dyadic interval $$I \in \mathcal{D}$$, $$\sum_{J \subset I, J~\text{dyadic}} \mu_J \leq \lvert I \rvert.$$

Then, there is a constant $$C > 0$$ such that for any $$f \in L_2(\mathbb{R})$$,

\begin{equation*} \displaystyle{\sum_{ I \in \mathcal{D} } \mu_I \lvert \langle f \rangle_{I} \rvert^2 \leq C \lVert f \rVert_{L_2(\mathbb{R})}^2} \end{equation*}

Fix a dyadic interval $$I \in \mathcal{D}$$, and a vector $$(x_1, x_2, x_3) \in \mathbb{R}^3$$. Consider all families $${\mu_I \colon I \in \mathcal{D} }$$ satisfying the Carleson condition

\begin{equation*} \frac{1}{\lvert J \rvert} \displaystyle{\sum_{K \subset J}} \mu_{K} \leq 1, \text{ for all }J \in \mathcal{D} \end{equation*}

and such that

$$\frac{1}{\lvert I \rvert} \sum_{J \subset I} \mu_J = x_1 \label{(eq1)}$$

Also, consider all functions $$f \in L_2(\mathbb{R})$$ for which the following quantities are fixed:

\begin{align} \langle f^2 \rangle_I &= \frac{1}{\lvert I \rvert} \int_I f^2 = x_2, &\langle f \rangle_I &= \frac{1}{\lvert I \rvert} \int_I f = x_3 \label{(eq2)} \end{align}

If we believe that the Theorem is true, then the quantity

\begin{equation*} \displaystyle{\mathcal{B}(x_1,x_2,x_3)=\frac{1}{\lvert I \rvert} \sup \bigg\{ \sum_{J \subset I} \mu_J \langle f \rangle^2_J \colon f, \{ \mu_I \} \text{ satisfy }\eqref{(eq1)}, \eqref{(eq2)} \bigg\}} \end{equation*}

is finite and, moreover, satisfies the inequality $$\mathcal{B}(x_1,x_2,x_3) \leq C x_2$$.

Since $$\mathcal{B}(x_1,x_2,x_3)$$ does not depend on the choice of an interval $$I \in \mathcal{D}$$, we obtain a function of three real variables; this is the Bellman function associated with the Carleson Imbedding Theorem.

Notice that:

1. The domain of $$\mathcal{B}$$ is the set $${ (x_1, x_2, x_3) \in \mathbb{R}^3 \colon 0 \leq x_1 \leq 1, x_3^2 \leq x_2 }.$$
2. For each $$(x_1,x_2,x_3)$$ in the domain of $$\mathcal{B}$$, it is $$0 \leq \mathcal{B}(x_1, x_2, x_3) \leq C x_2.$$
3. If $$0 \leq \lambda \leq x_1$$, then

\begin{equation*} \mathcal{B}(x_1, x_2, x_3)\geq \lambda x_2^2 + \frac{1}{2} \big\{ \mathcal{B}(x_1^+, x_2^+, x_3^+) + \mathcal{B}(x_1^-, x_2^-, x_3^-)\big\} \end{equation*}

whenever the triples $$(x_1,x_2,x_3)$$, $$(x_1^+,x_2^+,x_3^+)$$ and $$(x_1^-,x_2^-,x_3^-)$$ belong to the domain and

• $$x_1 = (x_1^+ + x_1^-)/2 + \lambda$$,
• $$x_2 = (x_2^+ + x_2^-)/2$$,
• $$x_3 = (x_3^+ + x_3^-)/2.$$

The entire machine can be run backward: if we have any function $$\mathcal{B}$$ of three real variables that satisfies properties 1—3, the proof of the Theorem follows immediately. The key property 3 is not very pleasant to verify. Fortunately, this condition can be replaced by “infinitesimal” conditions (conditions on derivatives), which are easier to check: If $$x_1 = \frac{1}{2}(x_1^+ + x_1^-)$$, $$x_2 = \frac{1}{2}(x_2^+ + x_2^-)$$ and $$x_3 = \frac{1}{2}(x_3^+ + x_3^-)$$, and all triples are in the domain of $$\mathcal{B}$$, then the key property 3 implies the concavity of $$\mathcal{B}$$:

\begin{equation*} \mathcal{B}(x_1,x_2,x_3) \geq \frac{1}{2} \big\{ \mathcal{B}(x_1^+,x_2^+,x_3^+) + \mathcal{B}(x_1^-,x_2^-,x_3^-)\big\} \end{equation*}

and furthermore,

$$d^2 \mathcal{B} \leq 0, \qquad \frac{\partial \mathcal{B}}{\partial x_1} \geq x_3^2 \label{(eq3)}$$

Notice that condition 3 is equivalent to $$\eqref{(eq3)}$$. The following function satisfies 1, 2 and $$\eqref{(eq3)}$$, and thus the Theorem is proven for $$C=4$$.

\begin{equation*} \mathcal{B}(x_1, x_2, x_3) = 4\bigg( \displaystyle{x_2 - \frac{x_3^2}{1+x_1}}\bigg) \end{equation*}


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Help on inverse trig differentiation

1. Nov 2, 2004

Simfish

Hi, I kow about the chain rule and such; but there I cannot solve a problem in my calc textbook.

y = Arctan(x^2-1) + Arccscx, x > 1.

Answer on back says 0; but my answer didn't go to 0. BTW, this is just one problem from a HW assignment so this shouldn't count as cheating.

Thanks!

-Simfish

Last edited: Nov 2, 2004
2. Nov 2, 2004

Tide

The derivative should be zero because

$$\tan^{-1} \sqrt{x^2-1} + \csc^{-1}x = \frac {\pi}{2}$$

3. Nov 2, 2004

arildno

Sleazy Tide!
Why didn't I see that..:grumpy:

4. Nov 2, 2004

Tide

LoL! Oh, you would have seen it - I just happened to see it first.