Critical mass

As part of a re-creation of a 1945 criticality accident, a simulated sphere of plutonium, is surrounded by blocks of neutron reflective tungsten carbide. The original experiment was designed to measure the radiation produced when an extra block was added. Instead, the mass went supercritical.
A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (e.g. the nuclear fission cross-section), its density, its shape and its enrichment.

Explanation of criticality

The term critical refers to an equilibrium fission reaction (steady-state or continuous chain reaction), this is where there is no increase in power, temperature, or neutron population.

A numerical measure of a critical mass is dependent on the neutron multiplication factor, k, where:

k = f − l

where f is the average number of neutrons released per fission event and l is the average number of neutrons lost by either leaving the system or being captured in a non-fission event. When k = 1 the mass is critical.

A subcritical mass is a mass of fissile material without the ability to sustain a fission reaction. A population of neutrons introduced to a subcritical assembly will decrease in number over time. In this case, k < 1.

A supercritical mass is one where there is an increasing rate of fission until natural feedback mechanisms cause the reactor to settle into equilibrium (i. e. be critical) at an elevated temperature/power level or destroy itself (disassembly is an equilibrium state). In this case, k > 1.

Changing the point of criticality

The point, and therefore the mass, where criticality occurs may be changed by modifying certain attributes, such as fuel, temperature, density, and the installation of a neutron-reflective substance.
• Varying the amount of fuel
It is possible for an assembly to be critical at near zero power. If the perfect quantity of fuel were added to a slightly subcritical mass to create an "exactly critical mass", fission would be self-sustaining for one neutron generation (fuel consumption makes the assembly subcritical).

If the perfect quantity of fuel were added to a slightly subcritical mass, to create a barely supercritical mass, the temperature of the assembly would increase to an initial maximum (for example: 1 K above the ambient temperature) and then decrease back to room temperature after a period of time, because fuel consumed during fission brings the assembly back to subcriticality once again.
• Varying the temperature and density of the mass
At an exactly critical state, a mass at room temperature will become subcritical if warmed and supercritical if cooled. Fission reduces as the fuel temperature increases. This is called the negative coefficient of reactivity. Thermal expansion of a critical mass also contributes to a negative coefficient of reactivity. This is because a decrease in fuel density, associated with increase in temperature, also makes the fission reaction less probable.
• Use of a neutron reflector
Surrounding a spherical critical mass with a neutron reflector further reduces the mass needed for criticality. A good neutron reflector is beryllium metal. This increases the rate of neutron collisions, resulting in criticality.

Critical mass of a bare sphere

Top: A sphere of fissile material is too small to allow the chain reaction to become self-sustaining as neutrons generated by fissions can too easily escape. Middle: By increasing the mass of the sphere to a critical mass, the reaction can become self-sustaining. Bottom: Surrounding the original sphere with a neutron reflector increases the efficiency of the reactions and also allowing the reaction to become self-sustaining.

The shape with minimal critical mass and the smallest physical dimensions, is a sphere.

Bare-sphere critical masses at normal density of some other isotopes whose half-lives exceed 100 years are listed in the following table.

protactinium-231750±180 kg45±3 cm
uranium-23315 kg11 cm[1]
uranium-23552 kg17 cm[2]
neptunium-2367 kg8.7 cm[3]
neptunium-23760 kg18 cm[4],[5]
plutonium-2389.04–10.07 kg9.5-9.9 cm[6]
plutonium-23910 kg9.9 cm[7],[8]
plutonium-24040 kg15 cm[9]
plutonium-24112 kg10.5 cm[10]
plutonium-24275–100 kg19-21 cm[11]
americium-24155–77 kg20-23 cmDias et. al.
americium-242m9–14 kg11-13 cmibid.
americium-243180–280 kg30-35 cmibid.
curium-2437.34–10 kg10-11 cm[12]
curium-244(13.5)–30 kg(12.4)–16 cm[13]
curium-2459.41–12.3 kg11-12 cm[14]
curium-24639–70.1 kg18-21 cm[15]
curium-2476.94–7.06 kg9.9 cm[16]
californium-2496 kg9 cm[17]
californium-2515 kg8.5 cm[18]

The critical mass for lower-grade uranium depends strongly on the grade: with 20 % U-235 it is over 400 kg; with 15 % U-235, it is well over 600 kg.

The critical mass is inversely proportional to the square of the density: if the density is 1% more and the mass 2% less, then the volume is 3% less and the diameter 1% less. The probability for a neutron per cm travelled to hit a nucleus is proportional to the density, so 1% more, which compensates that the distance travelled before leaving the system is 1% less. This is something that must be taken into consideration when attempting more precise estimates of critical masses of plutonium isotopes than the rough values given above, because plutonium metal has a large number of different crystal phases which can have widely varying densities.

Note that not all neutrons contribute to the chain reaction. Some escape. Others undergo radiative capture.

Let denote the probability that a given neutron induces fission in a nucleus. Let us consider only prompt neutrons, and let denote the number of prompt neutrons generated in a nuclear fission. For example, for uranium-235. Then, criticality occurs when . The dependence of this upon geometry, mass, and density appears through the factor .

Given a total interaction cross section (typically measured in barns), the mean free path of a prompt neutron is where is the nuclear number density. Most interactions are scattering events, so that a given neutron obeys a random walk until it either escapes from the medium or causes a fission reaction. So long as other loss mechanisms are not significant, then, the radius of a spherical critical mass is rather roughly given by the product of the mean free path and the square root of one plus the number of scattering events per fission event (call this ), since the net distance travelled in a random walk is proportional to the square root of the number of steps:

Note again, however, that this is only a rough estimate.

In terms of the total mass , the nuclear mass , the density , and a fudge factor which takes into account geometrical and other effects, criticality corresponds to

which clearly recovers the aforementioned result that critical mass depends inversely on the square of the density.

Alternatively, one may restate this more succinctly in terms of the areal density of mass, :

where the factor has been rewritten as to account for the fact that the two values may differ depending upon geometrical effects and how one defines . For example, for a bare solid sphere of Pu-239 criticality is at 320 kg/m², regardless of density, and for U-235 at 550 kg/m². In any case, criticality then depends upon a typical neutron "seeing" an amount of nuclei around it such that the areal density of nuclei exceeds a certain threshold.

This is applied in implosion-type nuclear weapons, where a spherical mass of fissile material that is substantially less than a critical mass, is made supercritical by very rapidly increasing (and thus as well), see below. Indeed, sophisticated nuclear weapons programs can make a functional device from less material than more primitive weapons programs require.

Aside from the math, there is a simple physical analog that helps explain this result. Consider diesel fumes belched from an exhaust pipe. Initially the fumes appear black, then gradually you are able to see through them without any trouble. This is not because the total scattering cross section of all the soot particles has changed, but because the soot has dispersed. If we consider a transparent cube of length on a side, filled with soot, then the optical depth of this medium is inversely proportional to the square of , and therefore proportional to the areal density of soot particles: we can make it easier to see through the imaginary cube just by making the cube larger.

Several uncertainties contribute to the determination of a precise value for critical masses, including (1) detailed knowledge of cross sections, (2) calculation of geometric effects. This latter problem provided significant motivation for the development of the Monte Carlo method in computational physics by Nicholas Metropolis and Stanislaw Ulam. In fact, even for a homogeneous solid sphere, the exact calculation is by no means trivial. Finally note that the calculation can also be performed by assuming a continuum approximation for the neutron transport, so that the problem reduces to a diffusion problem. However, as the typical linear dimensions are not significantly larger than the mean free path, such an approximation is only marginally applicable.

Finally, note that for some idealized geometries, the critical mass might formally be infinite, and other parameters are used to describe criticality. For example, consider an infinite sheet of fissionable material. For any finite thickness, this corresponds to an infinite mass. However, criticality is only achieved once the thickness of this slab exceeds a critical value.

Criticality in nuclear weapon design

If two pieces of subcritical material are not brought together fast enough, nuclear predetonation (fizzle) can occur, whereby a very small explosion will blow the bulk of the material apart.
Until detonation is desired, a nuclear weapon must be kept subcritical. In the case of a uranium bomb, this can be achieved by keeping the fuel in a number of separate pieces, each below the critical size either because they are too small or unfavorably shaped. To produce detonation, the uranium is brought together rapidly. In Little Boy, this was achieved by firing a smaller piece of uranium down a gun barrel into a corresponding hole in a larger piece, a design referred to as a gun-type fission weapon.

A theoretical 100% pure Pu-239 weapon could also be constructed as a gun-type weapon. In reality, this is impractical because even "weapons grade" Pu-239 is contaminated with a small amount of Pu-240, which has a strong propensity toward spontaneous fission. Because of this, a reasonably sized gun-type weapon would suffer nuclear reaction before the masses of plutonium would be in a position for a full-fledged explosion to occur. Even accounting for Pu-240 impurity, a gun type weapon could still be constructed. It would not be a very practical weapon, however, as it would have to be very long in order to accelerate a mass of plutonium to very high velocities to overcome the effects just mentioned. A better solution exists.

Instead, the plutonium is present as a subcritical sphere (or other shape), which may or may not be hollow. Detonation is produced by exploding a shaped charge surrounding the sphere, increasing the density (and collapsing the cavity, if present) to produce a prompt critical configuration. This is known as an implosion type weapon.

Over a thousand riders took part in the 10th anniversary ride in Melbourne during November 2005.
Critical Mass is an event typically held on the last Friday of every month in cities around the world where bicyclists and, less frequently, unicyclists, skateboarders, inline skaters, roller skaters and other self-propelled commuters take to the streets en masse. While the ride was originally founded with the idea of drawing attention to how unfriendly the city was to bicyclists,[] the leaderless structure of Critical Mass makes it impossible to assign it any one specific goal. In fact, the purpose of Critical Mass is not formalized beyond the direct action of meeting at a set location and time and traveling as a group through city streets.

Background

Critical Mass rides are self-organized, non-commercial and non-competitive, and they operate with diffused and informal decision-making, independent of leaders. They are often also unofficial, foregoing permits and official sanction from municipal authorities. Typically, only the meeting place, date, and time are fixed. In some cities, the route, finishing point, or attractions along the way may be planned ahead. Participants have differing purposes for the event, such as celebrating their choice of the bicycle for transportation, [1] and enjoying car-free social time on city streets. [2]

Critical Mass rides have been perceived as protest activities. A 2006 New Yorker magazine article described Critical Mass' activity in New York City as "monthly political-protest rides", and characterized Critical Mass as a part of a social movement; [3] and the UK e-zine Urban75, which advertises as well as publishes photographs of the Critical Mass event in London, describes this as "the monthly protest by cyclists reclaiming the streets of London".[4] However, Critical Mass participants have insisted that these events should be viewed as "celebrations" and spontaneous gatherings, and not as protests or organized demonstrations.[5][6] This stance allows Critical Mass to argue a legal position that its events can occur without advance notification of local police.[7][8]

Critical Mass rides vary greatly in many respects, including frequency and number of participants. For example, many small cities have monthly Critical Mass rides with fewer than twenty riders, while on the opposite extreme, in what have been the largest events using the name Critical Mass, cyclists in Budapest, Hungary hold only two rides each year on 22 September (International Car Free Day) and 22 April (Earth Day). They attract tens of thousands of riders.[9] The April 22, 2007 Budapest ride participation was generally estimated at 50,000 riders.

History

San Francisco Critical Mass, April 29, 2005.
The first ride took place on Friday, September 25, 1992 at 6 P.M. in San Francisco. At that time, the event was known as Commute Clot and was composed of a couple of dozen cyclists who had received flyers on Market Street.[0]

Shortly after this, some participants in that ride went to a local bicycle shop for a screening of Ted White's documentary Return of the Scorcher, about bike culture overseas. In that film, American human powered vehicle and pedicab designer George Bliss noted that, in China, both motorists and bicyclists had an understood method of negotiating intersections without signals. Traffic would "bunch up" at these intersections until the back log reached a "critical mass" at which point that mass would move through the intersection. The term caught on and replaced Commute Clot as a name at the time of the second event.[0]

By the time of the fourth ride, the number of cyclists had increased to around 100 and participation continued to grow dramatically, reaching about 1,000 riders, on average.[0]

The name was soon adopted as a generic label by participants in similar but independent mass rides that were either initiated in various locations around the world at around the same time, or had already existed before 1992 under other names. It is estimated that there are Critical Mass-type rides in more than 325 cities to date. The term "Masser" is sometimes applied to frequent participants.

Structure

Critical Mass differs from many other social movements in its rhizomal (rather than hierarchical) structure. Critical Mass is sometimes called an "organized coincidence", with no leadership or membership. The routes of some rides are decided spontaneously by whoever is currently at the front of the ride, others are decided prior to the ride by a popular vote of suggested routes often drawn up on photocopied flyers. The term xerocracy was coined to describe a process by which the route for a Critical Mass can be decided: anyone who has an opinion makes their own map and distributes it to the cyclists participating in the Mass. Still other rides decide the route by consensus. The "disorganized" nature of the event allows it to largely escape clampdown by authorities who may view the rides as forms of parades or organized protest. Additionally, the movement is free from the structural costs associated with a centralized, hierarchical organization. In order for the event to function, the only requirement is a sufficient turn-out to create a "critical mass" of riders dense enough to occupy a piece of road to the exclusion of motorized road users. Authorities in New York, California and Oregon have expressed concern with the difficulty of coordinating with the riders, due to the lack of leadership.[11][12] [13]

Detail from the November 20, 1992 flyer by Joel Pomerantz which introduced the concept of corking.

The city of New Haven includes the event in its city-published Green Map. [14]

Corking

Because Critical Mass takes place without an official route or sanction, participants practice a tactic known as "corking" in order to maintain the cohesion of the group. This tactic consists of a few riders blocking traffic from side roads so that the mass can freely proceed through red lights without interruption. Corking allows the mass to engage in a variety of activities, such as circling in an intersection, or lifting their bikes in a tradition known as a Chicago hold-up. The 'Corks' sometimes take advantage of their time corking to distribute flyers.

Critics argue that the practice of corking roads in order to pass through red lights as a group is contrary to Critical Mass' claim that "we are traffic", since ordinary traffic (including bicycle traffic) does not usually have the right to go through intersections once the traffic signal has changed to red, unless issued with a specific permit or residing in jurisdictions where bicyclists have this right (such as the Idaho, USA Bicycle Law [15]). Corking has sometimes translated into hostility between motorists and riders, even erupting into violence and arrests during Critical Mass rides.[16]

Criticism

Critical Mass has been the subject of criticism from authorities and motorists in the various cities in which it takes place.

Conflicts with motorists

Critics have claimed that Critical Mass is a deliberate attempt to obstruct automotive traffic and cause a disruption of normal city functions, asserting that individuals taking part in Critical Mass refuse to obey the vehicular traffic laws that apply to cyclists the same as they do to drivers of other vehicles.[17]

In the San Francisco Bay Area, there have been several incidents of violence during Critical Mass events.[18]

On the evening of March 30, 2007 in San Francisco, toward the end of Critical Mass, Susan Ferrando of Redwood City, California claimed to have found herself in the middle of a group of bicyclists and tried to drive through them resulting in hundreds of bicyclists surrounding her minivan while her 11 and 13 year old daughters watched from inside. Ferrando denies striking a cyclist but claims they banged on the sides of her car, "keyed" the paint, and threw a bicycle through the rear window of the vehicle, causing \$5,300 in damage.[19]

On May 11, 2007, a similar incident occurred in Berkeley, Calfornia. According to a Bicycle Civil Liberites Union press release, a "motorist with his wife deliberately ran into the side of the monthly Berkeley Critical Mass bicycle demonstration"[20] and caused approximately \$3,000 worth of damage to bicycles.[21] However, the driver and two third-party witnesses told police that the bikers threw their bicycles under the vehicle. Subsequently, Critical Mass participants pounded on the hood and windows of the car and the windshield of the vehicle was shattered.[22]

On July 27, 2007, while the Chicago ride was heading to the Spindle in Berwyn, Illinois, an allegedly drunk driver plowed into the mass while attempting to flee the scene of a previous accident. Ten year old Will Healy, who was riding with his mother and sister, was directly hit by the car. Healy flew up onto the hood of the car, but was not severely injured. Several other bicyclists were injured or had their bicycles damaged while attempting to move out of the way of the car. The driver, Robert Rogers, 34, of Maywood, IL was quickly apprehended by police who were riding with and monitoring the group.[23] [24]

San Francisco Mayor Gavin Newsom, in April 2007, requested that Critical Mass riders "police themselves." "It does the bicycle-advocacy community no good to have people that are aggressive and dispirit the entire movement,” Newsom said. “I would encourage the bicycle coalition to say, ‘Look, we don’t put up with this, enough is enough.’”[25]

Conflicts with authorities

Metropolitan Police officers with their cycles awaiting the start of Critical Mass London, April 2006.
In 1997, the Mayor of San Francisco, Willie Brown, was asked by a journalist at a press conference how he planned to control Critical Mass. The Mayor was quoted in the press as threatening the riders with arrest, along with various belittling of bicyclists. The reaction and extensive press coverage grew into a confrontation at the July 25, 1997 ride. The local newspapers had published a route, although many riders were hesitant about—or flatly against—cooperation with it. On Friday the Mayor addressed the crowd at the Embarcadero meeting place but was shouted down. The crowd of approximately 7,000 bicyclists quickly split into many parts, each being chased or monitored by police units, including helicopters. This resulted in extensive turmoil throughout the downtown area and many arrests and bicycle confiscations.

Bennett Hall, a professional photographer, claimed to have witnessed a San Francisco police officer writing a citation for a bicyclist who had committed no offense. While photographing the event, Hall further alleges that the police then improperly arrested him and seized his camera. Another pedestrian attempted to take the camera to bring it to the San Francisco Chronicle, but he was also arrested.[26]

After the US 2004 Republican National Convention coincided with the August 2004 New York City Critical Mass, many court cases resulted regarding the legality of the ride, confronting issues of whether police have the right to arrest cyclists and seize their bicycles, and whether the event needs a permit. In December of 2004, a federal judge threw out New York City's injunction against Critical Mass as a "political event."[27] On March 23, 2005, the city filed a lawsuit, seeking to prevent TIME'S UP!, a local nonprofit, direct action, environmental group, from promoting or advertising Critical Mass rides. The lawsuit also stated TIME'S UP! and the general public could not participate in riding or gathering at the Critical Mass bike ride, claiming a permit was required. A documentary film, Still We Ride shows the nature of these bike rides before and after the police took notice.[28][29][30]

In September 2005, Critical Mass in London found itself in conflict with the law when the Metropolitan Police gave out notices announcing a requirement that the organisers of the mass provide a route six days before the event. In addition, they stated that the Mass may be restricted in the future, and arrests would result if their orders were not followed. The threat was quickly moderated when politicians and cyclist groups voiced objections. The following ride, that of October 2005, was tremendously well attended, with estimates approaching the figure of 1200 participants. There was a long stop in Parliament Square, part of the Government's exclusion area in the Serious Organised Crime and Police Act 2005. However, this event also led to a particularly slow and cumbersome ride which brought some debate from London cycling groups.

Another consequence of the police notice was that a participant sought a declaration from the High Court of England and Wales that there was no requirement to notify police about the Critical Mass rides. After what the judgment describes as a "friendly action" in which the claimant and the police agreed not to seek damages, the Court ruling[31] on June 27, 2006 agreed with the claimant that the Critical Mass rides were exempt from notification under Section 11 of the Public Order Act 1986.

On March 14, 2007 the issue was taken to the Court of Appeal by the Metropolitan Police. On May 21, 2007 the court ruled in their favour[32] by a majority of 2 to 1.[33] Friends of the Earth, who are helping Critical Mass with the legal action, have now indicated that the case will be going to England's highest legal authority, the House of Lords.

Police in Oregon and New York have cited concerns that Critical Mass may delay emergency vehicles, such as ambulances, due to the traffic disruption.[33][33] An expert retained by bicyclists suing New York City gave the opinion that such claims are without merit.[34]

On July 27, 2007 in Vilnius, Lithuania, police took five critical mass participants into custody, including two minors, for not following orders to disband. At least two of them later reported to have been beaten and injured by police officers. A court case is set to take place in August. [35]

On August 31, 2007 in Minneapolis, police arrested nineteen critical mass participants, including two minors.[36] The adults were reported to have been arrested on suspicion of rioting, a gross misdemeanor. [37]

Also on August 31, 2007, seven riders in the Chicago Critical Mass were arrested on charges of obstructing traffic and disobeying police. The seven were held overnight. [38]

Reaction of other cyclists

Some bicycling advocacy groups have expressed concern that the controversial nature of Critical Mass and altercations with motorists could weaken public support for bicyclists.[33] Though it does not condone incidents of violence and rudeness, the San Francisco Bicycle Coalition credits Critical Mass with spotlighting bicycle issues and aiding their efforts in advocating for cyclists.[0]

Critical Manners

In San Francisco, a splinter event known as "Critical Manners," was created as a response to Critical Mass. Critical Manners rides through the city on the second Friday of the month, but in contrast with Critical Mass, the riders obey all traffic laws, such as stopping at red lights and signaling.[39][40]

There are also conversations about starting Critical Manners in Portland, Oregon.[41]

General Impact

Although there is no consensus as to the overall effect of the ride on street conditions for cyclists or on public perceptions of bicycling, a few examples show the extent to which the ride has permeated various subcultures:

The name of the event has been subjected to word play in many contexts, ranging from advertising campaigns for commercial products to numerous other public events,[42] some with only remote similarities to Critical Mass. The extensive news coverage of San Francisco's July 1997 ride spawned an international celebration of bicycling, called Bike Summer.[43] The Rand Corporation produced a white paper entitled "What Next for Networks and Netwars?" analyzing the tactics of the ride, as part of an evaluation of decentralized decision-making for potential military battlefield use.[44] The ride has generated books,[45] documentary films,[46] murals,[47] and other secondary artifacts.

Gallery

 Critical Mass gathering in Chicago. London Critical Mass, April 28, 2006 - 12th Anniversary. Rome Critical Mass, 29th July, 2005. Cyclists in Critical Mass ride through Times Square in New York City on July 30, 2004. Critcal Mass at Heroes' Square, Budapest, April 22, 2006.

References

1. ^ Carlsson, Chris (2002), "Introduction", in Carlsson, Chris, Critical Mass: Bicycling's Defiant Celebration, Edinburgh, Scotland: AK Press, pp. 6, 1-902593-59-6, <[19]
2. ^ Bernie, Blaug (2002), "Crit Mass", in Carlsson, Chris, Critical Mass: Bicycling's Defiant Celebration, Edinburgh, Scotland: AK Press, pp. 73, 1-902593-59-6, <[20]
3. ^ Mcgrath, Ben. "Holy Rollers", 2006-11-13.
4. ^ Critical Mass London. Urban75 (2006).
5. ^ Pittsburgh Critical Mass.
6. ^ Critical Mass: Over 260 Arrested in First Major Protest of RNC. Democracy Now! (2004-08-30).
7. ^ Seaton, Matt. "Critical crackdown", The Guardian, 2005-10-26.
8. ^ Rosi-Kessel, Adam (2004-08-24). [*BCM* Hong Kong Critical Mass News].
9. ^ [21]
10. ^ Garofoli, Joe. "Critical Mass turns 10.", San Francisco Chronicle, September 28, 2002. Retrieved on 2007-07-02.
11. ^ [22]
12. ^ [23]
13. ^ [24]
14. ^ [25]
15. ^ Idaho Statutes.
16. ^ Gutierrez, Scott. "2 bicyclists arrested at Critical Mass get out of jail", Seattle Post-Intelligencer, 2006-07-03.
17. ^ [26]
18. ^ Cabanatuan, Michael, Van Derbeken, Jaxon; Vega, Cecilia M.. "Clash reignites road wars", San Francisco Chronicle, April 5, 2007.
19. ^ Rubenstein, Steve, Lee, Henry K; Zamora, Jim. "Critical Mass pedals politely through S.F.", San Francisco Chronicle, April 28, 2007. Retrieved on 2007-07-02.
20. ^ [27]
21. ^ [28]
22. ^ Lee, Henry K.. "Elderly couple caught up in altercation with Critical Mass bicyclists", San Francisco Chronicle, May 13, 2007. Retrieved on 2007-07-02.
23. ^ Gardiner, Kate. "Driver runs through Critical Mass, injures young rider", Chi-Town Daily News, July 30, 2007. Retrieved on 2007-08-27.
24. ^ Newbart, Dave. "Has 'Mass' ride run its course?", Chicago Sun Times, August 5, 2007. Retrieved on 2007-08-27.
25. ^ [29]
26. ^ [30]
27. ^ [31]
28. ^ [32]
29. ^ [33]
30. ^ [34]
31. ^ [35]
32. ^ [36]
33. ^ [37]
34. ^ [38] Declaration of Charles Komanoff
35. ^ [39] (in Lithuanian)
36. ^ [40]
37. ^ [41]
38. ^ [42]
39. ^ Steve, Rubenstein. "Critical Manners takes a stand for sharing, harmony, red lights.", San Francisco Chronicle, April 14, 2007. Retrieved on 2007-07-02.
40. ^ [43]
41. ^ Would Critical Manners Catch On In Portland?
42. ^ [44]
43. ^ [45]
44. ^ [46]
45. ^ [47]
46. ^ [48]
47. ^ [49]

A supercritical fluid is any substance at a temperature and pressure above its thermodynamic critical point. It has the unique ability to diffuse through solids like a gas, and dissolve materials like a liquid.
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation. Pitchfork bifurcations, like Hopf bifurcations have two types - supercritical or subcritical.
Critical mass is the amount of fissile material needed to sustain fission. The term may also be used in one of the following meanings.
• Critical Mass, a monthly bicycle-centred social movement
• Critical Mass (anime), a subdivision of The Right Stuf International

In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission.

All known fissile materials are capable of sustaining a chain reaction in which either thermal or slow neutrons or fast neutrons predominate.
nuclear chain reaction occurs when on average more than one nuclear reaction is caused by another nuclear reaction, thus leading to an exponential increase in the number of nuclear reactions.
The nucleus of an atom is the very small dense region of an atom, in its center consisting of nucleons (protons and neutrons). The size (diameter) of the nucleus is in the range of 1.
Nuclear fission is the splitting of the nucleus of an atom into parts (lighter nuclei) often producing photons (in the form of gamma rays), free neutrons and other subatomic particles as by-products.
In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles.

The term is derived from the purely classical picture of (a large number of) point-like projectiles directed to an area that includes a solid
Shape (OE. sceap Eng. created thing), refers to the external two-dimensional outline, appearance or configuration of some thing — in contrast to the matter or content or substance of which it is composed.
Enrichment may mean:
• Education.
• The process of making enriched uranium, i.e. isotope separation.
• The process of adding nutrients to cereals or grain (e.g. in enriched flour).

The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero — the coldest possible temperature — is zero kelvins
Beryllium (IPA: /bəˈrɪliəm/) is the chemical element that has the symbol Be and atomic number 4.
For , see .
The half-life of a quantity, subject to exponential decay, is the time required for the quantity to decay to half of its initial value.
5
(weakly basic oxide)
Electronegativity 1.5 (scale Pauling)
Ionization energies 1st: 568 kJ/mol
Miscellaneous
Magnetic ordering no data
Electrical resistivity (0 C) 177 nΩ·m
Uranium-233 is a fissile artificial isotope of uranium, which has been used in a few nuclear reactors and has been proposed for much wider use as a nuclear fuel. It has a half-life of 160,000 years.

Uranium-233 is produced by the neutron irradiation of thorium-232.
Uranium-235 is an isotope of uranium that differs from the element's other common isotope, uranium-238, by its ability to cause a rapidly expanding fission chain reaction, i.e., it is fissile. In fact, U-235 is the only fissile isotope found in any economic quantity in nature.
Neptunium-236 is a radioactive isotope of neptunium with 93 electrons and protons and 143 neutrons. It has a half-life of 154,000 years. It can decay by the following methods -
• Electron capture - here, the decay energy is 0.95 MeV and the decay product is Uranium-236.

5, 4, 3
(amphoteric oxide)
Electronegativity 1.36 (scale Pauling)
Ionization energies 1st: 604.5 kJ/mol
Miscellaneous
Magnetic ordering ?
Electrical resistivity (22 °C) 1.220 µΩ·m
Thermal conductivity (300 K) 6.
Plutonium 238, is a radioactive isotope of plutonium with a half-life of 87.7 years and is a very powerful alpha emitter. Because of its high level of alpha activity, it is used for radioisotope thermoelectric generators and radioisotope heater units.
Plutonium-239 is an isotope of plutonium. Plutonium-239 is one of the three fissile isotopes used for the production of nuclear weapons and in nuclear reactors as a source of energy. Other fissile isotopes used are uranium-235 and uranium-233.
Plutonium-240 (Pu-240) is an isotope of the metal plutonium formed when plutonium-239 captures a neutron. About 62% to 73% of the time when Pu-239 captures a neutron it undergoes fission; the rest of the time it forms Pu-240.
4, 3
(amphoteric oxide)
Electronegativity 1.28 (scale Pauling)
Ionization energies 1st: 584.7 kJ/mol
Miscellaneous
Magnetic ordering no data
Electrical resistivity (0 C) 1.
Americium (Am) has no stable isotopes. A standard atomic mass cannot be given.

19 radioisotopes of americium have been characterized, with the most stable being 243Am with a half-life of 7370 years, and 241Am with a half-life of 432.7 years.
Americium-242 is a radioactive isotope of Americium with 95 protons and electrons and 147 neutrons and a mass of 242.0595492 g/mol. It has a half-life of approximately 141 years. It either decays by isomeric transition (with a decay energy is 0.
Americium-243 is a radioactive isotope of americium having 95 electrons and protons and 148 neutrons and has a mass of 243.06138 g/mol. It has a half-life of 7370 years and is highly unstable, hence it is not found in nature.
Curium (IPA: /ˈkjuːriəm/) is a synthetic chemical element with the symbol Cm and atomic number 96.
Curium (IPA: /ˈkjuːriəm/) is a synthetic chemical element with the symbol Cm and atomic number 96.
3, 4
Electronegativity 1.3 (scale Pauling)
Ionization energies 1st: 608 kJ/mol
Miscellaneous
CAS registry number 7440-71-3
Selected isotopes
Main article: Isotopes of californium
iso NA half-life DM DE (MeV) DP
248Cf syn 333.