A report on Stanislaw Ulam

Stanisław Ulam
Stanisław Ulam
The Scottish Café's building now houses the Universal Bank in Lviv, Ukraine.
Ulam's ID badge photo from Los Alamos
Stan Ulam holding the FERMIAC
Ivy Mike, the first full test of the Teller–Ulam design (a staged fusion bomb), with a yield of 10.4 megatons on 1 November 1952
The Sausage device of Mike nuclear test (yield 10.4 Mt) on Enewetak Atoll. The test was part of the Operation Ivy. The Sausage was the first true H-Bomb ever tested, meaning the first thermonuclear device built upon the Teller-Ulam principles of staged radiation implosion.
An artist's conception of the NASA reference design for the Project Orion spacecraft powered by nuclear propulsion
When the positive integers are arrayed along the Ulam spiral, prime numbers, represented by dots, tend to collect along diagonal lines.
An animation demonstrating the lucky number sieve. The numbers in red are lucky numbers

Polish-American scientist in the fields of mathematics and nuclear physics.

- Stanislaw Ulam
Stanisław Ulam

56 related topics with Alpha

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Ulam's packing conjecture

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Ulam's packing conjecture, named for Stanislaw Ulam, is a conjecture about the highest possible packing density of identical convex solids in three-dimensional Euclidean space.

An animation demonstrating the lucky number sieve. The numbers on a reddish orange background are lucky numbers. When a number is eliminated its background changes from grey to purple.

Lucky number

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Natural number in a set which is generated by a certain "sieve".

Natural number in a set which is generated by a certain "sieve".

An animation demonstrating the lucky number sieve. The numbers on a reddish orange background are lucky numbers. When a number is eliminated its background changes from grey to purple.

The term was introduced in 1956 in a paper by Gardiner, Lazarus, Metropolis and Ulam.

A graph and the associated deck of single-vertex-deleted subgraphs. Note some of the cards show isomorphic graphs.

Reconstruction conjecture

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Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs.

Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs.

A graph and the associated deck of single-vertex-deleted subgraphs. Note some of the cards show isomorphic graphs.

It is due to Kelly and Ulam.

Measurable cardinal

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Certain kind of large cardinal number.

Certain kind of large cardinal number.

The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930.

A re-creation of the 1945 criticality accident using the Demon core: a plutonium pit 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. The mass went supercritical when the block was placed improperly by being dropped.

Critical mass

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Smallest amount of fissile material needed for a sustained nuclear chain reaction.

Smallest amount of fissile material needed for a sustained nuclear chain reaction.

A re-creation of the 1945 criticality accident using the Demon core: a plutonium pit 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. The mass went supercritical when the block was placed improperly by being dropped.
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 allows the reaction to become self-sustaining.
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.

This latter problem provided significant motivation for the development of the Monte Carlo method in computational physics by Nicholas Metropolis and Stanislaw Ulam.

Kremlinology

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Study and analysis of the politics and policies of the Soviet Union while Sovietology is the study of politics and policies of both the Soviet Union and former communist states more generally.

Study and analysis of the politics and policies of the Soviet Union while Sovietology is the study of politics and policies of both the Soviet Union and former communist states more generally.

Adam Ulam, brother of Stanisław Ulam and head of the Russian Research Center at Harvard University

Santa Fe, New Mexico

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Capital of the U.S. state of New Mexico.

Capital of the U.S. state of New Mexico.

The trading post established in 1603
Mapa de los Estados Unidos de Méjico, by John Distrunell, the 1847 map used during the negotiations of the Treaty of Guadalupe Hidalgo
Santa Fe, 1846–1847
Santa Fe, 1882, the railroad era
The reconstruction of the St. Francis Cathedral, with the plaza visible (1885)
1921 Fiesta parade, Santa Fe. Palace of the Governors in background.
February 2003 astronaut photography of the valley of the Rio Grande (including the Rio Grande Gorge) and the Sangre de Cristo Mountains from Santa Fe (bottom center) to north of Taos, taken from the International Space Station (ISS). Santa Fe Baldy peak at lower right. Los Alamos, White Rock, the Valles Caldera, and the Rio Chama at lower left.
Palace of the Governors, established 1609–10, pictured in 2006
Cathedral Basilica of Saint Francis of Assisi, built in 1869, pictured in 2004
Homes are territorial- or pueblo-style and stuccoed with flat roofs, 2011.
The Inn at Loretto, a Pueblo Revival-style building near the Plaza in Santa Fe, 2005
Santa Fe wall with mural on doorway
A covered portal on Cathedral Place outside the Museum of Contemporary Native Arts in Santa Fe, New Mexico
The public sculpture Santa Fe Current at City Hall Park
Interior of the Crosby Theatre at the Santa Fe Opera, from the mezzanine
Panoramic view from E. Palace Ave., with Cathedral Park and Cathedral Basilica of St. Francis of Assisi (left), and Museum of Contemporary Native Arts (right)
San Miguel Chapel in Santa Fe is said to be the oldest standing church structure in the U.S. The adobe walls were constructed around A.D. 1610.
El Santuario de Guadalupe, 100 S. Guadalupe St. (downtown), is the oldest extant shrine to the Virgin of Guadalupe in the United States.
The New Mexico Rail Runner Express, with its northern terminus in Santa Fe, services multiple locations in the state.
The Santa Fe Public Library, located downtown, 2009
Fashion designer and filmmaker Tom Ford was raised in Santa Fe after moving from Texas.
Actress Anna Gunn moved to Santa Fe from Oklahoma during her childhood.
Visual artist Georgia O'Keeffe took up residency in Santa Fe during the later years of her life, eventually dying in the city. The Georgia O'Keeffe Museum was built in her honor.

Stanislaw Ulam (1909–1984), mathematician associated with the Manhattan Project

Thermal motion of an α-helical peptide. The jittery motion is random and complex, and the energy of any particular atom can fluctuate wildly. Nevertheless, the equipartition theorem allows the average kinetic energy of each atom to be computed, as well as the average potential energies of many vibrational modes. The grey, red and blue spheres represent atoms of carbon, oxygen and nitrogen, respectively; the smaller white spheres represent atoms of hydrogen.

Equipartition theorem

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In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies.

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies.

Thermal motion of an α-helical peptide. The jittery motion is random and complex, and the energy of any particular atom can fluctuate wildly. Nevertheless, the equipartition theorem allows the average kinetic energy of each atom to be computed, as well as the average potential energies of many vibrational modes. The grey, red and blue spheres represent atoms of carbon, oxygen and nitrogen, respectively; the smaller white spheres represent atoms of hydrogen.
Figure 2. Probability density functions of the molecular speed for four noble gases at a temperature of 298.15 K (25 °C). The four gases are helium (4He), neon (20Ne), argon (40Ar) and xenon (132Xe); the superscripts indicate their mass numbers. These probability density functions have dimensions of probability times inverse speed; since probability is dimensionless, they can be expressed in units of seconds per meter.
Figure 3. Atoms in a crystal can vibrate about their equilibrium positions in the lattice. Such vibrations account largely for the heat capacity of crystalline dielectrics; with metals, electrons also contribute to the heat capacity.
Figure 4. Idealized plot of the molar specific heat of a diatomic gas against temperature. It agrees with the value (7/2)R predicted by equipartition at high temperatures (where R is the gas constant), but decreases to (5/2)R and then (3/2)R at lower temperatures, as the vibrational and rotational modes of motion are "frozen out". The failure of the equipartition theorem led to a paradox that was only resolved by quantum mechanics. For most molecules, the transitional temperature Trot is much less than room temperature, whereas Tvib can be ten times larger or more. A typical example is carbon monoxide, CO, for which Trot ≈ 2.8 K and Tvib ≈ 3103 K. For molecules with very large or weakly bound atoms, Tvib can be close to room temperature (about 300 K); for example, Tvib ≈ 308 K for iodine gas, I2.
Figure 6. A combined X-ray and optical image of the Crab Nebula. At the heart of this nebula there is a rapidly rotating neutron star which has about one and a half times the mass of the Sun but is only 25 km across. The equipartition theorem is useful in predicting the properties of such neutron stars.
Figure 7. Typical Brownian motion of a particle in three dimensions.
Figure 9. Energy is not shared among the various normal modes in an isolated system of ideal coupled oscillators; the energy in each mode is constant and independent of the energy in the other modes. Hence, the equipartition theorem does not hold for such a system in the microcanonical ensemble (when isolated), although it does hold in the canonical ensemble (when coupled to a heat bath). However, by adding a sufficiently strong nonlinear coupling between the modes, energy will be shared and equipartition holds in both ensembles.
Figure 10. Log–log plot of the average energy of a quantum mechanical oscillator (shown in red) as a function of temperature. For comparison, the value predicted by the equipartition theorem is shown in black. At high temperatures, the two agree nearly perfectly, but at low temperatures when kBT << hν, the quantum mechanical value decreases much more rapidly. This resolves the problem of the ultraviolet catastrophe: for a given temperature, the energy in the high-frequency modes (where hν >> kBT) is almost zero.

In 1953, Fermi, Pasta, Ulam and Tsingou conducted computer simulations of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third).

Hyers–Ulam–Rassias stability

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The stability problem of functional equations originated from a question of Stanisław Ulam, posed in 1940, concerning the stability of group homomorphisms.

George David Birkhoff

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American mathematician best known for what is now called the ergodic theorem.

American mathematician best known for what is now called the ergodic theorem.

However, Birkhoff took a particular liking to certain Jewish mathematicians, including Stanislaw Ulam.