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The Stability of Matter: From Atoms to Stars. Selecta of Elliott H. Lieb. Edited by W. Thirring, and with a preface by F. Dyson. Fourth edition. Springer, Berlin, 2005. Elliott H. Lieb and Robert Seiringer, The Stability of Matter in Quantum Mechanics. Cambridge Univ. Press, 2010. Elliott H. Lieb, The stability of matter: from atoms to stars ...
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides , separated from known stable and long-lived primordial radionuclides .
Lieb has been awarded several prizes in mathematics and physics, including the Heineman Prize for Mathematical Physics of the American Physical Society and the American Institute of Physics (1978), [9] the Max Planck Medal of the German Physical Society (1992), [10] the Boltzmann medal of the International Union of Pure and Applied Physics (1998), [11] the Schock Prize (2001), [12] the Henri ...
However, stability of large systems with many electrons and many nucleons is a different question, and requires the Pauli exclusion principle. [ 15 ] It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume.
For this reason, the valley of stability does not follow the line Z = N for A larger than 40 (Z = 20 is the element calcium). [3] Neutron number increases along the line of beta stability at a faster rate than atomic number. The line of beta stability follows a particular curve of neutron–proton ratio, corresponding to the most stable ...
The existence of a topological defect can be demonstrated whenever the boundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are ...
For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to = (), where () is the enclosed mass, is the pressure, () is the density of the gas (at radius ), is the gravitational constant, and is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are ...
Floquet theory shows stability in Hill differential equation (introduced by George William Hill) approximating the motion of the moon as a harmonic oscillator in a periodic gravitational field. Bond softening and bond hardening in intense laser fields can be described in terms of solutions obtained from the Floquet theorem.