Search

There is disagreement over how much Werner Heisenberg knew about reactors and the bomb 1939–1945. A critical paper, declassified and returned to the Germans in 1971, has been inadequately understood in the controversy. Heisenberg calculated the critical radius for a spherical reactor with a tamper but the same formula applies whether spherical reactor or spherical bomb because his result is independent of the reactor's neutron source at criticality (a bomb has no external neutron source). He didn't emphasize the source-independence of the critical radius but instead misinterpreted it. Under captivity at Farm Hall in England in 1945 with eight other leading German nuclear researchers and Max v. Laue, Heisenberg recalled his 1939 theory from memory and made the same critical radius calculation for a bomb with a tamper that Serber had made in 1943 at Los Alamos. Heisenberg's 1945 formula for a bomb is identical to his 1939 critical radius formula derived for a reactor. His 1945 predictions for the numerical values of the critical radius are close to Serber's, except that Heisenberg only knew the fast fission cross section within two bounds, 0.5 and 2.5 barn. Serber's fast fission cross section was in the middle at 1.5 barn. This places Heisenberg's 1939 and 1945 theory and calculations, finally, in the correct historic context. Editor's Note: Historians debate whether Heisenberg was aware, before the launching of the American Manhattan project, of the possible characteristics of a U-235 bomb. This paper presents convincing evidence that in 1939 Heisenberg had already performed the calculation that was presented in 1943 by Serber to the Los Alamos group that predicted a critical radius. This paper will be of interest to those who teach about the development of the atomic bomb. [ABSTRACT FROM AUTHOR]

The adaptation underlying many realistic processes plays a pivotal role in shaping the collective dynamics of diverse systems. Here, we untangle the generic conditions for synchronization transitions in a system of coupled phase oscillators incorporating the adaptive scheme encoded by the feedback between the coupling and the order parameter via a power-law function with different weights. We mathematically argue that, in the subcritical and supercritical correlation scenarios, there exists no critical adaptive fraction for synchronization transitions converting from the first (second)-order to the second (first)-order. In contrast to the synchronization transitions previously deemed, the explosive and continuous phase transitions take place in the corresponding regions as long as the adaptive fraction is nonzero, respectively. Nevertheless, we uncover that, at the critical correlation, the routes toward synchronization depend crucially on the relative adaptive weights. In particular, we unveil that the emergence of a range of interrelated scaling behaviors of the order parameter near criticality, manifesting the subcritical and supercritical bifurcations, are responsible for various observed phase transitions. Our work, thus, provides profound insights for understanding the dynamical nature of phase transitions, and for better controlling and manipulating synchronization transitions in networked systems with adaptation. [ABSTRACT FROM AUTHOR]

Recently, Das et al. [J. Chem. Phys. 125, 024506 (2006)] established that computer simulations of critical dynamics in a binary Lennard-Jones mixture are consistent with the predicted Stokes-Einstein behavior of the asymptotic decay rate of the order-parameter fluctuations near criticality. Here, we show that the noncritical or “background” contributions to the computed diffusion coefficient are also in agreement with both theory and experiment, thus further validating the feasibility of molecular dynamics simulations for studying dynamic critical behavior. [ABSTRACT FROM AUTHOR]

Analyzes the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition by molecular dynamics simulations. Details of the simulation; Molecular dynamics simulation of Lennard-Jones ellipsoids; Implication for isotropic-nematic transition.

Investigates the heat capacity of the restricted primitive model near criticality. Use of the Monte Carlo technique in studying the phase transition of the model; Absence of indication of Isong-type divergence of the heat capacity; Occurrence of Ising behavior close to critical point in some electrolyte solution.

Double criticality and its nonlinear implications are considered for stratified N-layer shallow water flows with N = 1, 2, 3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector and one generalized eigenvector) and semi-simple (two independent eigenvectors). Using a multiple scales argument, dictated by the type of singularity, it is shown that the weakly nonlinear problem near double criticality is governed by a two-way Boussinesq equation (non-semisimple case) and a coupled Kortewegde Vries equation (semisimple case). Parameter values and reduced equations are constructed for the examples of two-layer and three-layer stratified shallow water hydrodynamics. [ABSTRACT FROM AUTHOR]

Examines the physical and mathematical descriptions of self-organized criticality. Use of a stochastic model with long-time correlations; Formula for the frequency spectrum of uncorrelated and overlapping avalanches; Argument on the Eulerian correlation functions and local transport coefficients.

In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259-262 (1988)] in the context of random neural networks. When system size is infinite, it is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the sub-critical regime for finite size systems: the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices. [ABSTRACT FROM AUTHOR]