228 research outputs found
Ginzburg-Landau vortices, Coulomb Gases, and Renormalized Energies
This is a review about a series of results on vortices in the Ginzburg-Landau
model of superconductivity on the one hand, and point patterns in Coulomb gases
on the other hand, as well as the connections between the two topics.Comment: review paper, submitted to J. Stat. Phy
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Indexes of the Proceedings for the Ten International Symposia on Detonation 1951-93
The Proceedings of the ten Detonation Symposia have become the major archival source of information of international research in explosive phenomenology, theory, experimental techniques, numerical modeling, and high-rate reaction chemistry. In many cases, they contain the original reference or the only reference to major progress in the field. For some papers, the information is more complete than the complementary article appearing in a formal journal; yet for others, authors elected to publish only an abstract in the Proceedings. For the large majority of papers, the Symposia Proceedings provide the only published reference to a body of work. This report indexes the ten existing Proceedings of the Detonation Symposia by paper titles, topic phrases, authors, and first appearance of acronyms and code names
Distribution of cracks in a chain of atoms at low temperature
We consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy
Distribution of cracks in a chain of atoms at low temperature
We consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy
Surface Energies Arising in Microscopic Modeling of Martensitic Transformations
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic
lattice. The two wells of the Hamiltonian are prescribed by two rank-one
connected martensitic twins, respectively. By constraining the deformed
configurations to special 1D atomic chains with position-dependent elongation
vectors for the vertical direction, we show that the structure of ground states
under appropriate boundary conditions is close to the macroscopically expected
twinned configurations with additional boundary layers localized near the
twinning interfaces. In addition, we proceed to a continuum limit, show
asymptotic piecewise rigidity of minimizing sequences and rigorously derive the
corresponding limiting form of the surface energy
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