1,260 research outputs found
Singular kernels, multiscale decomposition of microstructure, and dislocation models
We consider a model for dislocations in crystals introduced by Koslowski,
Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel
behaving as the norm of the slip. We obtain a sharp-interface limit
of the model within the framework of -convergence. From an analytical
point of view, our functional is a vector-valued generalization of the one
studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement
argument no longer applies. Instead we show that the microstructure must be
approximately one-dimensional on most length scales and exploit this property
to derive a sharp lower bound
Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters
Semiempirical orthogonalization-corrected methods (OM1, OM2, and OM3) go beyond the standard MNDO model by explicitly including additional interactions into the Fock matrix in an approximate manner (Pauli repulsion, penetration effects, and core–valence interactions), which yields systematic improvements both for ground-state and excited-state properties. In this Article, we describe the underlying theoretical formalism of the OMx methods and their implementation in full detail, and we report all relevant OMx parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. For a standard set of mostly organic molecules commonly used in semiempirical method development, the OMx results are found to be superior to those from standard MNDO-type methods. Parametrized Grimme-type dispersion corrections can be added to OM2 and OM3 energies to provide a realistic treatment of noncovalent interaction energies, as demonstrated for the complexes in the S22 and S66×8 test sets
Three-Dimensional Quantum Percolation Studied by Level Statistics
Three-dimensional quantum percolation problems are studied by analyzing
energy level statistics of electrons on maximally connected percolating
clusters. The quantum percolation threshold \pq, which is larger than the
classical percolation threshold \pc, becomes smaller when magnetic fields are
applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to
be consistent with the recently obtained values of the Anderson model,
supporting the conjecture that the quantum percolation is classified onto the
same universality classes of the Anderson transition. Novel critical level
statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
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