We report the first atomistic determination of the minimum energy path for a series of bond ruptures to advance a crack front. Saddle-point configurations on (111) cleavage planes in Si reveal a steplike distribution of atomic displacements, implying a kink mechanism which is known to control dislocation mobility. Manifestations of lattice trapping and directional cleavage anisotropy are furthe...

We study the generalized free energy of five dimensional charged Gauss-Bonnet anti--de Sitter (AdS) black holes in grand canonical ensemble by treating hole radius and charge as order parameters. On two landscape, lowest points basins represent local stable saddle point represents unstable hole. show that is topological defect gradient field landscape. The stability determined topography landsc...

For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babušca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In the light of the new spectral results ...

We present a unified approach in analyzing Uzawa iterative algorithms for saddle point problems. We study the classical Uzawa method, the augmented Lagrangian method, and two versions of inexact Uzawa algorithms. The target application is the Stokes system, but other saddle point systems, e.g., arising from mortar methods or Lagrange multipliers methods, can benefit from our study. We prove con...

Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spira...

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortun...

We extend recent work on the connection between loopy belief propagation and the Bethe free energy. Constrained minimization of the Bethe free energy can be turned into an unconstrained saddle-point problem. Both converging double-loop algorithms and standard loopy belief propagation can be interpreted as attempts to solve this saddle-point problem. Stability analysis then leads us to conclude ...

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be mapped onto an autonomous dynamical system in a three-dimensional phase space. The corresponding flux has a polynomial form and in general displays four fixed ...

The nearest neighbor level spacing and D3 distributions indicate that the vibrational spectrum of CH2ð~aA1Þ is largely chaotic. Nevertheless, regular localized states coexist with the chaotic ones and they are related to overtone states of the principal vibrational modes. Periodic orbits accompanied by a stability analysis identify these states and explain their topologies and localization in c...