Search results for "singularity."
showing 10 items of 346 documents
Decoherence in a fermion environment: Non-Markovianity and Orthogonality Catastrophe
2013
We analyze the non-Markovian character of the dynamics of an open two-level atom interacting with a gas of ultra-cold fermions. In particular, we discuss the connection between the phenomena of orthogonality catastrophe and Fermi edge singularity occurring in such a kind of environment and the memory-keeping effects which are displayed in the time evolution of the open system.
High-Temperature Series Analysis of the Free Energy and Susceptibility of the 2D Random-Bond Ising Model
1999
We derive high-temperature series expansions for the free energy and susceptibility of the two-dimensional random-bond Ising model with a symmetric bimodal distribution of two positive coupling strengths J_1 and J_2 and study the influence of the quenched, random bond-disorder on the critical behavior of the model. By analysing the series expansions over a wide range of coupling ratios J_2/J_1, covering the crossover from weak to strong disorder, we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form $\chi \sim t^{-7/4} |\ln t|^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig. For the specific heat our results are less…
Dynamical susceptibility from simulations of a mean field Potts glass
2004
Abstract We present results of the non-linear dynamic susceptibility χ(t) in a mean field Potts glass from simulations in a wide range of temperatures above the theoretically predicted dynamical transition, for various system sizes up to 2560 spins. χ(t) has a maximum, with a height that diverges like (T−TD)−α, with α≈1. The timescale t ∗ associated with this maximum also approaches a singularity, and we show that its behavior is compatible with the relaxation time of the standard time-dependent spin autocorrelation function, also with respect to finite size effects. We find that χ(t) for temperatures near the transition temperature TD satisfies a dynamical scaling property.
Fatigue crack growth in welds based on a V-notch model for the short crack propagation at the toe
2018
Abstract This work presents a new fatigue crack growth prediction model for non-load-carrying fillet welded steel joints. For this joint configuration the fatigue cracks will emanate from the weld toe region. Due to the presence of a V-notch in this region the crack initiation point becomes a point of singularity for the stress field. This may in many cases make it difficult to determine the Stress Intensity Factor Range (SIFR) for small cracks by conventional methods based on Linear Elastic Fracture Mechanics (LEFM). The present approach solves this problem by using the Energy Release Rate (ERR) to determine the SIFR in the small crack growth regime. The model is fitted to crack growth cur…
Mixed mode energy release rates for bonded composite joints
2011
Abstract: Analytical formulae developed by Luo and Tong (2009) to determine the mixed mode strain energy release rates of laminated and co-cured composite structures and joints are reviewed. The effects of varying loading conditions and geometries on the mode mixity found analytically are investigated via a parametric study. A critical evaluation of the analytical formulae indicates that the formulae are robust in calculating the total strain energy release rate, but may underestimate the mode II component compared with the finite element analysis and experimental results. Possible reasons for this discrepancy are discussed, including the effect of stress concentrations and singularities at…
Metal–Metal Distances, Electron Counts, and Superconducting TC's in AM2B2C
2001
Abstract We present first principles band structure calculations on representative boron carbides belonging to the class of superconducting compounds with the general formula AM 2 B 2 C with A =Lu, La, or Th and M =Ni or Pd. The compounds are analyzed within the framework of the so-called van Hove scenario, where superconductivity is linked to certain kinds of instabilities in the band structure. We attempt to determine why the addition of the extra electron on replacing the rare earth with Th does not make a significant difference to the superconducting properties, and why the compound LaNi 2 B 2 C is not superconducting.
Ni-based superconductor: Heusler compoundZrNi2Ga
2008
This work reports on the novel Heusler superconductor ZrNi2Ga. Compared to other nickel-based superconductors with Heusler structure, ZrNi2Ga exhibits a relatively high superconducting transition temperature of Tc=2.9 K and an upper critical field of 1.5 T. Electronic structure calculations show that this relatively high transition temperature is caused by a van Hove singularity, which leads to an enhanced density of states at the Fermi energy. The van Hove singularity originates from a higher order valence instability at the L-point in the electronic structure. The enhanced density of states at the Fermi level was confirmed by specific heat and susceptibility measurements. Although many He…
Inflection points and topology of surfaces in 4-space
2000
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
ASYMPTOTIC CURVES ON SURFACES IN ℝ5
2008
We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.
Appendix: Diophantine Approximation on Hyperbolic Surfaces
2002
In this (independent) appendix, we study the Diophantine approximation properties for the particular case of the cusped hyperbolic surfaces, in the spirit of Sect. 2 (or [11]), and the many still open questions that arise for them. We refer to [9], [10]for fundamental results and further developments. We study in particular the distance to a cusp of closed geodesics on a hyperbolic surface.