Search results for "singular"
showing 10 items of 589 documents
Genericity of dimension drop on self-affine sets
2017
We prove that generically, for a self-affine set in $\mathbb{R}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
Integrable Hamiltonian systems with swallowtails
2010
International audience; We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovski´ı and Zhilinski´ı (2007 Ann. Phys. 322 164–200) is discussed.
Higher order matrix differential equations with singular coefficient matrices
2015
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
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…
A Unified Approach to Portfolio Optimization with Linear Transaction Costs
2004
In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the p…
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…
Change of the vortex core structure in two-band superconductors at the impurity-scattering-driven s±/s++ crossover
2017
We report a nontrivial transition in the core structure of vortices in two-band superconductors as a function of interband impurity scattering. We demonstrate that, in addition to singular zeros of the order parameter, the vortices there can acquire a circular nodal line around the singular point in one of the superconducting components. It results in the formation of the peculiar ``moat''-like profile in one of the superconducting gaps. The moat-core vortices occur generically in the vicinity of the impurity-induced crossover between ${s}_{\ifmmode\pm\else\textpm\fi{}}$ and ${s}_{++}$ states.
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.