Search results for "Degree"

Subgroup S-commutativity degrees of finite groups

2012

Volumetric Behaviour of Lime Treated High Plasticity Clay Subjected to Suction Controlled Drying and Wetting Cycles

2017

The paper presents some experimental results collected on samples recovered from an experimental embankment obtained by compacting a lime-treated clay. Samples were collected soon after the in situ compaction and they were cured in controlled environmental conditions for at least 18 months. Mercury intrusion porosimetry tests (MIP) were carried out on freeze-dried specimens to characterize the microstructure of the material. In order to assess the durability of the improved material, laboratory tests focused on the effects of cyclic variations of the degree of saturation on the water retention properties and the volumetric behaviour of the stabilized clay. Collected results show that the li…

Experimental analysis of the water retention behaviour of shales

2014

Shales are among the most commonly considered geomaterials in current energy-related geomechanical investigations, as they are involved in engineering applications such as the unconventional extraction of natural gas, CO2 sequestration and nuclear waste geological storage. A deep understanding of their behaviour with regard to variations in the degree of saturation is of primary significance for such applications. With the aim to establish a sound protocol for shale retention behaviour analysis, this paper presents an advanced experimental methodology that takes into account the specificities of shales such as small pore size dimensions and the large variations in water potential to be appl…

Disordered hyperuniformity in superconducting vortex lattices

2020

Particles occupying sites of a random lattice present density fluctuations at all length scales. It has been proposed that increasing interparticle interactions reduces long range density fluctuations, deviating from random behaviour. This leads to power laws in the structure factor and the number variance that can be used to characterize deviations from randomness which eventually lead to disordered hyperuniformity. It is not yet fully clear how to link density fluctuations with interactions in a disordered hyperuniform system. Interactions between superconducting vortices are very sensitive to vortex pinning, to the crystal structure of the superconductor and to the value of the magnetic …

Skyrmion formation due to unconventional magnetic modes in anisotropic multiband superconductors

2018

Multiband superconductors have a sufficient number of degrees of freedom to allow topological excitations characterized by Skyrmionic topological invariants. In the most common, clean s-wave multiband, systems the interband magnetic coupling favours composite vortex solutions, without a Skyrmionic topological charge. It was discussed recently that certain kinds of anisotropies lead to hybridisation of the interband phase difference (Leggett) mode with magnetic modes, dramatically changing the hydromagnetostatics of the system. Here we report this effect for a range of parameters that substantially alter the nature of the topological excitations, leading to solutions characterized by a nontr…

Time-domain analysis of electronic spectra in superfluid 4He

2004

Abstract Electronic absorption spectra of impurities in superfluid helium is developed in time domain, using time-dependent density functional theory to describe liquid 4 He and time-dependent perturbation theory to describe the electronic degrees of freedom of the impurity. Angularly isotropic potentials are used to describe the molecule–helium interactions in the ground and excited electronic states. The calculations rationalize experimentally observed phonon side-bands in 4 He droplets and in bulk helium, and allow assignments of spectral features to specific motions of the liquid.

Reaction coordinates and transition states in enzymatic catalysis

2017

Enzymatic reactions are complex chemical processes taking place in complex dynamic environments. Theoretical characterization of these reactions requires the determination of the reaction coordinate and the transition state ensemble. This is not an easy task because many degrees of freedom may be involved in principle. We present recent efforts to find good enzymatic reaction coordinates and the implications of these findings in the interpretation of enzymatic efficiency. In particular, we analyze different strategies based on the use of minimum free energy paths and direct localization of the dividing surface on multidimensional free energy surfaces. Another strategy is based on the genera…

Topological classification of 4-dimensional complete intersections

1996

Let X,,(d) C C P "+r denote a complete intersection, the transversal intersection of r hypersurfaces in C P ~+r defined by r homogeneous polynomials of degrees (d l , . . . ,dr) =: d, with dld2...d,. =: d the total degree. It is well-known that the diffeomorphism type of X,,(d) is determined by n and d. In [7] and [8], Libgober and Wood showed that in dimension n -~ 2, there exist k distinct multidegrees ibr any integer k 6 N such that the corresponding complete intersections are all diffeomorphic. For n = 1,3, the diffeomorphism classification of Xn(d) is well-known by surface theory and the classification of 1-connected six-manifolds [12] respectively. For 7z = 2, at least the topological…

Design and synthesis of the first triply twisted Möbius annulene.

2014

As long as 50 years ago theoretical calculations predicted that Mobius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Huckel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Mobius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower deg…

Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points

2021

Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…