When the associated graded ring of a semigroup ring is Complete Intersection

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and gamma-rectangular Ap\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterisation for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection.Comment: 24 page

Correlation Functions for an Elastic String in a Random Potential: Instanton Approach

We develop an instanton technique for calculations of correlation functions characterizing statistical behavior of the elastic string in disordered media and apply the proposed approach to correlations of string free energies corresponding to different low-lying metastable positions. We find high-energy tails of correlation functions for the case of long-range disorder (the disorder correlation length well exceeds the characteristic distance between the sequential string positions) and short-range disorder with the correlation length much smaller then the characteristic string displacements. The former case refers to energy distributions and correlations on the distances below the Larkin correlation length, while the latter describes correlations on the large spatial scales relevant for the creep dynamics.Comment: 5 pages; 1 .eps figure include

Peak effect in YBCO crystals: Statics and dynamics of the vortex lattice

Oscillatory dynamics and quasi-static Campbell regime of the vortex lattice (VL) in twinned YBa2Cu3O7 single crystals has been explored at low fields near the peak effect (PE) region by linear and non-linear ac susceptibility measurements. We show evidence that the PE is a dynamic anomaly observed in the non-linear response, and is absent in the Labusch constant derived from the linear Campbell regime. Static properties play a major role however, and we identify two H(T) lines defining the onset and the end of the effect. At H1(T) a sudden increase in the curvature of the pinning potential wells with field coincides with the PE onset. At a higher field, H2(T), a sudden increase in linear ac losses, where dissipative forces overcome pinning forces, marks the end of Campbell regime and, simultaneously, the end of the PE anomaly. Vortex dynamics was probed in frequency dependent measurements, and we find that in the PE region, vortex dynamics goes beyond the description of a power law with a finite creep exponent for the constitutive relation.Comment: 8 pages, 5 figure

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Double sign reversal of the vortex Hall effect in YBa2Cu3O7-delta thin films in the strong pinning limit of low magnetic fields

Measurements of the Hall effect and the resistivity in twinned YBa2Cu3O7-delta thin films in magnetic fields B oriented parallel to the crystallographic c-axis and to the twin boundaries reveal a double sign reversal of the Hall coefficient for B below 1 T. In high transport current densities, or with B tilted off the twin boundaries by 5 degrees, the second sign reversal vanishes. The power-law scaling of the Hall conductivity to the longitudinal conductivity in the mixed state is strongly modified in the regime of the second sign reversal. Our observations are interpreted as strong, disorder-type dependent vortex pinning and confirm that the Hall conductivity in high temperature superconductors is not independent of pinning.Comment: 4 pages, 4 figure

Melting of Flux Lines in an Alternating Parallel Current

We use a Langevin equation to examine the dynamics and fluctuations of a flux line (FL) in the presence of an {\it alternating longitudinal current} $J_{\parallel}(\omega)$. The magnus and dissipative forces are equated to those resulting from line tension, confinement in a harmonic cage by neighboring FLs, parallel current, and noise. The resulting mean-square FL fluctuations are calculated {\it exactly}, and a Lindemann criterion is then used to obtain a nonequilibrium `phase diagram' as a function of the magnitude and frequency of $J_{\parallel}(\omega)$. For zero frequency, the melting temperature of the mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a limiting current. However, for any finite frequency, there is a non-zero melting temperature.Comment: 5 pages, 1 figur

Patterns on the numerical duplication by their admissibility degree

We develop the theory of patterns on numerical semigroups in terms of the admissibility degree. We prove that the Arf pattern induces every strongly admissible pattern, and determine all patterns equivalent to the Arf pattern. We study patterns on the numerical duplication $S \Join^d E$ when $d \gg0$. We also provide a definition of patterns on rings

A thermodynamic unification of jamming

Fragile materials ranging from sand to fire-retardant to toothpaste are able to exhibit both solid and fluid-like properties across the jamming transition. Unlike ordinary fusion, systems of grains, foams and colloids jam and cease to flow under conditions that still remain unknown. Here we quantify jamming via a thermodynamic approach by accounting for the structural ageing and the shear-induced compressibility of dry sand. Specifically, the jamming threshold is defined using a non-thermal temperature that measures the 'fluffiness' of a granular mixture. The thermodynamic model, casted in terms of pressure, temperature and free-volume, also successfully predicts the entropic data of five molecular glasses. Notably, the predicted configurational entropy avoids the Kauzmann paradox entirely. Without any free parameters, the proposed equation-of-state also governs the mechanism of shear-banding and the associated features of shear-softening and thickness-invariance.Comment: 16 pgs double spaced. 4 figure

Ionic Liquids–Cobalt(II) Thermochromic Complexes: How the Structure Tunability Affects “Self-Contained” Systems

With the aim of obtaining thermochromic systems with potential applications in solar energy storage, we evaluated the behavior of some sugar-based ionic liquids (ILs) 12Co(NTf2)2 complexes, in IL solution, as a function of temperature. Different structural changes on the cation, the nature of the anion, and the nature of the IL used as the solvent were considered. The analysis of the above factors was carried out through a combined approach of different techniques, that is, variable temperature UV 12vis and NMR spectroscopies, conductivity, and thermal gravimetric analysis. The thermochromic systems were analyzed both as solutions and as thin films, and the data collected highlight the defining role played by both the cation structure and the solvent nature in determining their performance. Most of the investigated systems show a chromogenic transition from pink to blue, occurring in a temperature range suitable for practical applications (40 1260 \ub0C). Interestingly, when embedded in a polymeric matrix, thin films with high recyclability and long life are also described