Critical behavior at edge singularities in one dimensional spin models

In ferromagnetic spin models above the critical temperature ($T > T_{cr}$) the partition function zeros accumulate at complex values of the magnetic field ($H_E$) with a universal behavior for the density of zeros \rho (H) \sim | H - H_E |^{\sg}. The critical exponent \sg is believed to be universal at each space dimension and it is related to the magnetic scaling exponent $y_h$ via \sg = (d-y_h)/y_h. In two dimensions we have y_h=12/5 (\sg = -1/6) while y_h=2 (\sg=-1/2) in $d=1$. For the one dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperatures, that a new value y_h=3 (\sg =-2/3) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.Comment: to appear in Phys. Rev. E, 16 pages, 3 figure

Outcomes of ab interno trabeculectomy with the trabectome by degree of angle opening.

AimTo analyse ab interno trabeculectomy (AIT) with the trabectome and combined phacoemulsification with AIT (phaco-AIT) by Shaffer angle grade (SG).MethodsProspective study of AIT and phaco-AIT with narrow angles of SG≤2 versus open angles ≥3. Outcomes included intraocular pressure (IOP), medications, complications, secondary surgery and success (IOP <21 mm Hg and >20% reduction without further surgery). Exclusion criteria were missing preoperative data and <1 year follow-up.ResultsOf 671 included cases, at 1 year AIT SG≤2 (n=43) had an IOP reduction of 42% from 27.3±7.4 to 15.7±3.0 mm Hg (p<0.01) versus AIT SG≥3 (n=271) with an IOP reduction of 37% from 26.1±7.8 to 16.4±3.9 mm Hg (p<0.01). In phaco-AIT with SG≤2 (n=48), IOP was reduced 24% from 20.7±7.0 to 15.7±3.6 mm Hg (p<0.01) versus phaco-AIT with SG≥3 (n=309) with an IOP reduction of 25% from 22.6±6.4 to 17.0±3.4 mm Hg (p<0.01). There was no difference between SG≤2 and SG≥3 in reduction of IOP or medications, complications, secondary surgery and success rates (p>0.05).ConclusionsSG≤2 is not associated with worse outcomes in AIT or phaco-AIT

Influence of the sebaceous gland density on the stratum corneum lipidome

The skin surface lipids (SSL) result from the blending of sebaceous and epidermal lipids, which derive from the sebaceous gland (SG) secretion and the permeability barrier of the stratum corneum (SC), respectively. In humans, the composition of the SSL is distinctive of the anatomical distribution of the SG. Thus, the abundance of sebum biomarkers is consistent with the density of the SG. Limited evidence on the influence that the SG exerts on the SC lipidome is available. We explored the differential amounts of sebaceous and epidermal lipids in areas at different SG density with lipidomics approaches. SC was sampled with adhesive patches from forearm, chest, and forehead of 10 healthy adults (8F, 2M) after mechanical removal of sebum with absorbing paper. Lipid extracts of SC were analysed by HPLC/(-)ESI-TOF-MS. In the untargeted approach, the naïve molecular features extraction algorithm was used to extract meaningful entities. Aligned and normalized data were evaluated by univariate and multivariate statistics. Quantitative analysis of free fatty acids (FFA) and cholesterol sulfate (CHS) was performed by targeted HPLC/(-)ESI-TOF-MS, whereas cholesterol and squalene were quantified by GC-MS. Untargeted approaches demonstrated that the relative abundance of numerous lipid species was distinctive of SC depending upon the different SG density. The discriminating species included FFA, CHS, and ceramides. Targeted analyses confirmed that sebaceous FFA and epidermal FFA were increased and decreased, respectively, in areas at high SG density. CHS and squalene, which are biomarkers of epidermal and sebaceous lipid matrices, respectively, were both significantly higher in areas at elevated SG density. Overall, results indicated that the SG secretion intervenes in shaping the lipid composition of the epidermal permeability barrier. © 2018, The Author(s)

On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.Comment: 15 pages, 3 figure