Distribution of localized states from fine analysis of electron spin resonance spectra of organic semiconductors: Physical meaning and methodology

We develop an analytical method for the processing of electron spin resonance (ESR) spectra. The goal is to obtain the distributions of trapped carriers over both their degree of localization and their binding energy in semiconductor crystals or films composed of regularly aligned organic molecules [Phys. Rev. Lett. v. 104, 056602 (2010)]. Our method has two steps. We first carry out a fine analysis of the shape of the ESR spectra due to the trapped carriers; this reveals the distribution of the trap density of the states over the degree of localization. This analysis is based on the reasonable assumption that the linewidth of the trapped carriers is predetermined by their degree of localization because of the hyperfine mechanism. We then transform the distribution over the degree of localization into a distribution over the binding energies. The transformation uses the relationships between the binding energies and the localization parameters of the trapped carriers. The particular relation for the system under study is obtained by the Holstein model for trapped polarons using a diagrammatic Monte Carlo analysis. We illustrate the application of the method to pentacene organic thin-film transistors.Comment: 14 pages, 11 figure

Seizure outcomes and survival in adult low-grade glioma over 11 years: living longer and better

Background: There has been a trend toward earlier and more aggressive resection for low-grade gliomas (LGGs). This study set out to compare seizure control and survival of adults with LGG seen in the same neuro-oncology clinic over 11 years and to determine whether a change in surgical philosophy has led to a corresponding improvement in outcomes. / Methods: We conducted a retrospective analysis using case-note review of 153 adults with histologically verified or radiologically suspected LGG, collecting data on patient, tumor, and seizure characteristics between 2006 and 2017. / Results: We studied 79 patients in 2006 and 74 patients in 2017. There was no significant difference between the 2 groups in age at presentation, tumor location, or integrated pathological diagnosis. The numbers of complete or partial resections increased from 21.5% in 2006 to 60.8% in 2017 (P < .05). Five- and 10-year overall survival increased from 81.8% and 51.7% in 2006 to 100% and 95.8% in 2017 (P < .001); similarly, 5- and 10-year progression-free survival increased from 47.0% and 30.7% in 2006 to 93.1% and 68.7% in 2017. The proportion of patients with intractable epilepsy declined from 72.2% in 2006 to 43.2% in 2017 (P < .05). The neurosurgical morbidity rate was identical in both groups (11.8% in 2006 vs 11.1% in 2017). / Conclusion: Management of LGG over the last 11 years has led to substantial improvements in survival and seizure control. This is most likely thanks to a change in surgical philosophy, with early resection now favored over watchful waiting where possible

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Formation of Disk Galaxies: Warm Dark Matter and the Angular Momentum problem

We have performed TreeSPH simulations of disk galaxy formation in various warm dark matter (WDM) cosmologies. Our results indicate that for a range of WDM free-streaming masses, the disk galaxy formation angular momentum problem can be completely resolved by going to the WDM structure formation scenario, without having to invoke stellar feedback processes at all. We also confirm our previous suspicion, that part of the angular momentum problem is due to numerical effects, most likely related to the shock capturing, artificial viscosity used in SPH. Furthermore we find that we can match the observed I-band Tully-Fisher (TF) relation, provided that the I-band mass-to-light ratio of disk galaxies is about 0.8. We argue that this is quite a reasonable value in comparison with various dynamical and spectrophotometric estimates, including one given in this paper. We speculate that our success in matching the TF relation may be due to WDM halos being less centrally concentrated than CDM halos and suggest to check this exciting possibility with high resolution simulations, in particular in low Omega_M, WDM cosmologies. Finally, we discuss possible physical candidates for WDM particles extensively. We find that the most promising are neutrinos with weaker or stronger interactions than normal, majorons (light pseudogoldstone bosons) or mirror or shadow world neutrinos.Comment: 50 pages incl. 17 figures. Accepted for publication in Ap

Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model

We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$, versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ``Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ``connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of $\chi^{(3)}$ and $\chi^{(4)}$. We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the $n$-particle contributions $\chi^{(n)}$ and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for