Explicit kink solutions in several one-parameter families of higher-order field theory models

We present several one-parameter families of higher-order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink solutions with a power-law tail. Various properties of these families of kink solutions are examined in detail. Further, by applying the recent Manton formalism, we provide estimates for the kink–kink (KK) and antikink–kink (AK-K) acceleration and hence the ratio of the corresponding AK-K and KK forces.

A universal Urbach rule for disordered organic semiconductors

In crystalline semiconductors, absorption onset sharpness is characterized by temperature-dependent Urbach energies. These energies quantify the static, structural disorder causing localized exponential-tail states, and dynamic disorder from electron-phonon scattering. Applicability of this exponential-tail model to disordered solids has been long debated. Nonetheless, exponential fittings are routinely applied to sub-gap absorption analysis of organic semiconductors. Herein, we elucidate the sub-gap spectral line-shapes of organic semiconductors and their blends by temperature-dependent quantum efficiency measurements. We find that sub-gap absorption due to singlet excitons is universally dominated by thermal broadening at low photon energies and the associated Urbach energy equals the thermal energy, regardless of static disorder. This is consistent with absorptions obtained from a convolution of Gaussian density of excitonic states weighted by Boltzmann-like thermally activated optical transitions. A simple model is presented that explains absorption line-shapes of disordered systems, and we also provide a strategy to determine the excitonic disorder energy. Our findings elaborate the meaning of the Urbach energy in molecular solids and relate the photo-physics to static disorder, crucial for optimizing organic solar cells for which we present a revisited radiative open-circuit voltage limit.

A minimal nonlinearity logarithmic potential: Kinks with super-exponential profiles

We study a [Formula: see text]-dimensional field theory based on the [Formula: see text] potential which represents minimal nonlinearity in the context of phase transitions. There are three degenerate minima at [Formula: see text] and [Formula: see text]. There are novel, asymmetric kink solutions of the form [Formula: see text] connecting the minima at [Formula: see text] and [Formula: see text]. The domains with [Formula: see text] repel the linear excitations, the waves (e.g., phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. For illustrative purposes we provide a comparison of these results with the [Formula: see text] model and its half-kink solution, which has an exponential tail in contrast to the super-exponential tail for the [Formula: see text] potential. Finally, we place the results in the context of other logarithmic models.

Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain.

Exponential Tail Bounds for Chisquared Random Variables

The paper derives some exponential tail bounds for central and non-central chisquared random variables. The bounds are simple and can easily be applied in statistical analysis. Especially relevant are the tail bounds for non-central chisquares, which are different from some of the other exponential bounds available in the literature, for example the one given in [1].

A Universal Urbach Rule for Disordered Organic Semiconductors

In crystalline semiconductors, the sharpness of the absorption spectrum onset is characterized by temperature-dependent Urbach energies. These energies quantify the static, structural disorder causing localized exponential tail states, and the dynamic disorder due to electron-phonon scattering. The applicability of this exponential-tail model to molecular and amorphous solids has long been debated. Nonetheless, exponential fittings are routinely applied to the analysis of the sub-gap absorption of organic semiconductors alongside Gaussian-like spectral line-shapes predicted by non-adiabatic Marcus theory. Herein, we elucidate the sub-gap spectral line-shapes of organic semiconductors and their blends by temperature-dependent quantum efficiency measurements in photovoltaic structures. We find that the Urbach energy associated with singlet excitons universally equals the thermal energy regardless of static disorder. These observations are consistent with absorption spectra obtained from a convolution of Gaussian density of excitonic states weighted by a Boltzmann factor. A generalized Marcus charge transfer model is presented that explains the absorption spectral line-shape of disordered molecular matrices, and we also provide a simple strategy to determine the excitonic disorder energy. Our findings elaborate the true meaning of the dynamic Urbach energy in molecular solids and deliver a way of relating the photo-physics to static disorder, crucial for optimizing molecular electronic devices such as organic solar cells.

Flooding and diameter in general weighted random graphs

In this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two vertices in the graph, and the flooding time, which represents the time (weighted length) needed to reach all the vertices in the graph starting from a uniformly chosen vertex. Our result consists in describing the asymptotic behavior of the diameter and the flooding time, as the number of vertices n tends to infinity, in the case where the weight distribution G has an exponential tail behavior, and proving that this category of distributions is the largest possible for which the asymptotic behavior holds.