Exponential Tail Research Articles

Unveiling charge dynamics of visible light absorbing oxysulfide for efficient overall water splitting

Oxysulfide semiconductor, Y2Ti2O5S2, has recently discovered its exciting potential for visible-light-induced overall water splitting, and therefore, imperatively requires the probing of unknown fundamental charge loss pathways to engineer the photoactivity enhancement. Herein, transient diffuse reflectance spectroscopy measurements are coupled with theoretical calculations to unveil the nanosecond to microsecond time range dynamics of the photogenerated charge carriers. In early nanosecond range, the pump-fluence-dependent decay dynamics of the absorption signal is originated from the bimolecular recombination of mobile charge carriers, in contrast, the power-law decay kinetics in late microsecond range is dominated by hole detrapping from exponential tail trap states of valence band. A well-calibrated theoretical model estimates various efficiency limiting material parameters like recombination rate constant, n-type doping density and tail-states parameters. Compared to metal oxides, longer effective carrier lifetime ~6 ns is demonstrated. Different design routes are proposed to realize efficiency beyond 10% for commercial solar-to-hydrogen production from oxysulfide photocatalysts.

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.

Conformal growth rates and spectral geometry on distributional limits of graphs

For a unimodular random graph (G,ρ), we consider deformations of its intrinsic path metric by a (random) weighting of its vertices. This leads to the notion of the conformal growth exponent of (G,ρ), which is the best asymptotic degree of volume growth of balls that can be achieved by such a reweighting. Under moment conditions on the degree of the root, we show that the conformal growth exponent of a unimodular random graph bounds its almost sure spectral dimension. This has interesting consequences for many low-dimensional models. The consequences in dimension two are particularly strong. It establishes that models like the uniform infinite planar triangulation (UIPT) and quadrangulation (UIPQ) almost surely have spectral dimension at most two. It also establishes a conjecture of Benjamini and Schramm (Electron. J. Probab. 6 (2001) no. 23) by extending their recurrence theorem from planar graphs to arbitrary families of H-minor-free graphs. More generally, it strengthens the work of Gurel-Gurevich and Nachmias (Ann. of Math. (2) 177 (2013) 761–781) who established recurrence for distributional limits of planar graphs when the degree of the root has exponential tails. We further present a general method for proving subdiffusivity of the random walk on a large class of models, including UIPT and UIPQ, using only the volume growth profile of balls in the intrinsic metric.

A low-energy explosion yields the underluminous Type IIP SN 2020cxd

Context. We present our observations and analysis of SN 2020cxd, a low-luminosity (LL), long-lived Type IIP supernova (SN). This object is a clear outlier in the magnitude-limited SN sample recently presented by the Zwicky Transient Facility’s (ZTF) Bright Transient Survey. Aims. We demonstrate that SN 2020cxd is an additional member of the group of LL SNe and we discuss the rarity of LL SNe in the context of the ZTF survey. We consider how further studies of these faintest members of the core-collapse (CC) SN family might help improve the general understanding of the underlying initial mass function for stars that explode. Methods. We used optical light curves (LCs) from the ZTF in the gri bands and several epochs of ultraviolet data from the Neil Gehrels Swift observatory as well as a sequence of optical spectra. We constructed the colour curves and a bolometric LC. Then we compared the evolution of the ejecta velocity and black-body temperature for LL SNe as well as for typical Type II SNe. Furthermore, we adopted a Monte Carlo code that fits semi-analytic models to the LC of SN 2020cxd, which allows for the estimation of the physical parameters. Using our late-time nebular spectra, we also make a comparison against SN II spectral synthesis models from the literature to constrain the progenitor properties of SN 2020cxd. Results. The LCs of SN 2020cxd show a great similarity with those of LL SNe IIP in terms of luminosity, timescale, and colours. Also, the spectral evolution of SN 2020cxd is that of a Type IIP SN. The spectra show prominent and narrow P-Cygni lines, indicating low expansion velocities. This is one of the faintest LL SNe observed, with an absolute plateau magnitude of Mr = −14.5 mag and also one with the longest plateau lengths, with a duration of 118 days. Finally, the velocities measured from the nebular emission lines are among the lowest ever seen in a SN, with an intrinsic full width at half maximum value of 478 km s−1. The underluminous late-time exponential LC tail indicates that the mass of 56Ni ejected during the explosion is much smaller than the average of normal SNe IIP, we estimate M56Ni = 0.003 M⊙. The Monte Carlo fitting of the bolometric LC suggests that the progenitor of SN 2020cxd had a radius of R0 = 1.3 × 1013 cm, kinetic energy of Ekin = 4.3 × 1050 erg, and ejecta mass of Mej = 9.5 M⊙. From the bolometric LC, we estimated the total radiated energy Erad = 1.52 × 1048 erg. Using our late-time nebular spectra, we compared these results against SN II spectral synthesis models to constrain the progenitor zero-age main sequence mass and found that it is likely to be ≲15 M⊙. Conclusions. SN 2020cxd is a LL Type IIP SN. The inferred progenitor parameters and the features observed in the nebular spectrum favour a low-energy, Ni-poor, iron CC SN from a low-mass (∼12 M⊙) red supergiant.

Log-growth rates of CO2: An empirical analysis

We study the parametric distribution of log-growth rates of CO2 and CO2 per capita emissions for 207 countries and territories taking data from 1994 to 2010. We define the log-growth rates for different duration periods, from one year apart to fifteen years apart. The considered probability distributions have been the following: the normal (N), the asymmetric double Laplace normal (adLN), the exponential tails normal (ETN) and a mixture of two normal (2N) or three normal (3N) distributions. The main result is that the best one is different depending on the period considered, in such a way that there is not a systematically dominant distribution. Thus, the behavior may change from one year to the next one, and possibly this is influenced by policy measures such as the Kyoto protocol or the Clean Development Mechanism. Moreover, a policy measure that can be derived from this paper is that some countries can still reduce their emissions of CO2 compared with others, as seen by the non-uniformity of the preferred probability distribution for each period. We also model a stochastic differential equation whose associated Fokker–Planck equation has as a solution the observed time-dependent probability density function.

Energy diagram and parameters regarding localized states in InGaN/GaN nanocolumns

The parameters related to the localized states in green-emitting indium gallium nitride (InGaN) have been evaluated by considering the energy diagrams derived by five different methods: (1) the exponential tail of the low-energy side of photoluminescence (PL) spectra, (2) the photon energy dependence of PL decay time, (3) excitation energy dependence of the PL peak energy, (4) the PL excitation spectrum, and (5) the temperature dependence of PL peak energy. The results indicate that the energy diagram of InGaN is divided into four regions: deep localized states, migration region, transition region, and extended states. It is suggested that wider localized states and a narrower transition region are preferable in order to achieve higher PL efficiency. In addition, the dependence of carrier density on PL properties supports the fact of photo-generated carriers forming localized excitons in green-emitting InGaN, although the carriers do not form localized excitons in orange-emitting InGaN and instead exist as localized electrons and holes.

Primordial black holes in peak theory with a non-Gaussian tail

In this paper, we update the peak theory for the estimation of the primordial black hole (PBH) abundance,particularly by implementing the critical behavior in the estimation of the PBH mass and employing the averaged compaction function for the PBH formation criterion to relax the profile dependence.We apply our peak theory to a specific non-Gaussian feature called the exponential tail, which is characteristic in ultra slow-roll models of inflation. With this type of non-Gaussianity, the probability of a large perturbation is not suppressed by the Gaussian factor but decays only exponentially, so the PBH abundance is expected to be much enhanced.Not only do we confirm this enhancement even compared to the case of the corresponding nonlinearity parameter f NL = 5/2, but also we find that the resultant PBH mass spectrum has a characteristic maximal mass which is not seen in the simple Press-Schechter approach.

Tempered stable processes with time-varying exponential tails

In this paper, we introduce a new time series model with a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. It captures the stochastic exponential tail, which generates the volatility smile effect and volatility term structure in option pricing. Moreover, the model describes the time-varying volatility of volatility and empirically indicates stochastic skewness and stochastic kurtosis in the S&P 500 index return data. We present a Monte-Carlo simulation technique for parameter calibration of the model for S&P 500 option prices and show that a stochastic exponential tail improves the calibration performance.

Particle movement characteristics in a gas–solid vertical single helical ribbon agitated reactor

The gas–solid vertical single helical ribbon agitated reactor (G-S-VSAR) is a gas–solid dense-phase agitated reactor, in which the interaction between the agitator and the dense granules dominates the flow field and transfer behavior. The particle movement characteristics are essential for determining the reactor space–time yield and product quality. In this work, the particle residence time distribution (RTD) was measured through magnetic-particles pulse experiment to investigate the overall movement and mixing characteristics of a G-S-VSAR, with the effects of rotation speed and gas velocity studied. The RTD curves were featured by time lag, bypass peak and exponential tail, and thus a model of ‘PFR + double parallel CSTRs’ was established. Results showed that the increase in rotation speed could eliminate the bypass, but only reduce the lag time. The lag time adversely influenced the mixing. Photography was applied to characterize the local particle movements near the reactor wall. It was found that the particles spiraled upwardly along the wall in laminar-like flow and the fully mixed state reached after one circulation. During the spiraled process, the undulating displacement in the vertical direction was induced by agitation in the ribbon-wall gap, which inhibited the radial mixing. Therefore, a narrow gap was recommended for reducing such undulating movements and promoting radial mixing.

Verification of the accuracy of the SIR model in forecasting based on the improved SIR model with a constant ratio of recovery to infection rate by comparing with monitored second wave data.

The temporal evolution of second and subsequent waves of epidemics such as Covid-19 is investigated. Analytic expressions for the peak time and asymptotic behaviours, early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution of number of cases and fatalities, are derived, where the pandemic evolution exhibiting multiple waves is described by the semi-time SIR model. The asymmetry of the epidemic wave and its exponential tail are affected by the initial conditions, a feature that has no analogue in the all-time SIR model. Our analysis reveals that the immunity is very strongly increasing in several countries during the second Covid-19 wave. Wave-specific SIR parameters describing infection and recovery rates we find to behave in a similar fashion. Still, an apparently moderate change of their ratio can have significant consequences. As we show, the probability of an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the second wave, irrespective of the ongoing vaccination efforts. We compare with alternate approaches and data available at the time of submission. Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR model in predicting the evolution of pandemic outbreaks as long as the assumption underlying our analysis, an unchanged situation of the distribution of variants of concern and the fatality fraction, do not change dramatically during a wave. With the rise of the α variant at the time of submission the second wave did not terminate in some countries, giving rise to a superposition of waves that is not treated by the present contribution.

Probability distribution for heat exchange in plastic deformation.

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Unique Curve for the Radiative Photovoltage Deficit Caused by the Urbach Tail.

The photovoltage Voc of high-performance solar cells such as GaAs and metal halide perovskites is affected by the exponential Urbach tail in the absorption spectrum, with an energy parameter EU. It has been observed that increasing Urbach energy decreases the maximum photovoltage that can be achieved. On the basis of detailed balance and reciprocity of absorption and emission, we present a calculation that shows that the voltage loss due to the exponential tail in an absorption obeys a universal relation ΔVocrad = (kBT/q) ln(1 - EU/kBT) for EU < kBT, independently of the bandgap.

Urban noise distributions and the influence of geometric spreading on skewness.

Statistical distributions of urban noise levels are influenced by many complex phenomena, including spatial and temporal variations in the source level, multisource mixtures, propagation losses, and random fading from multipath reflections. This article provides a broad perspective on the varying impacts of these phenomena. Distributions incorporating random fading and averaging (e.g., gamma and noncentral Erlang) tend to be negatively skewed on logarithmic (decibel) axes but can be positively skewed if the fading process is strongly modulated by source power variations (e.g., compound gamma). In contrast, distributions incorporating randomly positioned sources and explicit geometric spreading [e.g., exponentially modified Gaussian (EMG)] tend to be positively skewed with exponential tails on logarithmic axes. To evaluate the suitability of the various distributions, one-third octave band sound-level data were measured at 37 locations in the North End of Boston, MA. Based on the Kullback-Leibler divergence as calculated across all of the locations and frequencies, the EMG provides the most consistently good agreement with the data, which were generally positively skewed. The compound gamma also fits the data well and even outperforms the EMG for the small minority of cases exhibiting negative skew. The lognormal provides a suitable fit in cases in which particular non-traffic noise sources dominate.

Limit Theorems for Random Non-uniformly Expanding or Hyperbolic Maps with Exponential Tails

We prove a Berry–Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain random (Young) tower extensions, which is the main focus of this paper. On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.

Numerical turbulence simulations of intermittent fluctuations in the scrape-off layer of magnetized plasmas

Intermittent fluctuations in the boundary of magnetically confined plasmas are investigated by numerical turbulence simulations of a reduced fluid model describing the evolution of the plasma density and electric drift vorticity in the two-dimensional plane perpendicular to the magnetic field. Two different cases are considered: one describing resistive drift waves in the edge region and another including only the interchange instability due to unfavorable magnetic field curvature in the scrape-off layer. Analysis of long data time series obtained by single-point recordings is compared to predictions of a stochastic model describing the plasma fluctuations as a superposition of uncorrelated pulses. For both cases investigated, the radial particle density profile in the scrape-off layer is exponential with a radially constant scale length. The probability density function for the particle density fluctuations in the far scrape-off layer has an exponential tail. Radial motion of blob-like structures leads to large-amplitude bursts with an exponential distribution of peak amplitudes and the waiting times between them. The average burst shape is well described by a two-sided exponential function. The frequency power spectral density of the particle density is simply that of the average burst shape and is the same for all radial positions in the scrape-off layer. The fluctuation statistics obtained from the numerical simulations are in excellent agreement with recent experimental measurements on magnetically confined plasmas. The statistical framework defines a new validation metric for boundary turbulence simulations.

Diffusion and escape from polygonal channels: extreme values and geometric effects

Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygons. Such pseudo-chaotic behaviour, often characterised by an algebraic separation of nearby trajectories, is believed to be linked to the wild dependence that particle transport has on the fine details of the billiard table. Here, we address this relation through a detailed numerical study of the statistics of displacement in a family of polygonal channel billiards with parallel walls. We show that transport is characterised by strong anomalous diffusion, with a mean square displacement that scales in time faster than linear, and with a probability density of the displacement exhibiting exponential tails and ballistic fronts. In channels of finite length, the distribution of first-passage times is characterised by fat tails, with a mean first-passage time that diverges when the aperture angle is rational. These findings have non-trivial consequences for a variety of experiments.

In-gap states of an amorphous In–Ga–Zn–O thin film studied via high-sensitivity ultraviolet photoemission spectroscopy using low-energy photons

Low-density electronic states in the energy gap of an amorphous In–Ga–Zn–O film control device performance. Herein, density of states (DOS) distribution from valence band to the in-gap states of 1014 cm−3 eV−1 level was determined using high-sensitivity UV photoemission spectroscopy. Exponential tail states accompanying two energetically-localized states were directly observed as reported previously. The observed slope of the exponential tail state was different from the Urbach energy derived using photothermal deflection spectroscopy, indicating the importance of directly observing the DOS of in-gap states.

Homeostatic swimming of zooplankton upon crowding: the case of the copepod Centropages typicus.

Crowding has a major impact on the dynamics of many material and biological systems, inducing effects as diverse as glassy dynamics and swarming. While this issue has been deeply investigated for a variety of living organisms, more research remains to be done on the effect of crowding on the behaviour of copepods, the most abundant metazoans on Earth. To this aim, we experimentally investigate the swimming behaviour, used as a dynamic proxy of animal adaptations, of males and females of the calanoid copepod Centropages typicus at different densities of individuals (10, 50 and 100 ind. l-1) by performing three-dimensional single-organism tracking. We find that the C. typicus motion is surprisingly unaffected by crowding over the investigated density range. Indeed, the mean square displacements as a function of time always show a crossover from ballistic to Fickian regime, with poor variations of the diffusion constant on increasing the density. Close to the crossover, the displacement distributions display exponential tails with a nearly density-independent decay length. The trajectory fractal dimension, D3D ≅ 1.5, and the recently proposed 'ecological temperature' also remain stable on increasing the individual density. This suggests that, at least over the range of animal densities used, crowding does not impact on the characteristics of C. typicus swimming motion, and that a homeostatic mechanism preserves the stability of its swimming performance.

A discussion of approaches for fitting asymmetric signals in X‐ray photoelectron spectroscopy (XPS), noting the importance of Voigt‐like peak shapes

Although the fundamental, theoretical peak shape in X‐ray photoelectron spectroscopy (XPS) is Lorentzian, some Gaussian character is observed in most XPS signals. Additional complexity in the form of asymmetry is also found in many XPS signals, which requires more advanced peak shapes than the traditional, symmetric Voigt and Gaussian‐Lorentzian sum and product (pseudo‐Voigt) functions. Here, we discuss the merits and disadvantages of four approaches that have been used to introduce asymmetry into XPS peak shapes: addition of a decaying exponential tail to a symmetric peak shape, the Doniach‐Sunjic peak shape, the double‐Lorentzian, DL, function, and the LX peak shapes, which include the asymmetric Lorentzian (LA), finite Lorentzian (LF), and square Lorentzian (LS) functions. The Doniach‐Sunjic peak shape is the only asymmetric, synthetic peak that has a theoretical basis. However, it has an infinite integral, which makes it problematic in quantitative work. The mathematical bases for the LX and DL peak shapes are discussed, and practical examples of their use in peak fitting are presented. The case is made for the Voigt function being the most appropriate function for XPS peak fitting, in general, which suggests that a modified Voigt function may be the most reasonable for fitting asymmetric XPS signals. The LX and DL functions include convolution with a Guassian, which, with the exception of the LS function, makes them Voigt‐like functions. The sources of asymmetry and its complexity are discussed. It is emphasized that not every asymmetric spectrum should be fit with an asymmetric peak shape.