USING A DOUBLE CONVOLUTION OF LORENTZ AND GAUSS FUNCTIONS FOR PROCESSING THE MÖSSBAUER SPECTRA OF THE SUPERSATURATED DISORDERED SOLID SOLUTIONS

An algorithm for mathematical processing of the Mössbauer spectra of supersaturated disordered solid solutions by the Tikhonov regularization method using a double convolution of the Lorentz function and two Gaussians is proposed. By the examples of spectra of supersaturated disordered solid solutions Fe100–xGex (x = 10—25 at.%) and Fe75Si15Al10, it is shown that the algorithm allows more correct processing, which provides a reliable distribution function of the hyperfine magnetic field. It is shown that to take into account the statistical ensemble of nonequivalent local atomic configurations of Fe atoms in disordered supersaturated solid solutions, it is necessary to use not only the convolution of two Gaussian functions, but also the projection scaling factor of the hyperfine magnetic field onto the velocity scale.

The analysis of the dynamics of the electorate system by using q-distribution-a case study

In this work we study the system of the votes, the mechanism of the electoral support formation, and also the elements of its dynamics, by analyzing the data from several election processes in Albania. Firstly, we evidence the specific features and the characteristics of the distributions of votes through a descriptive approach, and next we use those findings to identify the nature of the elementary processes of the agreement, the defects of the system and dynamical issues. The distributions of the votes for the majority or majority-like election as by polling stations reference results a two-parts function. The part of the distribution located in the small vote fraction fits to a power law or to a q-exponential function, therefore the foremost factor of the electoral support for the subjects populating this zone is based in the preferential attachment rule, with some modification. Consequently, the small subjects or independent candidates, realize their electoral attractiveness based on the individual performance. Also, their voters act rationally and usually gather sufficient information before deciding to support them. The bell-shaped part of the distribution which describes the votes of the candidates of the main parties, fits better to the q-gaussian functions. In this case, electoral support is affected strongly by the political activists (militants) which harvest local influences to convict people producing an extra support for the candidates of big parties, regardless of their performance and electoral values. This physiognomy is characteristic for all legislative and administrative majority voting or other majority-like elections as practically behave the closed-lists elections of 2009, 2013, 2017 and also the semi-opened list of the 2021. The distributions of the closed-list votes in the administrative elections are mostly of the exponential or q-exponential type. Also, the distributions based on the data from electoral constituencies which include many polling stations resulted q-exponentials for all types of elections. We connected the q-exponential form of the distribution with the electoral network failures, system deficiencies and heterogeneity effects. In 2021, the distributions of the votes for subjects is obtained similar to the typical recent majority voting distribution, a mix of the power law and q-gaussian functions. The distribution of the votes for the candidates on the semi-open list for those elections resulted a mix of two q-exponentials. We associated this last with the difficulties of the voters to understand new electoral rules and additional other causes of the non-electoral nature. Also, the electorate network might have suffered extra irregularity issues due to the inadequate sizes of elections units, etc. The distributions of the votes for the two main parties are found q-gaussians with q ∼ 1.32 and q ∼ 1.57 for the right and the left wing respectively. Based on the non-stationarity level measured by the q-value, significant redistribution events are expected for the left-wing network, whereas the right-wing network would experience fewer changes in ceteris paribus socio-electoral conditions. Interestingly, the mix of the votes for two main political parties has produced a q-gaussian with q=1.004, and subsequently, the joint system is found in a more relaxed state. Therefore, the compound network including two main parties is likely to not undergo significant redistribution of the votes in the near future. This means that the small subjects or the fresh-born ones are not likely to cause changes on the system. Based on the deductions for electoral agreement formation, we used our recently introduced q-opinion approach to model the electoral opinion formation. In this model, the q-opinion produces an additional term that multiplies the modified preferential attachment probability for the link establishment. Herein, the q-parameter is calculated by using an ad-hoc formula involving the performance of the candidate as utility function, which associates the agreement behavior as the response, with the candidate performance as the offer or the cause factor. The quantity q henceforth acts as activation-inhibition switch of the extra utility involved in the q-opinion model, and particularly it provides a nonzero voter’s support for the high-performance opponent candidates. The model has reproduced the distributions analyzed in this study. It resulted that many voters in this electorate system act rationally, despite their affiliations.

Matter Waves in the Talbot-Lau Interferometry

Particle paths, emitted from distributed sources and passing out through slits of two gratings, G0 and G1, up to detectors, have been computed in detail by the path integral method. The particles under consideration are fullerene molecules with a De Broglie wavelength equal to 5 pm. The slits are Gaussian functions that simulate fuzzy edges of the slits. Waves of the matter computed by this method show perfect interference patterns both between the gratings and behind the second grating. Coherent and non-coherent distributed particle sources reproducing the interference patterns are discussed in detail. Paraxial approximation results from removing the distributed sources onto innity. This approximation gives a wave function reproducing an exact copy of the Talbot carpet. PACS numbers: 03.75.-b, 03.75.Dg, 42.25.Hz

On Tribonacci Functions and Gaussian Tribonacci Functions

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

The Array Optimization of Vertical Axis Wind Turbine Based on a New Asymmetric Wake Model

With the increasing demand for wind energy, the vertical axis wind turbine (VAWT) is attracting more and more attention. In order to design the VAWT array for better performance, the VAWT wake model needs to reflect the wake characteristics well. Based on the asymmetric wake characteristic, a new VAWT wake model is proposed in this paper, which is a combination of two semi Gaussian functions with different deviations, and can be called the “double semi Gaussian functions wake model”. The model is simple and has only four parameters (mean, amplitude, left deviation and right deviation). Compared with the traditional Gaussian and Top-hat model, this model can better reflect the asymmetric characteristic of the VAWT wake. In particular, it can describe the behavior of wake merging in the case of counter-rotating twin turbines. Based on this wake model, the velocity field of VAWT array can be reproduced accurately. The goal function is mainly based on the performance of a basic array unit, and it can ensure the rapidity of the optimization process. The optimal arrangements under two different criteria are analyzed. Moreover, the truncation ratio is introduced to ensure that the downstream turbine works at the rated condition, and the optimal arrangements under different truncation ratios are analyzed. In this paper, the proposed wake model provides a good choice for the preliminary design of the VAWT array, and some relevant suggestions on the array arrangement have been put forward.

Statistics on Jupiter's Current Sheet with Juno Data: Geometry, Magnetic Fields and Energetic Particles

<p>Jupiter's magnetosphere contains a current sheet of huge size near its equator. The current sheet not only mediates the global mass and energy cycles of Jupiter's magnetosphere, but also provides an occurring place for many localized dynamic processes, such as reconnection and wave-particle interaction. To correctly evaluate its role in these processes, a statistical description of the current sheet is required. To this end, here we conduct statistics on Jupiter's current sheet, with four-year Juno data recorded in the 20-100 Jupiter radii, post-midnight magnetosphere. The results suggest a thin current sheet whose thickness is comparable with the gyro-radius of dominant ions. Magnetic fields in the current sheet decrease in power-law with increasing radial distances. At fixed energy, the flux of electrons and protons increases with decreasing radial distances. On the other hand, at fixed radial distances, the flux decreases in power-law with increasing energy. The flux also varies with the distances to the current sheet center. The corresponding relationship can be well described by Gaussian functions peaking at the current sheet center. In addition, the statistics show the flux of oxygen- and sulfur-group ions is comparable with the flux of protons at the same energy and radial distances, indicating the non-negligible effects of heavy ions on current sheet dynamics. From these results, a statistical model of Jupiter's current sheet is constructed, which provides us with a start point of understanding the dynamics of the whole Jupiter's magnetosphere.</p>

Gaussian Parameters Correlate with the Spread of COVID-19 Pandemic: The Italian Case

Until today, numerous models have been formulated to predict the spreading of Covid-19. Among them, the actively discussed susceptible-infected-removed (SIR) model is one of the most reliable. Unfortunately, many factors (i.e., social behaviors) can influence the outcomes as well as the occurrence of multiple contributions corresponding to multiple waves. Therefore, for a reliable evaluation of the conversion rates, data need to be continuously updated and analyzed. In this work, we propose a model using Gaussian functions, coming from the solution of an ordinary differential equation representing a logistic model, able to describe the growth rate of infected, deceased and recovered people in Italy. We correlate the Gaussian parameters with the number of people affected by COVID-19 as a function of the large-scale anti-contagion control measures strength, and also of vaccines effects adopted to reach herd immunity. The superposition of gaussian curves allow modeling the growth rate of the total cases, deceased and recovered people and reproducing the corresponding cumulative distribution and probability density functions. Moreover, we try to predict a time interval in which all people will be infected or vaccinated (with at least one dose) and/or the time end of pandemic in Italy when all people have been infected or vaccinated with two doses.