Density Distribution Function Research Articles

Mathematical and Statistical Model for Assessing the Impact of COVID-19 Waves on the Regional System (on the Example of the Kirov Region)

Since the f rst outbreak in China and the spread of COVID-19 in dif erent countries of the world, the study of mathematical models of the spread of the epidemic has begun and is intensively continuing. Such models are dynamic and of en based on dif erential or dif erence equations. As a rule, these models require an identif cation procedure to determine unknown parameters. But for a number of reasons, unambiguous identif cation of such parameters cannot be performed. For example, the preparation of statistical data for the identif cation procedure may be performed in various ways. T erefore, the preferred method of data preprocessing is to approximate them with the most appropriate functional dependence.T e study shows that epidemic curves may be represented by a superposition of several local waves — an outbreak of an epidemic in a particular region consists of many local waves and some of them may merge into one common wave. In this article, it is proposed to use analogs of the normal distribution density function to predict waves of new COVID-19 cases. T e purpose of the article was to develop a model of the dynamics of the total number of cases and new cases of COVID-19, taking into account the waves of the epidemic and the impact on the regional socioeconomic system.T e study was conducted on the basis of data on the incidence of COVID-19 in the Kirov region4 in 2020—2022. It is shown that the chosen model describes statistical data well and allows making realistic forecasts for the total number of diseases and new cases of diseases. T e results of the study may be used to develop preventive measures to prevent the spread of the disease and allow assessing the impact of the epidemiological situation on the socio-economic system of the region.

The Effect of Ethanol on Lipid Nanoparticle Stabilization from a Molecular Dynamics Simulation Perspective.

Lipid nanoparticles (LNPs) have emerged as a promising delivery system, particularly for genetic therapies and vaccines. LNP formation requires a specific mixture of nucleic acid in a buffered solution and lipid components in ethanol. Ethanol acts as a lipid solvent, aiding the formation of the nanoparticle's core, but its presence can also affect LNP stability. In this study, we used molecular dynamics (MD) simulations to investigate the physicochemical effect of ethanol on LNPs and gain a dynamic understanding of its impact on the overall structure and stability of LNPs. Our results demonstrate that ethanol destabilizes LNP structure over time, indicated by increased root mean square deviation (RMSD) values. Changes in the solvent-accessible surface area (SASA), electron density, and radial distribution function (RDF) also suggest that ethanol affects LNP stability. Furthermore, our H-bond profile analysis shows that ethanol penetrates the LNP earlier than water. These findings emphasize the importance of immediate ethanol removal in lipid-based systems during LNP production to ensure stability.

Effect of SARA fractions on the physical, structural and dynamic properties of bitumen using molecular dynamics simulation

The utilization of molecular dynamics simulation on bituminous materials usually adopts three classical bitumen models (AAA-1, AAK-1, AAM-1). However, the chemical compositions of bitumen, namely SARA fractions, vary significantly in reality, depending on the source of bitumen. In this regard, this study investigated the influence of SARA fractions on the simulated properties of bitumen. To this end, 21 bitumen models with different SARA fractions collected from the literature were established. The radial distribution function (RDF), density, and self-diffusion coefficient (SDC) were derived to characterize the structural, physical, and dynamic properties, respectively. Results indicated that the SARA fractions would not significantly influence the density and radial distribution function of bitumen models. However, the influence of heavy components on the equilibrium of dynamic sampling was pronounced. In the MSD analysis, the temperature variation contributed little to the self-diffusion capability of bitumen when the asphaltene index was close to one. The correlation between SDC and asphaltene index varied depending on the value of the asphaltene index. Specifically, the correlation was positive when the asphaltene index was larger than one, and negative when it was smaller than one.

Effects of root systems on crack formation: experiments, modeling, and analyses

Plant roots can increase soil shearing resistance directly by mechanical reinforcing. The 2D crack pattern of the surface soil near the plant were observed experimentally, and it was found that the soil cracking near the plant roots was inhibited, which may be due to the influence of the plant roots. This paper focuses on the mechanical reinforcement of soil by plant roots and investigates the development rule and formation mechanism of desiccation cracking under the influence of plant roots. A numerical model describing the process of desiccation cracking of soils in the presence of root systems, which is based on a lattice of Hooke springs model, was combined with a non-stationary random field characterized by a trend term and a random fluctuation term. The root density distribution function was introduced to describe the root distribution, and an exponential function of critical strain and root density was constructed to obtain the trend of critical strain distribution of the root systems (the root systems of a single plant). The random fluctuation term was generated by the conditional simulation technique. Minkowski densities (i.e., area density, length density and Euler number density) were adopted to quantify the crack patterns. Parameters of the model were calibrated and verified by the field experimental results, and its precision was evaluated. The effect of most input parameters (include the new parameters maximum critical strain value hc and the lateral distribution radius of RDDF rm) on the model output was analyzed. The results show that in the validation process the coefficients of determination R2 for the Minkowski densities is between 0.749 and 0.948. Root mean square error is between 0.000 2–0.120 9. BIAS is between 0.049 5–0.139 0, and the consistency index is between 0.908 and 0.987. The model is effective in predicting the formation and development of cracks in farmland soils under the influence of the root systems. The model produces the dynamic development of the desiccation cracking network of farmland soils under the influence of the root systems. The simulation results provide ample indication of the reinforcing effect of the root systems on the soil and the limiting effect of the root systems on desiccation cracking.

Response prediction and fatigue life estimation of thin-walled structures under random excitation using the modified equivalent linearization method

This paper proposes a fast estimation method for the high-cycle fatigue of geometrically nonlinear thin-walled structures under random loading. The core idea of this method is utilizing a modified equivalent linearization method to obtain the statistical properties of the modal displacement response of the thin-walled structures, which is used to generate samples and then transform them into stress samples to determine the peak probability density function of the von Mises stress for fatigue life estimation. There are three critical issues addressed in implementing the method: (1) Using the implicit condensation technique to introduce the membrane softening effect in the regulated equivalent linearization method to improve the computational accuracy of the displacement statistical properties and convert the higher order moments into easily computable second order moments by separating the displacement mean values, so the regulated equations of motion for non-zero mean systems are derived, and fix the problem that the regulated equivalent linearization method does not apply to the prediction of the dynamic response of general thin-walled structures. (2) A nonlinear relationship between modal displacement and stress is derived with the implicit condensation and expansion method to transform the generated displacement samples to stress samples, which are used to determine probability density functions of stress and their derivatives. (3) Simplifying the probability density function of the three-dimensional joint distribution to the probability density function of the two-dimensional joint distribution by taking advantage of the Bayes rule, thus deriving a fast formula for the probability density function of the peak Mises stress.

Role of ionizing background on the statistics of metal absorbers in hydrodynamical simulations

ABSTRACT We study the statistical properties of O vi, C iv, and Ne viii absorbers at low-z (i.e. z < 0.5) using Sherwood simulations with ‘WIND’ only and ‘WIND + AGN’ feedback and massive black-II simulation that incorporates both ‘WIND’ i.e. outflows driven by stellar feedback and active galactic nucleus (AGN) feedbacks. For each simulation, by considering a wide range of metagalactic ionizing ultraviolet background (UVB), we show the statistical properties such as distribution functions of column density (N), b-parameter and velocity spread (ΔV90), the relationship between N and b-parameter, and the fraction of Ly α absorbers showing detectable metal lines as a function of N(H i) are influenced by the UVB used. This is because UVB changes the range in density, temperature, and metallicity of gas contributing to a given absorption line. For simulations considered here, we show the difference in some of the predicted distributions between different simulations is similar to the one obtained by varying the UVB for a given simulation. Most of the observed properties of O vi absorbers are roughly matched by Sherwood simulation with ‘WIND + AGN’ feedback when using the UVB with a lower O vi ionization rate. However, this simulation fails to produce observed distributions of C iv and fraction of H i absorbers with detectable metals. Therefore, in order to constrain different feedback processes and/or UVBs, using observed properties of H i and metal ions, it is important to perform simultaneous analysis of various observable parameters.

Observed dust surface density across cosmic times

ABSTRACT Our ability to interpret observations of galaxies and trace their stellar, gas, and dust content over cosmic time critically relies on our understanding of how the dust abundance and properties vary with environment. Here, we compute the dust surface density across cosmic times to put novel constraints on simulations of the build-up of dust. We provide observational estimates of the dust surface density consistently measured through depletion methods across a wide range of environments, going from the Milky Way up to z = 5.5 galaxies. These conservative measurements provide complementary estimates to extinction-based observations. In addition, we introduce the dust surface density distribution function – in analogy with the cold gas column density distribution functions. We fit a power law of the form log f(ΣDust) = −1.92 × log ΣDust − 3.65, which proves slightly steeper than that for neutral gas and metal absorbers. This observed relation, which can be computed by simulations predicting resolved dust mass functions through 2D projection, provides new constraints on modern dust models.

Dispersion‐type Anisotropic Viscoelasticity: Model Validation for Myocardium

AbstractThis contribution presents a novel constitutive model for rate‐dependent response of the passive myocardium. As a first step, we performed a comparative study on dispersion‐type anisotropic hyperelastic constitutive models [1–3] and assessed performance of various density distribution functions by fitting to experiments conducted on three distinct tissues [4]. Next, we proposed an angular integration type anisotropic viscoelastic constitutive model that uses bivariate von‐Mises distribution function to capture fiber dispersion in passive myocardium. The baseline hyperelasticity is described by a generalized structure tensor formulation proposed by GASSER ET AL. [1]. The non‐equilibrium part of the model utilizes a quadratic free energy function in the logarithmic strain space and a power‐type nonlinear evolution equation in orientation directions. The overstress response is then obtained by the numerical integration over the unit sphere by making use of 21 quadrature points. The proposed model parameters are obtained from cyclic triaxial shear and triaxial shear relaxation experiments on human passive myocardium [5].

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

The current research offers an enhanced three-parameter lifetime model that combines the unit Burr XII distribution with a power series distribution. The novel class of distribution is named the unit Burr XII power series (UBXIIPS). This compounding technique allows for the production of flexible distributions with strong physical meanings in domains such as biology and engineering. The UBXIIPS class includes the unit Burr XII Poisson (UBXIIP) distribution, the unit Burr XII binomial distribution, the unit Burr XII geometric distribution, and the unit Burr XII negative binomial distribution. The statistical properties of the class include formulas for the density and cumulative distribution functions, and limiting behaviour, moments and incomplete moments, entropy measures, and quantile function are provided. For estimating population parameters and fuzzy reliability for the UBXIIP model, maximum likelihood and Bayesian approaches are studied by the Metropolis–Hastings algorithm. For maximum likelihood estimators, the length of asymptotic confidence intervals is specified, whereas, for Bayesian estimators, the length of credible confidence intervals is assigned. A simulation investigation of the UBXIIP model was established to evaluate the performance of suggested estimates. In addition, the UBXIIP distribution is explored using real-world data. The UBXIIP distribution appears to offer some benefits in understanding lifetime data when compared to unit Weibull, beta, Kumaraswamy, Kumaraswamy Kumaraswamy, Marshall-Olkin Kumaraswamy, and Topp–Leone Weibull Lomax distributions.

Stationary distribution and probability density function of a stochastic waterborne pathogen model with saturated direct and indirect transmissions

We investigate the dynamical behavior of deterministic and stochastic waterborne pathogen models with saturated incidence rates. In particular, the indirect transmission via person–water–person contact is half‐saturated and the direct transmission by person–person contact takes the saturated form. Possible equilibrium points of the model are investigated, and their stability criterion is discussed. Basic reproduction number of the model is obtained through the next‐generation matrix method. It has been shown that the disease‐free equilibrium is locally stable when and unstable for . Furthermore, a stochastic Lyapunov method is adopted to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the proposed stochastic model, which reveals that the infection will persist if . We also obtain an exact expression of the probability density function near the quasi‐endemic equilibrium of stochastic system. Finally, numerical simulations are carried out to support our analytical findings. Results suggest that saturation constants in both direct and indirect transmissions play a positive role in controlling disease. Our results may provide some new insights for the elimination of waterborne disease.

Influence of the substrate on the density and infrared spectra of the adsorbed methanol ice of different thicknesses using molecular dynamics simulation

ABSTRACT In the interstellar medium, several complex organic molecules are found, and of these molecules, methanol is the simplest and the most ubiquitous one. By comparing the observed infrared (IR) spectra from astrochemical data, with laboratory experiments, one can deduce the composition and structure of these astrochemical ices. Computational studies are scarce, yet they could be greatly helpful in understanding the nature of these molecules. On that premise, the present study reports a molecular dynamics study of adsorbed methanol on the KBr substrate at 90 K and 130 K. After validating the potential parameters, two adsorbed phases differing in their thickness along the z-axis: 4 × 10 × 4 (4 layers) and 4 × 10 × 50 (50 layers) were simulated. Depending on this thickness, the IR spectra and density distribution functions were computed for the bottom and top 10 Å of the 4 layers of adsorbed methanol and the top, middle, and bottom 10 Å of the 50 layers of adsorbed methanol on the KBr substrate. The bottom 10 Å of the adsorbed phase exhibit considerable disorder. Additionally, the bands in the IR spectra of these bottom 10 Å show widening, referring to a heterogeneous environment. It is further reported that the slower heating and cooling of the adsorbed phase between 90 K and 130 K leads to a complete reversal of the changes seen in heating. Our findings here further clarify the recent observation of the amorphous phase of different astrochemical molecules seen at low temperatures and their crystalline phase seen at relatively higher temperatures.

A stochastic predator–prey model with Ornstein–Uhlenbeck process: Characterization of stationary distribution, extinction and probability density function

This paper concerns with a stochastic system modeling the population dynamical behavior of one prey and two predators. In this paper, we adopt a special method to simulate the effect of the environmental interference to the system instead of using the linear functions of white noise, i.e., the growth rate of the prey and the death rates of the two predators are all governed by Ornstein–Uhlenbeck processes, which is more practical and interesting. The dynamical behavior among the three species in the model is discussed in detail. The existence and uniqueness, moment boundedness and long time asymptotic behavior of the unique global solution are investigated. Through rigorous proof and theoretical derivation, some sharp sufficient conditions for the persistence and extinction of the three species have been established. Furthermore, we obtain that when one or two predators die out, the remaining species can be stable in time average under same conditions. Moreover, by constructing some suitable Lyapunov functions, the sufficient conditions for the existence of the stationary distribution are explicitly determined. Under the same parametric restrictions, it is worth noting that we obtain the six-dimensional probability density function of the stochastic one-prey two-predator model around the quasi-equilibrium E∗, which can reflect most statistical properties. Finally, several numerical simulations are carried out to illustrate the theoretical results.

Threshold dynamics of a stochastic single population model with Allee effect

A stochastic single species population model with Allee effect is considered in this paper. By using the theory of Random Dynamical System (RDS), the complete classification of the global dynamics of stochastic system is given. The theoretical results show that the dynamics of the system is completely determined by the threshold λ=2r−σ2: if λ≤0, the population will extinct, i.e., the solutions of the model will go to zero; if λ>0, the population is permanent. Moreover, the transition probabilities of the solutions weakly converge to the unique stationary distribution and the explicit density function of the stationary distribution is given.

Odd Mobility of a Passive Tracer in a Chiral Active Fluid.

Chiral active fluids break both time-reversal and parity symmetry, leading to exotic transport phenomena unobservable in ordinary passive fluids. We develop a generalized Green-Kubo relation for the anomalous lift experienced by a passive tracer suspended in a two-dimensional chiral active fluid subjected to an applied force. This anomalous lift is characterized by a transport coefficient termed the odd mobility. We validate our generalized response theory using molecular dynamics simulations, and we show that the asymmetric tracer mobility may be understood mechanically in terms of asymmetric deformations of the tracer-fluid density distribution function. We show that the even and odd components of the mobility decay at different rates with tracer size, suggesting the possibility of size-based particle separation using a chiral active working fluid.

Multi-patch isogeometric topology optimization for cellular structures with flexible designs using Nitsche’s method

Cellular structures have recently been received a tremendous growth in discussions and applications in the engineering due to their several fascinating structural properties, such as the ultra-lightweight, high stiffness and crashworthiness. However, the discussions on the design of cellular structures in the complex structural domain with the non-conforming mesh are still unavailable, resulting from the fact that the non-conforming mesh causes several difficulties in numerical analysis and design optimization. Hence, the main purpose of the work is to propose a Multi-Patch Isogeometric Topology Optimization (MP-ITO) method with powerful capabilities for periodic or graded cellular structures. Firstly, the Nitsche’s method is applied to couple non-conforming meshes in multiple NURBS patches and conduct multi-patch isogeometric analysis. Secondly, a multi-patch topology description model is developed, in which a local smoothing mechanism and the two-resolution scheme of discretization meshes are constructed to avoid terrible structural features and improve smoothness and continuity of boundaries at the interfaces within adjacent subdomains. The separation and independency of the Density Distribution Function (DDF) at each subdomain can offer high flexibility for cellular designs with the imposing of several kinds of periodic constraints. Thirdly, the MP-ITO method is proposed for complex structures and the mathematical formulation for cellular designs considering periodic constraints is developed. Finally, the effectiveness and indispensability of the local smoothing mechanism and the two-resolution scheme in the MP-ITO are discussed, and several numerical examples are addressed to present the compelling effectiveness and capabilities of the MP-ITO method with the high flexibility on the designs of periodic and graded cellular structures.

Density distribution functions of Constrained-degree percolation model on the square lattice

We study the Constrained-degree percolation model on the square lattice. Through an analysis of this model on finite square lattices of length n we found numerical evidence that the distribution function of the density of open bonds converges, when n→∞, to the normal distribution around the average density.

Quasi-periodic oscillations in the γ-ray light curves of bright active galactic nuclei

Context. The detection of quasi-periodic oscillations (QPOs) in the light curves of active galactic nuclei (AGNs) can provide insights into the physics of the super-massive black holes (SMBHs) powering these systems and could represent a signature of the existence of SMBH binaries, setting fundamental constraints on SMBH evolution in the Universe. Aims. The identification of long-term QPOs, characterized by periods on the order of several months to years, is particularly challenging and can only be achieved via all-sky monitoring instruments that provide unbiased, continuous light curves of astrophysical objects. The Fermi-LAT satellite, thanks to its monitoring observing strategy, is an ideal instrument for such a goal. Here, we aim to identify QPOs in the γ-ray light curves of the brightest AGNs within the Fermi-LAT catalog. Methods. We analyzed the light curves of the 35 brightest Fermi-LAT AGNs, including data from the beginning of the Fermi mission (August 2008) to April 2021, with energies from 100 MeV to 300 GeV. Two time binnings were investigated: 7 and 30 days. The search for quasi-periodic features was then performed using the continuous wavelet transform. The significance of the result was tested via Monte Carlo simulations of artificial light curves with the same power spectral density and probability distribution function as the original light curves. The significances were then corrected for the look-elsewhere effect and provided as post-trials. Results. We identified 24 quasars with candidate QPOs. Several of our candidates coincide with previous claims in the literature, namely: PKS 0537−441, S5 0716+714, Mrk 421, B2 1520+31, and PKS 2247−131. All our candidates are transient. The most significant multi-year QPO, with a period of about 1100 days, was observed in the quasar S5 1044+71. It is reported here for the first time.

An Analytical Theory for the Growth from Planetesimals to Planets by Polydisperse Pebble Accretion

Pebble accretion is recognized as a significant accelerator of planet formation. Yet only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D accretion and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find accretion rates 1–2 orders of magnitude higher compared to monodisperse, also extending the onset of pebble accretion to 1–2 orders of magnitude lower in mass. We find megayear timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses 10−6 to 10−4 M ⊕, over a significant range of the parameter space. This mass range overlaps with the high-mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.

Evaluation and Analysis of Wind Speed with the Weibull and Rayleigh Distribution Models for Energy Potential Using Three Models

Medan has a tropical climate and has the potential to support additional renewable energy, one of which is wind energy. Analysis of wind speed in Medan in particular has not been conducted to determine the potential for renewable energy. Research on wind speed in Medan, which ranges from 3.5m/s to 7.5m/s, has been carried out, but its potential has not been analyzed and evaluated. This study was conducted to analyze the shape factor and scale for wind speed using the Weibull and Rayleigh distribution, and three evaluation models were proposed, namely the correlation coefficient (R2), Chi-Square (ꭓ2), and Root mean square error (RMSE). Wind speed data that is used to analyze and evaluate obtained from the Meteorology, Climatology, and Geophysics Agency for a period of three years, 2017 to 2019 in Medan. The probability density distribution function (Pdf) is described based on the shape (k) and scale (c) parameters obtained from the above data analysis. These two parameters are very important to be observed related to the potential of electrical energy produced in a place or area. The analysis result shows that Weibull is better than Rayleigh distribution based on Pdf. Meanwhile statistical analysis, Weibull distribution is better than Rayleigh distribution based on R2. But on the other hand, the Rayleigh distribution is better than the Weibull distribution based on Chi-Square and RMSE. In addition to the analysis and evaluation, the potential for wind energy to be obtained is around 79.5 Watt/m2.

The atomic-to-molecular hydrogen transition in the TNG50 simulation: Using realistic UV fields to create spatially resolved H i maps

ABSTRACT Cold gas in galaxies provides a crucial test to evaluate the realism of cosmological hydrodynamical simulations. To extract the atomic and molecular hydrogen properties of the simulated galaxy population, post-processing methods taking the local UV field into account are required. We improve upon previous studies by calculating realistic UV fields with the dust radiative transfer code SKIRT to model the atomic-to-molecular transition in TNG50, the highest-resolution run of the IllustrisTNG suite. Comparing integrated quantities such as the H i mass function, we study to what detail the UV field needs to be modelled in order to calculate realistic cold gas properties. We then evaluate new, spatially resolved comparisons for cold gas in galaxies by exploring synthetic maps of atomic hydrogen at redshift zero and compare them to 21-cm observations of local galaxies from the WHISP survey. In terms of non-parametric morphologies, we find that TNG50 H i maps are less concentrated than their WHISP counterparts (median ΔC ≈ 0.3), due in part to central H i deficits related to the ejective character of supermassive black hole feedback in TNG. In terms of the H i column density distribution function, we find discrepancies between WHISP and IllustrisTNG that depend on the total H i abundance in these data sets as well as the post-processing method. To fully exploit the synergy between cosmological simulations and upcoming deep H i/H2 data, we advocate the use of accurate methods to estimate the UV radiation field and to generate mock maps.