Density-dependent Model Research Articles

Systematic study of [formula omitted]-decay in neutron-deficient nuclei

The α-decay half-lives of 266 neutron-deficient nuclei in the 52 ≤Z≤ 118 range are calculated within the density-dependent cluster model. The realistic Michigan three-range Yukawa-Paris nucleon–nucleon interaction is used to calculate the α-core interaction potential within the double-folding model (DFM) context. In addition to the double-folding model, four analytical formulas are employed to compute the half-life time for the neutron-deficient nuclei. The obtained results from the five theoretical approaches are compared to the most recent experimental data. The calculated results from the DFM and the universal decay law (UDL) were in good agreement with the experimental data. A universal curve for α-decay of neutron-deficient nuclei has been analyzed, illustrating the correlation between the decimal logarithm of the experimental half-lives and the negative decimal logarithm of penetrability. We studied the variation of log10T with the neutron number of the daughter nuclei, Nd, for different neutron-deficient isotopes in the range 78 ≤Z≤ 92. We attempt to predict the neutron energy levels for each isotope from the behavior of log10T against Nd. Moreover, the impact of higher-multipolarity deformations, up to hexacontratetrapole, on the behavior of α-decay half-lives around the neutron shell closure N=126 is investigated, both with and without including octupole deformation.

Revisiting Fishery Sustainability Targets

Density-dependent population dynamic models strongly influence many of the world’s most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40–50 percent of carrying capacity to maximize sustainable harvest, no matter the species’ population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69–81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.

Structural and decay properties of even–even trans-lead nuclei

A systematic study of the ground-state properties of even–even Po, Rn, Ra and Th isotopes is conducted using the self-consistent Skyrme-Hartree–Fock–Bogoliubov (HFB) theory. Different Skyrme interactions are employed in the study. The bulk properties such as binding energy, two-neutron separation energies, two-proton separation energies and neutron skin thickness are investigated. The obtained results from the Skyrme-HFB formalism are compared with the calculated results from the Finite Range Droplet Model (FRDM) and the available experimental data. Our theoretical values were found to be consistent with their counterparts. In addition, the density-dependent cluster model is utilized to estimate [Formula: see text]-decay half-lives. A good agreement is achieved between the calculated results and the recent experimental data.

Strange Quark Stars: The Role of Excluded Volume Effects

We study cold strange quark stars employing an enhanced version of the quark-mass density-dependent model, which incorporates excluded volume effects to address non-perturbative QCD repulsive interactions. We provide a comparative analysis of our mass formula parametrization with previous models from the literature. We identify the regions within the parameter space where three-flavor quark matter is more stable than the most tightly bound atomic nucleus (stability window). Specifically, we show that excluded volume effects do not change the Gibbs free energy per baryon at zero pressure, rendering the stability window unaffected. The curves of pressure versus energy density exhibit various shapes—convex upward, concave downward, or nearly linear—depending on the mass parametrization. This behavior results in different patterns of increase, decrease, or constancy in the speed of sound as a function of baryon number density. We analyze the mass–radius relationship of strange quark stars, revealing a significant increase in maximum gravitational mass and a shift in the curves toward larger radii as the excluded volume effect intensifies. Excluded volume effects render our models compatible with all modern astrophysical constraints, including the properties of the recently observed low-mass compact object HESSJ1731.

Density dependent constitutive model for Bi-2212 powder compression deformation

Bi-2212 HTS materials are fabricated into multi-filamentary wires via powder-in-tube (PIT) method followed by proper heat treatment to obtain superconductivity, but how to predict the large compression deformation behaviors of the Bi-2212 powder is critical to design the processing of the Bi-2212 HTS wire. Drucker Prager/Cap (DPC) model was the most commonly used model for powders including Bi-2212 with soil-like mechanical behavior to consider its shear failure as well as hydrostatic compression. However, the parameters for DPC Cap evolve with densities change and the original model is inadequate to precisely describe the densification process of Bi-2212 powder with large strain. In this study, the modified DPC model with density dependent parameters was introduced for Bi-2212 powder compressions by measuring the failure strength and hydrostatic compressive behavior under different density states. The DPC yield surface was plotted with an evolution trend of non-linear outward expansion with density increased. FEM model of uniaxial compression based on the as-introduced model was built with subroutine VUSDFLD applied. The distribution of Mises stress and relative density were analyzed. The axial stress-density curve for FEM and experimental results were normalized and quantitively evaluated by Mean Square Error (MSE). The introduced model shows good convergence and could match the experimental results well with normalized MSE of 0.000207 and Root Mean Square Error (RMSE) of 0.0144, indicating the mean error percentage of 1.44%. The model introduced in this article provides supports toward large strain deformation simulation of Bi-2212 powder.

Proto-strange quark stars from density-dependent quark mass model

In this paper, we investigate the evolution of strange quark stars (SQS) from birth as proto-strange quark stars to maturity as stable SQSs at a zero temperature. We assume that self-bound free quarks form entirely the compact star and study its evolution through a series of snapshots using a density-dependent quark mass model. We consider β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-equilibrated stellar matter at two major stages of the star’s evolution: neutrino trapped regime and neutrino transparent regime during the deleptonization and cooling processes of the star. We fix the entropy density per baryon and the lepton fraction to investigate the nuclear equation of state (EoS), particle distribution, temperature profile inside the star, sound velocity, polytropic index, and the structure of the star. Our results show that stars with higher neutrino concentrations are slightly more massive than the neutrino-poor ones along the evolution lines of the SQS. We obtain EoSs in agreement with the conformal boundary set through sound velocity, and also the 2 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\\odot $$\\end{document} mass constraint for NSs was satisfied at all stages of the star’s evolution.

Radial oscillations of hybrid stars and neutron stars including delta baryons: the effect of a slow quark phase transition

We study radial oscillations of hybrid neutron stars composed of hadronic external layers followed by a quark matter core. We employ a density-dependent relativistic mean-field model including hyperons and Δ baryons to describe hadronic matter, and a density-dependent quark model for quark matter. We obtain the ten lowest eigenfrequencies and the corresponding oscillation functions of N, N+Δ, N+H, and N+H+Δ equations-of-state with a phase transition to the quark matter at 1.4 and 1.8 M ⊙, focusing on the effects of a slow phase transition at the hadron-quark interface. We observe that the maximum mass is reached before the fundamental mode's frequency vanishes for slow phase transitions, suggesting that some stellar configurations with higher central densities than the maximum mass remain stable even when they undergo small radial perturbations. Future gravitational wave detectors and multi-messenger astronomy, complemented by robust microscopic models enabling exploration of various neutron star compositions, including hyperon content, are anticipated to impose precise limitations on the equation of state of baryonic matter under high-density conditions.

Caterpillar movement mediates spatially local interactions and determines the relationship between population density and contact.

While interactions in nature are inherently local, ecological models often assume homogeneity across space, allowing for generalization across systems and greater mathematical tractability. Density-dependent disease models are a prominent example of models that assume homogeneous interactions, leading to the prediction that disease transmission will scale linearly with population density. In this study, we examined how the scale of larval butterfly movement interacts with the resource landscape to influence the relationship between larval contact and population density in the Baltimore checkerspot (Euphydryas phaeton). Our study was inspired by the recent discovery of a viral pathogen that is transmitted horizontally among Baltimore checkerspot larvae. We used multi-year larvae location data across six Baltimore checkerspot populations in the eastern U.S. to test whether larval nests are spatially clustered. We then integrated these spatial data with larval movement data in different resource contexts to investigate whether heterogeneity in spatially local interactions alters the assumed linear relationship between larval nest density and contact. We used Correlated Random Walk (CRW) models and field observations of larval movement behavior to construct Probability Distribution Functions (PDFs) of larval dispersal, and calculated the overlap in these PDFs to estimate conspecific contact within each population. We found that all populations exhibited significant spatial clustering in their habitat use. Subsequent larval movement rates were influenced by encounters with host plants and larval age, and under many movement scenarios, the scale of predicted larval movement was not sufficient to allow for the "homogeneous mixing" assumed in density dependent disease models. Therefore, relationships between population density and larval contact were typically non-linear. We also found that observed use of available habitat patches led to significantly greater contact than would occur if habitat use were spatially random. These findings strongly suggest that incorporating larval movement and spatial variation in larval interactions is critical to modeling disease outcomes in E. phaeton. Epidemiological models that assume a linear relationship between population density and larval contact have the potential to underestimate transmission rates, especially in small populations that are already vulnerable to extinction.

Quark star matter in the color-flavor-locked state with a density-dependent quark mass model

The properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter are investigated in quark stars (QSs) at zero temperature case within confined-isospin-density-dependent-mass (CIDDM) model. The mass–radius relation of QSs are also studied by considering newly proposed mass–radius constraints in CFL phase. Our results indicate that we can obtain more stable and stiffer equation of state (EOS) by considering CFL phase within CIDDM model at zero temperature. While the GW190814's secondary component with a mass around 2.6 M ⊙ cannot be QSs within CIDDM model in SQM case, it can be well described as QSs by considering CFL phase within CIDDM model in this work. In particular, we further construct a density-dependent pairing energy gap to connect the EOS of SQM and CFL quark matter with constant pairing energy gap Δ, and the results indicate that by extending the paring energy gap to include density dependence, the mass–radius lines within CIDDM model can satisfy most of the mass–radius region constraints in recent pulsar observations.

Understanding How Parasites from Farmed Fish May Influence Wild Fish Declines Using Epidemiological Modelling

Beside various fields of its applications, in this study epidemiological modelling was used to understand how parasites from farmed fish may cause wild fish declines. Two separate strategic models were constructed addressing the transmission of micro-parasites and macro-parasites between farmed and wild fish: A SIR (Susceptible-Infective-Removed) model for micro-parasite infections and a compartmental density-dependent model for macro-parasite infestations. The results indicated that parasites originated in wild fish populations, after infecting farmed fish can cause epizootics. Subsequently, these parasites can be transmitted from farmed to wild fish and might have negative impact on the dynamics of wild fish populations. Sensitivity analysis of the basic model parameters in both models showed that model parameters, which are influenced by abiotic factors and allow passive manipulation, such as pathogen specific transmission rate (β), pathogen specific transmission rate between infected farmed and susceptible wild fish (δ), the rate of production of infective stages by an adult parasite (λ) and transmission rate between host and parasite infective stages (β) are more sensitive compared to model parameters which encompass chemical control and fallowing. This emphasizes the importance of the preventive medicine rather than intervention procedures in aquaculture aiming at eradicating epizootics caused by parasites and protecting wild fish stocks.

Excluded volume effects in the quark-mass density-dependent model: Implications for the equation of state and compact star structure

Excluded volume effects in the quark-mass density-dependent model: Implications for the equation of state and compact star structure

Weak evidence of density dependent population regulation when using the ability of two simple density dependent models to predict population size

The relative importance of density dependence regulation in natural population fluctuations has long been debated. The concept of density dependence implies that current abundance is determined by historical abundance. We have developed four models—two density dependent and two density independent—to predict population size one year beyond the training set and used predictive performance on more than 16,000 populations from 14 datasets to compare the understanding captured by those models. For 4 of 14 datasets the density dependent models make better predictions (i.e., density dependent regulated) than either of the density independent models. However, neither of the density dependent models is statistically significantly superior to density independent models for any of the 14 datasets. We conclude that the evidence for widespread density dependent population regulation in the forms represented by these two simple density-dependent models is weak. However, the density dependent models used here—the Logistic and Gompertz models—are simple representations of how population density might regulate natural populations and only examine density-dependent effects on population size. A comprehensive assessment of the relative importance of density-dependent population regulation will require testing the predictive ability of a wider range of density-dependent models including models examining effects on population characteristics other than population size.

Finite element solution of crack-tip fields for an elastic porous solid with density-dependent material moduli and preferential stiffness

In this paper, the finite element solutions of crack-tip fields for an elastic porous solid with density-dependent material moduli are presented. Unlike the classical linearized case in which material parameters are globally constant under a small strain regime, the stiffness of the model presented in this paper can depend upon the density with a modeling parameter. The proposed constitutive relationship appears linear in the Cauchy stress and linearized strain independently. From a subclass of the implicit constitutive relation, the governing equation is bestowed via the balance of linear momentum, resulting in a quasi-linear partial differential equation (PDE) system. Using the classical damped Newton’s method, the sequence of linear problems is then obtained, and the linear PDEs are discretized through a bilinear continuous Galerkin-type finite element method. We perform a series of numerical simulations for material bodies with a single edge-crack subject to a variety of loading types (i.e. the pure mode-I, II, and mixed-mode). Numerical solutions demonstrate that the modeling parameter in our proposed model can control preferential mechanical stiffness with its sign and magnitude along with the change of volumetric strain. This study can provide a mathematical and computational foundation to further model the quasi-static and dynamic evolution of cracks, utilizing the density-dependent moduli model and its modeling framework.

Global boundedness of a density-dependent SIRS epidemic model with nonlinear infection mechanism

Global boundedness of a density-dependent SIRS epidemic model with nonlinear infection mechanism

Microstructure Based Flow Stress Modelling of Superalloy 718

In order to get the insights about microstructural changes that occurs under the thermo-mechanical processing conditions, the physics based modelling approach is very useful. Therefore, the flow curves of alloy 718 are theoretical simulated using a dislocation density dependent constitutive model for different conditions. Presented model considers the microstructural ingredients that are immobile dislocation density, effective grain size and dislocation cell size as the variables to address the creep. The simulated flow curves show a good agreement with the experimental flow curves. The magnitude of immobile dislocation density and dislocation cell size in between 3.87× 1014 - 3.87× 1014­ m-2 and 8.29-8.45 μm, respectively, at the completion of the simulation. Furthermore, this approach also provides the possibility to quantify and depict the variation in each strengthening contributions.

Constraints on density dependent MIT bag model parameters for quark and hybrid stars

We compute the equation of state (EoS) of strange quark stars (SQSs) with the MIT Bag model using density dependent bag pressure, characterized by a Gaussian distribution function. The bag pressure's density dependence is controlled by three key parameters namely the asymptotic value (Bas), ΔB(=B0−Bas), and β. We explore various parameter combinations (Bas, ΔB, β) that adhere to the Bodmer-Witten conjecture, a criterion for the stability of SQSs. Our primary aim is to analyze the effects of these parameter variations on the structural properties of SQSs. However we find that none of the combinations can satisfy the NICER data for PSR J0030+0451 and the constraint on tidal deformability from GW170817. So it can be emphasized that this model cannot describe reasonable SQS configurations. We also extend our work to calculate structural properties of hybrid stars (HSs). With the density dependent bag model (DDBM), these astrophysical constraints are fulfilled by the HSs configurations within a very restricted range of the three parameters. The present work is the first to constrain the parameters of DDBM for both SQS and HSs using the recent astrophysical constraints on tidal deformability from GW170817 and that on mass-radius relationship from NICER data.

Theoretical predictions on cluster radioactivity of superheavy nuclei with Z = 119, 120* *Supported by the National Natural Science Foundation of China (12035011, 11975167, 11947211, 11905103, 11881240623, 11961141003), and by the National Key R&D Program of China (2018YFA0404403)

In this study, we investigate the cluster radioactivity (CR) of new superheavy elements with and 120 based on two successful theoretical methods with modified parameters: the density-dependent cluster model (DDCM) and unified decay formula (UDF). First, we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions, which demonstrates the high reliability of our theoretical methods. Then, we systematically predict the probable cluster modes of 293-311119 and 293-302120 as well as their corresponding decay energies and half-lives. The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF. Therefore, our results reveal that the cluster emission of 8Be, emitted from the 119 and 120 isotopic chains, exhibits the minimum half-life for cluster emission, and hence, 8Be emission is considered the most probable cluster decay mode. Moreover, we explore the competition between α decay and CR and find that α decay may be the dominant decay mode against CR. Furthermore, the good linear relationship between the decay energy and the number of α particles within the emitted cluster is extended to the range of superheavy nuclei (SHN). We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.

Global Asymptotic Stability Analysis of Fixed Points for a Density-Dependent Single-Species Population Growth Model

In a density-dependent single-species population growth model, a simple method is proposed to explicitly and directly derive the analytic expressions of reliable regions for local and global asymptotic stability. Specifically, first, a reliable region ΛLAS is explicitly represented by solving the fixed point and utilizing the asymptotic stability criterion, over which the fixed point is locally asymptotically stable. Then, two types of auxiliary Liapunov functions are constructed, where the variation of the Liapunov function is decomposed into the product of two functions and is always negative at the non-equilibrium state. Finally, based on the Liapunov stability theorem, a closed-form expression of reliable region ΛGAS is obtained, where the fixed point is globally asymptotically stable in the sense that all the solutions tend to fixed point. Numerical results show that our analytic expressions of reliable regions are accurate for both local and global asymptotic stability.

Economically optimised target state of uneven-aged forest management for main forest types in Slovakia

Abstract The study presented a bioeconomic modelling approach for an uneven-aged mixed forest management planning. Regression models for transition (increment), and ingrowth (regeneration) used the National Forest Inventory (NFI) of Slovakia and regional inventory data. Mortality was based on salvage logging records. Models were specific for five tree species within three forest types (FT) (oak with hornbeam and beech, beech, mixed fir-beech-spruce). Net timber prices were calculated with regard to stem quality. Tree growth depended on crown characteristics. The regression models were adjusted to three main geobiotope (GBT) sites per FT. Forest growth was simulated with the density-dependent stand-level matrix transition model. Financial optimisation of harvest was sensitive to an interest rate. Long-time optimisation stabilised in a steady state equilibrium characterised by a stable diameter distribution. Target diameters were specific for site and tree species, and were highest for fir, a dense crown, a good stem quality, and a lower interest rate. Standing timber volume varied from 150 m3 ha–1 (oak forests, 2% interest rate) to 400 m3 ha–1 (beech and fir-beech-spruce forests, 0.5% interest rate). Harvested volume varied from 38 to 93 m3 ha–1 per 10 years, stand basal area (ba) varied from 19 to 36 m2 ha–1 depending on the site, timber price, and interest rate. The discussion pointed out that the relative low volume of the oak FT resulted from the light-demanding characteristics of oak. The mean of oak mosaic structures was lower compared to the high level of more storeys present in the single tree selection structures in beech and mixed fir-beech-spruce forests.

Semi-microscopic optical-model with channel coupling analysis to describe neutron-nucleus scattering of light and heavy nuclei

Many studies utilizing various potential models have been conducted on the scattering of nucleons from nuclei. In our study, we added channel coupling to a semi-microscopic optical model. With incident energies between 10 and 30 MeV, we sought to compare the predicted reaction observables for the neutron scattering of the following nuclei: 12C, 16O, 54Fe, 58Ni, 120Sn, and 208Pb. We did this twice, once using the density-dependent M3Y-Reid nucleon-nucleon effective bare interaction and once using the density-independent M3Y-Reid effective bare interaction. The remaining terms of the optical potential model take the form of Woods-Saxon and its derivatives, and the real volume term is obtained by folding the NN effective bare potential over the density of the nuclear target using the density-dependent M3Y-Reid NN effective bare interaction and density-independent M3Y-Reid NN effective bare interaction. To investigate how the potential characteristics depend on energy, the ground state is connected to a select few low-lying collective excited states. The density-dependent M3Y-Reid NN effective bare interaction-based semi-microscopic model reproduces the reaction features and forecasts the experimental total cross sections. The parameters of potential depth exhibit a linear energy dependence. We contrast the outcomes of the M3Y-Reid density-dependent model with those attained using the M3Y-Reid nucleon-nucleon effective bare interaction, which is density-independent. The M3Y Reid density-dependent model performs well when the two models are compared.