Constant Equation Research Articles

Boiling heat transfer by phase-field method

AbstractIn this work, we propose and test the validity of a phase-field method tailored specifically for modeling boiling phenomena. The method relies on numerical solutions of the Navier–Stokes equations coupled with a phase-field method and the energy equation. The continuity and Navier–Stokes equations have been modified introducing a source term that accounts for phase change. Likewise, in the conservative Allen–Cahn equation (phase-field method) a source term that accounts for the volume is introduced. The system of governing equations is solved using a projection-correction method and equations are discretized using a second-order finite difference approach. Thanks to the numerical discretization employed, a constant coefficient Poisson equation for pressure is obtained, which can be efficiently solved using FFT-based direct solvers. The proposed method is validated against several benchmarks: an interface undergoing vaporization at a constant rate, the Stefan problem, the adsorption problem, and the growth of a 2D vapor bubble. For all the benchmarks, the present method well matches with analytical and archival literature results for a wide range of vapor-to-liquid density ratios, from $$\rho _v/\rho _l = 1$$ ρ v / ρ l = 1 down to $$\rho _v/\rho _l \simeq 5 \times 10^{-4}$$ ρ v / ρ l ≃ 5 × 10 - 4 (where $$\rho _v$$ ρ v identifies the vapor density and $$\rho _l$$ ρ l the liquid density).

The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in f(R)CDM and wCDM cosmologies

In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of $f(R)$ gravity models. We also extended e-MANTIS to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state $w$CDM. We used a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than $10000$ $N$-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the HMF for redshifts $ 1.5$ and for halo masses $M_h M_ The typical HMF errors for SO haloes with $ c $ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of the order of $ up to a transition mass $M_t M_ ($M_t M_ For larger masses, the errors are dominated by the shot noise and scale as $ with $ up to $M_h M_ Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the $f(R)$CDM and $w$CDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.

Partially and fully implicit multi-step SAV approaches with original dissipation law for gradient flows

The scalar auxiliary variable (SAV) approach was considered by Shen et al. in Shen et al. (2019) and has been widely used to simulate a series of gradient flows. However, the SAV-based schemes are known for the stability of a ‘modified’ energy. In this paper, we construct a series of modified SAV approaches with unconditional energy dissipation law based on several improvements to the classic SAV approach. Firstly, by introducing the three-step technique, we can reduce the number of constant coefficient linear equations that need to be solved at each time step, while retaining all of its other advantages. Secondly, the addition of energy-optimal technique and Lagrange multiplier technique can make the numerical schemes have the advantage of preserving the original energy dissipation. Thirdly, we use the first-order approximation of the energy balance equation in the GSAV approach, instead of discretizing the dynamic equation of the auxiliary variable, so that we can construct the high-order unconditional original energy stable numerical schemes. Finally, representative numerical examples show that the efficiency and accuracy of the proposed schemes are improved.

Evaluating extensions to LCDM: an application of Bayesian model averaging and selection

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter ΩK, a spectral index ns = 1 and a varying n run, a constant dark energy equation of state (EOS) w 0CDM and a time-dependent one w 0 w aCDM. We also assess cosmological data against a varying effective number of neutrino species N eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results.We reinforce the standard ΛCDM model statistical preference when combining CMB data withCMB lensing, BAO, and Bicep-KECK 2018 data against the K-ΛCDM model anddns /d ln k-ΛCDM with a probability > 80%. Whenevaluating the dark energy EOS, we find that this dataset does not exhibit a strong preferencebetween the standard ΛCDM model and the constant dark energy EOS model w 0CDM,with a model posterior probability distribution of approximately ≈ 40%:60% in favour of w 0CDM, while the time-varying dark energy EOS model only holds below 1%probability. We find a similar result also when considering the N eff-ΛCDM model, with asplit probability almost 50%-50% from both our datasets.Overall, our application of BMA reveals that including model uncertainty in these cases does notsignificantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmologicalmodel evaluation.

The Dark Energy Survey: Cosmology Results with ∼1500 New High-redshift Type Ia Supernovae Using the Full 5 yr Data Set

We present cosmological constraints from the sample of Type Ia supernovae (SNe Ia) discovered and measured during the full 5 yr of the Dark Energy Survey (DES) SN program. In contrast to most previous cosmological samples, in which SNe are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia, we find 1635 DES SNe in the redshift range 0.10 < z < 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-quality z > 0.5 SNe compared to the previous leading compilation of Pantheon+ and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints, we combine the DES SN data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0.025 < z < 0.10. Using SN data alone and including systematic uncertainties, we find ΩM = 0.352 ± 0.017 in flat ΛCDM. SN data alone now require acceleration (q 0 < 0 in ΛCDM) with over 5σ confidence. We find (ΩM,w)=(0.264−0.096+0.074,−0.80−0.16+0.14) in flat wCDM. For flat w 0 w a CDM, we find (ΩM,w0,wa)=(0.495−0.043+0.033,−0.36−0.30+0.36,−8.8−4.5+3.7) , consistent with a constant equation of state to within ∼2σ. Including Planck cosmic microwave background, Sloan Digital Sky Survey baryon acoustic oscillation, and DES 3 × 2pt data gives (ΩM, w) = (0.321 ± 0.007, −0.941 ± 0.026). In all cases, dark energy is consistent with a cosmological constant to within ∼2σ. Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified SN analyses.

Revealing Building Information Modeling Adoption Factors in Indonesia: A Mixed-Methods Exploration Through Constant Comparative Method and Structural Equation Modeling

This study explores factors affecting Building Information Modeling (BIM) adoption in Indonesia’s architecture, engineering, and construction (AEC) industry. The researchers adopt a mixed-methods approach, utilizing interview data from 15 experienced BIM specialists and questionnaire responses from 206 AEC professionals. Using the constant comparative method and structural equation modeling, this study identifies key determinants of BIM adoption. Research findings highlight individual innovativeness as the primary factor, followed by perceived benefits, internal organizational readiness, and external influences. A structural analysis reveals that not all factors directly impact BIM adoption. Perceived benefits and internal organizational readiness have direct structural paths to BIM adoption, with individual innovativeness mediating external influences and perceived benefits. This study result also emphasizes the importance of internal organizational readiness in supporting individual innovativeness during BIM adoption. Overall investigation enriches the understanding of BIM adoption strategy and critical factors, especially in the context of developing nation like Indonesia.

Spatio-temporal distribution and peak prediction of energy consumption and carbon emissions of residential buildings in China

With the acceleration of urbanization and the improvement of people's living standards, the carbon emissions of residential buildings (BCE) in China have been increasing, hindering the achievement of carbon peaking and carbon neutrality goals. It has become increasingly urgent and important to analyze and grasp the dynamic trends of BCE. Given the notable regional variations in carbon emissions, it is necessary to delve into the distribution characteristics of BCE and the underlying factors influencing them. First, based on the emission factor method, the energy consumption and carbon emissions calculation models are established. Next, the main influencing factors are obtained by improving Kaya's constant equation. Meanwhile, the GA-PPC-Kmeans model is established to divide BCE into different regions. Then, the STIRPAT-Ridge model is built to predict the peak carbon emissions. Finally, a combination of static and dynamic methods is used to forecast peaks under three scenarios, which are low-carbon (LC) scenario, baseline (BA) scenario, and high-carbon (HC) scenario. The results show that five pivotal factors significantly impact BCE in China, which are energy carbon emission intensity (ECEI), energy intensity (EI), economic density (ED), residential housing level (RHL) and population size(P). Furthermore, BCE is categorized into five distinct regions: low-carbon demonstration area, energy efficiency improvement area, carbon concentration and innovation area, high-carbon optimization area, and carbon poverty development area. Under BA scenario, the peaks for BCE in these regions converge primarily around 2040 and 2045. This study provides a regional research perspective for China's residential buildings to reach the peak of carbon emissions, and serves as a reference for formulating carbon emission reduction plans in different regions.

Enhanced pilot protection scheme for half-wavelength transmission line based on the conservation of traveling wave energy

The half-wavelength transmission system is a viable technology for long-distance and large-capacity power transmission. It can safely and efficiently transmit a large amount of clean energy to remote load centers. However, the traditional traveling wave protection methods have reliability and speed limitations for HWTL lines. To overcome these limitations, this paper proposes a novel and robust pilot protection scheme based on the conservation of traveling wave energy at the protection installation. The proposed scheme uses the constant equation relationship between fault-traveling waves, reflected waves and refracted waves at the measurement end to significantly improve the reliability and effectiveness of the protection mechanism. The blocking protection operation logic constructed by the inequality directional element is used to improve the rapidity of the pilot protection scheme. The theoretical analysis and real-time digital simulator (RTDS) digital-analog hybrid test demonstrate that the action equation of the proposed protection scheme is explicit to the operating value. The novel scheme exhibits enhanced resilience against high transition resistance and the impact of impulse corona while ensuring both reliability and rapidity.© 2017 Elsevier Inc. All rights reserved.

First description of immature stages and notes on the biology of the blow fly, Calliphora lopesi Mello, 1962.

Several species of the worldwide distributed genus Calliphora Robineau-Desvoidy (Insecta, Diptera, Calliphoridae) are medically important vectors and agents of myiasis. Furthermore, these flies are relevant in forensics because they are found in corpses. Information regarding the taxonomy, bionomics and distribution of Calliphora species endemic to South America, including Calliphora lopesi Mello, is scarce. To expand knowledge on C. lopesi, this study presents descriptions of eggs, larvae, puparia and developmental data at 14, 17, 20, 23 and 26 ± 1°C for the first time. Adult flies were collected from the field and kept in the laboratory to obtain samples for morphological and biological studies. Immatures were examined using light and scanning electron microscopy. To assess the growth rate, 10 specimens from each temperature group were randomly removed from the diet and weighed every 24 h from larval hatching until pupation. The minimum developmental threshold, thermal constant and linear development-rate equations were calculated for each stage. Considering weight gain records and survival rates, the optimum temperature for the development of C. lopesi ranges from 23 to 26°C. A key to third-instar larvae of known Neotropical species of Calliphora was also provided to assist in identification. The information provided in this study should be useful in expanding knowledge about Neotropical Calliphoridae species of forensic importance.

On the Qualitative Analysis of Solutions of Two Fractional Order Fractional Differential Equations

In applied sciences, besides the importance of obtaining the analytical solutions of differential equations with constant coefficients, the qualitative analysis of the solutions of such equations is also very important. Due to this importance, in this study, a qualitative analysis of the solutions of a delayed and constant coefficient fractal differential equation with more than one fractional derivative was performed. In the equation under consideration, the derivatives are the Riemann–Liouville fractional derivatives. In the proof of the obtained results, Laplace transform formulas of the Riemann–Liouville fractional derivative and some inequalities are used. We also provide some examples to check the accuracy of our results.

Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method

This document elaborates on a newly introduced analytical method known as the “Variable Coefficient Generalized Abel Equation Method,” as proposed by Hashemi in Hashemi (2024), designed specifically for addressing the two-mode Cahn–Allen equation. Diverging from conventional techniques that heavily rely on constant coefficient ordinary differential equations and auxiliary ordinary differential equations, our method innovatively incorporates variable coefficient ordinary differential equations within a sub-equation framework. Demonstrating its versatility, we apply this innovative technique to the two-mode Cahn–Allen equation, showcasing its effectiveness and efficiency through the derivation of analytical solutions. Notably, this method emerges as a promising tool for tackling complex nonlinear partial differential equations prevalent in fluid dynamics and wave propagation scenarios. Beyond merely expanding the repertoire of available analytical tools, our approach contributes to advancing solutions for various models within the realm of mathematical physics. Various forms of exact solutions, including exponential-type solutions, Kink solitons, dark solitons, and bright soliton solutions, are obtained for the model under consideration. Moreover, we delve into the analysis of bifurcation, chaotic behavior, and sensitivity within the context of the two-mode Cahn–Allen model, further enhancing the depth and breadth of our study. Three equilibria are analyzed across various classifications, including center point, focus point, saddle point, and node point. Chaotic behavior of the corresponding dynamical system is considered by adding the function ω1sin(ω2ζ). Lastly, sensitivity analysis of the system is conducted by examining different parameters of the model and imposing noise to the initial conditions.

Commentary: Pharmacokinetic Theory Must Consider Published Experimental Data.

Recently, we have proposed simple methodology to derive clearance and rate constant equations, independent of differential equations, based on Kirchhoff's Laws, a common methodology from physics used to describe rate-defining processes either in series or parallel. Our approach has been challenged in three recent publications, two published in this journal, but notably what is lacking is that none evaluate experimental pharmacokinetic data. As reviewed here, manuscripts from our laboratory have evaluated published experimental data, demonstrating that the Kirchhoff's Laws approach explains (1) why all of the experimental perfused liver clearance data appear to fit the equation that was previously believed to be the well-stirred model, (2) why linear pharmacokinetic systemic bioavailability determinations can be greater than 1, (3) why renal clearance can be a function of drug input processes, and (4) why statistically different bioavailability measures may be found for urinary excretion versus systemic concentration measurements. Our most recent paper demonstrates (5) how the universally accepted steady-state clearance approach used by the field for the past 50 years leads to unrealistic outcomes concerning the relationship between liver-to-blood Kpuu and hepatic availability FH , highlighting the potential for errors in pharmacokinetic evaluations based on differential equations. The Kirchhoff's Laws approach is applicable to all pharmacokinetic analyses of quality experimental data, those that were previously adequately explained with present pharmacokinetic theory, and those that were not. The publications that have attempted to rebut our position do not address unexplained experimental data, and we show here why their analyses are not valid. SIGNIFICANCE STATEMENT: The Kirchhoff's Laws approach to deriving clearance equations for linear systems in parallel or in series, independent of differential equations, successfully describes published pharmacokinetic data that has previously been unexplained. Three recent publications claim to refute our proposed methodology; these publications only make theoretical arguments, do not evaluate experimental data, and never demonstrate that the Kirchhoff methodology provides incorrect interpretations of experimental pharmacokinetic data, including statistically significant data not explained by present pharmacokinetic theory. We demonstrate why these analyses are invalid.

Constraints on the Minimally Extended Varying Speed of Light Model Using Pantheon Dataset+

In the context of the minimally extended varying speed of light (meVSL) model, both the absolute magnitude and the luminosity distance of type Ia supernovae (SNe Ia) deviate from those predicted by general relativity (GR). Using data from the Pantheon+ survey, we assess the plausibility of various dark energy models within the framework of meVSL. Both the constant equation of state (EoS) of the dark energy model (ωCDM) and the Chevallier–Polarski–Linder (CPL) parameterization model (ω=ω0+ωa(1−a)) indicate potential variations in the cosmic speed of light at the 1−σ confidence level. For Ωm0=0.30,0.31, and 0.32 with (ω0,ωa)=(−1,0), the 1−σ range of c˙0/c0(10−13yr−1) is (−8.76, −0.89), (−11.8, 3.93), and (−14.8, −6.98), respectively. Meanwhile, the 1−σ range of c˙0/c0(10−12yr−1) for CPL dark energy models with −1.05≤ω0≤−0.95 and 0.28≤Ωm0≤0.32 is (−6.31, −2.98). The value of c at z=3 can exceed that of the present by 0.2∼3% for ωCDM models and 5∼13% for CPL models. Additionally, for viable models except for the CPL model with Ωm0=0.28, we find −25.6≤G˙0/G0(10−12yr−1)≤−0.36. For this particular model, we obtain an increasing rate of the gravitational constant within the range 1.65≤G˙0/G0(10−12yr−1)≤3.79. We obtain some models that do not require dark matter energy density through statistical interpretation. However, this is merely an effect of the degeneracy between model parameters and energy density and does not imply that dark matter is unnecessary.

Restoring cosmological concordance with axion-like early dark energy and dark matter characterized by a constant equation of state?

The Hubble tension persists as a challenge in cosmology. Even early dark energy (EDE) models, initially considered the most promising for alleviating the Hubble tension, fall short of addressing the issue without exacerbating other tensions, such as the S 8 tension. Considering that a negative dark matter (DM) equation of state (EoS) parameter is conducive to reduce the value of the σ 8 parameter, we extend the axion-like EDE model in this paper by replacing the cold dark matter (CDM) with DM characterized by a constant EoS w dm (referred to as WDM hereafter). We then impose constraints on this axion-like EDE extension model, along with three other models: the axion-like EDE model, ΛWDM, and ΛCDM. These constraints are derived from a comprehensive analysis incorporating data from the Planck 2018 cosmic microwave background, baryon acoustic oscillations, and the Pantheon compilation, as well as a prior on H 0 (i.e. H 0 = 73.04 ± 1.04, based on the latest local measurement by Riess et al) and a Gaussianized prior on S 8 (i.e. S 8 = 0.766 ± 0.017, determined through the joint analysis of KID1000+BOSS+2dLenS). We find that although the new model maintains the ability to alleviate the Hubble tension to ∼1.4σ, it still exacerbates the S 8 tension to a level similar to that of the axion-like EDE model.

Photocatalytic activity of ZnO doped Nano hydroxyapatite/GO derived from waste oyster shells for removal of Methylene blue.

Hydroxyapatite (HAp) stands as an inorganic compound, recognized as a non-toxic, bioactive ceramic, and its composition closely resembles that of bone material. In this study, nHAp was prepared from waste oyster shells, which are biowaste rich in calcium carbonate. nHAp with its unique catalytic property can be used as an adsorbent in various fields, including wastewater treatment. nHAp with an exceptional surface adsorbent with excellent chemical stability, enabling its catalytic function. Nano hydroxyapatite doped with Zinc oxide (ZnO) by wet chemical precipitation and made into a composite with Graphene oxide (GO) by modified hummers method followed by grinding, which was taken as 9:1 ratio (nHAp/ZnO and GO) of weight, enhances its tensile and mechanical strength. The energy band gap of nHAp photocatalyst was evaluated as 3.39eV and that of the in nHAp/ZnO/GO photocatalyst was narrowed to 1.77eV. The ternary nanocomposites are very efficient in generating the photogenerated electrons and holes, thereby improving the degradation potential of dye effluents to by-products such as CO2 and H2O. The nanocomposites photocatalyst were characterized by FTIR, XRD, SEM, TEM, EDS, XPS, DRS, and BET techniques. The UV-visible study shows the complete dye degradation efficiency of the prepared nanocomposites photocatalyst. In this study, the prepared nanocomposites nHAp/ZnO/GO have studied their efficiency for the removal of MB dye in a batch process by varying the dosage from 0.1 to 0.5g, and the effects of dosage variations, pH, kinetic, scavenger study were evaluated at a time interval of 30min. The removal of dye was found to be 99% at 150min of 0.3g dosage and pH = 12 is most favorable as it reached the same percentage at 90min. The as-prepared nanocomposite nHAp/ZnO/GO fits the kinetic rate constant equation and shows a pseudo-first-order reaction model. This study indicates the suitability for dye removal due to the synergistic effect and electrostatic interaction of the synthesized ternary nanocomposite, which shows the potential, socially active, low-cost-effective, eco-friendly, and safe for photocatalytic degradation of MB from wastewater.

Influence of vegetation on heavy metal Cr release process from bottom sediment under unidirectional flows and regular waves

As human activities become more intensive, a substantial number of heavy metals are discharged into estuarine or wetland environments. Due to the poor degradability, heavy metals are prone to adsorption and deposition on suspended particles in bottom sediments. Subsequently, under the influence of disturbances, there is a potential for their re-release, causing secondary pollution. To investigate the release process of the heavy metal Cr from sediment, laboratory experiments were conducted under both unidirectional flow and regular wave conditions. At the initial stage, the temporal trends of particulate (CrP) and dissolved (CrD) Chromium concentrations were both characterized by initial increments followed by stabilization and continuous escalation. Vertically, the stable concentrations of CrP and CrD increased with the presence of vegetation and the enhancement of hydrodynamics. The Elovich equation, pseudo-second-order kinetic equation, Double constant equation (Freundlich model), and parabolic diffusion equation were employed to predict the release process of CrD from bottom sediment. The Elovich equation proved most suitable for describing the release process of CrD, with an R2 exceeding 0.9. In order to assess the influence of vegetation on the Cr release process, the Stem-Reynolds were introduced to modify the Elovich equation. The final maximum error was 12 % (excluding the initial stage), which was much lower than that using the original Elovich equation (maximum error of 32 %). The study findings provide practical support for estuarine and wetland managers to formulate effective heavy metal management measures, which contribute to the conservation and sustainable management of aquatic ecosystems.

Some classes of interacting two-fluid model of the expanding universe

We consider interacting dark matter-dark energy models arising out of a general interaction term Q=f(ρm,ρd,ρ̇m,ρ̇d). Here f is a functional relation connecting the energy densities ρ m and ρ d and their derivatives w.r.t. time t. In our model we consider two interacting barotropic fluid with constant equation of state ω m and ω d . By considering a dynamical interaction between them we trace out the cosmological evolution dynamics of the Universe. We analytically solve the model by considering a constant ratio between the two fluids and then track the corresponding analytical results using observational data from the baryon acoustic oscillation measurements, Type Ia supernovae measurements and the local Hubble constant measurements. From this general setting we introduce three different models and nine different interaction function. Our final aim is to set up a comparative analysis of the various class of models under the different interaction function using common theoretical and numerical analysis.

Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach

This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and monotonically decreasing delay intervals, respectively. Based on the constructed augmented Lyapunov functionals and the employed time-varying zero equation, less conservative stability criteria are obtained separately for bounded and periodic time-varying delays. Lastly, three examples are used to verify the superiority of the stability conditions obtained in this paper.

De Sitter-like configurations with asymptotic quintessence environment

We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to an isotropic de Sitter-like solution that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state parameter near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.

Traversable wormholes in minimally geometrical deformed trace-free gravity using gravitational decoupling

In this work, we investigate wormhole solutions through the utilization of gravitational decoupling, employing the Minimal Geometric Deformation (MGD) procedure within the framework of Trace-Free Gravity. We base our investigation on static and spherically symmetric Morris-Thorne traversable wormholes, considering both constant and variable equation of state parameters. We derive the field equations and extract the shape function for each scenario. Moreover, we explore the gravitational decoupling technique and examine various forms of energy density for both a smeared and particle-like gravitational source, encompassing the realm of noncommutative geometry and a statically charged fluid. We also examinethe wormhole geometry through the utilization of embedding diagrams. Through our analysis, we uncover a violation of the Null Energy Condition (NEC). To conclude, we employ the Gauss-Bonnet theorem to determine the weak deflection angle for the wormhole configurations.