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We study a cosmological model in Rastall's theory of gravity in the framework of the flat FLRW metric. We formulate the value of the Hubble parameter, which contains two model parameters, $ \alpha $ and $ j $. Employing the Markov Chain Monte Carlo (MCMC) sampling technique, we determine the values of these model parameters along with their uncertainties. Moreover, we derive the equation of state (EoS) parameter, which converges around the quintessence region. We perform a dynamical system analysis using the linearization technique to validate the results independently. Also, we discuss various physical attributes of the model, highlighting the transition to acceleration and the violation of the strong energy condition (SEC) in the late stages of evolution. In conclusion, our model mimics the behavior of a dark matter fluid during the past epoch and transitions into a quintessence dark energy model in the future epoch., Comment: 18 pages, 17 figures

We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m + 2 \lambda T^n$, where $\lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10 \leq z_{tr} \leq 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration., Comment: 14 pages, 12 figures

This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared with the results obtained by the method using orthonormal Bernoulli wavelets. Using fractional-order generalized Bernoulli wavelets, product and integral operational matrices have been obtained. By using these operational matrices, the multi-dimensional fractional optimal control problems have been reduced into a system of algebraic equations. To confirm the efficiency of the proposed numerical technique involving fractional-order generalized Bernoulli wavelets, numerical problems have been solved by using both orthonormal Bernoulli wavelets and fractional-order generalized Bernoulli wavelets and obtaining an approximate cost function value, which has been found by approximating state and control functions. In addition, the convergence rate and error bound of the proposed numerical method have also been derived., Comment: arXiv admin note: substantial text overlap with arXiv:2310.06570

This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine fractional derivatives and integral fractional wavelets, operational matrices were devised and utilised to solve fractional optimal control problems. The proposed method reduced the fractional optimal control problems into a system of algebraic equations. To validate the effectiveness of the presented numerical approach, some illustrative problems were solved using fractional Taylor and Taylor wavelets, and the approximate cost function value derived by approximating state and control functions was compared. In addition, convergence rate and error bound of the proposed method have been derived.

We investigate a bounce realization in the framework of higher order curvature in $ f(R,T) $ modified theory of gravity. We perform a detailed analysis of the cosmological parameters to explain the contraction phase, the bounce phase, and the expansion phase. Furthermore, we observe a violation of the null energy condition, instability of the model, and a singularity upon deceleration at the bouncing point, which are the supporting results for a bouncing cosmology. The outcome of the slow roll parameters is satisfactory to understand the inflation era and the equation of state parameter exhibits a ghost condensate behavior of the model near the bounce. Additionally, we discuss the stability of the model using linear perturbations in the Hubble parameter as well as the energy density., Comment: 15 pages, 16 figures

The homogeneous and isotropic cosmological model in generalized $ f(R,T^\phi) $ theories associated with scalar field is discussed, which is motivated by the $ f(R,T) $ theory of gravity studied by Harko et al. \cite{Harko:2011kv, Harko:2014pqa}. The $ f(R,T^\phi) $ gravity can be explained as $ f(R,T) $ gravity with a self-interacting scalar field $ \phi $, where $ T^\phi $ is the trace of the energy-momentum tensor. The parametrization of Hubble parameter $ H(t) $ is taken as $ \alpha-\beta e^{-\gamma t} $, where $ \alpha $, $\beta$ and $\gamma$ are arbitrary constants such that $ \alpha, \gamma>0 $ and $ \beta<0 $. The model shows no space-time singularity and the expansion of the universe will continue forever, i.e., the future scenario of the universe attains Big Freeze. The model predicts the moderate inflationary scenario at the time of the evolution of the universe and it is consistent with $ \Lambda $CDM in late times. The consistency of the model has also been examined using recent observational Hubble dataset and supernovae dataset. Finally, the physical features of the model have been discussed in some detail., Comment: 12 pages, 13 figures

Medium-voltage back-to-back (MVB2B) converters can connect two distribution systems and quantifiably transfer power between them. This function can enable the MVB2B converter to exchange distributed energy resource (DER)-generated power between two systems and bring significant value to enhancing distribution system DER adoption. Our previous work analyzed and demonstrated the value the MVB2B converter can bring to DER integration. As continuous work, this paper presents a methodology that helps address the MVB2B converter sizing and location selection problem in distribution systems with high DER penetrations. The proposed methodology aims to address three critical problems for MVB2B converter implementation in the real world: 1) which distribution systems are better to be connected, 2) what converter size is appropriate for connecting the distribution systems, and 3) where the optimal connection points are in the systems for connecting the MVB2B converter. The proposed methodology has been demonstrated by case studies that include various scenarios involving distribution systems with different dominated load types and high photovoltaic penetrations.

We investigate a flat FLRW-model in $f(R,T)$-gravity, which includes the quadratic variation in scalar curvature $R$ and the linear term of the trace of the stress-energy tensor $T$. In turn, we establish the model has the behaviour of the late time Universe, which is accelerated expanding and ends up in a big rip. Using the parametrization of scale factor $a(t)$, we propose a model, which begins with point-type singularity, i.e., the model starts with a point of zero volume, infinite energy density and infinite temperature. The model's behaviour is accelerated expanding at present and $\Lambda$CDM in late times. Finally, the proposed model behaves like a quintessence dark energy model in the present time and is consistent with standard cosmology $\Lambda$CDM in late times., Comment: 15 pages, 20 figures

In this work, we consider the case of a strongly coupled dark/hidden sector, which extends the Standard Model (SM) by adding an additional non-Abelian gauge group. These extensions generally contain matter fields, much like the SM quarks, and gauge fields similar to the SM gluons. We focus on the exploration of such sectors where the dark particles are produced at the LHC through a portal and undergo rapid hadronization within the dark sector before decaying back, at least in part and potentially with sizeable lifetimes, to SM particles, giving a range of possibly spectacular signatures such as emerging or semi-visible jets. Other, non-QCD-like scenarios leading to soft unclustered energy patterns or glueballs are also discussed. After a review of the theory, existing benchmarks and constraints, this work addresses how to build consistent benchmarks from the underlying physical parameters and present new developments for the PYTHIA Hidden Valley module, along with jet substructure studies. Finally, a series of improved search strategies is presented in order to pave the way for a better exploration of the dark showers at the LHC., Comment: Uniform notation, fixed typos, improved numerical analysis, added references, comments welcome

This paper presents an analysis of the value that can be realized by medium-voltage back-to-back (MVB2B) converters in terms of increased utilization rate of distributed energy resource (DER) and the improvement in operational conditions. A systematic, transferrable, and scalable methodology has been designed to analyze and quantify the increased DER value from three perspectives: 1) curtailment reduction of the DER generation, 2) size reduction of the energy storage needed to otherwise realize DER hosting levels, and 3) hosting capacity improvement of DER compared to base distribution circuit capability. In the case study, the proposed methodology is applied to two utility distribution systems for analysis and quantification of the grid value of the MVB2B converter, installed in the distribution circuit, and provided to the solar photovoltaic (PV) DERs. The analysis results demonstrate that the MVB2B converter can deliver significant value to PV hosting enhancement of two adjacent distribution systems when they are connected by the MVB2B converter. Based on this case study, this paper analyzes and summarizes the approximate realized grid value of the MVB2B converter for distribution systems dominated by different shares of customer classes.