arXiv subjects

Saddam Hussain

Publications and source records attributed to Saddam Hussain.

33 records · Page 2Linked to original sources

arXiv2024

Hybridized Projected Differential Transform Method For collisional-breakage equation

The non-linear collision induced fragmentation plays a crucial role in modeling several engineering and physical problems. In contrast to linear breakage, it has not been thoroughly investigated in the existing literature. This study introduces an innovative method that leverages the Elzaki integral transform as a preparatory step to enhance the accuracy and convergence of domain decomposition, used alongside the projected differential transform method to obtain closed-form or series approximations of solutions for the collisional breakage equation (CBE). A significant advantages of this technique is its capability to directly address both linear and nonlinear differential equations without the need for discretization or linearization. The mathematical framework is reinforced by a thorough convergence analysis, applying fixed point theory within an adequately defined Banach space. Additionally, error estimates for the approximated solutions are derived, offering more profound insights into the accuracy and dependability of the proposed method. The validity of this approach is demonstrated by comparing the obtained results with exact or finite volume approximated solutions considering several physical examples. Interestingly, the proposed algorithm yields accurate approximations for the number density functions as well as moments with fewer terms and maintains higher precision over extended time periods.

cs.CE↗

arXiv2024

Stability analysis of a dark energy model in Rastall gravity

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, $ α$ 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.

gr-qc↗

arXiv2024

Semi-Analytical Methods for Population Balance models involving Aggregation and Breakage processes: A comparative study

Population balance models often integrate fundamental kernels, including sum, gelling and Brownian aggregation kernels. These kernels have demonstrated extensive utility across various disciplines such as aerosol physics, chemical engineering, astrophysics, pharmaceutical sciences and mathematical biology for the purpose of elucidating particle dynamics. The objective of this study is to refine the semi-analytical solutions derived from current methodologies in addressing the nonlinear aggregation and coupled aggregation-breakage population balance equation. This work presents a unique semi-analytical approach based on the homotopy analysis method (HAM) to solve pure aggregation and couple aggregation-fragmentation population balance equations, which is an integro-partial differentia equation. By decomposing the non-linear operator, we investigate how to utilize the convergence control parameter to expedite the convergence of the HAM solution towards its precise values in the proposed method.

math.NA↗

arXiv2024

Non-linear collision-induced breakage equation: finite volume and semi-analytical methods

The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number and the total mass of the particles in the system. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. To justify the applicability and accuracy of these methods, numerical simulations are compared with the findings of FVM and analytical solutions considering three physical problems.

math.NA↗

arXiv2024

The Role of LLMs in Sustainable Smart Cities: Applications, Challenges, and Future Directions

Smart cities stand as pivotal components in the ongoing pursuit of elevating urban living standards, facilitating the rapid expansion of urban areas while efficiently managing resources through sustainable and scalable innovations. In this regard, as emerging technologies like Artificial Intelligence (AI), the Internet of Things (IoT), big data analytics, and fog and edge computing have become increasingly prevalent, smart city applications grapple with various challenges, including the potential for unauthorized disclosure of confidential and sensitive data. The seamless integration of emerging technologies has played a vital role in sustaining the dynamic pace of their development. This paper explores the substantial potential and applications of Deep Learning (DL), Federated Learning (FL), IoT, Blockchain, Natural Language Processing (NLP), and large language models (LLMs) in optimizing ICT processes within smart cities. We aim to spotlight the vast potential of these technologies as foundational elements that technically strengthen the realization and advancement of smart cities, underscoring their significance in driving innovation within this transformative urban milieu. Our discourse culminates with an exploration of the formidable challenges that DL, FL, IoT, Blockchain, NLP, and LLMs face within these contexts, and we offer insights into potential future directions.

cs.AI↗

arXiv2023

Stability analysis of warm quintessential dark energy model

A dynamical system analysis is performed for a model of dissipative quintessential inflation realizing warm inflation at early primordial times and dissipative interations in the dark sector at late times. The construction makes use of a generalized exponential potential realizing both phases of accelerated expansion. A focus is given on the behavior of the dynamical system at late times and the analysis is exemplified by both analytical and numerical results. The results obtained demonstrate the viability of the model as a quintessential inflation model and in which stable solutions can be obtained.

gr-qc↗

arXiv2023

Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature

This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.

gr-qc↗

arXiv2023

Realizing late-time cosmology in the context of Dynamical Stability Approach

We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.

gr-qc↗

arXiv2023

Dynamical Analysis of the Dirac-Born-Infeld type of Tachyon field minimally coupled with barotropic fluid using EOS parametrization of a field

In this paper, we present a dynamical system analysis of the tachyon dark energy model by parametrization of the equation of state (EoS) of the dark energy. The choice of parametrization can constrain the form of the field potential, and as a result, the theory can be directly constrained from the observation without assuming a particular form of the potential.

gr-qc↗

arXiv2023

Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the $k$-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the $k$-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the $k$-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the $k$-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

gr-qc↗

arXiv2023

Dynamical systems analysis of tachyon dark energy model from a new perspective

In this work we present a new scheme to study the tachyon dark energy model using dynamical systems analysis by considering parametrization of the equation of state(EoS) of the dark energy. Both the canonical and phantom field dynamics are investigated. In our method we do not require any explicit form of the tachyon potential. Instead of the potential we start with an approximate form of the EoS of the tachyon field. This EoS is phenomenologically motivated and contains some dimensionless parameters. Using our method we can construct the dynamical system which gives rise to the time evolution of the universe. We have considered two different parametrizations of the EoS and studied the phase space dynamics in details. Our analysis shows Taylor series parametrization of the EoS has serious cosmological limitations. Our proposal is generic in nature and can be applied to other scalar field dark energy models.

gr-qc↗

arXiv2023

Ghost condensates and pure kinetic $k$-essence condensates in presence of field-fluid non-minimal coupling in the dark sector

In this article we try to find out the conditions when a ghost field in conjunction with a barotropic fluid produces a stable accelerating expansion phase of the universe. It is seen that in many cases the ghost field produces a condensate and drives the fluid energy density to zero in the final accelerating phase, but there can be other possibilities. We have shown that a pure kinetic $k$-essence field (which is not a ghost field) interacting with a fluid can also form an interaction induced condensate and produce a stable accelerating phase of the universe. In the latter case the fluid energy density does not vanish in the stable phase.

gr-qc↗

arXiv2022

The nature of cosmological metric perturbations in presence of gravitational particle production

The present paper tries to answer the question: Can a de Sitter phase in presence of radiation be a competitor of the standard inflationary paradigm for the early universe? This kind of a de Sitter phase can exist in cosmological models where gravitational particle production takes place. To address the issue the metric perturbations in the de Sitter phase in presence of radiation must be known. The evolution of metric perturbations are explicitly calculated in the paper. It is seen that the evolution of scalar and vector perturbations are considerably different from standard inflationary models. These differences arise due to the particle production mechanism. The scalar perturbation power spectrum grows exponentially at small length scales. However, one cannot uniquely specify the scale at which this exponential growth starts because of the dependence of the power spectrum on the initial perturbation value. The time slice on which the initial perturbation starts is arbitrary. The arbitrariness of the initial time slice is related to the problem of setting the initial condition on the perturbations in the present model. The paper briefly opines on vector and tensor perturbations in the de Sitter space filled with radiation. It is seen that quantization of the perturbation modes in the present model is considerably difficult. One has to modify the present model to provide a consistent scheme of quantization of the perturbation modes.

gr-qc↗

arXiv2021

Dynamical stability of K-essence field interacting non-minimally with a perfect fluid

We study models of non-minimally coupled relativistic fluid and $k$-essence scalar field in the background of a flat Friedmann-Lemaitre-Robertson-Walker universe. The non-minimal coupling term is introduced in the Lagrangian level. We employ the variational approach with respect to independent variables that produce modified $k-$essence field equations and the Friedmann equations. We have analyzed the coupled field-fluid framework explicitly using the dynamical system technique considering two different models based on inverse power-law potential. After examining these models it is seen that both models are capable of producing accelerating attractor solutions satisfying adiabatic sound speed conditions.

gr-qc↗

arXiv2017

Segmentation of Glioma Tumors in Brain Using Deep Convolutional Neural Network

Detection of brain tumor using a segmentation based approach is critical in cases, where survival of a subject depends on an accurate and timely clinical diagnosis. Gliomas are the most commonly found tumors having irregular shape and ambiguous boundaries, making them one of the hardest tumors to detect. The automation of brain tumor segmentation remains a challenging problem mainly due to significant variations in its structure. An automated brain tumor segmentation algorithm using deep convolutional neural network (DCNN) is presented in this paper. A patch based approach along with an inception module is used for training the deep network by extracting two co-centric patches of different sizes from the input images. Recent developments in deep neural networks such as drop-out, batch normalization, non-linear activation and inception module are used to build a new ILinear nexus architecture. The module overcomes the over-fitting problem arising due to scarcity of data using drop-out regularizer. Images are normalized and bias field corrected in the pre-processing step and then extracted patches are passed through a DCNN, which assigns an output label to the central pixel of each patch. Morphological operators are used for post-processing to remove small false positives around the edges. A two-phase weighted training method is introduced and evaluated using BRATS 2013 and BRATS 2015 datasets, where it improves the performance parameters of state-of-the-art techniques under similar settings.

cs.CV↗