arXiv subjects

Bappa Ghosh

Publications and source records attributed to Bappa Ghosh.

8 recordsLinked to original sources

arXiv2026

Qualitative and Numerical Simulation of a Time-Fractional SEIR Mpox Model Arising in Population Epidemiology

Epidemiological modeling is vital in understanding disease dynamics and guiding public health interventions. This study presents a time-fractional SEIR model to describe the transmission dynamics of Mpox, incorporating memory effects via the fractional derivative. We perform an extensive qualitative investigation, proving that there is a unique solution and that the solutions are Hyers-Ulam stable. To approximate the model numerically, we implement the L1 finite difference scheme for the Caputo derivative and solve the resulting nonlinear system using the Newton-Raphson technique. A detailed error analysis is provided, demonstrating that the scheme achieves algebraic convergence. Comparative results with the Fractional Modified Euler method (FMEM) confirm the superior accuracy and stability of the proposed approach. Numerical simulations under biologically relevant parameters illustrate the impact of the non-integer order and vaccination rate on disease progression. The study underscores the effectiveness of fractional order models in capturing epidemic memory effects and positions the L1 scheme as a robust numerical tool for simulating such dynamics.

math.NA↗

arXiv2026

Qualitative analysis and numerical investigations of time-fractional Zika virus model arising in population dynamics

Epidemic models play a crucial role in population dynamics, offering valuable insights into disease transmission while aiding in epidemic prediction and control. In this paper, we analyze the mathematical model of the time-fractional Zika virus transmission for human and mosquito populations. The fractional derivative is considered in the Caputo sense of order $\alpha\in(0,1).$ We begin by conducting a qualitative analysis using the stability theory of differential equations. The existence and uniqueness of the solution are established, and the model's stability is examined through Hyers-Ulam stability analysis. Furthermore, an efficient difference scheme utilizing the standard L1 technique is developed to simulate the model and analyze the solution's behavior under key parameters. The resulting nonlinear algebraic system is solved using the Newton-Raphson method. Finally, illustrative examples are presented to validate the theoretical findings. Graphical results indicate that the fractional model provides deeper insights and a better understanding of disease dynamics. These findings aid in controlling the virus through contact precautions and recommended therapies while also helping to predict its future spread.

math.DS↗

arXiv2025

On two notions of torsion and metric compatibility of connections in noncommutative geometry

We compare the notions of metric-compatibility and torsion of a connection in the frameworks of Beggs-Majid and Mesland-Rennie. It follows that for $\ast$-preserving connections, compatibility with a real metric in the sense of Beggs-Majid corresponds to Hermitian connections in the sense of Mesland-Rennie. If the calculus is quasi-tame, the torsion zero conditions are equivalent. A combination of these results proves the existence and uniqueness of Levi-Civita connections in the sense of Mesland-Rennie for unitary cocycle deformations of a large class of Riemannian manifolds as well as the Heckenberger-Kolb calculi on all quantized irreducible flag manifolds.

math.QA↗

arXiv2025

The Levi-Civita connection and Chern connections for cocycle deformations of K\"{a}hler manifolds

We consider unitary cocycle deformations of covariant $\ast$-differential calculi. We prove that complex structures, holomorphic bimodules and Chern connections on the deformed calculus are twists of their untwisted counterparts. Moreover, for cocycle deformations of a class of classical K\"ahler manifolds, the Levi-Civita connection on the space of one-forms of the deformed calculus is shown to be a direct sum of the Chern connections on the twisted holomorphic and the anti-holomorphic bimodules. Our class of examples also includes cocycle deformations of the Heckenberger-Kolb calculi.

math.QA↗

arXiv2024

Levi-Civita connection on the irreducible quantum flag manifolds

We classify covariant metrics (in the sense of Beggs and Majid) on a class of quantum homogeneous spaces. In particular, our classification implies the existence of a unique (up to scalar) quantum symmetric covariant metric on the Heckenberger--Kolb calculi for the quantized irreducible flag manifolds. Moreover, we prove the existence and uniqueness of Levi-Civita connection for any real covariant metric for the Heckenberger--Kolb calculi. This generalizes Matassa's result for the quantum projective spaces.

math.QA↗

arXiv2023

Designing, Synthesizing and Modeling Active Fluids

We review recent advances in the design, synthesis, and modeling of active fluids. Active fluids have been at the center of many technological innovations and theoretical advances over the past two decades. Research on this new class of fluids has been inspired by the fascinating and remarkably efficient strategies that biological systems employ, leading to the development of biomimetic nano- and micro-machines and -swimmers. The review encompasses active fluids on both the nano- and micro-scale. We start with examples of biological active systems before we discuss how experimentalists leverage novel propulsion mechanisms to power nano- and micro-machines. We then examine how the study of these far-from-equilibrium systems has prompted the development of new simulation methods and theoretical models in nonquilibrium physics to account for their mechanical, thermodynamic and emergent properties. Recent advances in the field have paved the way for the design, synthesis, and modeling of autonomous systems at the nano- and micro-scale and open the door to the development of soft matter robotics.

cond-mat.soft↗

arXiv2019

Pulling a folded polymer through a nanopore

We investigate the translocation dynamics of a folded linear polymer which is pulled through a nanopore by an external force. To this end, we generalize the iso-flux tension propagation (IFTP) theory for end-pulled polymer translocation to include the case of two segments of the folded polymer traversing simultaneously trough the pore. Our theory is extensively benchmarked with corresponding Molecular Dynamics (MD) simulations. The translocation process for a folded polymer can be divided into two main stages. In the first stage, both branches are traversing the pore and their dynamics is coupled. If the branches are not of equal length, there is a second stage where translocation of the shorter branch has been completed. Using the assumption of equal monomer flux of both branches, we analytically derive the equations of motion for both branches and characterise the translocation dynamics in detail from the average waiting time and its scaling form. Moreover, MD simulations are used to study additional details of translocation dynamics such as the translocation time distribution and individual monomer velocities.

cond-mat.soft↗

arXiv2017

Dynamics of end-pulled polymer translocation through a nanopore

We consider the translocation dynamics of a polymer chain forced through a nanopore by an external force on its head monomer on the trans side. For a proper theoretical treatment we generalize the iso-flux tension propagation (IFTP) theory to include friction arising from the trans side subchain. The theory reveals a complicated scenario of multiple scaling regimes depending on the configurations of the cis and the trans side subchains. In the limit of high driving forces $f$ such that the trans subchain is strongly stretched, the theory is in excellent agreement with molecular dynamics simulations and allows an exact analytic solution for the scaling of the translocation time ${\tau}$ as a function of the chain length $N_0$ and $f$. In this regime the asymptotic scaling exponents for ${\tau} \sim N_0^{\alpha} f^{\beta}$ are $\alpha=2$, and $\beta =-1$. The theory reveals significant correction-to-scaling terms arising from the cis side subchain and pore friction, which lead to a very slow approach to $\alpha =2$ from below as a function of increasing $N_0$.

cond-mat.soft↗