The late-time cosmological behavior of the f(T, L_m) gravity framework is examined by adopting a linear functional form, f(T, L_m) = α T + β L_m . To characterize the expansion history, a redshift-dependent EoS is employed, ω (z) = ω _0 + ω _1 z , which allows for an analytical determination of the Hubble parameter. A joint fitting procedure using CC, DESI DR2 BAO and Type Ia supernova datasets (Pantheon+, DES-SN5Y and Union 3) is employed to constrain the model parameters. The combined observational datasets provide consistent constraints on the cosmological parameters, yielding H_0 ≈ 67.4 km; s^-1 Mpc^-1 , in close agreement with the Planck measurement. The present-day EoS parameter is constrained to ω _0 ≈ -0.59 , while the positive value ω _1 ≈ 0.27 indicates an evolving effective cosmological fluid. Furthermore, the torsion–matter coupling parameter is constrained to β≈ 0 , suggesting that the background expansion data considered here do not require a statistically significant deviation from the vanishing–coupling limit. AIC results suggest compatibility between the model and Λ CDM, whereas BIC indicates a strong preference for Λ CDM owing to its simpler structure. The behavior of the deceleration parameter shows a smooth transition from a decelerating phase to an accelerating epoch at z_tr∼ 0.65 –0.70, consistent with observational constraints. In addition, the NEC and DEC hold, whereas the SEC fails to hold, which provide support for the mechanism responsible for cosmic acceleration. The Universe’s age, t_0 ≈ 13.2 –13.4 Gyr matches well with values reported from current observations. Overall, the f(T, L_m) model offers a coherent and observationally viable description of the late-time evolution of the Universe.
We derive new exact traveling wave solutions for coupled partial differential equations whose terms involve both odd and even order derivatives. The Extended Generalized Riccati Equation Mapping Method (EGREM) does the work, and it returns several kinds of solutions, among them bright solitons, periodic waves, breathers, and lump solitons. We also look at stability and conservation laws in some detail. Because the method balances nonlinear and dispersive effects in a systematic way, the solutions give a useful picture of how these waves behave and what they might mean physically. A qualitative comparison with other analytical methods points out where EGREM helps and where it falls short. Our test case is the coupled nonlinear Drinfel'd-Sokolov-Wilson (DSW) equation, though the same approach should apply to a wider range of coupled NPDEs.
This paper investigates the global boundedness of classical solution to a weakly singular chemotaxis system with density-dependent and general production under homogeneous Neumann boundary conditions: u_t = Δ u - ∇· ( S(u)/v^α∇ v ), 0 = Δ v - v + u^β in a smooth bounded domain Ω⊂R^n ( n ≥ 2 ) with S(u) ⩽ s_0u^δ for δ , s_0> 0 and α∈ (0,1) , β >0 . It is proved that the system possesses a globally bounded classical solution if δ >0 suitably small relative to β >0 for given α∈ (0,1) . This result reveals the effect of weakly singular sensitivity in preventing blow-up of solution.
We consider a multiscale approach to study the effective electrophysiological properties of nervous tissue, specifically focusing on unmyelinated axon bundles. To this purpose, we employ the asymptotic homogenisation technique to bridge the explicit microstructural geometry and membrane interface laws with macroscopic equations. We start by formulating a two-phase conduction problem where intracellular and extracellular media interact via transmembrane currents, including capacitive, stimulus, and FitzHugh-Nagumo ionic currents. The theoretical framework is then specialised to represent the microstructure as a periodic distribution of uniaxially aligned cylindrical axons. In this context, we simplify the relevant cell problems to the cross section of the medium and derive closed-form expressions for the effective conductivity coefficients utilising complex-potential methods. To inform our model with experimental data, we associate the analytical expressions with experimentally obtained morphological data, specifically, axon radii and packing densities extracted from transmission electron microscopy (TEM) images of porcine brain tissue across various ages and brain regions. Finally, we conduct electrophysiological simulations to explore how age and region microstructural characteristics affect macroscale responses.
