Abstract It is shown that algebraic techniques based on the Lie algebra so (4, 2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay (“Dynamical symmetries of the H atom, one of the most important tools of modern physics: SO (4) to SO (4, 2), background, theory and use in calculating radiative shifts,” Symmetry , vol. 12, no. 1323, pp. 1–66, 2020). In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case.
Abstract This paper investigates the role of higher-order nonlinearities in the propagation of heavy ion-acoustic shock waves (HIASWs) within a magnetized, collisionless plasma comprising inertial heavy ions and kappa-distributed electrons and positrons. Employing a reductive perturbation technique, we derive a magnetized Burgers equation governing the first-order electrostatic potential, alongside an extended, linearly inhomogeneous Burgers-type equation that encapsulating significantly higher-order corrections. Analytical stationary solutions for both the wave potential and the associated electric field are obtained. A comprehensive parametric analysis reveals that the fundamental properties of the shock waves, including phase velocity, amplitude, and width, are critically sensitive to the plasma parameters. A key finding is the identification of a substantial moderating influence from the higher-order terms, which manifest as a negative contribution to the total wave potential and introduce a complex, opposing structure to the electric field. This effect acts as a stabilizing mechanism, mitigating nonlinear wave steepening and refining the shock profile. The results provide a more robust framework for understanding the dynamics of nonlinear coherent structures in astrophysical and laboratory plasmas where non-Maxwellian, multicomponent environments are prevalent, underscoring the necessity of incorporating higher-order effects for accurate physical description.
Abstract This work presents a symmetry-based analytical study of a frictional Aw–Rascle–Zhang (ARZ) traffic-flow model with Chaplygin-type pressure laws. The governing system is formulated as a nonlinear hyperbolic balance law with a Coulomb-like friction term. Local Lie point symmetries and invariant reductions are considered for the Classical, Generalized, and Modified Chaplygin pressure laws. For the classical Chaplygin case, the analysis is further extended through conservation-law potentials to identify nonlocal symmetry structures and associated invariant solutions. The reductions yield explicit solution families, including inverse-time density profiles, nonlinear-power and logarithmic velocity corrections, branches with moving singular density boundaries, and bounded traveling fronts in the frictionless limit. The regularity and physical admissibility of these solutions are assessed on explicitly stated domains through density positivity and finite velocity behavior. The obtained profiles provide exact analytical benchmarks for comparison and numerical validation. Stability, entropy admissibility, shock formation, and evolution from general initial data remain outside the scope of the present symmetry-based analysis.
Abstract A well-known integrable nonlinear model that arises in dispersive fluid dynamics, the Drinfeld–Sokolov–Wilson (DSW) system frequently serves to explain the evolution of dispersive tidal waves. In order to develop new classes of exact solitary wave solutions that are essential to understanding the model’s underlying dispersion and diffusion mechanisms, we examine the dynamical properties of the DSW system in this work. The governing nonlinear system is examined through effective analytical methods that provides mathematical derivation for a wide range of accurate solutions. Periodic wave structures, bright and dark solitons, and singular soliton solutions achieved under suitable parametric constraints are among them. Furthermore, the system is reduced to an analogous planar dynamical system enabling a bifurcation analysis, and phase-plane portraits are used to analyze the qualitative behavior of the solutions. In order to gain a deeper understanding of the DSW system’s nonlinear dynamics and wave propagation characteristics, the stability properties of the generated solitary waves are also examined. Three-dimensional, two-dimensional, and contour plots are used to graphically represent the calculated solutions in order to improve physical interpretation. Mathematica and Maple are used to do all symbolic calculations and visualizations, verifying the precision, effectiveness, and resilience of the analytical techniques used. The findings show that the suggested techniques are quite successful and can be expanded to study increasingly complex nonlinear models that arise in fluid mechanics, engineering, and mathematical physics.
Abstract This study explores the wave dynamics of the (2 + 1)-dimensional Pavlov equation, a significant model in differential geometry and fluid dynamics, using two powerful semi-analytical methods: the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). A rigorous mathematical foundation is provided through convergence analysis based on the Banach fixed-point theorem. Methodologically, while both schemes effectively capture the stable propagation of kink-type solitary waves, they follow distinct algorithmic pathways. HPM operates directly through homotopy parameter expansions without spatial integration constraints, whereas ADM involves inverse spatial operators that inherently require careful treatment of integration constants. We demonstrate that when identical boundary conditions ( u n (0, y , t ) = 0) are strictly imposed on the spatial integration constants in ADM, both semi-analytical approaches converge to structurally comparable series terms. Numerical evaluations within the valid radius of convergence ( t = 0.01 and t = 0.05) reveal that ADM consistently achieves approximately twice the accuracy of HPM, with absolute errors roughly half those of HPM across the tested spatial domain, while both schemes retain rapid convergence to the exact solution.
Abstract The identification of gas–liquid two-phase flow patterns is crucial to fluid dynamics research and industrial applications. This study proposes a novel flow pattern identification framework that integrates variational mode decomposition (VMD), complex network analysis, and deep learning. First, the four-channel conductance signals are decomposed into intrinsic mode functions (IMFs) using VMD to capture subtle flow characteristics. Then, mutual information (MI) is used to quantify the nonlinear correlation between each pair of IMFs. Subsequently, a weighted complex network is constructed by assigning each IMF as a node and quantifying the MI between IMFs pairs as edge weights, thereby uncovering the underlying nonlinear interactions within the gas–liquid two-phase flow. In addition, multiple topological indicators, including the total length of the maximum spanning tree and the maximum participation coefficient, are extracted and analyzed to investigate the structural characteristics of different flow regimes. Finally, the topology of each complex network is represented as an adjacency matrix, which serves as input to deep learning frameworks for gas–liquid flow pattern identification. Experimental results on a self-constructed dataset demonstrate that the proposed method can effectively identify different gas–liquid two-phase flow patterns, achieving an accuracy of 95.56 %. This research establishes a complex network based on VMD and MI, effectively eliminates noise interference in the signals, extracts key structural features, and improves the accuracy and interpretability of gas–liquid two-phase flow pattern identification.
Abstract We present a proposed E 8 × E 8 kinematic scaffolding for the standard model with pre-gravitation. The notation E 8 × ωE 8 used below records a split-complex exchange grading of two factors; it is not a tensor product of groups. Each factor branches through SU (3) × E 6 and thence through trinification, E 6 → SU (3) 3 . The first factor supplies representation labels associated with the standard-model lineage, and the second supplies a mirror, pre-gravitational lineage. The identification of a single vector-like colour group across the two factors, and the proposed gravitational reading of the right-sector SU (2), remain dynamical hypotheses. Physical chiral fermions are not assigned to the E 8 adjoints: they are modelled by minimal ideals of the complex Clifford algebra C l 6 ( C ) $C{l}_{6}\left(\mathbb{C}\right)$ , while the 496 adjoint dimensions are used only as a representation-label ledger. The numerical split 208 + 288 is therefore a declared roster-matching convention, not an invariant decomposition and not a particle count. Spacetime enters through a selected six-dimensional split-biquaternionic vector space with a separately specified quadratic form of signature (3, 3). Its full frame group is SO (3, 3); deriving a soldering form and the proposed BF /Plebański dynamics remains open. The conventional Clifford–Dirac operator is constructed independently and exactly: J 2 ( H s ) ${J}_{2}\left({\mathbb{H}}_{s}\right)$ realises the vector space R 3,3 ${\mathbb{R}}^{3,3}$ through its determinant, and after choosing H s ≅ M 2 ( R ) ${\mathbb{H}}_{s}\cong {M}_{2}\left(\mathbb{R}\right)$ its matrix gradient and adjugate act between real four-dimensional Weyl modules and factorise the wave operator in both orderings. The rank-two algebra supplies the quadratic spacetime layer, whereas J 3 ( O C ) ${J}_{3}\left({\mathbb{O}}_{\mathbb{C}}\right)$ supplies the proposed internal, generation and cubic spectral layer through the magic-star decomposition of e 8 C ${\mathfrak{e}}_{8}^{\mathbb{C}}$ . We distinguish established algebraic identities from model identifications and list the missing real-form, anomaly, localisation and invariant-coupling constructions explicitly.
Abstract Expressions for the heterodyne detection efficiency of the partially coherent electromagnetic Gaussian–Schell model (EGSM) in atmospheric turbulence were derived. In this study, the signal and local oscillator beams were configured in five different polarization states: linear (LP), left/right-handed circular (LHCP/RHCP), and left/right-handed elliptical (LHEP/RHEP). The results show that as the spatial coherence length increases, the detection efficiency rises rapidly before gradually saturating. A dynamic “critical spatial coherence length” exists, which varies with propagation distance. Furthermore, the detection efficiency decreases with increasing zenith angle, turbulence intensity, and detector aperture. The influence of inner turbulence scale is significant, while that of the outer turbulence scale is negligible. Finally, the partially coherent heterodyne detection experimental system we constructed revealed that, although polarization matching is most efficient under perfectly matched conditions, the relative attenuation of circular and elliptical polarization is relatively small under turbulent conditions.
The objective of the present study is to investigate the electroosmotic flow of Casson fluid through a porous channel under slip-dependent boundary conditions, with emphasis on velocity and thermal characteristics. The flow is further influenced by the presence of a magnetic field, thermal radiation, and constant transport properties. The model incorporates silver nanoparticles uniformly dispersed in the Casson fluid, representing a blood-based nanofluid system. The governing equations are transformed into dimensionless nonlinear ordinary differential equations (ODEs) using appropriate dimensionless parameters and the electric potential distribution function. The resulting boundary value problem is solved numerically using Runge-Kutta-Fehlberg method to obtain the numerical solution. Graphical results are presented for velocity and temperature profiles over a suitable range of governing dimensionless parameters. The effects of the governing parameters on the velocity and temperature profiles of the electroosmotic flow are discussed graphically. The results indicate that the Casson fluid parameter, velocity slip, and porous medium strength enhance the velocity distribution. In contrast, increasing the Debye length, electroosmotic parameter, nanoparticle concentration, Hartmann number, and pressure gradient leads to a reduction in the velocity profile. The temperature field is significantly enhanced by Joule heating effects and the Casson fluid parameter. However, strong magnetic fields, thermal radiation, velocity slip, nanoparticle concentration, and pressure gradient tend to suppress the thermal distribution. The combined influence of porous media, slip velocity, and nanoparticle dispersion improves flow modulation and heat dissipation in electroosmotic filtration systems, enhancing separation efficiency in chemical and industrial processing.
We analytically investigate the generation of terahertz (THz) radiation via interaction of two counter propagating radially polarized q-Gaussian laser beams in homogeneous collisional plasma modulated by periodic (sinusoidal) chirp. In contrast to the linear chirp, the periodic chirp offers an oscillatory modulation of the instantaneous laser frequency that is time dependent, allowing a dynamic synchronization of the nonlinear plasma current with the emitted THz wave. Parametric analysis shows that the maximum THz emission is obtained in the low normalized frequency regime (omega/omega p approximate to 1.08-1.15) with the best output at smaller chirp modulation indices (alpha approximate to 0.4), higher q-parameter values and intermediate radial beam positions (r/r 0 approximate to 0.7-1.0). The THz amplitude is moderately increased with increasing plasma electron density and the emission is suppressed by collisional damping with increasing collision frequency, where the peak normalized field decreases from about 0.62 to 0.31 as nu increases from 0.04 omega p to 0.08 omega p . The normalized THz energy analysis reveals a monotonic decrease with increasing chirp index, corresponding to a drop of similar to 70-75 % at higher chirp values, implying the existence of an optimal chirp window for phase-coherent energy transfer. These results show that periodic chirp modulation and q-Gaussian beam shaping is an efficient and flexible method to control and optimize plasma-based THz sources.
Abstract This paper proposes an image encryption scheme based on the logic of the Tetris game and a ring oscillator coupled with a Van der Pol oscillator. The proposed scheme relies on simultaneous permutation–diffusion mechanism, in which the permutation stage involves pixel extraction and recombination in patterns similar to Tetris tetrominoes. Both encryption phases exploit a chaotic sequence generated by the coupled oscillator system. Prior to encryption, the dynamics of the coupled oscillator system is studied thoroughly, extending beyond previous studies that were limited to bifurcation illustrations. Results of dynamical study reveal complex behaviors such as bifurcation, multistability, and chaos. The latter dynamic property is critical in the encryption process and leads to strong performance results, demonstrating the robustness of the proposed encryption scheme.
In this study, the onset of double-diffusive convection in a nanofluid layer is analyzed when a uniform vertical throughflow is applied, with the velocity of the fluid at the confining boundaries described by slip conditions. The model also incorporates the effects of buoyancy forces arising from temperature and concentration variations in the nanofluid, leading to a coupled system of linear eigenvalue equations governing perturbations about the throughflow basic state. The steady-state temperature and nanoparticle concentration are obtained using the Adomian decomposition method, while the stability problem is solved numerically via the Chebyshev collocation method. Neutral stability curves and critical values are computed to examine the influence of parameters such as the nanofluid Lewis number, nanoparticle and solutal Rayleigh numbers, throughflow velocity, Brownian motion parameter, thermophoretic parameter, and slip coefficient. The results indicate that stationary instability dominates over the parameter range considered, and the role of each parameter on the critical conditions is discussed. In particular, the sign of the nanoparticle Rayleigh number plays a key role in determining how nanoparticle-induced buoyancy affects the onset of instability, as well as how throughflow and slip conditions influence the critical thresholds. Overall, the study presents a detailed analysis of the onset of double, diffusive convection in a nanofluid model of higher complexity than those based on simplified slip and no-slip formulations.
Abstract Direct laser acceleration (DLA) of electrons in vacuum is investigated using a radially polarized Gaussian and Super-Gaussian (RP SG) laser beam in the presence of an externally applied wiggler magnetic field. SG beam profiles exhibit a flatter transverse intensity distribution and reduced diffraction compared to conventional Gaussian beams, thereby providing a more uniform accelerating field over an extended interaction region. A normalized relativistic model is employed to examine the influence of the SG order on the longitudinal electric field and the resulting electron energy gain. It is found that increasing the Super-Gaussian order enhances the field uniformity and extends the effective acceleration length up to 12.7 µm, leading to improved energy transfer to electrons. The presence of the wiggler magnetic field induces transverse oscillations that enable sustained phase synchronism with the laser field through an inverse free-electron laser (IFEL)-type interaction, resulting in significant energy enhancement. For a laser wavelength of 800 nm and intensity I ∼ 3.4 × 10 19 W/cm 2 , the maximum electron energy increases from 0.82 GeV for a Gaussian beam ( m = 1) without a wiggler magnetic field to 1.42 GeV in the presence of the wiggler field, and further to 4.15 GeV for an RP SG order ( m = 4) combined with wiggler-assisted acceleration. These results demonstrate the strong synergistic effect of beam shaping and IFEL-based phase synchronization in enhancing vacuum electron acceleration. These results demonstrate that the combined use of Super-Gaussian beam shaping and magnetic modulation provides an efficient and controllable mechanism for vacuum electron acceleration, with potential applications in compact accelerators.
Abstract This study explores the formation of capillary ridges in a two-layer flow of immiscible viscous Newtonian fluids down a non-uniformly heated inclined plate. Temperature gradients induced by the heated substrate generate surface-tension variations that, in turn, produce thermocapillary (Marangoni) stresses, driving fluid flow and leading to liquid accumulation at the advancing front and the formation of pronounced capillary ridges. A comprehensive mathematical model is developed based on the conservation of mass, momentum, and energy, together with appropriate boundary and interfacial conditions. Long-wave theory is employed based on the aspect ratio of the fluid domain to derive the transient thin-film equations. The resulting coupled non-linear equations are discretized using the finite volume method and solved with a nonlinear solver. The study systematically investigates how key parameters, including temperature gradients, inclination angle, and fluid properties, influence the formation and morphology of capillary ridges. The results reveal that increased thermal gradients enhance Marangoni stresses and ridge prominence. The findings provide new insights into the interplay between thermal effects and flow behavior, offering valuable guidance for optimizing thin-film processes in applications such as coating technologies and heat-transfer systems.
In numerous branches of physics, the nonlinear cubic Schr & ouml;dinger equation serves as a fundamental model with profound applications, particularly in optics, plasma physics, fluid dynamics, and quantum mechanics. In this study, four analytical techniques have been employed to explore and derive soliton solutions of the complex Schr & ouml;dinger equation. The obtained solutions, expressed via hyperbolic, trigonometric, exponential, and rational functions, exhibit rich wave structures and dynamics. To elucidate the physical significance and practical applicability of the proposed model, several graphical simulations have been performed by assigning appropriate values to the key parameters, thereby illustrating the influence of these parameters on wave propagation characteristics. The proposed methods efficiently generate diverse traveling solutions in physics and applied sciences.
This paper investigates dust-acoustic waves in a polarized, self-gravitating dusty plasma with kappa-distributed superthermal ions. We resolve the longstanding degeneracy in the common Psi = Gamma Phi assumption by demonstrating that polarization and self-gravity, though mathematically coupled, exert physically distinct influences on wave dynamics. Linear analysis reveals that polarization actively suppresses wave propagation, while self-gravity controls Jeans instability thresholds; their competition creates tunable stability boundaries scalable with plasma parameters. Through reductive perturbation theory, we derive a gravitationally modified Korteweg-de Vries equation whose coefficients explicitly depend on polarization strength R, self-gravity parameter (Gamma), and ion superthermality kappa i . Analytical solutions obtained via the (g '/g) expansion method yield a spectrum of coherent structures, including bright solitons, kinks, and singular waves. The joint modification of wave propagation arises from a scale-dependent competition: self-gravity acts as a long-range attractive force that reduces phase velocity and fosters clumping, while the polarization force provides a repulsive correction sensitive to plasma gradients. The physical mechanism is driven by ion superthermality; a lower spectral index kappa i provides a more energetic ion population that more easily deforms the Debye shielding cloud around dust grains, thereby strengthening the polarization force and intensifying nonlinear steepening. Strong ion superthermality (lower kappa i ) amplifies both mechanisms by increasing the polarization coefficients c kappa 1 ${c}_{{\kappa }_{1}}$ , c kappa 2 ${c}_{{\kappa }_{2}}$ and reducing the effective Jeans length, thereby promoting the formation of persistent, macroscopic structures. These results provide a unified mechanism to explain transient "spokes" in Saturn's rings and initial dust clumping in protoplanetary disks, bridging grain-scale interactions to collective astrophysical phenomena.
In this work, using the transfer matrix method, we calculated the transmittance spectrum of an optical biosensor based on a defective one-dimensional photonic crystal for detecting cells infected with the Chikungunya virus. The heterostructure consists of alternating layers of GaAs and the high-critical-temperature superconductor Hg-1223, where the crystal's periodicity is disrupted by the insertion of a cavity that acts as a sensing layer. Given that the cavity is infiltrated with plasma, platelets, and uric acid in both normal and infected states, we measured the transmittance spectrum under controlled variations in hydrostatic pressure and temperature. The results show the presence of a confined mode within the photonic band gap, whose position shifts with increasing applied pressure, enabling us to distinguish between healthy and infected cells. A maximum quality factor of 3.06 & times; 103 is reported for plasma at 10 GPa, and the confined energy decreases as the temperature is raised to 120 K. Additionally, we found that the biosensor is sensitive to increases in pressure or temperature across all cell types.
