Abstract Ion-acoustic solitary waves offer a useful test bed for separating plasma nonthermality from memory effects. Starting from a cold-ion fluid model with suprathermal κ-distributed electrons, we derive the κ-dependent Kortewegde Vries (KdV) and Kadomtsev-Petviashvili (KP) coefficients by reductive perturbation theory. A Caputo derivative of order 0 < α ≤ 1 is introduced only afterwards as a phenomenological slow-time memory closure, so the roles of κ and α remain distinct. At α = 1, the classical KdV equation is integrable and exact Hirota one-and two-soliton solutions provide demanding benchmarks for the numerical solver. For α < 1, we evolve the fractional KdV and KP-II equations directly with an L1-Fourier pseudospectral scheme, without assuming a fractional soliton form. The implementation reproduces secondorder convergence in the classical limit, keeps KdV invariant drifts below 1.1 × 10 -4 , and passes fractional time-step and KP spatial-resolution checks. The simulations show that stronger memory reduces crest speed and peak amplitude and postpones overtaking interactions for every tested κ. In KP-II, it also produces a small additional decrease in a weak transverse displacement modulation over the simulated interval, together with longitudinal reshaping. These results identify a measurable departure from integrable ion-acoustic dynamics while keeping suprathermal statistics and temporal memory as separate modeling controls.
Abstract To address the unclear mechanisms regarding how different spatial energy distributions of laser spots affect powder-laser interaction and multi-physical field responses in the melt pool during off-axis powder feeding laser cladding on curved substrates, this study conducted a comparative investigation on powder transport and cladding processes under rectangular and circular laser spot conditions. Continuous-discrete phase and thermo-fluid-stress multi-field coupled numerical model was established for laser cladding of Fe31 powder with off-axis powder feeding on a Q235 curved substrate. The model employs a 1200 W laser power, a scanning speed of 6 mm/s, and a powder feed rate of 10 g/min. Considering the particle size distribution and the temperature-dependent thermal properties of the material, it conducts a comparative analysis of the transient evolution of powder temperature, concentration, flow velocity, as well as the temperature field, flow field, and stress field in the melt pool under both rectangular and circular beam spot conditions. The results show that, under the same total laser power, the rectangular light spot has a wider and more uniform energy distribution area, reducing the concentration of local heat input. When the laser irradiation lasts for 2 seconds, the maximum flow velocity of the rectangular light spot increases by approximately 21.1%; the maximum transient thermal stress decreases by approximately 7.9%. The rectangular light spot model was subjected to 12 repeated measurements using infrared thermal imaging experiments, and the relative error between the simulated temperature and the experimental measurement results was 1.47%. The calculations show that, rectangular light spots have a more uniform distribution of heat input, which can reduce local peak temperatures and alter the flow and stress distribution characteristics of the molten pool. This study provides a theoretical reference for the selection of different light spot shapes and the optimization of process parameters in oblique-axis powder-fed laser cladding.
Abstract Local unitary (LU) equivalence classifies quantum states up to changes of local bases and preserves their entanglement properties. Polynomial LU invariants provide an algebraic approach to determining whether two quantum states are LU equivalent. We revisit the ring of complex polynomial LU invariants on the full two-qubit operator space, equivalently the invariant ring under the local conjugation action of $\GL(2,\bbC)\times\GL(2,\bbC)$. For the two-qubit system, King \emph{et al.} previously determined a generating set of 21 invariants and the Cohen--Macaulay structure of this ring. Using a unified notation, we provide a self-contained derivation of the known Molien series and a systematic graphical reconstruction of the known generators. The Molien series is derived by explicit contour integration over the maximal torus, supplying computational steps not given in the earlier treatment. We systematically reconstruct the known generators using the graphical tensor method and provide explicit algebraic reductions of the candidate invariants. This work clarifies the calculations and graphical construction underlying the established results.
Abstract We introduce a geometry‑dependent tight‑binding model for graphene π‑electrons—the Tan‑Bo model—in which nearest‑neighbour hopping integrals are parametrized by a Möbius angular factor combined with exponential decay. This construction naturally captures bond‑orientation anisotropy while preserving the gapless Dirac cone at the K point under Hermitian assembly. When the reverse‑bond hopping violates the complex‑conjugation relation, the non‑Hermitian assembly yields complex eigenenergies that diagnose non‑reciprocal band structures rather than quasiparticle lifetimes. Benchmarking against the Slater–Koster scaling demonstrates exact equivalence in the isotropic limit. Embedding the Tan‑Bo intralayer fk into the Bernal bilayer McCann model recovers the robust linear gap‑bias relation ΔK≈2δ. Under uniaxial strain, a hybrid scheme combining Harrison/Pereira distance scaling with Möbius angular modulation generates tunable real‑band separation and non‑Hermitian imaginary components. Kubo optical conductivity reproduces the universal Dirac plateau, the TB van Hove structure, and strain‑induced σxx/σyy dichroism qualitatively consistent with polarized transmittance trends. This work provides a reproducible single‑particle benchmark and parametrization reference for future non‑Hermitian calculations including correlation effects.
Abstract In this paper, we study isotropic as well as anisotropic polytropic stellar configurations within the framework of exponential f (R, T ) gravity, defined as f (R, T ) = R + γe χT . This f (R, T ) model introduces a non-minimal coupling between matter and geometry through an exponential dependence on the trace of the energy-momentum tensor. The modified field equations, together with the hydrostatic equilibrium and Lane-Emden equations, are derived for two different polytropic equations of state. The resulting system is solved numerically, and the behavior of matter variables, energy conditions, and stability criteria is analyzed graphically for different model parameters and for polytropic indices n = 1 and n = 1.5. The role of anisotropy in determining the structural properties of the compact configurations is also emphasized. It is found that anisotropy significantly impacts the compactness, with the surface compactness decreasing as the anisotropy parameter increases. The results indicate that the proposed model remain physically viable and stable, leading to consistent stellar configurations within the exponential f (R, T ) gravity framework.
