The dynamic magnetic phase behavior of a mixed-spin (1,7/2) Blume-Capel Ising system on a hexagonal lattice is investigated using the Path Probability Method in the presence of a periodically oscillating magnetic field. The effects of the magnetic-field amplitude and crystal-field interaction on the dynamic order parameters and phase diagrams are examined systematically for both ferrimagnetic (J AB < 0) and ferromagnetic (J AB > 0) exchange regimes. Thermal variations in dynamic magnetizations are used to determine the phase-transition temperatures and the nature of the transitions. Dynamic phase diagrams constructed in the (T, h 0 ) and (T, d) planes reveal first-order and second-order dynamic phase transitions, tricritical points, and parameter-dependent phase boundaries. Various Néel-type compensation behaviors are observed in the ferrimagnetic regime, whereas no compensation phenomenon occurs in the ferromagnetic case. The results demonstrate that competition among exchange interactions, crystal-field effects, thermal fluctuations, and the oscillating magnetic field strongly influences the stability of the dynamically ordered phases and the topology of the phase diagrams. The present study provides a systematic dynamic phase-diagram analysis of the mixed-spin (1,7/2) Blume-Capel system on a hexagonal lattice within the PPM framework.
The dynamic magnetic properties of the mixed-spin (3/2,7/2) Blume-Capel Ising system on an interpenetrating square lattice are investigated using the path probability method in the presence of a time-dependent oscillating magnetic field. The thermal variations of the dynamic magnetizations, stationary magnetization oscillations, compensation behavior, and dynamic phase diagrams are examined for both errimagnetic and ferromagnetic exchange interactions. The system exhibits dynamically ordered and disordered phases separated by first- and second-order dynamic phase transition lines, together with dynamic tricritical points. For the ferrimagnetic case, coexistence regions and P-, Q-, R-, S-, and N-type compensation behaviors are observed, whereas W-, or M-type characteristics are absent within the investigated parameter ranges. Increasing the crystal-field interaction stabilizes the ordered phase, while increasing the magnetic-field amplitude promotes dynamic disordering and bistability. In contrast, the ferromagnetic case exhibits a simpler phase structure, with broader ordered regions, weaker coexistence effects, and no compensation behavior. The results demonstrate that the interplay among exchange interactions, crystal-field interactions, and oscillating magnetic field governs the nonequilibrium phase topology and dynamic critical behavior of the mixed-spin (3/2,7/2) system.
Reciprocal-space phonon spectra are commonly used as material descriptors rather than as coordinates of a dynamical space. We show that a finite retained set of normalized phonon and neutron-weighted spectra defines an observable quotient of microscopic descriptions and, for three selected endpoint materials, an explicit two-dimensional simplex of spectral mixtures in retained-observable space. The simplex is a reduced model: its vertices are realized material observables, whereas no microscopic source description is assumed to realize every interior mixture. For the B2 TlBr–CsBr–RbI trio, the square-root immersion of this simplex has a positive-definite pullback metric. Comparison with an affine density-[Formula: see text] reference yields a coordinate-invariant logarithmic contrast field with a boundary-controlled saddle at barycentric weights [Formula: see text]. Using this contrast as the reduced potential and the pullback metric as the kinetic metric defines a natural saddle–center Hamiltonian on the cotangent bundle of the observable simplex. Its quartic canonical normal form has hyperbolic rate [Formula: see text], elliptic angular frequency [Formula: see text], and quartic action coefficients [Formula: see text]. Restriction of the quartic normal form to the transition-state normally hyperbolic invariant manifold (NHIM) fixes the fourth-order excess reduced-energy law [Formula: see text], where [Formula: see text] is the elliptic action. Trajectories of the complete fourth-order local Hamiltonian validate nonrecrossing transport, the signed threshold, and the predicted logarithmic delay. The saddle-weighted full-Brillouin-zone phonon density-of-states (DOS) centroid, [Formula: see text] meV, fixes the Hamiltonian time unit to [Formula: see text] ps. An exhaustive census finds saddles in 28 of 56 eligible B2 triples, while matched B1/B3 and elemental face-centered-cubic (FCC) controls show that the construction can be applied across distinct symmetries without implying universal saddle occurrence. The resulting dynamics belongs to the constructed observable-mixture space and is not an atomistic anharmonic lattice Hamiltonian.
Density functional theory (DFT) calculations were used to investigate how CO adsorption sites affect the structural, electronic, charge transfer, vibrational, and optical properties of Ge-doped Si quantum dots. Three adsorption sites, namely hollow, top, and valley, were investigated. Among the three configurations, the top site exhibits the strongest adsorption, with an adsorption energy of -0.915 eV, whereas the valley site shows the weakest interaction, with E ads = -0.124 eV. CO adsorption at the top site produces the largest geometric deformation and surface buckling, indicating a stronger interaction between CO and the SiGe surface. CO adsorption substantially modifies the electronic structure of the quantum dot. The HOMO-LUMO gap decreases, while the density of states near the Fermi level increases, particularly for the top configuration. HOMO-LUMO distributions, charge density differences, and Bader charge analysis further reveal pronounced charge redistribution and orbital overlap at the top site. Adsorption was also found to increase low frequency soft vibrational modes and reduce the dynamical stability of the system. The optical properties of the system, including the dielectric function, absorption coefficient, reflectivity, and joint density of states (JDOS), show the appearance of new peaks or changes in peak intensity, most clearly at the top site. These findings demonstrate that the adsorption site strongly influences the gas-surface interaction and the resulting electronic and optical responses. The results suggest that the investigated SiGe quantum dot model may be relevant to CO sensing and related nano-optoelectronic applications.
We examine the influence of hole doping on superconducting pairing symmetries in the two-dimensional Hubbard model extended by next-nearest-neighbor hopping, nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair-hopping processes. Using Lanczos exact diagonalization supported by projector quantum Monte Carlo method, we calculate superconducting correlation functions corresponding to s-wave, extended s-wave, and d-wave pairing over a broad range of electron concentrations and interaction parameters. We find that hole doping acts as an efficient control parameter of superconducting pairing symmetry, giving rise to robust crossovers between the dominant pairing correlations. While extended s-wave pairing dominates throughout most of the overdoped regime, reducing the hole concentration progressively enhances d-wave correlations over large regions of the ground-state diagram. The critical doping associated with these crossovers depends strongly on the underlying interaction mechanism. In particular, correlated hopping and next-nearest-neighbor hopping substantially modify the location of the pairing-symmetry boundaries, whereas the local Hubbard interaction exhibits a comparatively weaker effect. In contrast to all other interaction channels, a finite nearest-neighbor Coulomb interaction additionally stabilizes conventional s-wave state over a sizeable region of parameter space. Our results demonstrate that superconducting pairing symmetry in the extended Hubbard model is governed by a subtle interplay between carrier concentration and nonlocal electronic interactions.
Rogue waves and lump solutions are crucial for describing extreme waves in higher dimensions. This paper reports the (3+1)-dimensional higher-order Kadomtsev-Petviashvili (hKP) equation, which governs the propagation of weakly nonlinear dispersive waves in shallow water. We present a bilinear neural network-based framework for symbolic computation to derive novel localized wave solutions. By configuring the network with a single hidden layer, we successfully obtain three distinct hybrid lump solutions consists of lump-sine, lump-exponential and lump-hyperbolic solutions. We reveal that each lump returns to its initial form, amplitude and velocity after a collision due to the elastic features exhibited in lump-sine interaction. Similarly, we establish a double hidden layer configuration to generate a rogue wave solution. The dynamic characteristics and evolutionary behaviors of the derived wave solutions are illustrated through surface, line and density plots, utilizing constraints and suitable selective parameter values. These solutions are reported for the first time by this method and enrich the analysis of hKP equation in fluid dynamics.
The elliptic cylindrical Kadomtsev–Petviashvili (ecKP) equation is an integrable variable-coefficient model for weakly nonlinear dispersive waves in elliptic cylindrical geometry. In this paper, a decay mode means a line-type localized component whose amplitude decays away from an oblique core while the complete field remains supported by a nontrivial background. Exact line-type decay mode solutions of the ecKP equation are constructed by a simplified homogeneous balance method. The main theoretical step is the introduction of a geometry-compatible background field, which makes it possible to derive a logarithmic nonlinear transformation directly from the balance between nonlinear and dispersive terms. The resulting homogeneous auxiliary equation is solved by a finite exponential expansion and yields explicit one-decay and two-decay mode families. Direct symbolic substitution verifies that the background field, the one-decay solution, and the two-decay auxiliary function satisfy their corresponding equations identically. Physically, the plotted localized components describe oblique ridges whose amplitude, width and phase are modulated by the elliptic cylindrical spreading factor [Formula: see text]. They therefore represent straight-fronted decay modes on a nonuniform geometry-induced background, rather than the curved or horseshoe-like waves generated by KP–ecKP variable transformations.
Ultrafast fibre lasers in the 2[Formula: see text]m spectral region are highly desirable for applications such as laser surgery, environmental sensing and micromachining. Saturable absorbers (SAs) currently used to generate pulses in this region perform admirably in laboratory settings. Still, their high costs, complex fabrication processes and narrow operating bandwidths prevent their widespread adoption in real-world applications. In this work, we demonstrate, for the first time, the use of Quinaldine Red as a highly effective and viable alternative. The fabrication of the SA only requires dissolving Quinaldine Red powder in isopropyl alcohol to form an aqueous solution at a 10[Formula: see text]mg/mL concentration before being drop-casted onto an arc-shaped single-mode fibre (SMF-28) to form the SA. The SA showed good nonlinear optical properties including a high modulation depth of 12.0% and a low saturation intensity of 0.56[Formula: see text]MW/cm 2 , and when integrated into a thulium-holmium-doped fibre laser (THDFL) the SA was able to generate stable mode-locked pulses at 1911.8[Formula: see text]nm as well as a pulse width of 1.96[Formula: see text]ps, repetition rate of 13.4[Formula: see text]MHz and pulse energy of 0.16[Formula: see text]nJ with a peak power of 83[Formula: see text]W. The laser also demonstrated a slope efficiency of 1.78% and exceptional long-term stability over a 2-h observation period and after a 2-week dormant state, with a measured signal-to-noise ratio (SNR) of 43[Formula: see text]dB. These findings suggest that dye-based SAs like Quinaldine Red offer a robust, giving a pathway for the development of future optical modulators.
Phoxonic crystals (PXCs) are artificial composite periodic structures that simultaneously exhibit both phononic and photonic bandgaps. This paper proposes a liquid-sensing structure based on a heterogeneously structured cavity PXCs and investigates its sensing characteristics using the finite element method (FEM). In addition, the temperature dependence of the sensing performance is analyzed by considering the influence of the thermo-optic effect on the refractive index and sound velocity. The results demonstrate that the proposed structure can effectively confine both phononic and photonic energy at specific frequencies within the cavity, enabling high-sensitivity sensing for both acoustic and optical signals. The acousto-optic (AO) resonance peak shifts with variations in solution concentration, yielding sensitivities of up to 3.65 MHz/ms -1 and 750.48 nm/RIU for acoustic and optical sensing, respectively. With temperature variation, the sensitivities reach 11.6 MHz/K for acoustic sensing and -146 pm/K for optical sensing. Furthermore, the structure exhibits dual characteristic acoustic peaks, which significantly enhance the stability and accuracy of acoustic sensing. These findings establish a platform for multiphysical sensing in liquid environments, with potential applications in biomedicine, environmental monitoring, and food safety.
This paper retrieves optical solitons in birefringent fibers modeled by the complex Ginzburg-Landau equation and introduces application of its chaotic characteristics in image encryption and decryption. The model incorporates cubic-quintic-septic-nonic law of nonlinear refractive index structure and perturbation terms of the Hamiltonian type as well as multiplicative white noise effect. Two integration schemes, that are the generalized exponential rational function approach, and the solution procedure that utilizes the Cole-Hopf transformation with several direct assumptions in conjunction, are implemented to derive exact solitary wave solutions. Also, sequences generated from the perturbed chaotic system are employed for Walsh–Hadamard transform coefficient permutation, deoxyribonucleic acid key generation, and dynamic deoxyribonucleic acid rule selection. The proposed color image encryption method is evaluated through histogram, adjacent-pixel correlation, information entropy, differential-attack, surface-plot, key-space, known-plaintext, chosen-plaintext, computational-complexity, execution-time, memory-consumption, and comparative analyses.
2D functionalized nanomaterials like metal oxides and 2D grown perovskites have emerged as auspicious candidates for electrochemical charge diffusion and storage applications. Integrating the functionality of metal oxide into 2D modeled perovskite has efficiently proved to enhance the pseudo capacitor competence in field of electrochemical energy cycle. SrCrO 3 perovskite fabricated using Sol Gel technique was studied for morphology and electrochemical redox energy storage capacity. The successful synthesis of 2D structural nanoscopic lamellae flakes with nano crystalline size was acknowledged using XRD, SEM, and FTIR. UV was utilized to validate an effective bandgap of 2.4-2.9 eV using absorption characteristics. The substantial potential pseudo-supercapacitive behavior of SrCrO 3 perovskite-Ni foam electrode was analyzed in three electrode setup using 2M KOH alkaline aqueous electrolyte. Duck-shaped CV curve of Sr-Perovskite demonstrated the maximum specific capacitance of 983 Fg -1 at the scan rate of 10 mV/s exposing the pseudocapacitive nature. The GCD exposed specific capacitance of 1618 Fg -1 at a current density of 1 Ag -1 pointed to significant charge storage capability. The electrode proved to be cyclic stable and preserved about 82% of its capacitance even after 40 hrs. These results exhibit Strontium Chromate Perovskite as a noteworthy electrocatalytic nanocomposite material for electrical energy storage.
Many technical systems rely on efficient temperature regulation. These systems include thermal shields for aircraft, metal forming, microelectronics, solar energy collectors, nuclear cooling units, polymer extrusion, and nuclear power plants. It is common for these technologies to function in environments with very hot and uneven surfaces, which calls for fluids with exceptional performance. To address this challenge, the heat transfer and nonlinear flow characteristics of a hybrid nanofluid, which includes water-dispersed copper (Cu) nanoparticles and aluminium oxide (Al2O 3 ) nanoparticles are investigated over an inclined stretching/shrinking sheet. The combined impacts of heat source and thermal radiation are considered in the study. The physical model has highly coupled, nonlinear governing equations due to the incorporation of nonlinear surface motion, inclination-induced gravity effects, and hybrid nanoparticle interactions. We transform them into a system of MATLAB-solvable nonlinear ordinary differential equations by utilizing similarity variables. There is also strong agreement when results from certain limiting circumstances are compared to previously published data. Several physical parameters control the problem, and the impact of these parameters on different flow distributions is studied extensively using both tabular and graphical methods. This study analyzed nonlinear hybrid nanofluid flow over an inclined stretching/shrinking surface influenced by magnetic forces, radiation, suction, and heat generation, with machine learning and Sensitivity analysis applied for predictive modeling. Furthermore, a global sensitivity analysis based on Sobol indices is performed to quantify the relative importance of governing parameters and their interaction effects on the skin-friction coefficient and local Nusselt number. The results identify the dominant parameters controlling momentum and heat transfer characteristics. Multiple Linear Regression (MLR) served as an efficient surrogate, achieving high accuracy (R 2 = 0.98 for C f , R 2 = 0.92 for N ux ) in estimating flow and thermal characteristics.
We report experimental and first-principles studies of bulk NiCrMnAl alloy. X-ray diffraction of annealed, arc-melted sample shows a cubic Heusler phase. The (111) and (200) superlattice peaks are absent, indicating site disorder. Annealing restores the (400) peak and improves crystallinity but does not yield full long-range order. Calculated elastic and mechanical properties indicate mechanical stability, brittle behavior, and mainly covalent bonding. Phonon calculations show no imaginary modes, confirming dynamical stability. Electronic structure calculations using hybrid-functional (HSE06) method suggest half metallic behavior. Measured resistivity of NiCrMnAl increases with temperature. From 6 to 50 K resistivity follows a power law close to temperature to the 2.63 power. Low temperature fits prefer a disorder dependent model with square root of temperature plus a quadratic term. From 50 to 300 K transport is mainly linear in temperature with a smaller higher-order correction. Chemical disorder likely suppresses the intrinsic half metallic nature.
Water contamination by persistent organic pollutants has become a major environmental concern, creating an urgent need for efficient and sustainable treatment technologies. Visible-light-driven semiconductor photocatalysis offers a promising approach for pollutant degradation; however, its practical efficiency is often limited by rapid recombination of photogenerated charge carriers. In this study, thermally exfoliated g-C 3 N 4 nanosheets were integrated with GdFeO 3 through an ultrasonication-assisted assembly approach, and the CNNS/GdFO composition was systematically optimized to enhance visible-light photocatalytic performance. The optimized composite achieved approximately 94% rhodamine B (RhB) removal based on the decrease in UV–Vis absorbance after 120[Formula: see text]min of visible-light irradiation. The enhanced photocatalytic activity was consistent with a proposed S-scheme charge-transfer mechanism involving h[Formula: see text], O[Formula: see text] and [Formula: see text]OH reactive species. Photoluminescence (PL) and electrochemical impedance spectroscopy (EIS) studies show that enhanced photocatalytic activity is linked to better separation and reduced recombination of photogenerated electron–hole pairs. These findings open the path for more sustainable industrial practices by emphasizing the advantages of CNNS/GdFO composites in lowering environmental pollution and expanding our understanding of effective visible-light photocatalysts.
Al-Mg alloys have been identified as having significant potential for application in energetic materials and propulsion systems. The thermophysical properties of these alloys directly influence a number of processes, including propellant preparation, storage safety, and combustion efficiency. In this study, a high-precision NNP for Al-Mg alloys was constructed based on first-principles data covering the phase diagram composition. This potential function demonstrates excellent performance in predicting a number of key properties, including energy, atomic forces, crystal structure, mechanical properties, vibrational characteristics, and dynamic evolution over a wide temperature range. This renders it a dependable instrument for atomic-scale thermal property research. Employing the innovative NNP potential, molecular dynamics simulations were employed to systematically investigate the effects of Mg content on the melting point, thermal expansion coefficient, specific heat capacity, thermal conductivity, radial distribution function, and Warren-Cowley parameters of Al-Mg alloys. The findings suggest that even a minimal amount of Mg doping can substantially reduce the alloy's melting point and thermal conductivity, while concurrently increasing the thermal expansion coefficient and specific heat capacity. As the Mg content rises, the thermal expansion coefficient and thermal conductivity demonstrate non-monotonic trends, with inflection points at 40 wt.% and 30 wt.%, respectively. This phenomenon is intimately linked to the stability of the Al-Mg alloys crystal structure. These findings reveal, at the atomic scale, the regulatory mechanisms of Mg content on the thermal properties of Al-Mg alloys, providing an atomic-scale basis for composition design and performance control in propellants.
This work investigates how frequency-comb spacing patterns influence the nonlinear dynamics of optically injected semiconductor lasers through numerical simulation. Equal, unequal, and logarithmic comb-spacing configurations are compared over a detuning–injection parameter grid using bifurcation diagrams, time-domain analysis, and a finite-time reconstructed divergence diagnostic, denoted Λts, derived from the simulated field-amplitude sequence. The results show that irregular comb spacing modifies the distribution of high-complexity response regimes. Unequal spacing reduces the classified high-complexity fraction from 62.57% for the equal-spacing baseline to 57.29%, corresponding to an absolute reduction of 5.28 percentage points and a relative reduction of 8.44% under the adopted numerical conditions. It also produces a smoother diagnostic landscape, indicating fewer strongly irregular post-transient responses across the investigated parameter grid. Because Λ ts is derived from scalar time-series reconstruction rather than direct variational-equation integration, we use it as an auxiliary comparative diagnostic, not as a strict calculation of the maximum Lyapunov exponent λmax or as sole proof of deterministic chaos. These findings suggest that comb-spacing irregularity influences nonlinear response regimes; however, full Lyapunov-spectrum analysis is necessary for definitive chaos classification.
Galitskii-Migdal-Feynman (GMF) model is employed to compute the total scattering cross section σ T and the viscosity scattering cross section σ η for a mixture of 20 Ne and 40 Ar atoms over a temperature range of 90-120 K and at various number densities. Both σ T and σ η are determined as a function of relative momentum at different temperatures and densities. It is observed that, at higher density, both cross sections exceed their corresponding values at lower density. The influence of temperature on σ T and σ η is also examined to investigate the thermal effects on transport properties; no significant temperature-induced variation is detected between 90 and 120 K. Additionally; the contribution of partial scattering waves is analyzed. The results reveal a rich resonance spectrum with multiple sharp peaks corresponding to different partial waves. At low energy, the S-wave dominates the scattering. As the relative momentum increases, a D-wave resonance emerges. With further increase in relative momentum, additional quasi-states corresponding to ℓ=4, ℓ=6 and ℓ=8 are also observed. Finally, the average values of σ T and σ η are computed as a function of temperature: 〈σ T 〉 decreases with increasing temperature, whereas 〈σ η 〉 shows a slight increase.
In this paper, Monte Carlo calculations with the Blume-Capel model are used to investigate the magnetic properties of a butterfly graphene nanostructure. A particular emphasis is placed on the formation of magnetization plateaus influenced by exchange fields, anisotropy, and temperature. The stability of a discrete magnetic state influenced by lattice structure as well as competition between different lattice parameters is considered. It should be noted that this paper offers general guidance on magnetization plateaus in graphene nanostructures with potential applications at the nano scale.
Nonlinear partial differential equations are used to describe complicated physical systems, ranging from fluid mechanics to optical solitons. The physical meaning of the equations can only be understood by thoroughly examining the terms that constitute the equations since each term usually accounts for a basic physical phenomenon. This review is intended to give an overview of the physical significance of the different terms in nonlinear partial differential equations and discuss the various transformations that are used to solve such equations. We address how the terms relate to physical factors like wave propagation, dispersion, nonlinearity, and external forces. The study systematically classifies the principal terms appearing in nonlinear partial differential equations according to their physical roles, including nonlinear, dispersive, diffusive, and dissipative effects. Furthermore, it provides a comparative analysis of widely used transformations such as traveling wave, scaling, Cole–Hopf, Hirota bilinear, and Painlevé transformations, while highlighting their applicability, limitations, and physical significance across fluid dynamics, nonlinear optics, plasma physics, Bose–Einstein condensates, and biological systems.
The accurate detection of hazardous gases such as methane (CH 4 ), carbon monoxide (CO), and ammonia (NH 3 ) is critical for ensuring miner safety in coal mines. Conventional gas sensors suffer from significantly reduced performance in harsh mining environments characterized by high humidity and dust levels. Two-dimensional transition metal dichalcogenides (TMDs) have emerged as promising materials for next-generation gas sensors due to their unique electronic structures and tunable surface reactivity. Using first-principles calculations, this study systematically investigates how transition metal doping (Ni, Cu, Pd, Ag) modulates the gas-sensing properties of NbSe 2 . The results demonstrate that metal doping substantially improves NbSe 2 's gas adsorption capacity. Ni-doped NbSe 2 shows optimal performance for CH 4 (-0.367 eV) and NH 3 (-1.845 eV), while Pd-doped NbSe 2 exhibits the strongest CO adsorption (-1.525 eV). Electronic structure analysis, charge transfer calculations, and work function studies reveal the structure-activity relationship between surface electron emission and gas adsorption. Notably, recovery time calculations suggest Ni-NbSe 2 maintains excellent adsorption-desorption equilibrium for CH 4 at room temperature, indicating strong practical applicability. This work elucidates the atomic-scale gas adsorption mechanisms in doped NbSe 2 , providing crucial theoretical guidance for designing advanced gas sensors for mine safety monitoring.
