Search Results (618)

We derive an analytical solution to the one-dimensional linearized Boussinesq equation with mixed boundary conditions (Dirichlet–Neumann), formulated to describe drainage in porous media. The solution is obtained via the unified transform method (Fokas method), extending its previous applications in infiltration problems and illustrating its utility in soil hydrology. An explicit integral representation is constructed, considering different types of initial conditions. Numerical examples are presented to demonstrate the accuracy of the solution, with direct comparisons to the classical Fourier series approach. Full article

This main focus of this work is the fractional-order nonlinear Schrödinger equation with wave operators. First, a conservative difference scheme is constructed. Then, the discrete energy and mass conservation formulas are derived and maintained by the difference scheme constructed in this paper. Through rigorous theoretical analysis, it is proved that the constructed difference scheme is unconditionally stable and has second-order precision in both space and time. Due to the completely implicit property of the differential scheme proposed, a linearized iterative algorithm is proposed to implement the conservative differential scheme. Numerical experiments including one example with the fractional boundary conditions were studied. The results effectively demonstrate the long-term numerical behaviors of the fractional nonlinear Schrödinger equations with wave operators. Full article

This paper investigates the teleparallel Robertson–Walker (TRW) $F\left(T\right)$ gravity solutions for a Chaplygin gas, and then for any polytropic gas cosmological source. We use the TRW $F\left(T\right)$ gravity field equations (FEs) for each k-parameter value case and the relevant gas equation of state (EoS) to find the new teleparallel $F\left(T\right)$ solutions. For flat $k=0$ cosmological case, we find analytical solutions valid for any cosmological scale factor. For curved $k=\pm 1$ cosmological cases, we find new approximated teleparallel $F\left(T\right)$ solutions for slow, linear, fast and very fast universe expansion cases summarizing by a double power-law function. All the new solutions will be relevant for future cosmological applications on dark matter, dark energy (DE) quintessence, phantom energy, Anti-deSitter (AdS) spacetimes and several other cosmological processes. Full article

We present a model of superfluidity based on the internal variable theory. We consider a two-component fluid endowed with a scalar internal variable whose gradient is the counterflow velocity. The restrictions imposed by the second law of thermodynamics are obtained by applying a generalized Coleman–Noll procedure. A set of constitutive equations of the Landau type, with entropy, entropy flux and stress tensor depending on the counterflow velocity, is obtained. The propagation of acceleration waves is investigated as well. It is shown that the first-and-second sound waves may propagate along the system with speeds depending on the physical parameters of the two fluids. First sound waves may propagate in the same direction or in the opposite direction of the counterflow velocity, depending on the concentration of normal and superfluid components. The speeds of second sound waves have the same mathematical form of those propagating in dielectric crystals. Full article

This paper investigates the quasi-concircular curvature tensor on sequential warped product manifolds, which extend the classical singly warped product structure. We examine various curvature conditions associated with this tensor, including quasi-concircular flatness, quasi-concircular symmetry, and the divergence-free quasi-concircular condition, and we explore the properties of related soliton structures. In addition, we analyze the implications of these results in Lorentzian geometry by deriving explicit expressions for the Ricci tensor and scalar curvature of the considered manifolds. The study concludes with an illustrative example that emphasizes the geometric significance and potential applications of the investigated structures. Full article

This work presents a numerical investigation of Richtmyer–Meshkov instability (RMI) in shock-driven single-mode stratified heavy fluid layers, with emphasis on the influence of the Atwood number. High-order modal discontinuous Galerkin simulations are carried out for Atwood numbers ranging from $A=0.30$ to $0.72$, allowing a systematic study of interface evolution, vorticity dynamics, and mixing. The analysis considers diagnostic quantities such as interface trajectories, normalized interface length and amplitude, vorticity extrema, circulation, enstrophy, and kinetic energy. The results demonstrate that the Atwood number plays a central role in instability development. At low A, interface deformation remains smooth and coherent, with weaker vorticity deposition and delayed nonlinear roll-up. As A increases, baroclinic torque intensifies, leading to rapid perturbation growth, stronger vortex roll-ups, and earlier onset of secondary instabilities such as Kelvin–Helmholtz vortices. Enstrophy, circulation, and interface measures show systematic amplification with increasing density contrast, while the total kinetic energy exhibits relatively weak sensitivity to A. Overall, the study highlights how the Atwood number governs the transition from linear to nonlinear dynamics, controlling both large-scale interface morphology and the formation of small-scale vortical structures. These findings provide physical insight into shock–interface interactions and contribute to predictive modeling of instability-driven mixing in multicomponent flows. Full article

We study a class of circular restricted planar Newtonian four-body problems in which three masses are positioned at the vertices of a Lagrange equilateral triangle configuration, each mass revolving around the center of mass in circular orbits. Assuming that the value of the fourth mass is negligibly small (i.e., it does not perturb the motion of the other three masses, though its own motion is influenced by them), we use variational minimization methods to prove the existence of noncollision periodic solutions with some fixed winding numbers. These noncollision solutions exist for both equal and unequal mass values for the three bodies located at the vertices of the Lagrange equilateral configuration. Full article

Resonance self-shielding in multi-resonant nuclide media is a dominant physical process in reactor neutronics analysis. This study proposes an improved subgroup method (ISM) based on Padé rational approximation, constructing a high-order rational function mapping between effective and background cross-sections to overcome the precision bottleneck of traditional DSMs and BIMs in nonlinear resonance interference scenarios. The method first generates cross-section relation data via ultra-fine group calculations, then solves subgroup parameters using a positive definite system, with a Spatial Homogenization (SPH) factor introduced for reaction rate conservation. Validation results show that ISM + SPH reduces k-infinity errors from −708 pcm (DSM) to +5 pcm for UO₂ fuel, and from −269 pcm to +45 pcm for MOX fuel with ²³⁹Pu, significantly enhancing neutron transport accuracy in complex fuel systems. This work provides a theoretically rigorous and practically applicable approach for efficient resonance modeling in advanced reactor fuel design. Full article

The quantum Hall effect is a paradigmatic example of topological order, characterized by precisely quantized Hall resistance and dissipationless edge transport. These edge states are chiral, propagating unidirectionally along the boundary, and their directionality is determined by the external magnetic field. While chirality is a central feature of the quantum Hall effect, directly probing it remains experimentally nontrivial. In this study, we introduce a simple and effective method to probe the chirality of edge transport using two independently controlled current sources in a Hall bar geometry. The system under investigation is monolayer epitaxial graphene grown on a silicon carbide substrate, exhibiting robust quantum Hall states. By varying the configurations of the two current sources, we measure terminal voltages and analyze the transport characteristics. Our results demonstrate that the observed behavior can be understood as a linear superposition of chiral contributions to the edge transport. This superposition enables tunable combinations of longitudinal and Hall resistances and enables additive or canceling behavior of Hall voltages depending on current source configuration. The Landauer–Büttiker formalism provides a quantitative framework to describe these observations, capturing the interplay between edge state chirality and the measurement configuration. This research offers a simple yet effective experimental and analytical approach for probing chiral edge currents and highlights the linear superposition principle in the quantum Hall effect. Full article

The low thermal conductivity of phase change material (PCM) critically constrains the cooling performance of PCM-based battery thermal management system (BTMS). To address this limitation, embedding high-thermal-conductivity fins into PCM was recently explored. However, it may increase the overall BTMS mass, degrading vehicle performance. Therefore, a quantitative evaluation of the effects of fin design on cooling performance and system mass is required. In this study, the effects of fin design factors in a PCM–fin structured BTMS on the maximum cell temperature and BTMS mass was analyzed using design of experiments (DoE) and analysis of variance (ANOVA). To characterize BTMS thermal behavior, a numerical model was developed by applying thermal fluid partial differential equations (PDEs) with the enthalpy–porosity method to represent the phase change of the PCM. Fin number, thickness, and angle were selected as design factors; responses were calculated through thermal fluid analysis. The results showed a trade-off between thermal performance and mass across all design factors. The number of fins had the greatest effect on maximum cell temperature (78.27%) but less on mass (28.85%). Fin thickness moderately affected temperature (16.71%) but strongly increased mass (63.93%). Fin angle had minimal impact, 4.10% on temperature and 3.10% on mass. Full article

This article focuses on modeling counterflows within pedestrian social groups in a corridor using the kinetic theory approach, specifically when two social groups move in opposite directions. The term social group refers to a set of pedestrians with established social relationships who stay as close as possible to one another and share a common goal or destination, such as friends or family. The model accounts for interactions both within the same social group and between pedestrians from different social groups. Numerical simulations based on a Monte Carlo particle method are performed. A key criterion for evaluating simulation models is their ability to reproduce empirically observed collective motion patterns. One of the most significant emergent behaviors in bidirectional pedestrian flows is lane formation. To analyze this phenomenon, we employ Yamori’s band index to quantify the evolution of lane structures. Full article

In this work, we analyze a scalar field model which gives rise to stable bound states in field space characterized by nonzero motion that breaks the underlying time translation symmetry of its Hamiltonian, known as time crystals. We demonstrate that an ideal fluid made up of these time crystals behaves as phantom dark energy characterized by an equation of state $w<-1$, speed of sound squared $c_s^2\ge 0$, and nonnegative energy density $\rho \ge 0$. Full article

We found analytic approximations for the Bessel function of the first kind $J_{\nu }\left(x\right)$, valid for any real value of x and any value of $\nu$ in the interval (−1/2, 3/2). The present approximation is exact for $\nu =-1/2$, $\nu =1/2$, and $\nu =3/2$, where an exact function for each case is well known. The maximum absolute errors for $\nu$ near these peculiar values are very small. Throughout the interval, the absolute values remain below 0.05. The structure of the approximate function is defined considering the corresponding power series and asymptotic expansions, and they are quotients of three polynomials of the second degree combined with trigonometrical functions and fractional powers. This is, in some way, the Multipoint Quasi-rational Approximation (MPQA) technique, but now only two variables are considered, x and $\nu$, which is novel, since in all previous publications only the variable x was considered and $\nu$ was given. Furthermore, in the case of $J_{-1/2}\left(x\right)$, $J_{1/2}\left(x\right)$, and $J_{3/2}\left(x\right)$, the corresponding exact function was also a condition to be considered and fulfilled. It is important to point out that the zeros of the exact functions and the approximate ones are also almost coincident with small relative errors. Finally, the approximation presented here has the property of preservation of symmetry for $\nu >0$, i.e., when there is a sign change in the variable x, the corresponding change agrees with a similar change in the power series of the exact function. Full article