Search Results (287)

The design and optimization of drive distribution strategies are critical for enhancing the performance of Formula Student electric racing cars, which face demanding operational conditions such as rapid acceleration, tight cornering, and variable track surfaces. Given the increasing complexity of racing environments and the need for adaptive control solutions, a multi-mode adaptive drive distribution strategy for four-wheel-drive Formula Student electric racing cars is proposed in this study to meet specialized operational demands. Based on the dynamic characteristics of standardized test scenarios (e.g., straight-line acceleration and figure-eight loop), two control modes are designed: slip-ratio-based anti-slip control for longitudinal dynamics and direct yaw moment control for lateral stability. A CarSim–Simulink co-simulation platform is established, with test scenarios conforming to competition standards, including variable road adhesion coefficients (μ is 0.3–0.9) and composite curves. Simulation results indicate that, compared to conventional PID control, the proposed strategy reduces the peak slip ratio to the optimal range of 18% during acceleration and enhances lateral stability in the figure-eight loop, maintaining the sideslip angle around −0.3°. These findings demonstrate the potential for significant improvements in both performance and safety, offering a scalable framework for future developments in racing vehicle control systems. Full article

Compared to spiral bevel gear drives with localized conjugation, line contact spiral bevel gears possess a significantly larger meshing area, theoretically achieving full tooth surface contact and substantially enhancing load capacity. To accurately support the root strength calculation and parameter design of line contact spiral bevel gear drives, this paper presents a theoretical analysis and experimental study of the root bending stress of gear pairs. First, based on the analysis of the meshing characteristics of line contact spiral bevel gear pairs, the load distribution along the contact lines is investigated. Using the slicing method, the load distribution characteristics along the contact line are obtained, and the load sharing among multiple tooth pairs during meshing is further studied. Then, by applying a cantilever beam bending stress model, the root bending stress on such a gear drive is calculated. A root bending moment distribution model is proposed based on the characteristics of the line load distribution previously obtained, from which a formula for calculating root bending stress is derived. Finally, static-condition experiments are conducted to test the root bending stress. The accuracy of the proposed calculation method is verified through experimental testing and finite element analysis. The results of this study provide a foundation for designing lightweight and high-power-density spiral bevel gear drives. Full article

Field foundation pile loading tests were conducted in the context of an actual bridge pile foundation project. The test data were analyzed to determine the reasons for the variation in the complex geological conditions of the seashore. Moreover, finite element analysis was conducted to evaluate the influence of pile length and diameter on the settlement of coastal friction foundation piles. Increasing the pile length from 65 m to 75 m reduced the settlement by 25.7%, while increasing the diameter from 1.5 m to 2.0 m led to a 35.9% reduction. Increasing the pile spacing reduced the amount of structural settlement. Group pile foundation pile spacings should be 2.5–3.0 D. Pile group superposition reduced the most obvious effects and the settlement reduction rate was the fastest. Under seismic conditions, the pile group foundation exhibited 5.60 times greater horizontal displacement, 3.57 times higher bending moment, and 5.30 times increased shear force relative to static loading. The formula for predicting the settlement of oversized friction pile group foundations was modified based on settlement values calculated using finite elements. The revised formula is suitable for calculating the settlement of friction pile group foundations in coastal areas. Full article

The structural, elastic, electronic, magnetic, and half-metallic properties of full-Heusler ${\mathrm{Fe}}_2$LiSi and ${\mathrm{Fe}}_2$LiGe compounds were investigated using first-principles calculations. Among the studied configurations, the cubic XA structures in the ferromagnetic state for both compounds are the most stable. They exhibit mechanical stability, elastic anisotropy, and ductility. Compared to ${\mathrm{Fe}}_2$LiGe, ${\mathrm{Fe}}_2$LiSi demonstrates higher stability, stronger anisotropy, greater brittleness, higher Debye and melting temperatures, and a smaller Grüneisen parameter. Both compounds exhibit metallic majority-spin channels and semiconducting minority-spin channels. At the equilibrium lattice constant, ${\mathrm{Fe}}_2$LiSi and ${\mathrm{Fe}}_2$LiGe exhibit half-metallic gaps of 0.141 eV and 0.179 eV, respectively. Both compounds exhibit 100% spin-polarization ratio in specific lattice constant ranges. The total magnetic moment per formula unit (3.000 ${\mu }_{\mathrm{B}}$) follows the generalized Slater–Pauling rule and depends on Fe atomic magnetic moments. These properties indicate that ${\mathrm{Fe}}_2$LiSi and ${\mathrm{Fe}}_2$LiGe hold promise for spintronic applications. Full article

LK-99, with chemical formula Pb_10−xCu_x(PO₄)₆O, was recently reported to be a room-temperature superconductor. While this claim has met with little support in a flurry of ensuing work, a variety of calculations (mostly based on density-functional theory) have demonstrated that the system possesses some unusual characteristics in the electronic structure, in particular flat bands. We have established previously that within DFT, the system is insulating with many characteristics resembling the classic cuprates, provided the structure is not constrained to the P3(143) symmetry nominally assigned to it. Here we describe the basic electronic structure of LK-99 within self-consistent many-body perturbative approach, quasiparticle self-consistent GW (QSGW) approximation and their diagrammatic extensions. QSGW predicts that pristine LK-99 is indeed a Mott/charge transfer insulator, with a bandgap gap in excess of 3 eV, whether or not constrained to the P3(143) symmetry. When Pb₉Cu(PO₄)₆O is hole-doped, the valence bands modify only slightly, and a hole pocket appears. However, two solutions emerge: a high-moment solution with the Cu local moment aligned parallel to neighbors, and a low-moment solution with Cu aligned antiparallel to its environment. In the electron-doped case the conduction band structure changes significantly: states of mostly Pb character merge with the formerly dispersionless Cu d state, and high-spin and low spin solutions once again appear. Thus we conclude that with suitable doping, the ground state of the system is not adequately described by a band picture, and that strong correlations are likely. Irrespective of whether this system class hosts superconductivity or not, the transition of Pb₁₀(PO₄)₆O from being a band insulator to Pb₉Cu(PO₄)₆O, a Mott insulator, and multi-determinantal nature of doped Mott physics make this an extremely interesting case-study for strongly correlated many-body physics. Full article

The squared Bessel process plays a central role in stochastic analysis, with broad applications in mathematical finance, physics, and probability theory. While explicit expressions for its transition probability density function (TPDF) under constant parameters are well known, analytical results in the case of time-dependent dimensions remain scarce. In this paper, we address a significantly challenging problem by deriving an analytical formula for the TPDF of a conic combination of independent squared Bessel processes with time-dependent dimensions. The result is expressed in terms of a Laguerre series expansion. Furthermore, we obtain closed-form expressions for the conditional moments of such conic combinations, represented via generalized hypergeometric functions. These results also yield new analytical formulas for the TPDF and conditional moments of both squared Bessel processes and Bessel processes with time-dependent dimensions. The proposed formulas provide a unified analytical framework for modeling and computation involving a broad class of time-inhomogeneous diffusion processes. The accuracy and computational efficiency of our formulas are verified through Monte Carlo simulations. As a practical application, we provide an analytical valuation of an interest rate swap, where the underlying short rate follows a conic combination of independent squared Bessel processes with time-dependent dimensions, thereby illustrating the theoretical and practical significance of our results in mathematical finance. Full article

The stochastic correlation for Brownian motions is the integrand in the formula of their quadratic covariation. The estimation of this stochastic process becomes available from the temporally localized correlation of latent price driving Brownian motions in stochastic volatility models for asset prices. By analyzing this process for Apple and Microsoft stock prices traded minute-wise, we give statistical evidence for the roughness of its paths. Moment scaling indicates fractal behavior, and both fractal dimensions (approx. 1.95) and Hurst exponent estimates (around 0.05) point to rough paths. We model this rough stochastic correlation by a suitably transformed fractional Ornstein–Uhlenbeck process and simulate artificial stock prices, which allows computing tail dependence and the Herding Behavior Index (HIX) as functions in time. The computed HIX is hardly variable in time (e.g., standard deviation of 0.003–0.006); on the contrary, tail dependence fluctuates more heavily (e.g., standard deviation approx. 0.04). This results in a higher correlation risk, i.e., more frequent sudden coincident appearance of extreme prices than a steady HIX value indicates. Full article

This study employs DFT+U calculations to investigate the ferromagnetic properties of ErAl₂ and ErNi₂ Laves phases under an external hydrostatic pressure P (0 GPa ≤ P ≤ 1.0 GPa). The calculated magnetic moments per formula unit for both crystalline structures align with experimentally reported values: 4.40 μ_B/f.u. in the hard magnetization <001> axis for ErAl₂ and 5.56 μ_B/f.u. in the easy magnetization <001> axis for ErNi₂. The DFT results indicate that the magnetic moment remains unchanged up to 1 GPa of hydrostatic pressure, with no structural instabilities observed, as evidenced by a nearly constant formation energy for ErAl₂ and ErNi₂ alloys. The simulations confirm that the magnetic behavior of ErAl₂ is primarily driven by the electrons localized in the f orbitals. In contrast, for ErNi₂, both d and f orbitals significantly contribute to the total magnetic moment. Finally, the electronic specific heat coefficient was calculated and reported as a function of hydrostatic pressure up to P = 1.0 GPa for each Laves phase. Full article

This study presents, for the first time, a detailed linear stability analysis (LSA) of bedform evolution under low-flow conditions using a one-dimensional vertically averaged and moment (1D-VAM) approach. The analysis focuses exclusively on bedload transport. The classical Saint-Venant shallow water equations are extended to incorporate non-hydrostatic pressure terms and a modified moment-based Chézy resistance formulation is adopted that links bed shear stress to both the depth-averaged velocity and its first moment (near-bed velocity). Applying a small-amplitude perturbation analysis to an initially flat bed, while neglecting suspended load and bed slope effects, reveals two distinct modes of morphological instability under low-Froude-number conditions. The first mode, associated with ripple formation, features short wavelengths independent of flow depth, following the relation F² = 1/(kh), and varies systematically with both the Froude and Shields numbers. The second mode corresponds to dune formation, emerging within a dimensionless wavenumber range of 0.17 to 0.9 as roughness increases and the dimensionless Chézy coefficient $C^{\ast }$ decreases from 20 to 10. The resulting predictions of the dominant wavenumbers agree well with recent experimental observations. Critically, the model naturally produces a phase lag between sediment transport and bedform geometry without empirical lag terms. The 1D-VAM framework with Exner equation offers a physically consistent and computationally efficient tool for predicting bedform instabilities in erodible channels. This study advances the capability of conventional depth-averaged models to simulate complex bedform evolution processes. Full article

We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally, we demonstrate that the same approach extends to a broad family of non-affine, time-varying diffusions, providing a general framework for obtaining transition PDFs and moments in advanced models. Full article

Multivariate normal moments are foundational for statistical methods. The derivation and simplification of these moments are critical for the accuracy of various statistical estimates and analyses. Normal moments are the building blocks of the Hermite polynomials, which in turn are the building blocks of the Edgeworth expansions for the distribution of parameter estimates. Isserlis (1918) gave the bivariate normal moments and two special cases of trivariate moments. Beyond that, convenient expressions for multivariate variate normal moments are still not available. We compare three methods for obtaining them, the most powerful being the differential method. We give simpler formulas for the bivariate moment than that of Isserlis, and explicit expressions for the general moments of dimensions 3 and 4. Full article

To enhance the seismic performance of existing reinforced concrete (RC) columns, this study proposes a novel strengthening method that combines steel strips with ultra–high–performance concrete (UHPC). The seismic behavior of the proposed method is investigated through quasi–static cyclic tests conducted on four strengthened columns and one control column. The experimental parameters include the type of reinforcement (UHPC–only and UHPC combined with steel strips) and the thickness of the UHPC strengthening layer. The failure modes, hysteretic behavior, energy dissipation capacity, and stiffness degradation of the specimens are systematically analyzed. The results show that, compared to the unstrengthened column, the UHPC–strengthened columns achieved maximum increases of 73.73% in peak load and 23.68% in ductility coefficient, while the columns strengthened with composite steel strips achieved further improvements of up to 84.79% and 50.23%, respectively. The composite strengthening method significantly improved the failure mode, with crack distribution changing from localized crushing to multiple fine cracks. The displacement ductility coefficient reached as high as 6.28, and the hysteretic curve fullness and cumulative energy dissipation increased by a factor of two to three. Finally, based on moment equilibrium theory, a theoretical formula is proposed to calculate the lateral ultimate flexural capacity of RC columns strengthened with steel strip–UHPC composites, which shows good agreement with the experimental results. Full article

This study investigates the flexural performance of desert sand concrete-filled steel tube (DS-CFST) members through experimental validation and finite element modeling (FEM). An extensive database of square and circular CFST specimens subjected to pure bending was analyzed to validate an ABAQUS-based FEM. Parametric studies evaluated the influence of steel yield strength, steel ratio, stirrup confinement, and desert sand replacement ratio (r) on ultimate bending moment, stiffness, and failure modes. The results indicated that steel yield strength and section geometry significantly affected bending capacity, while desert sand substitution (r ≤ 1) had a negligible impact on capacity, reducing it by less than 3%. The FEM accurately predicted buckling patterns, moment-curvature relationships, and failure modes. New design formulas for predicting ultimate bending moment and flexural stiffness were proposed, demonstrating superior accuracy (mean error < 1%) compared to existing design codes (AIJ, AISC, GB). This study highlights that DS-CFST members, particularly circular sections, offer robust flexural performance, with enhanced ductility and uniform stress distribution. The findings underscore the potential of using desert sand as a sustainable material in concrete-filled steel tube structures without compromising structural integrity. Full article

This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). Unlike conventional approaches relying on moment-generating functions or Fokker–Planck equations, which often yield intractable expressions, we derive explicit closed-form formulas for these moments. Our methodology leverages the Wick–Itô calculus (fractional Itô formula) and the properties of Hermite polynomials to express moments efficiently. Additionally, we establish a recurrence relation for moment computation and propose an alternative approach based on generalized binomial expansions. To validate our findings, Monte Carlo simulations are performed, demonstrating a high degree of accuracy between theoretical and empirical results. The proposed framework provides novel insights into stochastic processes with long-memory properties, with potential applications in statistical inference, mathematical finance, and physical modeling of anomalous diffusion. Full article

This paper presents a new model of the term structure of interest rates that is based on the continuous Ho–Lee one. In this model, we suggest that the drift and volatility coefficients depend additionally on a generalized inverse Gaussian (GIG) distribution. Analytical expressions for the bond price and its moments are found in the new GIG continuous Ho–Lee model. Also, we compute in this model the prices of European call and put options written on bond. The obtained formulas are determined by the values of the Humbert confluent hypergeometric function of two variables. A numerical experiment shows that the third and fourth moments of the bond prices differentiate substantially in the continuous Ho–Lee and GIG continuous Ho–Lee models. Full article