Search Results (47)

Regulatory risk measurement under Basel III’s Fundamental Review of the Trading Book places Expected Shortfall (ES) at the center of market risk capital, yet the fourth-order Edgeworth expansion, still widely used for Value-at-Risk (VaR) and ES calculations, can produce negative densities in the tail regions where these measures concentrate, while saddlepoint approximations preserve positivity but face their own limits in heavy-tailed and sub-Gaussian settings. Whether either method delivers reliable tail estimates in the rare-disaster regimes documented in the empirical consumption-disaster literature therefore remains an open question. We address it by comparing the two approximations across 648 rare-disaster parameter combinations and five additional distributional families (Student-t, Hansen skewed-t, generalised error distribution (GED), two-sided jump mixture, and generalised hyperbolic), and by deriving a closed-form characterisation of the Edgeworth validity envelope. We establish three core findings. First, the validity envelope is bounded above by a sharp kurtosis ceiling at ${\gamma }_2=4$ and laterally by a non-monotone skewness boundary peaking at $|{\gamma }_1^{\ast ,\max }| \approx 0.685$ at ${\gamma }_2\approx 2.533$; $87.5\%$ of the rare-disaster grid falls outside it. Second, accuracy is threshold-dependent: Edgeworth dominates at moderate quantiles, saddlepoint at extreme quantiles, with negative-density regions inflating Edgeworth ES error from $6.20\%$ inside the envelope to $47.04\%$ outside it. Third, these results reconcile only when point probability, density validity, and integrated-tail accuracy are treated as distinct accuracy criteria. The findings have direct implications for ES-based regulatory capital in heavy-tailed regimes and motivate a regime-conditional rather than universal approximation choice. Full article

Multi-block structured mesh is widely used for high-precision aerodynamic simulation, but mesh blocking usually requires substantial manual intervention, which is time-consuming and demands a high level of user expertise. In this study, a potential field-based blocking algorithm for mesh generation around an aircraft is proposed, and a corresponding multi-block grid generation workflow is established. First, the hyperbolic partial differential equation (PDE) method is used to march boundary layer grids from the body surface. Next, the potential field is solved on an unstructured background grid, and the grid topology is flexibly designed by adjusting boundary conditions. The gradient lines of the potential field are then determined and employed to partition the external domain into blocks. Finally, the elliptic PDE method is applied to generate structured grids within each sub-block. A low-aspect-ratio flying-wing configuration is adopted as the test case. Structured grids of both H-type and O-type topologies are generated and compared with the benchmark grid released by the China Aerodynamics Research and Development Center (CARDC). The grid quality analysis and aerodynamic calculation results demonstrate that the two generated grids possess good quality, and the computational results show satisfactory agreement with experimental data. The O-type mesh yields more accurate predictions for the lift coefficient and pitching moment coefficients. Furthermore, two test cases, namely a rocket sled and a V-tail aircraft, are presented to demonstrate that the proposed method can flexibly design either O-type or H-type topologies to accommodate different geometric characteristics. In summary, the proposed method enables efficient generation of high-quality multi-block structured grids for the configurations examined in this study. Full article

This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address hyperbolic conservation laws on structured grids. Firstly, we propose three unequal-degree reconstruction polynomials in the new trigonometric polynomial space to devise a novel fifth-order US-TWENO scheme. Then, we devise a novel troubled cell indicator capable of accurately identifying troubled cells containing strong discontinuities: the existence of extreme points of the trigonometric polynomials within the smallest interval (the target cell itself) is determined by whether the estimated minimum and maximum values of their derivative trigonometric polynomials have opposite signs. To the best of our knowledge, this is the first troubled cell indicator devised specifically within the target cell interval. The HUS-TWENO scheme is improved, offering greater efficiency, lower dissipation, and higher resolution. Numerical experiments demonstrate the effectiveness of the HUS-TWENO scheme. Full article

Power line sag monitoring is critical for ensuring transmission system reliability and optimizing grid capacity utilization. Traditional sag detection methods rely on hyperbolic cosine models that assume ideal catenary behavior under uniform loading conditions. However, these models impose restrictive assumptions about weight distribution and suspension conditions that limit accuracy under real-world scenarios involving wind loading, ice accumulation, and non-uniform environmental forces. This study introduces a novel Bézier curve-based mathematical framework for transmission line sag detection and monitoring. Unlike traditional hyperbolic cosine approaches, the proposed methodology eliminates idealized assumptions and provides enhanced flexibility for modeling actual conductor behavior under variable environmental conditions. The Bézier curve approach offers enhanced precision and computational efficiency through intuitive control point manipulation, making it well suited for Dynamic Line Rating (DLR) applications. Experimental validation was performed using a controlled laboratory setup with a 1:100 scaled transmission line model. Results demonstrate improvement in sag measurement accuracy, achieving an average error of 1.1% compared to 6.15% with traditional hyperbolic cosine methods—representing an 82% improvement in measurement precision. Statistical analysis over 30 independent experiments confirms measurement consistency with a 95% confidence interval of [0.93%, 1.27%]. The framework also demonstrates a 1.5 to 2 times increase in computational efficiency improvement over conventional template matching approaches. This mathematical framework establishes a robust foundation for advanced transmission line monitoring systems, with demonstrated advantages for power grid applications where traditional catenary models fail due to non-ideal environmental conditions. The enhanced accuracy and efficiency support improved Dynamic Line Rating implementations and grid modernization efforts. Full article

Curved roofs constructed using hyperbolic paraboloid (HP) modules are gaining popularity in structural engineering due to their unique aesthetic and structural advantages. Consequently, these studies have investigated steel bar modules based on HP geometry, focusing on how variations in geometric configuration and bar topology affect internal force distribution and overall structural performance. Each module was designed on a 4 × 4 m square plan, incorporating external bars that formed the spatial frame and internal grid bars that filled the frame’s interior. Parametric modeling was conducted using Dynamo, while structural analysis and design were performed in Autodesk Robot Structural Analysis Professional (ARSAP). Key variables included the vertical displacement of frame corners (0–1.0 m at 0.25 m intervals), the orientation and spacing of internal bar divisions, and the overall mesh topology. A total of 126 structural models were analyzed, representing four distinct bar topology variants, including both planar and non-planar mesh configurations. The results demonstrate that structural efficiency is significantly influenced by the geometry and topology of the internal bar system, with notable differences observed across the various structural types. Computational analysis revealed that asymmetric configurations of non-planar quadrilateral subdivisions yielded the highest efficiency, while symmetric arrangements proved optimal for planar panel applications. These findings, along with observed design trends, offer valuable guidance for the development and optimization of steel bar structures based on HP geometry, applicable to both single-module and multi-module configurations. Full article

The increasing incorporation of renewable energy into power grids has significantly reduced system inertia and damping, posing challenges to frequency stability and power quality. To address this issue, an adaptive virtual synchronous generator (VSG) control strategy is proposed, which dynamically adjusts virtual inertia and damping in response to real-time frequency variations. Virtual inertia is modulated by an exponential function according to the frequency variation rate, while damping is regulated via a hyperbolic tangent function, enabling minor support during small disturbances and robust compensation during severe events. Control parameters are optimized using an enhanced particle swarm optimization (PSO) algorithm based on a composite performance index that accounts for frequency deviation, overshoot, settling time, and power tracking error. Simulation results in MATLAB/Simulink under step changes, load fluctuations, and single-phase faults demonstrate that the proposed method reduces the frequency deviation by over 26.15% compared to fixed-parameter and threshold-based adaptive VSG methods, effectively suppresses power overshoot, and eliminates secondary oscillations. The proposed approach significantly enhances grid transient stability and demonstrates strong potential for application in power systems with high levels of renewable energy integration. Full article

The paper presents the control of the ablated gap of required dimensions in an axisymmetric domain made of metal. For this purpose, two parameters of the laser interacting on this layer were identified, which means laser intensity and characteristic time of the laser pulse. A hyperbolic two-temperature model was applied. This is a model in which there are two coupled equations for electrons and phonons. The model was supplemented with appropriate boundary and initial conditions. The direct problem was solved using the finite difference method with a staggered grid. An artificial immune system was used for the identification process. Full article

This paper develops a numerical simulation method for polymer-flooding reservoirs using the high-order Weighted Essentially Non-Oscillatory (WENO) scheme. The research begins by leveraging the WENO method to obtain high-order approximations of the saturation and polymer concentration functions and formulates a sequential solution strategy for the hyperbolic mass conservation equations of the water phase and polymer component in these reservoirs. Three numerical tests compare the WENO scheme with the traditional first-order upwind difference method. The results show that the WENO scheme has higher computational accuracy, especially in predicting fronts, which improves the prediction of water cut and polymer production concentration. Under the same accuracy, the WENO method requires fewer grids and has much higher computational efficiency. A sensitivity analysis of the polymer solution viscosity parameters verifies that the WENO method can accurately simulate reservoir production behavior, providing an efficient and accurate reservoir simulation alternative. Full article

A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed a finite-difference time-domain (FDTD) method based on a rotating ellipsoidal hyperbolic coordinate system. Due to intense field variations near the explosion center, non-uniform grids were employed for both spatial and temporal steps, and an OpenMP parallel algorithm was utilized to enhance computational efficiency. Analysis focused on the following two scenarios: varying angles at a constant distance and varying distances at a constant angle, considering both transverse magnetic (TM) and transverse electric (TE) waves. The results indicate that the spatial field value distribution characteristics differ between the two wave types. For TM waves, the electric and magnetic fields share the same polarity, but their waveform polarities are opposite above and below the explosion center. A TE wave is exactly the opposite. Compared with a TM wave, a TE wave has stronger peak electromagnetic fields but narrower pulse widths and lower overall energy. This research provides significant support for the development of nuclear explosion detection technology and offers theoretical foundations for the protection of surrounding environmental facilities. Full article

This paper investigates the emerging field of grid-connected wind-powered pumping kite generator system (PKGS), focusing on the challenges associated with the generator/motor speed control. Conventional use of proportional–integral (PI) controllers faces difficulties in meeting requirements for dynamic response, tracking performance, stability, and disturbance rejection encountered in this technology, notably the periodical variation in the rotational speed reference in maximum power point tracking in generation phases and the dynamic response for the step reference in transient ones. To overcome these limitations, a model-free controller (MFC) approach is introduced, also known as intelligent PID controllers. Unlike traditional methods, MFC does not rely on a control model of the system and adapts to uncertainties and disturbances through online estimation based on the system’s input–output behavior. To further improve the control performances, a tracking differentiator based on a nonlinear hyperbolic tangent function is integrated in the MFC. The effectiveness of the proposed strategy is proved through simulations in MATLAB/Simulink. The results highlight the superior performances of the proposed MFC approach in terms of speed control accuracy, response time, and robustness. Full article

Steel is an important construction material in civil engineering. In addition, the building industry is one of the global economy’s largest sectors, responsible for one-third of the energy consumption and significant CO₂ emissions. For this reason, there is a need to design effective structures that are characterized by the lowest possible steel consumption. This article presents an approach to sustainability considerations in steel structures, namely the approach of shaping efficient steel canopies with modular roofs using genetic algorithms. The shed structures, which were designed based on a regular polygonal plan, were constructed from grid modules that were formed on the basis of the hyperbolic paraboloid (HP) units arranged radially, supported by the columns, and covered by metal sheets. The algorithmic definitions allowed for the creation of numerous variants of the structures with the adopted preliminary criteria and for the performance of genetic optimization in order to select the best results. Twenty-four kinds of structures were analyzed and compared, differing in the quantity of modules, module shapes, arrangements, and dimensions. This made it possible to observe changes in the efficiency of the structures depending on the form of the roof applied. As a measure of structural efficiency, the coefficient representing the mass of the shed structure per square meter of the covered area was utilized. The presented design approach and optimal solutions can be helpful in shaping more complex sustainable structures, for which the analyzed sheds constitute modules. Full article

To tackle the issue of poor accuracy in single-snapshot data processing for Direction of Arrival (DOA) estimation in passive radar systems, this paper introduces a method for judiciously leveraging multi-snapshot data. This approach effectively enhances the accuracy of DOA estimation and spatial angle resolution in passive radar systems. Additionally, in response to the non-convex nature of the mixed norm, we propose a hyperbolic tangent model as a replacement, transforming the problem into a directly solvable convex optimization problem. The rationality of this substitution is thoroughly demonstrated. Lastly, through a comparative analysis with existing discrete grid DOA estimation methods, we illustrate the superiority of the proposed approach, particularly under conditions of medium signal-to-noise ratio, varying numbers of snapshots, and close target angles. This method is less affected by the number of array elements, and is more usable in practices verified in real-world scenarios. Full article

The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo simulations and an empirically inferred population distribution of period ratios, we prove that this apparent dearth of near-resonant systems is not statistically significant. The excess of systems with period ratios in the wider vicinity of the 2:1 resonance is significant, however. Long-term WHFast integrations of a synthetic two-planet system on a grid period ratios from 1.87 through 2.12 reveal that the eccentricity and inclination exchange mechanism between non-resonant planets represents the orbital evolution very well in all cases, except at the exact 2:1 mean motion resonance. This resonance destroys the orderly exchange of eccentricity, while the exchange of inclination still takes place. Additional simulations of the Kepler-113 system on a grid of initial inclinations show that the secular periods of eccentricity and inclination variations are well fitted by a simple hyperbolic cosine function of the initial mutual inclination. We further investigate the six known two-planet systems with period ratios within 2% of the exact 2:1 resonance (TOI-216, KIC 5437945, Kepler-384, HD 82943, HD 73526, HD 155358) on a grid of initial inclinations and for two different initial periastron longitudes corresponding to the aligned and anti-aligned states. All these systems are found to be long-term stable except HD 73526, which is likely a false positive. The periodic orbital momentum exchange is still at work in some of these systems, albeit with much shorter cycling periods of a few years. Full article

A new algorithm is developed to automatically detect rebar locations and diameters of reinforced concrete structures using the ground penetrating radar technique. The study uses two-way travel time and biquadratic equations to formulate electromagnetic wave speed in reinforced concrete structures where hyperbolic signatures are approximated. Leveraging an established algorithm, a computer code has been developed to offer automated analysis of ground-penetrating radar data obtained from survey grids. Four reinforced concrete slabs were designed, fabricated, and tested to validate the developed evaluation approach. The proposed methodology demonstrates outstanding signal processing proficiency and reliably and effectively identifies rebar information. Full article

Slope leveling is essential for the successful implementation of ground-mounted centralized photovoltaic (PV) plants, but currently, there is a lack of optimization methods available. To address this issue, a linear programming approach has been proposed to optimize PV slope leveling. This method involves dividing the field into blocks and grids and using hyperbolic paraboloids to simulate the design surface. By programming in MATLAB, the globally optimal solution for PV slope leveling can be calculated. Engineering case studies have demonstrated that this optimization method can achieve significant cut-and-fill volume savings ranging from 58% to 78%, when compared to the traditional segmented plane method. Additionally, the effectiveness of the optimization method improves with larger site areas and more complex terrains. A parameter analysis considering slope ratio, grid size, and block size reveals that grid size has a minimal impact on cut-and-fill volume, while slope ratio and block size have a significant influence. For typical PV projects, the recommended ranges of slope ratio, grid size, and block size are 3–7%, 5–20 m, and 30–50 m, respectively, for slope leveling design. In summary, the proposed linear optimization method provides an optimal slope leveling scheme for ground-mounted centralized PV plants, with convenient operation and fast computation. Full article