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Simple and accurate complete elliptic integrals for the full range of modulus arxiv.org/abs/2505.17159

Simple and accurate complete elliptic integrals for the full range of modulus

The complete elliptic integral of the first and second kind, K(k) and E(k), appear in a multitude of physics and engineering applications. Because there is no known closed-form, the exact values have to be computed numerically. Here, approximations for the integrals are proposed based on their asymptotic behaviors. An inverse of K is also presented. As a result, the proposed K(k) and E(k) reproduce the exact analytical forms both in the zero and asymptotic limits, while in the mid-range of modulus maintain average error of 0.06% and 0.01% respectively. The key finding is the ability to compute the integrals with exceptional accuracy on both limits of elliptical conditions. An accuracy of 1 in 1,000 should be sufficient for practical or prototyping engineering and architecture designs. The simplicity should facilitate discussions of advanced physics topics in introductory physics classes, and enable broader collaborations among researchers from other fields of expertise. For example, the phase space of energy-conserving nonlinear pendulum using only elementary functions is discussed. The proposed inverse of K is shown to be Never Failing Newton Initialization and is an important step for the computation of the exact inverse.

arXiv.org

Investigating the 2024 swarm like activity offshore Kefalonia Island aided by Machine Learning algorithms arxiv.org/abs/2505.17221

Investigating the 2024 swarm like activity offshore Kefalonia Island aided by Machine Learning algorithms

In March 2024, a swarm like seismic activity occurred north of Kefalonia Island, in the central Ionian Islands area. Following a machine-learning aided workflow, we compiled an enhanced seismic catalog of 2495 low to moderate magnitude earthquakes throughout a 2 month period. Spatiotemporal analysis reveals a narrow epicentral distribution of nearly E-W alignment, approximately 5km long, much longer than the length anticipated by common scaling laws for the aftershock area extension of the stronger earthquakes that did not exceed M4.0. The findings of the study indicate that the swarm like activity is possibly triggered by a combination of fluid movements and Coulomb stress changes. The strongest earthquakes appear beyond the diffusivity curves that are within the expected upper crust values and are possibly triggered by stress transfer by the first strong earthquake. Fluid effects rapidly diminish within the first days, while the changes in the stress field due to the combined effect of the two strongest earthquakes promote the triggering of most of the weaker earthquakes of the excitation. The findings of this study reinforce the idea of swarm-like activity initiating due to interactions between stress redistributions and fluid movements in the upper crust. The rapid employment of ML tools for the compilation of robust seismic catalogs can vastly improve our understanding of the processes that drive seismicity in highly productive areas such as the Central Ionian Islands, thus leading to improved seismic hazard assessment.

arXiv.org

Very fast general Electromagnetic Analysis with computational conformal geometry via Conformal Energy Minimization arxiv.org/abs/2505.17227

Very fast general Electromagnetic Analysis with computational conformal geometry via Conformal Energy Minimization

We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply computational conformal geometry with the conformal energy minimization (CEM) algorithm to make possible fast solution of finite-frequency electromagnetic problems involving arbitrarily shaped, simply-connected metallic surfaces. The CEM algorithm computes conformal maps with minimal angular distortion, enabling the transformation of arbitrary simply-connected surfaces into a disk, where orthogonal basis functions can be defined and electromagnetic analysis can be significantly simplified. We demonstrate the effectiveness and efficiency of our method by investigating the resonance characteristics of two metallic surfaces: a square plate and a four-petal plate. Compared to traditional finite element methods (e.g., COMSOL), our approach achieves a three-order-of-magnitude improvement in computational efficiency, requiring only seconds to extract resonant frequencies and fields. Moreover, it reveals low-energy, doubly degenerate resonance modes that are elusive to conventional methods. These findings not only provide a powerful tool for analyzing electromagnetic fields on complex geometries but also pave the way for the design of high-performance electromagnetic devices.

arXiv.org

Modification of the uniform electron gas polarizational stopping power due to the interaction of the projectile with new collective modes at moderate and strong coupling arxiv.org/abs/2505.17229

Modification of the uniform electron gas polarizational stopping power due to the interaction of the projectile with new collective modes at moderate and strong coupling

This paper presents a detailed study of the polarizational stopping power of a homogeneous electron gas in moderate and strong coupling regimes using the self-consistent version of the method of moments as the key theoretical approach capable of expressing the dynamic characteristics of the system in terms of the static ones, which are the moments. We develop a robust framework that relies on nine sum rules and other exact relationships to analyze electron-electron interactions and their impact on energy-loss processes. We derive an expression for the stopping power that takes into account both quantum statistical effects and electron correlation phenomena. Our results demonstrate significant deviations from classical stopping power predictions, especially under the strong coupling conditions when electron dynamics is highly dependent on collective behavior and a projectile interacts with the system collective modes revealed in Phys. Rev. B 107, 195143 (2023). This work not only advances the theoretical understanding of the homogeneous electron gas but also has implications for practical applications in fields such as plasma physics and materials science.

arXiv.org

A fast and automated approach for urban CFD simulations: integration with meteorological predictions and its application to drone flights arxiv.org/abs/2505.14703

A fast and automated approach for urban CFD simulations: integration with meteorological predictions and its application to drone flights

In past years, several studies have proposed new methods and applications for urban wind simulations. In this article, we present a fast and automatic methodology for reconstructing airflows within urban environments using LiDAR and cadastral data coupled with Computational Fluid Dynamics (CFD) simulations. Our approach integrates meteorological predictions with computational techniques to simulate the complex interactions between wind currents, buildings, vegetation, water zones and terrain morphology within urban environments. Accurate boundary conditions based on meteorological predictions are introduced into a coupled methodology that directly creates the terrain shape inside the simulation environment, simplifying the geometry creation process, which is one of the most prevalent problems in CFD urban simulations. The simulation results are confronted against ground-truth real data obtained from a meteorological station, showing strong agreement with the outcomes generated by the proposed CFD model, with a concordance correlation coefficient up to $ρ_c = 0.985$ for the wind direction and $ρ_c = 0.853$ for the wind speed. The results from these simulations are then used for validating a wind tunnel approach that mimics the interaction between a moving drone and the extracted wind currents, demonstrating a great improvement in computation times when compared to the most straightforward approach that consists in embedding the drone within the full urban landscape. This research contributes to the advancement of urban CFD modeling, and it has significant implications for various applications, providing valuable insights for urban development.

arXiv.org

Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations arxiv.org/abs/2505.14704

Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

arXiv.org

Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies arxiv.org/abs/2505.14712

Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies

We present a rigorous framework for determining the equilibrium configurations of uniformly rotating, self-gravitating fluid bodies. This work addresses the classical challenge of modeling rotational deformation in celestial objects such as stars and planets. By integrating foundational theory with modern mathematical tools, we develop a unified formalism that enhances the precision and generality of shape modeling in astrophysical contexts. Our method applies Lie group theory to vector flows and solves functional equations using the Neumann series. We extend Clairaut's classical linear perturbation theory into the nonlinear regime via Lie exponential mapping, yielding a system of nonlinear functional equations for gravitational potential and fluid density. These are analytically tractable using shift operators and Neumann series summation, enabling explicit characterization of density and gravitational perturbations. This leads to an exact nonlinear differential equation for the shape function, describing equilibrium deformation without assuming slow rotation. We validate the framework through exact solutions, including the Maclaurin spheroid, Jacobi ellipsoid, and unit-index polytrope. We also introduce spectral decomposition techniques for analyzing radial harmonics and gravitational perturbations. Using Wigner's formalism for angular momentum addition, we compute higher-order nonlinear corrections efficiently. The framework includes boundary conditions for Legendre harmonics, supporting the derivation of nonlinear Love numbers and gravitational multipole moments. This work offers a comprehensive, non-perturbative approach to modeling rotational and tidal deformations in astrophysical and planetary systems.

arXiv.org

Laser cooling Rydberg molecules -- a detailed study of the helium dimer arxiv.org/abs/2505.14798

Laser cooling Rydberg molecules - a detailed study of the helium dimer

The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He$_2^*$ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He$_2^*$ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He$_2^*$. The sensitivity of the vibrational levels of He$_2^+$ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.

arXiv.org

PANDAVA: Semantic and Reflexive Protocol for Interdisciplinary and Cognitive Knowledge Synthesis arxiv.org/abs/2505.13456

PANDAVA: Semantic and Reflexive Protocol for Interdisciplinary and Cognitive Knowledge Synthesis

Modern science faces the need to move from linear systematic review protocols to deeper cognitive navigation across fields of knowledge. In this context, the PANDAVA protocol (Protocol for Analysis and Navigation of Deep Argumentative and Valued Knowledge) is designed for analysing the semantic structures of scientific knowledge. It combines semantic mapping, assessment of concept maturity, clustering, and generation of new hypotheses. PANDAVA is interpreted as the first interdisciplinary protocol for knowledge systematization focused on semantic and cognitive mapping. The PANDAVA protocol integrates quantitative analysis methods with reflective procedures for comprehending the structure of knowledge and is applied in interdisciplinary, theoretically saturated fields where traditional models such as PRISMA prove insufficient. As an example, the protocol was applied to analyse the abiogenesis hypotheses. Modelling demonstrated how to structure theories of the origin of life through the integration of data on microlight, turbulent processes, and geochemical sources. PANDAVA enables researchers to identify strong and weak concepts, construct knowledge maps, and develop new hypotheses. Overall, PANDAVA represents a cognitively enriched tool for meaningful knowledge management, fostering the transition from the representation of facts to the design of new scientific paradigms.

arXiv.org
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