Physics

This paper examines whether a compact electron–proton configuration (“small hydrogen”) with a characteristic radius of a few femtometers is excluded by basic relativistic kinematics and simple stationarity constraints. Motivated by earlier discussions of formally deep relativistic energy scales in Dirac-based treatments, a phenomenological, virial-inspired energy-balance framework that incorporates relativistic kinetic energy, finite-size regularization of the central field, and order-of-magnitude spin–magnetic and spin–orbit contributions is developed in this paper. Within this framework, self-consistent characteristic scales associated is obtained with a hypothetical compact configuration without invoking Dirac or quantum-electrodynamics (QED) bound-state eigenvalues. The resulting scales—namely, a central energy scale of about 260 keV and a characteristic spin-dependent scale of order ΔE_spin ≈ 100 ± 20 keV—define concrete experimental and observational energy ranges of interest. The present study does not establish the existence, formation probability, lifetime, or dynamical stability of such states. Rather, it shows that relativistic kinematics, finite-size effects, and virial-inspired stationarity constraints do not, by themselves, rule out compact stationary electron–proton configurations within the assumptions of the model. If such states were realized in nature and possessed radiative or interaction channels, those states may have implications for astrophysics, fusion concepts, and dark-matter phenomenology.

We present a study of the mean transverse momentum $⟨p_{\mathrm{T}}⟩$ of identified strange hadrons ( ) produced in Au+Au collisions at RHIC-BES energies (the nucleon–nucleon center-of-mass energy and ). The mean transverse momentum is obtained from transverse momentum spectra of the strange hadrons as measured by the STAR experiment and its dependence on the number of participants $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$ is studied. For RHIC-BES energies, experimental data indicate a centrality dependence of $⟨p_{\mathrm{T}}⟩$, with an increase towards central collisions. This dependency is described using a power-law function to fit the data. The power-law exponent $\alpha$ is used to characterize the degree of flattening of $⟨p_{\mathrm{T}}⟩$ with respect to $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$ and its dependency on the collision energy and particle mass is studied. Special emphasis is placed on $\varphi$-meson that has a smaller interaction cross-section, thus reflecting the properties of the early stages of the system’s evolution. The $⟨p_{\mathrm{T}}⟩$ of $\varphi$-mesons produced in Au+Au collisions at RHIC-BES energies are compared with the results obtained in Au+Au collisions at higher RHIC energies and in Pb+Pb collisions at SPS and LHC energies. A distinct energy dependence of $\varphi ⟨p_{\mathrm{T}}⟩$ values is identified. Furthermore, data indicate, when comparing peripheral and central heavy-ion collisions, that $\varphi$-meson $⟨p_{\mathrm{T}}⟩$ increases with system size, following two distinct trends. The results are compared with the predictions of the default and string-melting versions of the AMPT generator. We observe that the string-melting AMPT version describes the strange meson $⟨p_{\mathrm{T}}⟩$, but underpredicts the strange baryon $⟨p_{\mathrm{T}}⟩$ centrality dependence. The default AMPT overpredicts the ${\mathrm{K}}_{\mathrm{S}}^0$ and $\varphi$ meson $⟨p_{\mathrm{T}}⟩$ centrality dependence, while the strange baryon data are in general better described by this version of the model. The exponent $\alpha$ obtained from AMPT-simulated results does not describe the measurements satisfactorily.

As a foundation for numerical solvers in computational electromagnetics, particularly for multiphysics and electromagnetic compatibility applications, Jefimenko’s equations offer a generalized solution to Maxwell’s equations, enabling the direct computation of electromagnetic fields from time-dependent source distributions without the boundary-condition artifacts inherent to grid-based methods. However, the numerical integration of these equations is computationally intensive, typically scaling as for $N_{\mathrm{s}}$ source points and $N_{\mathrm{o}}$ observation points. In this paper, we present JefiFast, a highly optimized graphics processing unit (GPU) implementation that significantly outperforms the state-of-the-art JefiGPU algorithm. We identify that previous implementations are strictly memory-bound due to inefficient global memory transactions and a lack of data reuse. JefiFast addresses these bottlenecks through four key optimizations: (i) a packed memory layout (PML) using an array-of-structures approach to ensure coalesced memory access for source densities and their derivatives; (ii) geometry-aware shared memory tiling strategies that maximize L2 (level-2) cache hit rates and on-chip data reuse; (iii) pre-computation of time derivatives to minimize redundant arithmetic operations; and (iv) a robust observation domain decomposition strategy that enables linear scaling across multiple GPUs. Benchmarks demonstrate that JefiFast achieves speedups ranging from $4.08$ times (for ${30}^3$ grids on a single NVIDIA V100 graphic processor) to $84.51$ times (for ${50}^3$ grids on 4 NVIDIA V100 processors) compared to the baseline. Notably, for a ${50}^3$ grid on a single GPU, JefiFast reduces execution time from about 51 min to just about 2.6 min ($19.54$ times speedup). These performance advances make high-resolution relativistic heavy-ion collision simulations feasible in near real-time.