We present a statistical analysis of the intense earthquake swarm near Santorini, Greece, in 2025. A change-point analysis of the b-value of the Gutenberg–Richter frequency-magnitude distribution indicates that, despite obvious spatiotemporal changes in seismicity characteristics during the crisis, there was no significant change of b with time. The high event rate provides a large statistical sample equivalent to a much longer catalog in terms of event numbers. This offers the chance to study the upper tail of the frequency-magnitude distribution in detail. While typical earthquake catalogs suffer from poor sampling in this domain, the Santorini crisis is suited for constraining the largest earthquakes. Assuming a truncated Gutenberg–Richter distribution and using well-established methods from frequentist statistics, like calculation of exact confidence intervals, we find that the maximum observed magnitude m=5.2 is close to the estimated maximum possible magnitude. We conclude that with 95 m>5.35 can be expected.
The Kadomtsev-Petviashvili equation is a fundamental nonlinear model with applications ranging from plasma physics and shallow water dynamics to ferromagnetism, Bose-Einstein condensation, and string theory. This manuscript investigates a newly formulated (3+1)-dimensional Kadomtsev-Petviashvili equation and presents its novel solution structures. By imposing constraints on the N-soliton solutions, resonant X-type, Y-type, XX-type, YY-type and parallel soliton solutions are derived. Furthermore, M-lump solutions are systematically constructed via the Long-wave limit method, enabling the exploration of higher-order lump dynamics. In addition, the interactions among lumps, soliton waves, and breathers are analyzed to reveal complex nonlinear behaviors. Finally, the physical properties and dynamical behaviors of these localized waveforms are illustrated through three-dimensional surface plots and corresponding contour representations. These results reveal new nonlinear phenomena and extend the theoretical understanding of soliton theory in higher dimensions.
The paper is a strict exploration of the existence, dynamic behavior, and stability of optical soliton states of a (3+1)-dimensional Boussinesq equation system, which is conventionally used to describe fluid mechanics systems but is here applied to the dynamics of waves in nonlinear optical materials. Through the application of two powerful analytic procedures, the expansion method of the ϕ ^6 -model expansion method and the modified exp(-ϕ (ϱ )) -expansion function method, we have been able to obtain a spectrum of new exact soliton solutions that explain the fine balance between higher-order dispersion and nonlinearity in the multidimensional setting. One of the most important contributions of the given work is the sensitivity analysis of the relevant dynamical system in which the transition between regular soliton behavior and the singular or chaotic one is determined systematically based on the values of the main physical parameters, including stratification and nonlinear gain, which determine the parametric regimes of stable propagation. The results do not merely add to the mathematical physics of the Boussinesq equation, but they provide a new theoretical basis to develop robust high-dimensional optical communications in which interactions between complex spatiotemporal dynamics are common. The physical relevance of the solutions is further confirmed by graphical simulations, which provide a clear picture of the underlying wave phenomena.
This study investigates the pressure distribution in porous media while accounting for the memory effects in fluid flow. A mathematical model is developed to describe fluid flow in both homogeneous and heterogeneous porous media under various boundary conditions. The presence of porous media can lead to anomalous diffusion, which preserves the history of the interactions between the fluid and medium. To capture this behavior, the Caputo-type fractional derivative is incorporated into Darcy’s law. The problem is analyzed numerically using a spectral method based on orthogonal polynomials. In this approach, the derivatives of orthogonal polynomials are represented in matrix form, which is known as the operational matrices. These matrices provide a systematic framework for handling polynomials, facilitating their application to fluid flow problems. By employing operational matrices, the original fractional differential equation is transformed into a system of linear algebraic equations. A closed-form approximation of the fluid pressure is then obtained. The convergence analysis of the proposed method is presented, and its stability is demonstrated numerically using a perturbation approach. The accuracy of the method is validated by comparing the results of the proposed operational matrix scheme with existing methods in the literature. Numerical results indicate that the influence of the fractional-order derivative on pressure distribution depends on both the boundary conditions and the permeability of the medium.
This paper introduces Lineal, a new linear algebra library optimized for runtime and especially memory efficiency to solve large sparse linear systems arising from PDE discretization on attainable hardware. Lineal supports general matrix-based linear systems using Compressed Sparse Row (CSR) matrices and matrix-free linear systems for stencil-based problems, which can store a single value per cell to minimize memory use. Both can be paired with MAMGO, Lineal’s Algebraic Multi-Grid implementation based on DUNE ISTL’s algorithm, which can use a matrix-free linear system on the finest, most memory-intensive level and CSR matrices on coarser levels, greatly reducing memory consumption—a novel approach, to our knowledge. Lineal also offers very flexible support for mixed precision to minimize memory use and the effect of reduced precision on convergence. Almost all components are fully multithreaded and many support explicit SIMD operations and/or tiling. Tests solving the stationary diffusion problem using two sets of high-resolution scans of soil samples show Lineal’s very good strong scaling and high performance. On the smaller dataset, Lineal outperforms hypre’s BoomerAMG, DUNE ISTL, and Ginkgo, requiring under half the time and memory with CSR matrices only and less than a quarter with the hybrid matrix-free approach. Unlike the other libraries, Lineal can handle the much larger dataset on the test system due to its low memory requirements. On the SPE10 Model 2 benchmark, Lineal is somewhat slower than BoomerAMG but uses much less memory, and it is faster than the other libraries.
