Fermat’s principle is fully generalized to the case where a smooth interface separates two cone structures—Lorentz-Finsler lightcones—representing wave propagation in a potentially inhomogeneous, anisotropic, time-dependent and discontinuous medium. The interface, wave source and receiver are assumed to be a hypersurface, a submanifold and a curve in the spacetime, respectively, of any causal character. For a trajectory to fulfill Fermat’s principle—i.e., to be a critical point of the arrival time functional—its direction must change at the interface, obeying a precise condition that generalizes Snell’s law of refraction when the wave crosses the interface, or the law of reflection when it remains in a single medium. Both laws are analyzed in detail to establish the conditions ensuring the existence and uniqueness of refracted and reflected trajectories, and to determine whether they actually minimize the arrival time. Applications to Zermelo’s navigation problem and the determination of geodesics in discretized spacetimes are also emphasized.
This paper develops a combined method between reduced order methods (ROM) and domain decomposition (DD) for a boundary value problem corresponding to a parametric linear elliptic partial differential equation. The convergence of the method and the error between the solution of the problem discretised using the finite element method and the solution of the problem posed on the reduced space are studied. The reduced space is composed of reduced spaces specific to each of the subdomains and a specific space for the interface that allows for a good approximation of the solution obtained by the method. In addition, numerical results on academic problems are presented that validate the theoretical results obtained.
The design of effective oral delivery systems represents a significant challenge in the biopharmaceutical field. In this study, hydrogel spheres were developed based on a polyelectrolyte matrix of chitosan and pectin, with the incorporation of extracts from three species of fungi with therapeutical benefits. FTIR and XRD analyses confirmed the successful incorporation and uniform dispersion of the extracts within a predominantly amorphous polymeric matrix. Mechanical tests demonstrated high elasticity and robustness, ensuring the structural integrity of the system. Furthermore, the matrices exhibited a controlled release through a pH-switch mechanism and mucoadhesive properties. These results demonstrate the development of stable and reproducible systems capable of providing an efficient delivery of bioactive fungal extracts.
This work explores the dynamics of nonlo cal reaction-diffusion equations under nonlinear growth conditions in thin domains. The nonlo cal effect appears in a viscosity term in front of the Laplacian operator. Existence of strong solutions and global attractors is ensured. By identifying a limit equation on the lower-dimensional domain, we compare the associated family of attractors, revealing upper-semicontinuity.
The second-order generalized integrator (SOGI), which can be used to attenuate the self-interference of the fundamental tone, is unable to fully reject DC offsets on the input signal. Consequently, the performance of any SOGI based synchrophasor estimation (SE) technique might be compromised in the presence of such DC components. The current work presents a SE algorithm which adopts an enhanced SOGI formulation, robust against DC, combined with a three-point IpDFT and a three nominal fundamental period Hanning observation window. Its simultaneous compliance with both phasor measurement unit (PMU) P and M performance classes is assessed by means of a simulated environment where all the operating conditions defined by the IEC/IEEE 60255-118-1:2018 standard are evaluated combined with a 10% static DC offset and under two different noise levels. Furthermore, the method adopts a dedicated mechanism for the detection of low amplitude 2nd harmonic tones and the correction of their impacts under off-nominal frequency conditions. Finally, its resilience against multiple simultaneous harmonic interferences is also analyzed together with its performance in the presence of decaying DC components.
