arXiv subjects

Daniel Fernández

Publications and source records attributed to Daniel Fernández.

9 recordsLinked to original sources

arXiv2026

Selective boundary condition reduction via learned error gating

Parametric PDEs can admit different boundary conditions with different accuracy and computational cost. We introduce a framework for learning when one reduced boundary condition can replace another: paired solutions train a neural network to estimate the resulting domain and boundary errors, and the simpler condition is used only when both predicted errors meet prescribed tolerances. We focus on singular limits in applications, in which a stiff Robin or nonlinear boundary law is replaced by its limiting Dirichlet form. We evaluate the method on a galvanic corrosion problem and other nonlinear stationary and evolution problems.

math.NA↗

arXiv2026

Beyond Equidistant Assumptions: An Autoregressive Ordered Stereotype Model for Ordinal Time Series

We propose an extension of the ordered stereotype model (OSM) for ordinal time series data, referred to as the Autoregressive OSM (AR-OSM). The model captures serial dependence by incorporating lagged values of the response as covariates in the systematic component. In contrast to existing regression models for ordinal time series, the AR-OSM does not assume equidistant categories, but instead allows the data to determine their relative spacing. This property makes the model particularly suitable for applications where the equidistance assumption is unrealistic. Such a case is illustrated through the analysis of infant sleep state data. Additionally, a comprehensive simulation study is conducted to assess the performance of the model under varying sample sizes and to investigate how parameter values influence the induced serial dependence structure.

stat.ME↗

arXiv2026

Singular limit phenomenon in a nonlinear elliptic model arising in electrochemistry

We study a singularly perturbed harmonic problem, with nonlinear Neumann boundary conditions of signed exponential type, arising in galvanic corrosion applications. We focus on the low-conductivity regime, which leads to a singular limit in which the solution presents a jump in the boundary. We prove convergence of the solution traces in the corresponding fractional Sobolev spaces, identify the interior limit solution, and obtain a sharp logarithmic energy expansion for smooth boundary junctions. The proofs rely mostly on trace Moser--Trudinger estimates for showing well-posedness and regularity, and on mollifier approximation techniques for the singular limit analysis. Numerical experiments test the predicted convergence rate.

math.AP↗

arXiv2025

Impedance Modeling of Magnetometers: A Path Toward Low-Noise Readout Circuits

Optimizing sensor readout schemes and integrated circuit designs for both open-loop and closed-loop implementations requires precise modeling and simulation strategies. This study introduces a novel two-port impedance model to estimate the behavior of a converse Magnetoelectric (cME) sensor. This model provides a possible framework for calculating transfer functions and simulating magnetometer behavior in both continuous- and discrete-time simulation environments, and it is also possibly transferable to other magnetometer types. Common S-parameters were measured experimentally using an impedance analyzer and converted to Z-parameters to create a transfer function for system-level simulations. The model was validated through an analysis of output-related noise using MATLAB and LTSpice simulations to optimize the noise of the analog circuit parts of the system. The simulation results were compared with experimental measurements using a Zurich Instruments lock-in amplifier and the custom-designed low-noise printed circuit board (PCB) under model considerations. The proposed methodology derives noise considerations and the transfer function of a magnetometer. These are essential for readout schemes for mixed-signal circuit design. This allows low-noise electronics to be designed and extended to other sensor interface electronics, broadening their applicability in high-performance magnetic sensing.

eess.SP↗

arXiv2025

Patterns in Growth and Distribution of Unbounded Prime Number Walks

In our previous work, we defined a prime walk (PW) on a square grid and presented several intriguing numerical results. Here, we demonstrate the main conjecture presented there, namely, that the area covered by the prime walk is unbounded. Taking this fact into account, we examine in further detail the properties of the PW and explore new questions that arise naturally in this analysis.

math.NT↗

arXiv2021

Design, Fabrication, Characterization and Reliability Study of CMOS-MEMS Lorentz-Force Magnetometers

This article presents several design techniques to fabricate micro-electro-mechanical systems (MEMS) using standard complementary metal-oxide semiconductor (CMOS) processes. They were applied to fabricate high yield CMOS-MEMS shielded Lorentz-force magnetometers (LFM). The multilayered metals and oxides of the back-end-of-line (BEOL), normally used for electronic routing, comprise the structural part of the MEMS. The most important fabrication challenges, modeling approaches and design solutions are discussed. Equations that predict the Q factor, sensitivity, Brownian noise and resonant frequency as a function of temperature, gas pressure and design parameters are presented and validated in characterization tests. A number of the fabricated magnetometers were packaged into Quad Flat No-leads (QFN) packages. We show this process can achieve yields above 95 % when the proper design techniques are adopted. Despite CMOS not being a process for MEMS manufacturing, estimated performance (sensitivity and noise level) is similar or superior to current commercial magnetometers and others built with MEMS processes. Additionally, typical offsets present in Lorentz-force magnetometers were prevented with a shielding electrode, whose efficiency is quantified. Finally, several reliability test results are presented, which demonstrate the robustness against high temperatures, magnetic fields and acceleration shocks.

physics.ins-det↗

arXiv2021

Prime numbers and random walks in a square grid

In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk. The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure -- both in 2d and 3d -- created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail.

math.NT↗

arXiv2016

Thermodynamics of anisotropic branes

We study the thermodynamics of flavor D7-branes embedded in an anisotropic black brane solution of type IIB supergravity. The flavor branes undergo a phase transition between a `Minkowski embedding', in which they lie outside of the horizon, and a `black hole embedding', in which they fall into the horizon. This transition depends on the black hole temperature, its degree of anisotropy, and the mass of the flavor degrees of freedom. It happens either at a critical temperature or at a critical anisotropy. A general lesson we learn from this analysis is that the anisotropy, in this particular realization, induces similar effects as the temperature. In particular, increasing the anisotropy bends the branes more and more into the horizon. Moreover, we observe that the transition becomes smoother for higher anisotropies.

hep-th↗

arXiv2015

Towards Collisions of Inhomogeneous Shockwaves in AdS

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that the considered inhomogeneities typically become hydrodynamical earlier or at the same moment when hydrodynamics applies to the background, even though they decay slowly.

hep-th↗