arXiv subjects

Lucas Timotheo Sanches

Publications and source records attributed to Lucas Timotheo Sanches.

7 recordsLinked to original sources

arXiv2026

Exploring Particle Geodesics in a Warp Drive Spacetime

Although the Alcubierre Warp Drive is theoretically capable of providing faster-than-light travel, it may be difficult to use for this purpose. But is it useful for slower-than-light travel? We begin by observing the that the warp bubble will act to protect the ship from dust particles and other space debris (a potentially serious hazard even at 10% the speed of light). We then explore several modifications of the Alcubierre Warp Drive, e.g. a "deflector shield", with the perspective of keeping a ship safe from collisions with particles, projectiles, rogue planets, and other dangers of space travel.

gr-qc↗

arXiv2026

Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.

cs.LG↗

arXiv2026

Accelerating Numerical Relativity Simulations with New Multistep Fourth-Order Runge-Kutta Methods

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires applications to evaluate four intermediate stages to take one time step. Depending on the complexity of the problem being solved, the evaluation of these intermediate stages can be computationally expensive. In this paper we develop explicit fourth-order accurate Multistep Runge-Kutta (MSRK) methods. The advantage of such methods is that they re-use data from previous time steps, thus requiring fewer intermediate stage evaluations and potentially speeding up applications. We outline a procedure to obtain and tune the method's coefficients by adjusting their stability regions in an attempt to maximize the size that a time step can take. We validate and evaluate our new methods in the context of Numerical Relativity applications using the EinsteinToolkit. We believe, however, that these methods and results should generalize to other applications using explicit Runge-Kutta methods.

gr-qc↗

arXiv2024

AsterX: a new open-source GPU-accelerated GRMHD code for dynamical spacetimes

We present AsterX, a novel open-source, modular, GPU-accelerated, fully general relativistic magnetohydrodynamic (GRMHD) code designed for dynamic spacetimes in 3D Cartesian coordinates, and tailored for exascale computing. We utilize block-structured adaptive mesh refinement (AMR) through CarpetX, the new driver for the Einstein Toolkit, which is built on AMReX, a software framework for massively parallel applications. AsterX employs the Valencia formulation for GRMHD, coupled with the Z4c formalism for spacetime evolution, while incorporating high resolution shock capturing schemes to accurately handle the hydrodynamics. AsterX has undergone rigorous testing in both static and dynamic spacetime, demonstrating remarkable accuracy and agreement with other codes in literature. Using subcycling in time, we find an overall performance gain of factor 2.5 to 4.5. Benchmarking the code through scaling tests on OLCF's Frontier supercomputer, we demonstrate a weak scaling efficiency of about 67%-77% on 4096 nodes compared to an 8-node performance.

astro-ph.HE↗

arXiv2022

QuasinormalModes.jl: A Julia package for computing discrete eigenvalues of second order ODEs

QuasinormalModes.jl is a Julia package for computing the quasinormal modes of any General Relativity model whose perturbation equation can be expressed as second order homogeneous ODE. Not only that, the package can be used to compute the discrete eigenvalues of any second order homogeneous ODE (such as the energy eigenstates of the time independent Schrödinger equation) provided that these eigenvalues actually exist. The package features a flexible and user friendly API where the user simply needs to provide the coefficients of the problem ODE after incorporating boundary and asymptotic conditions on it. The user can also choose to use machine or arbitrary precision arithmetic for the underlying floating point operations involved and whether or not to do computations sequentially or in parallel using threads. The API also tries not to force any particular workflow on the users so that they can incorporate and adapt the existing functionality on their research pipelines without unwanted intrusions.

gr-qc↗

arXiv2022

Revisiting the quasinormal modes of the Schwarzschild black hole: Numerical analysis

We revisit the problem of calculating the quasinormal modes of spin $0$, $1/2$, $1$, $3/2$, $2$, and spin $5/2$ fields in the asymptotically flat Schwarzschild black hole spacetime. Our aim is to investigate the problem from the numerical point of view, by comparing some numerical methods available in the literature and still not applied for solving the eigenvalue problems arising from the perturbation equations in the Schwarzschild black hole spacetime. We focus on the pseudo-spectral and the asymptotic iteration methods. These numerical methods are tested against the available results in the literature, and confronting the precision between each other. Besides testing the different numerical methods, we calculate higher overtones quasinormal frequencies for all the investigated perturbation fields in comparison with the known results. In particular, we obtain purely imaginary frequencies for spin $1/2$ and $3/2$ fields that are in agreement with analytic results reported previously in the literature. The purely imaginary frequencies for the spin $1/2$ field are exactly the same as the frequencies obtained for the spin $3/2$ field. In turn, the quasinormal frequencies for the spin $5/2$ perturbation field are calculated for the very first time, and purely imaginary frequencies are found also in this case. We conclude that both methods provide accurate results and they complement each other.

gr-qc↗

arXiv2021

Energy Extraction From Non-Coalescing Black Hole Binaries

We define and sketch the generalized ergosphere of the Majumdar-Papapetrou (MP) spacetime. In particular, we demonstrate the existence of closed orbits of negative energy that live outside the event horizon of such a spacetime. Relying on the Penrose process mechanism, we use these orbits to illustrate the possibility of energy extraction from a MP binary black hole by particle scattering. We also analyze the efficiency of the process, and construct explicit examples that optimize the extraction of energy. Lastly, we show how such concepts can be extended to a pair of non-coalescing Kerr black holes described by the Cabrera-Munguia, Manko and Ruiz (CMMR) metric.

gr-qc↗