arXiv subjects

Daniel Rodríguez

Publications and source records attributed to Daniel Rodríguez.

At least 19 recordsLinked to original sources

arXiv2026

Cyclotron-Frequency Stability via Single-Ion Fluorescence in a Penning Trap with a Cryogen-Free Superconducting Magnet

In this work, we investigate the magnetic-field stability of a Penning trap operated with a cryogen-free superconducting magnet through cyclotron-frequency measurements of a single laser-cooled calcium ion using two complementary photon-based detection techniques: a pulsed optical method for determining the three ion eigenfrequencies and Fluorescence-Detected Fourier-Transform Ion-Cyclotron-Resonance (FD-FT-ICR). For the former technique, the data-analysis procedure was revisited, considering it as the dominant contribution to the measurement uncertainty and yielding a long-term magnetic-field drift $(1/B)(dB/dt) = -3.07(32)\times10^{-9}$ $\mathrm{h}^{-1}$. This value is comparable to those reported for high-precision Penning-trap experiments employing liquid-helium-based superconducting magnets. The short-term stability was investigated using the FD-FT-ICR technique, resulting in a minimum relative magnetic-field variation of $δB/B \simeq 5\times10^{-8}$ for averaging times between 30 and 60 s. Furthermore, this technique enables direct cyclotron-frequency determinations on timescales as short as a few seconds, providing access to magnetic-field fluctuations that are generally not resolved in conventional Penning-trap experiments.

physics.ins-det↗

arXiv2026

Dynamical system for PageRank with a time-dependent memory

Inspired by the dynamical PageRank framework of Gleich and Rossi in 2012, we introduce a continuous-time PageRank model in which the personalization vector evolves as a weighted average of its past values, with the weights determined by a memory function. The resulting dynamics are formulated as an initial value problem for an integro-differential equation, where the initial condition is a probability vector. We investigate how the choice of memory function influences the long-time behavior of the PageRank vector. In particular, for strongly connected networks $\mathcal{G}$, we prove that broad classes of memory functions lead to convergence toward a stationary state that is independent of the initial condition. In contrast, when the memory function is exponential-oscillatory, $ω(t)=e^{at}\cos(bt)$ for $t\geq0$ with $a,b>0$, we show that the PageRank dynamics exhibit asymptotically periodic behavior, revealing that oscillatory memory can fundamentally alter the qualitative evolution of the ranking process. To establish these results, we first prove the existence and uniqueness of solutions using standard results from the theory of integro-differential equations and show that the solution remains a probability vector for all times, thereby preserving the essential properties of the PageRank model.

cs.SI↗

arXiv2026

Numerical method for strongly variable-density flows at low Mach number: flame-sheet regularisation and a mass-flux immersed boundary method

A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows at low Mach number, based on the fractional time-step method. The proposed approach is suitable for handling strong temperature gradients and thermal diffusion, as encountered in combustion systems. To address discontinuities at the flame front in reacting-flow cases, due to the hypothesis of infinitely fast chemistry, a regularisation procedure is employed. Additionally, the immersed boundary method (IBM) is extended to handle mass flux across the boundary surface, enabling simulations of fuel ejection from an arbitrary burner geometry, using a convenient Cartesian grid. The numerical method utilises a predictor-corrector scheme for time integration on a collocated grid, with flux interpolation to prevent numerical pressure oscillations (``odd-even decoupling''). Relevant test cases are used to verify the methods and their implementations, demonstrating correctness and robustness.

physics.flu-dyn↗

arXiv2026

Counterflow around a cylinder

The incompressible flow around a circular cylinder, positioned at the center of an unconfined planar counterflow, is studied by means of numerical solutions of the conservation equations and linear stability analysis. The flow is completely defined by the Reynolds number ($\Rey$) -- based on the cylinder radius, the strain rate defining the counterflow, and the kinematic viscosity. For very low values of $\Rey$, the flow is steady, two-dimensional, and fully attached to the cylinder wall. Increasing $\Rey$ above $\Rey_s \approx 16.86$, the flow separates, giving rise to two symmetric, counter-rotating recirculation regions on each side of the cylinder. Further increasing $\Rey$ leads to a progressive enlargement of the recirculation regions and the appearance of multiple recirculation centers, akin to Moffatt eddies. However, the convective acceleration imposed by the counterflow limits their size. An oscillatory mode becomes linearly unstable for $\Rey_{c} \approx 4146$. This mode gives rise to a sinuous meandering of the wake flow, on each side of the cylinder, being analogous to the well-known von Kármán instability. The frequency of this mode is directly proportional to the strain rate defining the counterflow.

physics.flu-dyn↗

arXiv2025

Plane-marching PSE wavepacket models for perfectly-expanded twin jets

The importance of wavepackets in the generation of mixing noise in twin jets is expected by extrapolation of the insights previously obtained from the study of single isolated jets. This work presents wavepacket models for supersonic round twin jets operating at perfectly-expanded conditions, computed via plane-marching parabolized stability equations based on mean flows obtained from the compressible RANS equations. High-speed schlieren visualizations and non-time-resolved PIV measurements are performed to obtain experimental datasets for validating the modelling strategy. The RANS solutions are found to be in good quantitative agreement with the PIV mean-flow measurements, confirming the ability of the approach to capture the interaction between jets at the mean-flow level. The obtained wavepackets consist of toroidal and flapping fluctuations of the twin-jet system, and show similarities with those of single axisymmetric jets. However, for the case of closely-spaced jets, they exhibit deviations in the phase speed of structures travelling in the outer mixing layer and those travelling in the inner one, leading to different non-axisymmetric behaviours. In particular, toroidal twin-jet wavepackets feature tilted ring-like structures with respect to the jet axis, while flapping twin-jet wavepackets are distorted and lose the clean checkerboard pattern typically observed in $m = 1$ modes in axisymmetric jets. A quantitative comparison of the modelled wavepackets with experimentally-educed coherent structures is performed in terms of their structural agreement measured through an alignment coefficient, providing a first validation of the modelling strategy. Alignment coefficients are found to be particularly high in the intermediate range of studied frequencies.

physics.flu-dyn↗

arXiv2025

Fixed points of Personalized PageRank centrality: From irreducible to reducible networks

In this paper we analyze the PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented includes the use of a feedback-PageRank in order to compute exactly the fixed points following the classic Power's Method in terms of the (left-hand) Perron vector of each strongly connected components.

cs.SI↗

arXiv2024

Enhancing non-destructive mass identification via Fourier-transform fluorescence analysis

Single-ion mass identification is important for atomic and nuclear physics experiments on ions produced with low yields. Cooling the ion to ultra-low temperatures by interacting with a laser-cooled ion will enhance the precision of the measurements. In this paper we present axial-common-mode frequency measurements of balanced and unbalanced Coulomb crystals from the Fourier transform of the fluorescence photons from a Doppler-cooling transition in calcium ions, after probing the ion/crystal with a 5-radiofrequency comb. A single ion non-destructively detected can be used for identification yielding a mass resolving power $m/Δm_\mathrm{FWHM}\approx 310$ from the axial common mode. This identification can be performed from a single measurement within times below one second.

physics.atom-ph↗

arXiv2024

High-performance in-vacuum optical system for quantum optics experiments in a Penning-trap

Accurate measurements with implications in many branches in Physics have been accessed using Penning traps and conventional techniques within a temperature regime where each eigenmotion of a charged particle is still a classical harmonic oscillator. Cooling the particle directly or indirectly with lasers allows reaching the quantum regime of each oscillator, controlling subtle effects in the precision frontier by detecting photons instead of electric current. In this paper, we present a new in-vacuum optical system designed to detecting 397-nm fluorescence photons from individual calcium ions and Coulomb crystals in a 7-T Penning trap. Based on the outcome of computer simulations, our design shows diffraction-limited performance. The system has been characterized using a single laser-cooled ion as a point-like source, reaching a final resolution of 3.69(3) $μ$m and 2.75(3) $μ$m for the trap's axial and radial directions, respectively, after correcting aberrations.

quant-ph↗

arXiv2023

Eduction of acoustics-related coherent structures from Schlieren images of supersonic twin jets by coupling Doak's decomposition and SPOD

This work proposes a methodology to improve the extraction of coherent structures associated with the generation of acoustic fluctuations in turbulent jets from high-speed Schlieren images. This methodology employs the momentum potential theory of Doak to compute potential (acoustic and thermal) energy fluctuations from the Schlieren images by solving a Poisson equation, in the manner introduced by Prasad and Gaitonde. The calculation of momentum potential fluctuations is then combined with the spectral proper orthogonal decomposition (SPOD) technique: the cross-spectral density is defined based on the momentum potential field, instead of the Schlieren images. While the latter are dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by acoustic fluctuations and its spatial structure in the frequency domain is remarkably coherent. This approach is applied here to Schlieren visualizations of a twin-jet configuration with a small jet separation and two supersonic operation conditions: a perfectly-expanded and a overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the Schlieren images. However, they result in a remarkably lower-rank decomposition than Schlieren-based SPOD and, as opposed to the latter, provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes.

physics.flu-dyn↗

arXiv2023

The impact of harmonic inflow variations on the size and dynamics of the separated flow over a bump

The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated by direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs, the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over all the period compared to the steady inflow case and would be the most desirable flow condition in a practical application.

physics.flu-dyn↗

arXiv2023

Penning-trap eigenfrequency measurements with optical radiofrequency detectors

We use an electric-dipole laser-driven transition to precisely measure the cyclotron-frequency ratios of the pairs $^{42}$Ca$^+$-$^{40}$Ca$^+$, $^{44}$Ca$^+$-$^{40}$Ca$^+$ and $^{48}$Ca$^+$-$^{40}$Ca$^+$ in a 7-tesla Penning trap. A single laser-cooled ($T\approx 1$~mK) ion serves, together with photon-counting and/or photon-imaging units, as a radiofrequency detector covering a broad-band frequency spectrum, in the present case from kHz to a few MHz. Such detectors ($^{40,42,44,48}$Ca$^{\scriptsize{+}}$) allow measuring extremely small forces, with measured normalized sensitivities down to $7.4(3.5)$ yN$/\sqrt{\text{Hz}}$ and $24.9(9.9)$ yN$/\sqrt{\text{Hz}}$ in the MHz and kHz regime, respectively. The direct determination of the ions' amplitudes makes a cyclotron-frequency measurement process more robust against inhomogeneities of the magnetic field and/or deviations of the electric quadrupole field due to mechanical imperfections of the trap.

physics.atom-ph↗

arXiv2022

A Coupled-Oscillators Model to Analyze the Interaction between a Quartz Resonator and Trapped Ions

The novel application of a piezoelectric quartz resonator for the detection of trapped ions has developed in the observation of the quartz-ions interaction under non-equilibrium conditions, opening new perspectives for high-sensitive motional frequency measurements of radioactive particles. Energized quartz crystals have (long) constant-decay times in the order of milliseconds, permitting the coherent detection of charged particles within short times. In this publication we develop in detail a model governing the interaction between trapped $^{40}$Ca$^+$ ions and a quartz resonator connected to a low-noise amplifier. We apply this model to experimental data and extract relevant information like the coupling constant $g=2π\times 1.449(2)$~Hz and the ions' modified-cyclotron frequency in our 7-tesla Penning trap. The study on the latter is specially important for the use of this resonator in precision Penning-trap mass spectrometry. The improvement in sensitivity can be accomplished by increasing the coupling constant through the quality factor of the resonator. This can develop in the use of the hybrid quartz-ion system for other applications.

quant-ph↗

arXiv2022

Formation of Two-Ion Crystals by Injection from a Paul-Trap Source into a High-Magnetic-Field Penning Trap

Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser-cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. $^{40}$Ca$^+$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energy of a few electronvolts with respect to the minimum of the Penning-trap potential well. Laser cooling of the two-ion crystal in a strong magnetic field towards reaching the quantum regime is also presented with particular emphasis on the cooling of the radial modes.

quant-ph↗

arXiv2022

Production of Fock Mixtures in Trapped Ions for Motional Metrology

We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband, measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the red sideband pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyze the parametric regime where these states can be reliably reproduced.

quant-ph↗

arXiv2021

Non-equilibrium Coupling of a Quartz Resonator to Ions for Penning-Trap Fast Resonant Detection

The coherent coupling between a quartz electro-mechanical resonator at room temperature and trapped ions in a 7-tesla Penning trap has been demonstrated for the first time. The signals arising from the coupling remain for integration times in the orders of seconds. From the measurements carried out, we demonstrate that the coupling allows detecting the reduced-cyclotron frequency ($ν_+$) within times below 10~ms and with an improved resolution compared to conventional electronic detection schemes. A resolving power $ν_+/Δν_+=2.4\times10^{7}$ has been reached in single measurements. In this publication we present the first results, emphasizing the novel features of the quartz resonator as fast non-destructive ion-trap detector together with different ways to analyze the data and considering aspects like precision, resolution and sensitivity.

physics.ins-det↗

arXiv2020

Efficient computation of global resolvent modes

Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows with large gain separation. Direct computation of force and response modes using a singular value decomposition of the full resolvent matrix is feasible only for simple problems; despite recent progress, the cost of resolvent analysis for complex flows remains considerable. In this paper, we propose a new matrix-free method for computing resolvent modes based on integration of the linearized equations and the corresponding adjoint system in the time domain. Our approach achieves an order of magnitude speedup when compared to previous matrix-free time stepping methods by enabling all frequencies of interest to be computed simultaneously. Two different methods are presented: one based on analysis of the transient response, providing leading modes with fine frequency discretization; and another based on the steady-state response to a periodic forcing, providing optimal and suboptimal modes for a discrete set of frequencies. The methods are validated using a linearized Ginzburg-Landau equation and applied to the three dimensional flow around a parabolic body.

physics.flu-dyn↗

arXiv2019

Dynamics of an unbalanced two-ion crystal in a Penning trap for application in optical mass spectrometry

In this article, the dynamics of an unbalanced two-ion crystal comprising the 'target' and the 'sensor' ions confined in a Penning trap has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron and reduced-cyclotron modes split up into the so-called 'stretch' and 'common' modes, that are generalizations of the well-known 'breathing' and 'center-of-mass' motions of a balanced crystal made of two ions. By measuring the frequency modes of the crystal and the sensor ion eigenfrequencies using optical detection, it will be possible to determine the target ion's free-cyclotron frequency. The measurement scheme is described and the non-harmonicity of the Coulomb interaction is discussed since this might cause large systematic effects.

physics.atom-ph↗

arXiv2018

The TRAPSENSOR Facility: an Open-Ring 7-Tesla Penning Trap for Laser-Based Precision Experiments

The Penning-trap electronic-detection technique that offers the precision and sensitivity requested in mass spectrometry for fundamental studies in nuclear and particle physics has not been proven yet to be universal. This has motivated the construction of a Penning-trap facility aiming at the implementation of a novel detection method, consisting in measuring motional frequencies of singly-charged trapped ions in strong magnetic fields, through the fluorescence photons from the 4s$^2$S$_{1/2}\rightarrow $4p$^2$P$_{1/2}$ atomic transition in $^{40}$Ca$^+$. The key element of this facility is an open-ring Penning trap, built and fully characterized, which is coupled upstream to a preparation Penning trap similar to those built at Radioactive Ion Beam facilities. Motional frequency measurements of trapped ions stored in the open-ring trap have been carried out by applying external dipolar and quadrupolar fields in resonance with the ions' eigenmotions, in combination with time-of-flight identification. The infrastructure to observe the fluorescence photons from $^{40}$Ca$^+$, comprising the twelve laser beams needed in 7~Tesla, and a two-meters long system to register the image in a high-sensitive CCD sensor, has also been successfully tested by observing optically the trapped $^{40}$Ca$^+$ ions. This demonstrates the capabilities of this facility for the proposed laser-based mass-spectrometry technique, and introduces it as a unique platform to perform laser-spectroscopy experiments with implications in different fields of physics.

physics.ins-det↗