arXiv subjects

Cristian Vega

Publications and source records attributed to Cristian Vega.

16 recordsLinked to original sources

arXiv2026

Distributions of particles accelerated by strong Alfvénic turbulence

This work presents a model for generating nonthermal power-law tails of particles' energy probability density functions in turbulent collisionless plasmas, applicable to both non-relativistic and relativistic scenarios. We propose that strong Alfvénic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the non-relativistic case, the momentum probability density function scales as $f(p) dp \propto p^{-3} dp $, while in the ultrarelativistic case, the energy probability density function scales as $ f(γ) dγ\propto γ^{-3} dγ$, where $γ$ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.

physics.plasm-ph↗

arXiv2026

Particle acceleration and pitch-angle evolution in relativistic turbulence

Synchrotron radiation detected from relativistic astrophysical objects such as pulsar-wind nebulae and {jets from active galactic nuclei} depends on the magnetic fields and the distribution functions of energetic electrons in these systems. Relativistic magnetically dominated turbulence has been recognized as an efficient mechanism for structure formation and non-thermal particle acceleration in these environments. Recent numerical simulations of relativistic turbulence have provided insights into the energy distribution functions of accelerated electrons. Much less is currently understood about their {pitch angle distributions}, which are crucial for accurately interpreting the spectra of synchrotron radiation. {We perform a detailed case study of} the pitch angle distributions formed during the process of turbulent acceleration {for $B_0/δB_0 = 10$ and $\tildeσ_0 \sim 40$, where $B_0$ is the uniform component of the magnetic field, $δB_0$ is the fluctuating component, and $\tildeσ_0$ is the plasma magnetization based on the magnetic fluctuations. We find that even minimal numerical noise can cause substantial pitch angle scattering, but we demonstrate techniques for overcoming the numerical challenges associated with the evolution of very small pitch angles. Our numerical results are consistent with the phenomenological model found in \cite[][]{vega2024b,vega2025}.}

astro-ph.GA↗

arXiv2026

Optimization Insights into Deep Diagonal Linear Networks

Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the mechanisms that make such methods effective has become a central problem in modern optimization. To investigate this question in a tractable setting, we study Deep Diagonal Linear Networks. These are multilayer architectures with a reparameterization that preserves convexity in the effective parameter, while inducing a nontrivial geometry in the optimization landscape. Under mild initialization conditions, we show that gradient flow on the layer parameters induces a mirror-flow dynamic in the effective parameter space. This structural insight yields explicit convergence guarantees, including exponential decay of the loss under a Polyak-Lojasiewicz condition, and clarifies how the parametrization and initialization scale govern the training speed. Overall, our results demonstrate that deep diagonal over parameterizations, despite their apparent complexity, can endow standard gradient methods with well-behaved and interpretable optimization dynamics.

cs.LG↗

arXiv2026

Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications

We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with a Lipschitz gradient or weakly smooth and, for each case, we ensure bounded dynamic regret in terms of cumulative path variation achieving sub-linear regret rates. Furthermore, we illustrate the flexibility of our framework by applying it to both theoretical settings such as zeroth-order (bandit) and also to practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions (Polyak 1966) are strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach.

math.OC↗

arXiv2025

Relaxed and inertial nonlinear Forward-Backward algorithm

The Nonlinear Forward-Backward (NFB) algorithm, also known as warped resolvent iterations, is a splitting method for finding zeros of sums of monotone operators. In particular cases, NFB reduces to well-known algorithms such as Forward-Backward, Forward-Backward-Forward, Chambolle--Pock, and Condat--Vũ. Therefore, NFB can be used to solve monotone inclusions involving sums of maximally monotone, cocoercive, monotone and Lipschitz operators as well as linear compositions terms. In this article, we study the weak and strong (linear) convergence of NFB with inertial and relaxation steps. Our results recover known convergence guarantees for the aforementioned methods when extended with inertial and relaxation terms. Additionally, we establish the convergence of inertial and relaxed variants of the Forward-Backward-Half-Forward and Forward-Primal--Dual-Half-Forward algorithms, which, to the best of our knowledge, are new contributions. We consider both nondecreasing and decreasing sequences of inertial parameters, the latter being a novel approach in the context of inertial algorithms. To evaluate the performance of these strategies, we present numerical experiments on optimization problems with affine constraints and on image restoration tasks. Our results show that decreasing inertial sequences can accelerate the numerical convergence of the algorithms.

math.OC↗

arXiv2025

Anisotropic particle acceleration in Alfvénic turbulence

Alfvénic turbulence is an effective mechanism for particle acceleration in strongly magnetized, relativistic plasma. In this study, we investigate a scenario where turbulent plasma is influenced by a strong guide magnetic field, resulting in highly anisotropic turbulent fluctuations. In such cases, the magnetic moments of particles are conserved, which means that acceleration can only occur along the direction of the magnetic field. Consistent with previous analytic studies, we find through PIC simulations of magnetically dominated pair plasma that the momenta of accelerated particles are closely aligned with the magnetic field lines. Notably, the alignment angle decreases as particle energy increases, potentially limited only by the inherent curvature and gradients of the turbulent magnetic fluctuations. This finding has significant implications for interpreting the synchrotron radiation emitted by highly accelerated particles.

physics.plasm-ph↗

arXiv2024

Relaxed and Inertial Nonlinear Forward-Backward with Momentum

In this article, we study inertial algorithms for numerically solving monotone inclusions involving the sum of a maximally monotone and a cocoercive operator. In particular, we analyze the convergence of inertial and relaxed versions of the nonlinear forward-backward with momentum (NFBM). We propose an inertial version including a relaxation step, and a second version considering a double-inertial step with additional momentum. By applying NFBM to specific monotone inclusions, we derive inertial and relaxed versions of algorithms such as forward-backward, forward-half-reflect-backward (FHRB), Chambolle-Pock, Condat-Vũ, among others, thereby recovering and extending previous results from the literature for solving monotone inclusions involving maximally monotone, cocoercive, monotone and Lipschitz, and linear bounded operators. We also present numerical experiments on image restoration, comparing the proposed inertial and relaxation algorithms. In particular, we compare the inertial FHRB with its non-inertial and momentum versions. Additionally, we compare the numerical convergence for larger step-sizes versus relaxation parameters and introduce a restart strategy that incorporates larger step-sizes and inertial steps to further enhance numerical convergence.

math.OC↗

arXiv2024

Particle acceleration in relativistic Alfvénic turbulence

Strong magnetically dominated Alfvénic turbulence is an efficient engine of non-thermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations $δB_0$ and the guide field $B_0$. If $δB_0\ll B_0$, the particle magnetic moments are conserved and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if $δB_0 \gtrsim B_0$, interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.

physics.plasm-ph↗

arXiv2024

Relativistic Alfvén turbulence at kinetic scales

In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in non-relativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close to $k^{-3}$ or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.

physics.plasm-ph↗

arXiv2023

Electron-Scale Current Sheets and Energy Dissipation in 3D Kinetic-Scale Plasma Turbulence with Low Electron Beta

3D kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is $β_e=0.1$ for electrons and $β_i=1$ for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth's magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (SPS) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure-strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20\% of the total volume. Some of the current sheets corresponding to the largest pressure-strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about $1$\% of all the current sheets identified.

physics.plasm-ph↗

arXiv2023

Spatial intermittency of particle distribution in relativistic plasma turbulence

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form non-thermal power-law distribution functions in the momentum (or energy) space, $f(γ)dγ\propto γ^{-α}dγ$, where $γ$ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has log-normal statistics, while the density of the accelerated particles, $n$, has a power-law distribution function, $P(n)dn\propto n^{-β}dn$. We argue that the scaling exponents are related as $β\approx α+1$, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

physics.plasm-ph↗

arXiv2023

Spectra of magnetic turbulence in a relativistic plasma

We present a phenomenological and numerical study of strong Alfvénic turbulence in a magnetically dominated collisionless relativistic plasma with a strong background magnetic field. In contrast with the non-relativistic case, the energy in such turbulence is contained in magnetic and electric fluctuations. We argue that such turbulence is analogous to turbulence in a strongly magnetized non-relativistic plasma in the regime of broken quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scaling $k^{-3/2}$, while the difference between the magnetic and electric energies, the so-called residual energy, has the scaling $k^{-2.4}$. The electric and magnetic fluctuations at scale $\ell$ exhibit dynamic alignment with the alignment-angle scaling close to $\cosϕ_\ell\propto \ell^{1/4}$. At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfvén turbulence steepens to $k^{-3.5}$.

physics.plasm-ph↗

arXiv2022

Fast iterative regularization by reusing data

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most applications the regularizer is convex, in many cases it is not smooth nor strongly convex. In this paper, we propose and study two new iterative regularization methods, based on a primal-dual algorithm, to solve inverse problems efficiently. Our analysis, in the noise free case, provides convergence rates for the Lagrangian and the feasibility gap. In the noisy case, it provides stability bounds and early-stopping rules with theoretical guarantees. The main novelty of our work is the exploitation of some a priori knowledge about the solution set, i.e. redundant information. More precisely we show that the linear systems can be used more than once along the iteration. Despite the simplicity of the idea, we show that this procedure brings surprising advantages in the numerical applications. We discuss various approaches to take advantage of redundant information, that are at the same time consistent with our assumptions and flexible in the implementation. Finally, we illustrate our theoretical findings with numerical simulations for robust sparse recovery and image reconstruction through total variation. We confirm the efficiency of the proposed procedures, comparing the results with state-of-the-art methods.

math.OC↗

arXiv2021

Turbulence and particle acceleration in a relativistic plasma

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a non-thermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter $σ\gg 1$) quickly evolves into a state with ultra-relativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent $α$ in the power-law particle energy distribution function, $f(γ)dγ\propto γ^{-α}dγ$, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent $α$ is in good agreement with the numerical results.

physics.plasm-ph↗

arXiv2020

Random Activations in Primal-Dual Splittings for Monotone Inclusions with a priori Information

In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite number of operators, and we propose and algorithm that activates the corresponding set by following a finite-valued random variable at each iteration. Our formulation is flexible and includes, for instance, deterministic and Bernoulli activations over cyclic schemes, and Kaczmarz-type random activations. The almost sure convergence of the algorithm is obtained by means of properties of stochastic Quasi-Fejér sequences. We also recover several primal-dual algorithms for monotone inclusions in the context without a priori information and classical algorithms for solving convex feasibility problems and linear systems. In the context of convex optimization with inequality constraints, any selection of the constraints defines the a priori information set, in which case the operators involved are simply projections onto half spaces. By incorporating random projections onto a selection of the constraints to classical primal-dual schemes, we obtain faster algorithms as we illustrate by means of a numerical application to a stochastic arc capacity expansion problem in a transport network.

math.OC↗

arXiv2020

Electron-only reconnection in kinetic Alfvén turbulence

We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfvén turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth's magnetosheath by Phan et al. (2018). Electron-only reconnection is thus an inherent property of kinetic-Alfvén turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to $0.1$.

physics.plasm-ph↗