arXiv subjects

Vincenzo Citro

Publications and source records attributed to Vincenzo Citro.

5 recordsLinked to original sources

arXiv2026

Aging Phase Diagram and Exact Asymptotic Energies of Mixed Spherical Spin Glasses

We determine the aging phase diagram of mixed spherical $(p+s)$-spin glasses quenched from random configurations to zero temperature. Solving the asymptotic dynamical equations of Cugliandolo and Kurchan, we find transitions between aging states with one, two, and continuously many effective temperatures, including phases in which discrete and continuous hierarchies coexist. We obtain analytic expressions for the energies reached asymptotically by the dynamics. In models combining pairwise and higher-order interactions, and sufficiently separated interaction orders ($s>3$), a fully continuous phase exists, where the gradient descent relaxation converges to the algorithmic energy lower bound. Instead, in mixed models with only high-order interactions ($p\ge3$) the energy relaxation remains strictly above it. Numerical integration of the dynamical equations is consistent with the predicted two-step and mixed discrete--continuous aging states.

cond-mat.dis-nn↗

arXiv2026

Flexibility as a Universal Nature-Inspired Mechanism for Thrust Enhancement

Nature has equipped jet-propelled swimmers with flexible nozzles that outperform rigid ones, yet the origin of this advantage has remained unexplained. By tracking where and when energy is exchanged between fluid and structure, three-dimensional numerical simulations resolve the underlying mechanism: a standing-wave response of the nozzle, in which the structure dilates and then recoils synchronously, charging and releasing energy to enhance thrust. Outside of this regime, the structure exhibits a traveling wave response, with expansion and contraction coexisting along the nozzle, reducing the thrust gain. We propose a physics-based model that captures the boundary between standing and traveling responses in a closed form, showing that the optimum occurs when the natural period of the structure matches the pulse duration. Beyond this optimum the strain imposed by the nozzle curvature required for steering selects the geometry observed across marine species. The propulsion and maneuverability are reconciled within a single framework that yields design principles for soft robotic propulsors.

physics.flu-dyn↗

arXiv2026

DYNAMITE: A high-performance framework for solving Dynamical Mean-Field Equations

Understanding the dynamics of systems evolving in complex and rugged energy landscapes is central across physics, economics, biology, and computer science. Disordered mean-field models provide a powerful framework, as exact Dynamical Mean-Field Equations (DMFE) can be derived. However, solving the DMFE -- a set of coupled integral-differential equations for two-time functions -- remains a major numerical challenge. So far, large-time solutions of DMFE rely either on analytical approaches, such as the Cugliandolo--Kurchan ansatz based on assumptions like weak ergodicity breaking (which is known to fail in some cases), or on numerical integrations that reliably reach times $O(10^3)$ and extend further only via poorly controlled approximations. Consequently, no general method currently exists to solve DMFE at very long times, limiting the study of slow dynamics in complex landscapes. We present \textsc{Dynamite} (DYNAmical Mean-fIeld Time Evolution solver), a high-performance framework for solving DMFE up to unprecedented times $t=O(10^7)$. It combines non-uniform interpolation, adaptive time stepping, and numerical `renormalization' of memory, enabling accurate evaluation of history integrals. Its asymptotic runtime is linear, with sublinear memory scaling. Stability and precision are ensured via an adaptive Runge--Kutta scheme and periodic sparsification of the past. \textsc{Dynamite} achieves orders-of-magnitude speedups over uniform-grid methods while maintaining accuracy and reproducibility on CPU and GPU architectures. Benchmarks on glassy mean-field models, including the mixed spherical $p$-spin system, demonstrate access to aging and relaxation regimes previously out of reach. The framework provides a reproducible and extensible foundation for studying long-memory dynamical systems.

cond-mat.dis-nn↗

arXiv2026

Residual Recombination Methods as Anderson-like Acceleration: An Algebraic Interpretation of BoostConv

BoostConv has been introduced in earlier works as an effective acceleration technique for nonlinear iterative processes and has been successfully employed in a variety of applications to enhance convergence rates or to compute unstable fixed points that are otherwise inaccessible through standard approaches. Despite its demonstrated practical effectiveness, the theoretical properties of the method have not yet been fully characterized. In this work, we present a more robust formulation of the BoostConv algorithm and, for the first time, provide a rigorous proof of its convergence. The proposed analysis places BoostConv within a precise mathematical framework, clarifying its interpretation as a nonlinear convergence accelerator and establishing sufficient conditions under which convergence to a fixed point is guaranteed. The theoretical findings are illustrated through several numerical examples, spanning from a linear problem to a low-dimensional benchmark and a large-scale incompressible Navier-Stokes simulation. These results demonstrate the robustness and practical relevance of the proposed method and bridge the gap between empirical performance and rigorous analysis, paving the way for further developments and applications to complex nonlinear problems.

math.NA↗

arXiv2025

Strong ergodicity breaking in dynamical mean-field equations for mixed p-spin glasses

The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the aging dynamics, the evolution becomes slower and slower, but keeps wandering in an unbounded space (a manifold of marginal states), thus forgetting any previously found configuration, has been one of the key hypotheses to achieve an analytical solution. This hypothesis, called weak ergodicity breaking, has recently been questioned by numerical simulations and attempts to solve the dynamical mean-field equations (DMFE). In this work, we introduce a new integration scheme for solving DMFE that allows us to reach very large integration times, $t=O(10^6)$, in the solution of the spherical 3+4-spin model, quenched from close to the mode coupling temperature down to zero temperature. Thanks to this new solution, we can provide solid evidence for \emph{strong ergodicity breaking} in the out-of-equilibrium dynamics on mixed $p$-spin glass models. Our solution to the DMFE shows that the out-of-equilibrium dynamics undergo aging, but in a restricted space: the initial condition is never forgotten, and the dynamics take place closer and closer to configurations reached at later times. During this new restricted aging dynamics, the fluctuation-dissipation relation is richer than expected.

cond-mat.dis-nn↗