arXiv subjects

Giovanni Russo

Publications and source records attributed to Giovanni Russo.

At least 19 recordsLinked to original sources

arXiv2026

Activation and Avalanche Length Scales in the Finite-Temperature Creep of an Elastic Interface

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, $\ell_{\mathrm{opt}}$, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, $\ell_{\mathrm{av}}$, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that $\ell_{\mathrm{av}}$ governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with $\ell_{\mathrm{opt}}$. We find that the avalanche scale follows $\ell_{\mathrm{av}}(T)\sim T^{-ν_{\mathrm{dep}}}$, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

cond-mat.stat-mech↗

arXiv2026

Haptic bilateral teleoperation system for free-hand dental procedures

Free-hand dental procedures are typically repetitive, time-consuming and require high precision and manual dexterity. Robots can play a key role in improving procedural accuracy and safety, enhancing patient comfort, and reducing operator workload. However, robotic solutions for free-hand procedures remain limited or completely lacking. To address this gap, we develop a haptic bilateral teleoperation system (HBTS) for free-hand dental procedures (FH-HBTS). The system includes a mechanical end-effector, compatible with standard clinical tools, and equipped with an endoscopic camera for improved visibility of the intervention site. By ensuring motion and force correspondence between the operator's and the robot's actions, monitored through visual feedback, we enhance the operator's sensory awareness and motor accuracy. Furthermore, to ensure procedural safety, we limit interaction forces by scaling the motion references provided to the admittance controller based solely on measured contact forces. This ensures effective force limitation in all contact states without requiring prior knowledge of the environment. The proposed FH-HBTS is validated through a technical evaluation and an in-vitro pre-clinical study conducted on a dental model under clinically representative, yet simplified, conditions. The results show that the system improves the naturalness, safety, and accuracy of teleoperation, highlighting its potential to enhance free-hand dental procedures.

cs.RO↗

arXiv2026

Deterministic and stochastic particle methods for the Fokker-Planck equation in S--formulation with application to point set registration

We present two particle methods for point set registration in bounded domains based on the Fokker-Planck equation. The first method relies on a moving least squares discretization of the S--formulation, in which moving grid points (particles) are advected by the drift with the target distribution, diffusion is resolved on a dynamically evolving particle cloud. This setting naturally leads to strong compression and expansion of the particle cloud. Obstacles are handled by enforcing reflective boundary conditions through a novel ghost point method. The second method is a Monte Carlo solver for the associated Langevin stochastic differential equation. It relies on a local approximation of the logarithmic gradient of the evolving particle density to extract macroscopic osmotic paths from individual stochastic trajectories. Owing to its inherent parallelism, this method exhibits excellent scalability and is well suited for high-dimensional registration problems. We illustrate the main features and performance of both approaches through extensive numerical experiments.

math.NA↗

arXiv2026

Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System

We study the application of exponential time integration methods, coupled with Fourier pseudospectral space discretization, to the hyperbolic Korteweg-de Vries (KdVH) system. We investigate the asymptotic preserving (AP) properties of such discretizations, showing that, in general, Lawson methods are not asymptotic preserving, because the auxiliary (derivative-approximating) variables do not satisfy the limit equilibrium manifold, whereas exponential time differencing (ETD) methods are AP for all components, including both the solution variable and the auxiliary variables. We also present an efficient numerical implementation based on an exact formula for the matrix exponential of this system, and compare it with previously-proposed ImEx Runge-Kutta time integration, showing that exponential methods can be competitive in this context.

math.NA↗

arXiv2026

Towards Interaction Regulation from Human Feedback via Free Energy Minimization

A central challenge across control and learning is the design of mechanisms regulating the interactions between humans and autonomous agents. Inspired by the free energy principle from computational neuroscience, we introduce a control-theoretical framework to integrate human preferences online into an agent policy. We turn the framework into an open control architecture and validate our approach using a human-in-the-loop experimental testbed involving a rover navigating via onboard sensing. The human, remotely located and equipped with virtual reality headsets, shares the same sensory information as the rover. Human preferences are provided to the rover via gestures which introduce both cooperative and competitive interactions between the agent goal and the preferences. The experiments show that interactions are regulated, validating the proposed approach.

eess.SY↗

arXiv2026

An Energy-Based Mechanism for Compositional Behavior

Flexible intelligence relies on the ability to reuse previously acquired behaviors and combine them differently as circumstances change. In biological and artificial systems, this ability is often attributed to gating mechanisms that determine how much each available behavior should contribute at a given time. Yet these gating rules, the dynamics that compute them, and the neural circuits that may implement them are usually introduced separately, leaving unclear whether they reflect a common underlying principle. Here, we show that they can all be derived from a single variational principle for behavioral composition. The resulting mechanism naturally gives rise to softmax gating, evolves as an energy-based dynamical system with guaranteed convergence, and admits a recurrent neural network instantiation featuring context-dependent and local interactions. Across collective behavior, human decision-making, and layered control, the same mechanism reproduces characteristic behavioral patterns, provides interpretable accounts of how different behaviors are combined, and matches or outperforms established approaches. These results provide a unified account of how behavioral composition can emerge from a common principle, with implications for understanding flexible behavior in natural systems and for designing artificial agents that can adapt by recombining existing capabilities.

math.OC↗

arXiv2026

Towards Tsallis Fully Probabilistic Design

Fully Probabilistic design (FPD) is a powerful framework offering an elegant and unifying account of stochastic control, learning and decision-making. Here we introduce a generalized FPD framework, which we term as Tsallis FPD. Tsallis FPD uses Tsallis divergence in place of the Kullback-Leibler divergence that defines the standard FPD cost term. Tsallis divergence is a natural generalization of the KL divergence, rooted in non-extensive statistical mechanics and providing flexibility towards modeling stochastic processes with non-Gaussian tail behavior. After formulating Tsallis FPD, we present a double iteration scheme that performs a sequence of backwards inductions, rather than a single pass down the stages that constitutes the proven approach for classical FPD.

math.OC↗

arXiv2026

An Adaptive Fourier Spectral Method for the Vlasov-Poisson system

Numerical simulation of the Vlasov-Poisson system faces fundamental challenges due to phase-space filamentation. Standard spectral methods rely on artificial filtering to suppress errors, which inadvertently degrades physical structures and accuracy over time. This paper proposes a dynamically adaptive Fourier spectral method combined with high-order time splitting to overcome these limitations. To prevent filamentation-induced aliasing, we dynamically expand the wavenumber domain via adaptive zero-padding whenever spectral tail monitoring detects emerging fine-scale structures. Acting as an exact trigonometric interpolation, it inherently avoids the artificial smoothing of traditional filters, preserving mass and effectively maintaining the $L^2$-norm within the dynamically resolved scales. Numerical experiments on Landau damping and various instability problems validate the robustness of our scheme.

math.NA↗

arXiv2026

Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these optimization problems, inspired by recent results, we introduce the \emph{proportional--integral proximal gradient dynamics} (PI--PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the stationary points of the minimization problem and the equilibria of the PI--PGD. Then for the case of affine constraints, by leveraging tools from contraction theory we give a comprehensive convergence analysis for the dynamics, showing convergence to a stationary point. Moreover, under suitable assumptions, we show linear--exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an exploratory application to nonlinear equality constraints.

math.OC↗

arXiv2026

A meshless MUSCL method for the BGK-Boltzmann equation

We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in which grid points move with the local mean velocity of the gas. The main advantage of the moving grid is that the algorithm can deal well with cases where the domain boundaries are time-dependent and the simulation domain contains rigid objects. Due to the irregular nature of the grid, we use a novel meshless MUSCL-like Moving Least Squares Method (MLS) for spatial discretisation coupled with a higher-order Implicit-Explicit Runge-Kutta method. To avoid spurious oscillations at discontinuities, we use the so-called Multi-dimensional Optimal Order Detection (MOOD) method with an adapted criterion to relax the discrete maximum property. Finally, we employ a new implementation of the boundary conditions that requires no iterative or extrapolation procedure. The method achieves fourth-order in 1D and second-order in 2D for simulations with moving boundaries. We demonstrate the method's effectiveness on classical test cases such as the driven square cavity, shear layer, and shock tube.

math.NA↗

arXiv2026

Solitary wave formation in the compressible Euler equations

We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength perturbations approximately obey a system of dispersive nonlinear wave equations. Computational experiments demonstrate that solutions of the 1D Euler equations agree well with this dispersive model, with solutions consisting mainly of solitary waves. Shock formation seems to be avoided for moderate-amplitude initial data, while shock formation occurs for larger initial data. We investigate the threshold for transition between these behaviors, validating a previously-proposed criterion based on further computational experiments. These results support the existence of large-time non-breaking solutions to the 1D compressible Euler equations, as hypothesized in previous works.

math.AP↗

arXiv2026

Nearly Parallel $\mathrm{G}_{2}$-Structures with Torus Symmetry

We study nearly parallel $\mathrm{G}_{2}$-structures with a three-torus symmetry via multi-moment map techniques. An effective three-torus action on a nearly parallel $\mathrm{G}_{2}$-manifold yields a multi-moment map. The torus acts freely on its regular level sets, so they are torus bundles over smooth three-dimensional manifolds. We show that the geometry of the base spaces is specified by two triples of closed two-forms related by a Riemannian metric. We then describe an inverse construction producing invariant nearly parallel $\mathrm{G}_{2}$-structures from three-dimensional data. We observe that locally this may produce examples with four-torus symmetry.

math.DG↗

arXiv2026

Asymptotic Preserving and Accurate scheme for Multiscale Poisson-Nernst-Planck (MPNP) system

In this paper, we propose and validate a two-species Multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a trap. Specifically, we aim to model surface traps whose attraction range, of length $δ$, is much smaller then the scale of the problem. The physical setup we refer to is an anchored gas drop (bubble) surrounded by a flow of charged surfactants {(composed by positive and negative ions) that diffuses in water. When the diffusing surfactants reach the surface of the trap, the negative ions are adsorbed because of their hydrophobic tail that is attracted by the air bubble}. As in our previous works, the effect of the attractive potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The novelty of this work is the extension of the model proposed in \cite{astuto2023multiscale}, now incorporating the influence of both carriers -- positive and negative ions -- simultaneously, which is often neglected in traditional approaches that treat ion species independently. The two carriers interact through the Coulomb potential, that is computed by a Poisson equation. [...]

math.NA↗

arXiv2026

Left-invariant harmonic spinors on three-dimensional Lie groups

We study the existence of left-invariant harmonic spinors on three-dimensional Lie groups equipped with a left-invariant pseudo-Riemannian metric. An existing formula for the spin Dirac operator acting on left-invariant spinors in the Riemannian setting is revised and specialised to our cases, in particular to almost Abelian Lie algebras. Focussing on dimension two and three, we find equivalent conditions for the Lie groups to admit left-invariant harmonic spinors in terms of constraints on the structure equations of the corresponding Lie algebras. We then identify those metrics (up to automorphism) carrying left-invariant harmonic spinors in each case.

math.DG↗

arXiv2026

Free-Energy Minimizing Policies Under Generative Model Ambiguity

We present a variational free-energy formulation for distributionally robust decision-making with ambiguity in the generative model. The formulation, related to a broad range of learning and control frameworks, yields a minimax optimal control problem where maximization is over an uncertainty set that represents ambiguities. We prove that computing the optimal policy requires solving a non-convex minimization problem and propose an algorithm with convergence guarantees to find the solution. The effectiveness of our results is illustrated via simulations on a pendulum swing-up problem.

math.OC↗

arXiv2026

High order ghost-FEM for incompressible Navier-Stokes equations on moving domains

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set function. The proposed approach relies on a space discretization based on the ghost finite element method (ghost-FEM), which allows computations on unfitted meshes and avoids costly remeshing as the domain evolves in time. Time integration is performed using an IMplicit-EXplicit (IMEX) scheme to address the nonlinearity of the convective term, ensuring high-order accuracy for incompressible flows. The error introduced by the geometrical approximation is handled using the Shifted Boundary Method, which allows higher order approximations of boundary conditions on unfitted meshes. Dirichlet boundary conditions are imposed weakly by means of Nitsche's method. The associated stabilization parameter is chosen by solving a generalized eigenvalue problem, ensuring stability and accuracy of the numerical scheme. We present a series of numerical experiments designed to validate the accuracy of the proposed method, as well as comparisons with established benchmark problems involving moving boundaries.

math.NA↗

arXiv2026

Learning-Based Robust Control: Unifying Exploration and Distributional Robustness for Reliable Robotics via Free Energy

A key challenge towards reliable robotic control is devising computational models that can both learn policies and guarantee robustness when deployed in the field. Inspired by the free energy principle in computational neuroscience, to address these challenges, we propose a model for policy computation that jointly learns environment dynamics and rewards, while ensuring robustness to epistemic uncertainties. Expounding a distributionally robust free energy principle, we propose a modification to the maximum diffusion learning framework. After explicitly characterizing robustness of our policies to epistemic uncertainties in both environment and reward, we validate their effectiveness on continuous-control benchmarks, via both simulations and real-world experiments involving manipulation with a Franka Research~3 arm. Across simulation and zero-shot deployment, our approach narrows the sim-to-real gap, and enables repeatable tabletop manipulation without task-specific fine-tuning.

cs.RO↗

arXiv2026

On the nu-invariant of two-step nilmanifolds with closed G2-structure

For every non-vanishing spinor field on a Riemannian spin seven-manifold, Crowley, Goette, and Nordström defined the so-called $ν$-invariant. This is an integer modulo $48$ that detects connected components of the moduli space of $\mathrm G_2$-structures on any seven-dimensional oriented spin manifold. The $ν$-invariant can be defined in terms of Mathai--Quillen currents, harmonic spinors, and $η$-invariants of spin Dirac and odd-signature operator. We compute these data for certain families of left-invariant closed $\mathrm G_2$-structures on compact two-step nilmanifolds with their natural spin structure. Specifically, we establish the existence of non-invariant harmonic spinors and determine the parity of the dimension of the space of harmonic spinors. We deduce the vanishing of $ν$ on invariant harmonic spinors.

math.DG↗