arXiv subjects

Arturo C. Marti

Publications and source records attributed to Arturo C. Marti.

At least 19 recordsLinked to original sources

arXiv2026

Multistability in the Duffing--Holmes oscillator: basins of antiperiodic, periodic, and chaotic attractors and their relative volumes

The periodically driven Duffing--Holmes oscillator is strongly multistable: for the same forcing amplitude and frequency, periodic, chaotic, and antiperiodic attractors coexist, each with its own basin of attraction. Antiperiodic orbits are periodic orbits invariant under a shift of half a driving period combined with a sign reversal of the coordinates, a symmetry of the equations of motion. Guided by a continuation map of the parameter plane, which locates the regimes but is blind to their coexistence, we explore the space of initial conditions along two one-parameter cuts, at fixed forcing frequency and at fixed forcing amplitude. Stochastic sampling of the full space yields an unbiased estimate of the relative volume of each basin as a function of the control parameter, on the same parameter grids on which single-trajectory bifurcation diagrams are computed by continuation. Basin maps on two-dimensional sections, complemented by maps of the order of the attractor reached from each initial condition, resolve the geometry of the coexisting basins where the competition between attractors is strongest. The relative volumes reveal windows of global antiperiodic dominance, in which the antiperiodic orbit attracts essentially every initial condition, separated by narrow intervals in which two or three qualitatively different attractors share the space in comparable proportions, as well as extended ranges of persistent coexistence; at large forcing amplitude, a single antiperiodic orbit of order one captures the whole space. Compared with the bifurcation diagrams, the abrupt changes of basin volume are the ensemble-level counterpart of the multistability-induced discontinuities of the sweeps, and the gradual shrinking of the antiperiodic basin explains why the branch followed by a sweep depends on the initial state and on the drive phase.

nlin.CD↗

arXiv2026

Antiperiodicity in the Duffing--Holmes oscillator: symmetry origin, parity selection, and transitions

We investigate the origin and distribution of antiperiodicity --- oscillations satisfying $x(t+T)=-x(t)$ --- in the periodically driven Duffing--Holmes oscillator, combining analytical arguments with extensive numerical exploration. Antiperiodic orbits are precisely the periodic orbits invariant under the half-period shift symmetry $S:(x,\dot{x},t)\mapsto(-x,-\dot{x},\,t+T_d/2)$ of the equations of motion, with $T_d$ the driving period. We map the antiperiodic regions across the plane spanned by the amplitude and the frequency of the forcing, together with the periodic and chaotic domains and the potential wells visited by each orbit. The invariance under $S$ imposes a parity selection rule, verified without exception across our parameter sweeps: antiperiodic orbits lock to the drive only at odd multiples of the forcing period. Periodic orbits that lack the antisymmetry occur instead as conjugate pairs related by $S$, each orbit being the point reflection of its twin. We further show that antiperiodic orbits cannot bifurcate through a direct period doubling: the symmetry must break first, in a supercritical pitchfork in which the antiperiodic orbit splits into two conjugate, symmetry-broken orbits; alternatively, the antiperiodic orbit disappears with its symmetry intact, in a saddle-node bifurcation with an antiperiodic saddle. Antiperiodicity thus emerges as the orbit-level manifestation of a discrete symmetry of the driven system.

nlin.CD↗

arXiv2026

AI-Assisted Assessment of Experimental Physics Laboratory Reports: Potential, Limitations, and Support for Teaching Practice

The incorporation of AI into the assessment of physics laboratory reports offers opportunities to support the review of student work and the provision of feedback. This article revisits an experience involving the use of ChatGPT models to analyze laboratory reports and examines the conditions that influence their usefulness in teaching practice. The analysis considers the evolution of AI models, document-processing procedures, and different modes of interaction, with particular attention to the effective availability of evidence contained in student reports. The findings indicate that differences between AI-generated and teacher assessments may be related not only to model capabilities but also to difficulties in retrieving and interpreting equations, graphs, tables, units, and other visual elements. The possibilities of systematic processing of sets of reports and conversational review of cases requiring more focused analysis are also examined. Based on these observations, a working strategy is proposed in which AI serves as a complementary resource for organizing assessment, supporting feedback, and identifying recurring difficulties in student work. The analysis highlights the importance of document-processing conditions and evidence availability, as well as the teacher's role in interpreting AI-generated information and making evaluative and pedagogical decisions.

physics.ed-ph↗

arXiv2026

Experimental observation of chaotic and multistable dynamics in a Duffing--Holmes--type analog circuit: antiperiodicity and attractor-coexistence signatures

An experimental study of a periodically forced Duffing--Holmes-type oscillator with a double-well potential, emulated by a piecewise-linear analog electronic circuit, is presented. By systematically varying the forcing amplitude and frequency, the full dynamical landscape of the system is characterized through bifurcation diagrams, Poincaré maps, and largest Lyapunov exponent calculations. The observed phenomenology includes period-doubling routes to chaos, periodic windows with multistability, intermittency, and antiperiodic orbits in which the trajectory recovers the global symmetry of the double-well potential. Multistability-induced discontinuities in the bifurcation diagrams are identified and interpreted as attractor-coexistence signatures arising from the sensitivity of the long-time dynamics to initial conditions, rather than as noise artifacts. These results are synthesized into a high-resolution two-dimensional map of the parameter space. The close agreement among all experimental diagnostics validates the fidelity of this analog implementation and demonstrates that continuous-time hardware provides a high-throughput platform for mapping complex nonlinear landscapes and resolving fine-scale multistable structures.

nlin.CD↗

arXiv2026

Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition

We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy $R$ and the squared frequency ratio $μ$. By randomly sampling the isoenergetic volume to classify trajectories as oscillatory, rotational, or chaotic across the $(μ, R)$ parameter plane, we obtain a global portrait of the coexistence and competition between dynamical regimes. The chaotic fraction is not uniformly distributed across the parameter plane but concentrates in a well-defined central cloud whose ridge follows a linear relation in the $(μ, R)$ plane and whose maximum does not exceed $70\%$ of the available phase space. The order-chaos-order transition is not a global property of the parameter plane but occurs specifically in the central region surrounding this cloud: along paths that traverse it, oscillatory orbits progressively give way to chaotic trajectories, which in turn yield to rotational orbits as the energy grows, revealing a clear sequential mechanism underlying the transition. The onset of rotational motion is gradual rather than sharp, reflecting a strong dependence on initial conditions. By decomposing the total energy into spring-like, pendulum-like, and coupling contributions, we establish a direct correspondence between the coupling power and the abundance of chaotic trajectories, showing that enhanced inter-mode energy exchange is a reliable indicator of dynamical complexity. These results provide a comprehensive and quantitative map of the dynamical regimes of the elastic pendulum, clarifying the structure of the chaotic cloud and connecting it to the underlying mode-coupling mechanisms.

nlin.CD↗

arXiv2026

3D-printed experimental devices for teaching dynamical systems in physics

We present the design, construction and classroom use of 3D-printed experimental devices aimed at introducing dynamical systems in physics courses. Theoretical, technical and pedagogical criteria are proposed for producing low-cost, modifiable resources suitable for experimental work. Three devices are analysed as examples: a magnetic pendulum, a wooden woodpecker toy and a double pendulum. The suggested activities are organised around prediction, observation, comparison between configurations, and the elaboration of physical explanations. The main contribution of this work is to show concrete implementation possibilities in secondary education, pre-service teacher training and introductory university courses, together with a discussion of the scope and limitations of 3D printing in experimental teaching.

physics.ed-ph↗

arXiv2026

Recurrence and anti-recurrence patterns reveal an antiperiodic fingerprint that survives into chaos in the Duffing--Holmes oscillator

The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive. When this symmetry is dynamically realized, the system supports \emph{antiperiodic} solutions, whose state at any instant is the point reflection of the state half a driving period earlier. We show that a standard recurrence plot (RP) is blind to this symmetry, whereas a complementary \emph{anti-recurrence plot} (anti-RP), built from the cross recurrence between a trajectory and its point-reflected image, detects it directly. Across four regimes -- periodic and chaotic single-well motion, and antiperiodic and chaotic two-well motion -- the anti-RP is empty when the attractor occupies one well and densely diagonal when the motion respects the symmetry. Crucially, the antiperiodic fingerprint persists into the chaotic two-well regime, where the anti-recurrence rate stays high relative to the ordinary one ($\mathrm{RR}_a/\mathrm{RR}\approx0.8$) despite the chaos. Recurrence quantification of both matrices separates order from chaos, while the anti-RP independently distinguishes one- from two-well, symmetry-respecting dynamics, giving a compact classification of all regimes. Requiring only a time series and the symmetry operation, the anti-RP is a model-free probe of dynamical symmetry for any system with a sign-reversal invariance, including experimental signals where phase-averaged observables fail.

nlin.CD↗

arXiv2026

Exploring the potential of ChatGPT for feedback and evaluation in experimental physics

This study explores how generative artificial intelligence, specifically ChatGPT, can assist in the evaluation of laboratory reports in Experimental Physics. Two interaction modalities were implemented: an automated API-based evaluation and a customized ChatGPT configuration designed to emulate instructor feedback. The analysis focused on two complementary dimensions-formal and structural integrity, and technical accuracy and conceptual depth. Findings indicate that ChatGPT provides consistent feedback on organization, clarity, and adherence to scientific conventions, while its evaluation of technical reasoning and interpretation of experimental data remains less reliable. Each modality exhibited distinctive limitations, particularly in processing graphical and mathematical information. The study contributes to understanding how the use of AI in evaluating laboratory reports can inform feedback practices in experimental physics, highlighting the importance of teacher supervision to ensure the validity of physical reasoning and the accurate interpretation of experimental results.

physics.ed-ph↗

arXiv2026

Elastic and Viscous Effects in Viscoelastic Flows: Elucidating the Distinct Roles of the Deborah and Weissenberg Numbers

The interpretation of the parameters appearing in constitutive models for viscoelastic fluids is essential for analyzing theoretical predictions and understanding the origin of phenomena observed in experiments. In this work, we examine the physical significance of the Deborah ($De$) and Weissenberg ($Wi$) numbers, along with other key parameters commonly used in these models. The central objective is to clarify the extent to which these dimensionless groups effectively characterise the competition between elastic and viscous effects in complex flows. While these parameters are ubiquitous in theoretical and experimental research, their interpretation is often context-dependent and prone to ambiguity. To address this, we analyse two representative scenarios: an analytical solution for unsteady planar flow and a numerical simulation of viscoelastic flow between rotating coaxial cylinders, governed by the Oldroyd-B constitutive equations. Our findings elucidate the distinct roles of these dimensionless numbers, offering guidelines for their rigorous interpretation in both analytical and numerical studies.

physics.flu-dyn↗

arXiv2026

Universal Second-Order Phase Transition from Integrability to Chaos

We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary $R(θ)=1+ε\cos(pθ)$. For $ε=0$, the phase space is {\it foliated} by invariant curves corresponding to periodic or quasiperiodic motion, whereas for small $ε$ a thin chaotic layer separates rotational and librational trajectories. As $ε$ increases, this layer grows according to a well-defined scaling law whose chaotic dispersion follows $ω_{\rm rms,sat}\simε^{\tildeα}$, where the exponent $\tildeα$ coincides with those of the Fermi-Ulam model, periodically corrugated waveguides, and a family of discrete mappings, revealing a universal mechanism for the onset of chaos in weakly perturbed integrable systems. The deviation of the reflection angle in the billiard, $ω_{\rm rms,sat}$, acts as an order parameter: it vanishes continuously as $ε\to 0$, signalling an ordered (integrable) phase, while its susceptibility $χ=dω_{\rm rms,sat}/dε$ diverges, indicating a second-order phase transition. A symmetry breaking and an analytically solvable diffusion process complete the near-critical phenomenology. These results establish a unified framework for the emergence of chaos from integrability.

nlin.CD↗

arXiv2026

Describing a Universal Critical Behavior in a transition from order to chaos

We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter $ε$, which modifies the boundary shape from circular, corresponding to $ε=0$ and an integrable dynamics, to oval for $ε\neq 0$, where non-integrability emerges. The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, we characterise the diffusive spreading of ensembles of trajectories and identify an observable, $ω_{rms,{\rm sat}}$, which plays the role of an order parameter for the transition. For small deformations, the saturation value of the diffusion obeys the scaling law $ω_{rms,{\rm sat}}\proptoε^{\tildeα}$, with a critical exponent $\tildeα=0.507(2)$, vanishing continuously as $ε\rightarrow 0$. The associated susceptibility, $χ=dω_{rms,{\rm sat}}/dε$, diverges in the same limit, signalling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics.

nlin.CD↗

arXiv2025

Enhancing Kinematics Understanding Through a Real-Time Graph-Based Motion Video Game

Kinematics is a core topic in early physics courses, yet students often struggle to interpret motion and its graphical representations. To tackle these difficulties, we developed MissionMotion, a physical-computational videogame where students reproduce target motion graphs using real-time data from their own movements or from sensors connected through micro:bit or Arduino. The system displays both the target and the user-generated graph, providing immediate visual feedback and a score based on similarity. We piloted the environment with ninth-grade students in different school contexts and evaluated their experience using the MEEGA+ instrument. The results show strong engagement, positive perceptions of usability, and evidence that the game promotes reflection on motion graphs in ways that rarely emerge in traditional lessons. MissionMotion runs on any web-enabled device and all materials are openly available, offering teachers an accessible tool to integrate experimentation, computational thinking, and playful learning into physics classrooms.

physics.ed-ph↗

arXiv2025

Code in Motion: Integrating Computational Thinking with Kinematics Exploration

Although physics has become increasingly computational, with computing even being considered the third pillar of physics, it is still not well integrated into physics education. Research suggests that integrating Computational Thinking (CT) into physics enhances conceptual understanding and strengthens students' ability to model and analyze phenomena. Building on this, we designed a didactic sequence for K9 students to foster specific CT practices while reinforcing fundamental kinematics concepts. The activity revealed students' ability to apply CT skills and is well suited for use in introductory kinematics courses.

physics.ed-ph↗

arXiv2025

Exploring the potential of ChatGPT for feedback and evaluation in experimental physics

physics.ed-ph↗

arXiv2025

Inconsistencies and errors in traditional approaches to energy in our introductory courses

We present a critical analysis of the classical approaches to energy subjects, based on the work-energy theorem and the conservation of mechanical energy proposed in the courses of the first years of tertiary education. We show how these approaches present a series of inconsistencies and errors that are a source of conceptual difficulties among students. We then analyze a modern treatment of mechanical courses based on the results of research in physics education over the last 40 years. We place special emphasis on the principle of conservation of energy as one of the fundamental principles of nature, prioritizing the concepts of system, surrounding, and energy transfer and transformation.

physics.ed-ph↗

arXiv2025

Light intensity does not always decay with the inverse of the square of the distance: an open-inquiry laboratory

The square inverse law with distance plays an important role in many fields of physics covering electromagnetism, optics or acoustics. However, as every law in physics has its range of validity. We propose an open-inquiry laboratory where we challenge these concepts by proposing experiments where the intensity of light decays linearly or even remains constant over a range of distances. Using the light sensors built into smartphones, it is possible to measure light curves for different sources: point, linear, planar and even LED ring lights. The analysis of these curves allows us to discuss the limits of the physical theories. This low-cost laboratory, initially proposed in the context of the COVID19 pandemic, has the virtue of challenging intuition and encouraging the critical spirit of the students.

physics.ed-ph↗

arXiv2025

Revisiting the displacement current: Two key examples showing when and why it can be neglected

This work explores the role of the displacement current in systems beyond capacitors, focusing on coaxial cables and resistors with alternating currents. Although its contribution, compared to that of the conduction current, is negligible at low frequencies, the displacement current becomes essential for accurately describing electromagnetic fields in dynamic regimes. Introductory physics textbooks typically restrict the discussion of displacement currents to capacitor charging, which can limit the students' understanding of its broader relevance and the interdependence of Maxwell's equations. By analyzing two specific cases, we clarify the conditions under which the displacement current can be neglected, when simplified laws like Biot-Savart are valid, and where coupled electromagnetic equations are essential. This approach highlights the boundaries of common models and promotes a deeper understanding of dynamic field interactions.

physics.ed-ph↗

arXiv2025

Differences in the attitudes and beliefs about science of students in the physics-mathematics and life sciences areas and their impact on teaching

For this study, we compared the attitudes and beliefs about science of physical science (physics and mathematics) and life science (biochemistry and biology) students at the beginning of their university degrees using the CLASS (Colorado Learning Attitudes about Science Survey) tool. It is worth noting that both groups of students received similar physics courses during their high-school education. Through a detailed analysis of the different categories of the test, we examined the differences in performance in each of the areas that make up the questionnaire. Among other aspects, we found that a considerable percentage of life science students (higher than that of physical science students) adopted a novice type of behavior in problem solving. Finally, we discussed the possible causes of the differences found and their implications for teaching.

physics.ed-ph↗