Dynamical Point Research Articles

War at the Gates

The conflict in Ukraine, now in its third year, has evolved into a complex geopolitical confrontation with limited prospects for resolution. Initially, diplomatic efforts focused on compromises or territorial concessions failed, as both Russia and NATO consolidated their positions. Strategic miscalculations on both sides have raised the stakes, transforming the conflict into a broader struggle for influence. For the West, the conflict represents a test of NATO unity and US global leadership, while for Russia it is an existential battle against perceived NATO encroachment. The protracted war has shifted the goals. Russia, initially seeking a quick victory, now prioritizes dismantling Ukraine’s military potential and providing a buffer against NATO expansion. In contrast, the US and its allies aim to shore up Ukraine’s resistance while preserving NATO cohesion, despite mounting financial and logistical challenges. With diplomatic solutions stymied by mutual distrust, military escalation seems increasingly likely. Demographic and economic constraints are further pushing both sides toward decisive action. Russia faces time pressures from demographic decline and NATO’s ongoing rearmament. Likewise, prolonged engagement strains NATO unity and risks exposing broader vulnerabilities in the Western alliance. A potential U.S. withdrawal under a new administration could shift responsibility to NATO’s European members, threatening Ukraine’s cohesion and defense capabilities. As entrenched positions and geopolitical imperatives harden, the conflict underscores a critical inflection point in global power dynamics, where the window for a negotiated solution is narrowing and the risk of a broader confrontation is growing.

Replicator dynamics generalized for evolutionary matrix games under time constraints.

One of the central results of evolutionary matrix games is that a state corresponding to an evolutionarily stable strategy (ESS) is an asymptotically stable equilibrium point of the standard replicator dynamics. This relationship is crucial because it simplifies the analysis of dynamic phenomena through static inequalities. Recently, as an extension of classical evolutionary matrix games, matrix games under time constraints have been introduced (Garay et al. in J Theor Biol 415:1-12, 2017; Křivan and Cressman in J Theor Biol 416:199-207, 2017). In this model, after an interaction, players do not only receive a payoff but must also wait a certain time depending on their strategy before engaging in another interaction. This waiting period can significantly impact evolutionary outcomes. We found that while the aforementioned classical relationship holds for two-dimensional strategies in this model (Varga et al. in J Math Biol 80:743-774, 2020), it generally does not apply for three-dimensional strategies (Varga and Garay in Dyn Games Appl, 2024). To resolve this problem, we propose a generalization of the replicator dynamics that considers only individuals in active state, i.e., those not waiting, can interact and gain resources. We prove that using this generalized dynamics, the classical relationship holds true for matrix games under time constraints in any dimension: a state corresponding to an ESS is asymptotically stable. We believe this generalized replicator dynamics is more naturally aligned with the game theoretical model under time constraints than the classical form. It is important to note that this generalization reduces to the original replicator dynamics for classical matrix games.

An optimization-based equilibrium measure describing fixed points of non-equilibrium dynamics: application to the edge of chaos

Understanding neural dynamics is a central topic in machine learning, non-linear physics, and neuroscience. However, the dynamics are non-linear, stochastic and particularly non-gradient, i.e., the driving force cannot be written as the gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory. Still, the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed-form solutions in general. From the associated Fokker–Planck equation, the steady-state solution is generally unknown. Here, we treat searching for the fixed points as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, can the distribution of the original fixed points be achieved. The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos. Furthermore, the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.

Geometric average of the digits with fast growth rates in d-decaying Gauss like iterated function system

For any x∈(0,1), its Khintchine exponent, standing for the geometric average growth rate of the partial quotients in the continued fraction expansion of x, has been extensively studied from dynamical systems point of view. This paper is concerned with the geometric average of the digits diverges at certain rates in a more general setting. As a result, the Hausdorff dimensions of such kinds of sets of divergence points with fast growth rates are obtained in the systems with polynomial decay of the derivative, which generalizes many results.

A novel strategy for activation technique for 6H-SiC substrates in electroless Ni-P plating processes

This study proposes a novel iron wire activation method for electroless Ni-P plating on 6H-SiC substrates, offering a sustainable alternative to traditional metal activation techniques, focusing on the surface roughness effect on the microhardness and Ni-P plating efficiency of 6H-SiC substrates. This experimental approach reveals insights into the relationship between substrate morphology and plating characteristics. It is found that the plating thickness (33.82 μm) of the non-polished substrates closely matched the expected (33.26 μm), with a deposition rate of 6.65 μm/h, which underscores the precision regulation of the plating process. In contrast, despite the faster deposition rate of 9.20 μm/h of the polished S500 substrate, it exhibited a minor thickness discrepancy, suggesting a saturation point in the deposition dynamics on fully polished surfaces. The research additionally sheds light on the adhesion characteristics of the plated layers, particularly emphasizing the role of surface roughness. Remarkably, non-polished substrates demonstrated better adhesion, categorized as HF3, indicating a significantly stronger bond compared to the polished substrates, which were categorized as HF4 to HF6. This distinction in adhesion categories underlines the critical influence of substrate morphology on the quality of the Ni-P layer's adherence.

Talking to Machado de Assis: Generative Artificial Intelligence to Simulate Dialogues with Prominent Figures

Generative artificial intelligence encompasses techniques for automatically generating content such as image, music, and text. A common application of these techniques, especially involving text generation, is the construction of conversational agents. In education, generative artificial intelligence has the potential to transform the learning process and enable new forms of teaching, such as the practical application of concepts studied in class and the acquisition of new knowledge through the interaction with computational tools. In Brazil, literature teachers often complain about students' resistance to the content and insufficient reading practice. To address these challenges, this work presents a serious game in which students can chat with Machado de Assis, an important writer of the Brazilian literature. The game was developed by integrating with ChatGPT. The validation was conducted with 15 high school students for them to interpret the book "Dom Casmurro". The MEEGA+ instrument was used to evaluate the usability and the experience with the game. The main findings were that students better understood the book, found the game easy to use, and felt immersed in the conversation with Machado de Assis, although they assessed the texts as long and tiring. In a world dominated by faster and visually stimulating forms of entertainment, such as video games and social networks, students may have different expectations regarding the reading experience. If they are not used to reading denser and more introspective texts, they may find it difficult to maintain interest when chatting with Machado de Assis. Finally, another implicit point in the game dynamics is observed: the (re)signification of the methodology to be adopted by the teacher, who will perceive the need to complement interactions with the writer in class according to what he can or should answer, tending to responses that stimulate students to study more about what is within the realm of knowledge about Machado de Assis.

Aspects concerning the factorial diagnostic of the breakeven point

The purpose of the article consists in applying breakeven point as a forecasting method to estimate the ability of the entity to fully cover expenses in business start up or in day-to-day diagnostics, identifying influencing factors. The calculation of the breakeven point shall be carried out in value and natural terms according to the heterogeneous and homogeneous charcter of production, on the basis of the division of the expenditure into variable and constant. The results allowed us to infer that at the entity the breakeven point in dynamics has an increasing trend. Thus, compared to the previous year , it increased by 14,7%, which proves an unfavorable situation. The security margin decreased by 29,7%, and the reduction in operational profit is 26,0%, which signals that the entity is in an unstable situation.

Birkhoff attractors of dissipative billiards

Abstract We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with ‘pinched’ curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that, generically, the Birkhoff attractor is complicated, both from the topological and the dynamical points of view.

Training neural networks with structured noise improves classification and generalization

Abstract The beneficial role of noise-injection in learning is a consolidated concept in the field of artificial neural networks, suggesting that even biological systems might take advantage of similar mechanisms to optimize their performance. The training-with-noise (TWN) algorithm proposed by Gardner and collaborators is an emblematic example of a noise-injection procedure in recurrent networks, which can be used to model biological neural systems. We show how adding structure to noisy training data can substantially improve the algorithm performance, allowing the network to approach perfect retrieval of the memories and wide basins of attraction, even in the scenario of maximal injected noise. We also prove that the so-called Hebbian Unlearning rule coincides with the TWN algorithm when noise is maximal and data are stable fixed points of the network dynamics.

Dynamic decoupling and compensation based on the inverted network technique and experiment research for multi-axis hydraulic road simulator

This paper presents a dynamic decoupling and compensation approach to eliminate channel interaction for a multi-axis hydraulic road simulator. Misalignment of the concentrated moving mass centroid on the entire test bench with the control point and inconsistencies in actuator dynamics leads to dynamic coupling, which deteriorates the motion performance of the system. To solve the problem, an inverted decoupling and compensation network based on an identification model is proposed. Firstly, the system is modeled using the recursive extended least square (RELS) identification method. In the feedforward compensation modeling process, the steady-state inverse is obtained using zero-magnitude error technology control (ZMETC). In addition, a finite impulse response (FIR) filter with an adaptive algorithm is employed to reduce the adverse impact of the modeling error. The proposed decoupling strategy is validated by conducting experiments using a multi-axis hydraulic road simulator. The experimental results indicate that the designed compensator can effectively decrease the cross-coupling of multi-input and multi-output (MIMO) systems. The suggested approach is also applicable to applications that necessitate the elimination of interactions between different control variables.

Long-term operation of a full-scale membrane bioreactor for industrial wastewater treatment using polyvinyl fluoride hollow fiber membranes: A systematic evaluation during 18-year operation

A membrane bioreactor (MBR) is a robust, high-performance technology for wastewater treatment that has been commercialized and disseminated worldwide since 1990. Despite broad implementation of this technology in the wastewater sector, ultralong operation beyond the membrane lifetime has rarely been reported. Therefore, the objectives of this study were to investigate (1) the effectiveness of a manually-operated feedback strategy to prevent membrane biofouling by dosing with sodium hypochlorite and oxalic acid and (2) the organic carbon removal of industrial wastewater treated by a full-scale MBR system in a chemical plant. The manually-operated feedback strategy consisted of monitoring the transmembrane pressure (TMP) by a test module in a bench-scale MBR to detect an inflection point, that is, the point (15 kPa) at which the TMP switched from growing gradually to exponentially in time. Biocake formation became noticeable at the inflection point, suggesting the TMP at which the membrane should be chemically washed to prevent severe biofouling. A full-scale MBR system was installed with a polyvinylidene fluoride (PVDF) membrane for organic carbon removal. The membrane was washed with 3000 mg/L of sodium hypochlorite and 1 wt% oxalic acid when the TMP reached 15 kPa during operation. The MBR was successfully operated for over 18 years without the PVDF membrane being damaged or compromised by biofouling. Characterization of the foulants on the membrane surface revealed that membrane washing removed inorganic (calcium and iron) and organic (acid amides and polysaccharides) foulants, plausibly by the action of oxalic acid and sodium hypochlorite, respectively. Installing a robust PVDF membrane and performing chemical washing at an inflection point in the TMP dynamics enabled ultralong MBR operation beyond the regular membrane lifetime. The implementation of the advocated strategy paves the way for the low CO2 footprint operation of a PVDF MBR, which does not require frequent membrane replacement and laborious membrane ex-situ cleaning.

Ergodic Concepts for a Self‐Organizing Trivalent Spin Network: A Path to (2+1)$(2+1)$‐D Black Hole Entropy

AbstractFrom a dynamical systems point of view, a trivalent spin network model in Loop Quantum Gravity is considered, which presents self‐organized criticality (SOC), arising from a spin propagation dynamics. A partition function is obtained for the domains of stability connecting gauge non‐invariant avalanches, leading to an entropy formula for the asymptotic SOC state. The microscopic origin of this SOC entropy is therefore given by the excitation‐relaxation spin dynamics in the avalanche cycle. The puncturing of trivalent spin networks (TSN) edges participating in the avalanche are counted in terms of an ensemble perimeter over the implicit avalanches. By identifying this perimeter with that of an isolated ‐D black hole horizon, it is conjectured that the SOC entropy reduces to the Bekenstein‐Hawking perimeter‐entropy law for the Bañados, Teitelboim, and Zanelli (BTZ) black hole, by an appropriate adjustment of a potential function based on the thermodynamical formalism of Sinai, Ruelle, and Bowen.

Chaotic nature of the electroencephalogram during shallow and deep anesthesia: From analysis of the Lyapunov exponent

In conscious states, the electrodynamics of the cortex are reported to work near a critical point or phase transition of chaotic dynamics, known as the edge-of-chaos, representing a boundary between stability and chaos. Transitions away from this boundary disrupt cortical information processing and induce a loss of consciousness. The entropy of the electroencephalogram (EEG) is known to decrease as the level of anesthesia deepens. However, whether the chaotic dynamics of electroencephalographic activity shift from this boundary to the side of stability or the side of chaotic enhancement during anesthesia-induced loss of consciousness remains poorly understood. We investigated the chaotic properties of EEGs at two different depths of clinical anesthesia using the maximum Lyapunov exponent, which is mathematically regarded as a formal measure of chaotic nature, using the Rosenstein algorithm. In 14 adult patients, 12 s of electroencephalographic signals were selected during two depths of clinical anesthesia (sevoflurane concentration 2% as relatively deep anesthesia, sevoflurane concentration 0.6% as relatively shallow anesthesia). Lyapunov exponents, correlation dimensions and approximate entropy were calculated from these electroencephalographic signals. As a result, maximum Lyapunov exponent was generally positive during sevoflurane anesthesia, and both maximum Lyapunov exponents and correlation dimensions were significantly greater during deep anesthesia than during shallow anesthesia despite reductions in approximate entropy. The chaotic nature of the EEG might be increased at clinically deeper inhalational anesthesia, despite the decrease in randomness as reflected in the decreased entropy, suggesting a shift to the side of chaotic enhancement under anesthesia.

How Fe-La-CS microspheres have selective adsorption capacity for As(V) over a wide pH range: Coupling molecular scale interpretation with experiments

In this study, an Fe-La-CS adsorbent with a reticulated structure was prepared by an in situ method, which was able to adsorb arsenate efficiently over a wide pH range of 3–11. The incorporation of iron and lanthanum ions broadened the tolerant pH range of the adsorbent compared with chitosan beads (CS). Arsenic was mainly present in the pH range of 3–9 as two forms, H2AsO4− and HAsO42−. Calculations using the density-functional theory (DFT) showed that in the Ligand interactions and electrostatic interactions dominate in the pH range, with surface precipitation, and hydrogen bonding interactions playing a facilitating role. The background ions mainly compete with arsenic adsorption for electrostatic interaction sites. However, due to the different valence states of the background ions, the competition intensity is different. Such as low valence state representative ions Na+, K+ competitiveness is weak, and arsenic competition adsorption first occupy different adsorption sites, therefore, from the quantum chemistry and molecular dynamics point of view of Na+, K+ on arsenic adsorption almost no effect. Cl−, SO42− will have some influence on arsenic adsorption because of the same charge with arsenic, but the charged amount is smaller than arsenic and the molecular structure is different from that of arsenic, so the influence is not very big. In summary, the material design of Fe-La-CS adsorbent has great potential and theoretical significance for selective purification of heavy metal wastewater at wide pH.

Critical charges for droplet collisions

Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and 20µm, we observe that the transition occurs at ∼103 elementary charges e. For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number (Kn, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon Kn. For droplets charged with the same polarity, we find the critical charge to be substantially larger (∼104e for the above radii) for reasons that we discuss. Published by the American Physical Society 2024

Dynamic Informed Bias RRT*-Connect: Improving Heuristic Guidance by Dynamic Informed Bias Using Hybrid Dual Trees Search

The RRT*-Connect algorithm enhances efficiency through dual tree bias growth, yet this bias can be inherently blind, potentially affecting the algorithm’s heuristic performance. In contrast, the Informed RRT* algorithm narrows the planning problem’s scope by leveraging an informed region, thereby improving convergence efficiency towards optimal solutions. However, this approach relies on the prior establishment of feasible paths. Combining these two algorithms can address the challenges posed by Informed RRT while also accelerating convergence towards optimality, albeit without resolving the issue of blind bias in dual trees.In this paper, we proposed a novel algorithm: Dynamic Informed Bias RRT*-Connect. This algorithm, grounded in potential and explicit informed bias sampling, introduces a dynamical bias points set that guides dual tree growth with precision objectives. Additionally, we enhance the evaluation framework for algorithmic heuristics by introducing two innovative metrics that effectively capture the algorithm’s characteristics. The improvements observed in traditional indicators demonstrate that the proposed algorithm exhibits greater heuristic compared to RRT*-Connect and Informed RRT*-Connect. These findings also suggest the viability of the new metrics introduced in our evaluation framework.

Vertical and Lateral Dynamics of 4L Freight Bogie

Freight wagons in Europe have used Y25 bogies since the 1960s. Although very cost-effective, Y25 suffers from intrinsic limitations due to its architecture and running behaviour. This study introduces an innovative lightweight bogie, named 4L bogie, aimed at removing those limitations as well as improving running dynamics and track friendliness. This task was particularly challenging as the high ratio between laden and tare weight (up to 5:1) forced us to use a non-conventional suspension system and an innovative architecture of frame, reducing the mass by about 15% and the yaw moment of inertia by about 30% with respect to the Y25 bogie. Maintenance issues were addressed by reducing the number of components and easing overhaul, while the new design was validated from both the structural and the running dynamics point of view, assessing its interaction with the track in terms of stability, curving behaviour and the vertical response of the 4L bogie. Stability was improved by about 20% even in empty conditions and high conicity at the wheel/rail contact. Vertical dynamic force on a straight track, evaluated according to the Ride Force Count metric, and wear behaviour on sharp and mild curves were considerably reduced, leading to an improved track friendliness of the bogie.

The role of taxation in an integrated economic-environmental model: a dynamical analysis

We propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected from taxation are used to reduce pollution. The resulting model consists of a two dimensional discrete dynamical system, and we study the role of taxation from both a static and a dynamical point of view. The focus is on the determination of the conditions under which taxation has a positive effect on the environment and leads to economic growth. Moreover, we show that a suitable environmental policy can allow recovering both local and global stability of the steady states. On the contrary, we show that, if the policy is not adequate, the system can exhibit endogenous oscillating and chaotic behavior and multistability phenomena.

Effect of ageing on housing prices: A perspective from an overlapping generation model

This paper suggests that ageing has divergent effects on housing prices, and the divergence sources from both aspects of ageing and housing. For the ageing, a fall in fertility and a rise in survival rate could have opposite effects on housing prices. For the housing, the prices of the two components – land and structure – respond to fertility rate decline and survival rate increase to different extent. Therefore, the effect of ageing on housing prices does not have a definite pattern in the long run. In the short run, the results suggest that ageing can produce a turning point in the price dynamics. To the left of the peak, ageing boosts prices while to the right, it has the opposite effect, therefore the impacts of ageing on housing prices are different with time.

Optimal attitude planning along torque equilibrium points using aerodynamic database for deorbiting large space debris

Currently, considerable attention is being directed toward active debris removal (ADR) using small, cost-effective satellites. From high altitude to re-entry, ADR missions use thrusters that consume significant amounts of fuel. The volume of the propulsion system in these satellites can be quite large, and it is difficult for a small satellite to accommodate a large-scale propulsion system. Thus, active utilization of atmospheric drag is being considered for small satellites with low capability. However, the principal challenge for small satellites to remove large debris is to deal with the large disturbance torque caused by strong atmospheric drag on the debris. This paper proposes attitude guidance around an equilibrium (balance) point in attitude dynamics acted on by gravity gradient and aerodynamic torques. The desired attitude is set to optimize two conflicting objectives: maximizing the projection area to generate large aerodynamic force and minimizing the disturbance torque. In this paper, we develop an aerodynamic database (ADDB) by rigorously calculating the aerodynamic torque for each altitude and solar array paddle (SAP) rotation based on an aerodynamic characteristic model of free molecular flow. Using the ADDB, the SAP angle and orbit altitude effects on the torque equilibrium attitude (TEA) are clarified. Then, the mean disturbance torque map at each orbit altitude is introduced to obtain the candidate TEA paths. The effectiveness of the proposed paths for debris descent is demonstrated through numerical simulations.