Deterministic Laws Research Articles

Chaos: From celestial mechanics to climate

Abstract Chaos is unpredictable behaviour arising in systems governed by deterministic laws. Since its ‘discovery’ in the 1960s by Edward Lorenz in his studies of meteorological systems, chaos has become an important way of understanding seemingly random behaviour in many other areas. These include the double pendulum, the climate, El Niño and electrical oscillators. Understanding chaos allows the limits of the predictability of a system to be determined. However, despite this recent activity this paper will show that the theory of chaos has a rich history and chaotic behaviour was originally identified in the 1890s by Henri Poincaré in his investigations of the three-body problem in celestial mechanics. But remarkably this paper will also show that chaotic behaviour can be found in such a simple problem as multiplication by 10 and it is closely linked to the question (studied by the ancient Greeks) of whether a number is rational or irrational.

Feedback-based quantum algorithms for ground state preparation

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024

Stochastic effects on plankton dynamics: Insights from a realistic 0-dimensional marine biogeochemical model

Marine ecosystems exist in a noisy and uncertain environment, not governed by deterministic laws. The development of ecological communities is significantly influenced by variability, and the interaction between nonlinearity and stochastic processes can lead to phenomena that deterministic models cannot explain. Plankton, forming the base of the marine food web, are highly affected by stochastic fluctuations due to their short reproductive timescales. Investigating the effects of noise on plankton growth is essential for accurately describing and predicting marine health. We present a realistic biogeochemical model where multiplicative white noise represents environmental stochasticity affecting plankton. The model suggests ergodic properties in the presence of stochastic fluctuations, with temporal and ensemble distributions being coherent. Analytical and numerical analyses reveal that, given sufficiently low noise intensity, dynamics near equilibrium resemble an Ornstein-Uhlenbeck additive process. With higher noise intensities, resonance occurs, particularly when endogenous dynamics are periodic. The results indicate that low noise intensity can positively influence plankton persistence with an higher number of species coexisting, while higher noise intensity can establish a new equilibrium in the system.

Reliability evaluation method for PID feedback control system considering performance degradation

The reliability of proportional-integration-derivative (PID) feedback control systems is crucial for products due to their critical functions. Traditional reliability evaluation methods of PID feedback control systems usually pose difficulties in comprehensively considering the performance compensation property of feedback mechanisms and the degradation phenomenon in operating processes. This paper proposes a new reliability evaluation method for the PID control system under the framework of belief reliability theory to consider both deterministic and uncertain laws regarding functional logics and degradation effects. For deterministic laws, the interdisciplinary, degradation, and margin equations are established with respect to the steady state error. Various internal and external influencing factors are integrated into these equations by modeling state space and characterizing degradation mechanisms. For uncertain laws, the metric equation is constructed accordingly considering diverse uncertain factors. A Monte Carlo-based algorithm and an analysis framework are further developed to calculate the belief reliability. Finally, the proposed method is implemented to an aero-power hydraulic servo control system as a specific illustration, demonstrating its effectiveness and rationality.

Acoustic emission applied to stochastic modeling of microdamage in compact bone

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain (εmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon _{\\max }$$\\end{document}).

Being prosocial and happy, and believing in life-determining forces across cultures

AbstractBelieving that your life is shaped by internal forces, such as your own free will, is usually thought to lead to positive outcomes, such as being prosocial and happy. Believing that it is shaped by external forces, such as deterministic laws of nature, is usually thought to lead to negative outcomes. However, whether that is the case might vary with culture and with the nature of the force, specifically, whether the force is teleological. To test this, we investigated beliefs in five countries: China, India, Lithuania, Mongolia, and the USA. We investigated beliefs in the importance of choice (an internal, teleological force), gods and fate (external, teleological forces), and chance and luck (external, non-teleological forces). Participants (N = 1035) played a hypothetical dictator game, rated their happiness, and rated how much, in their opinion, their life is determined by these forces. Choice was perceived as the most important and its perceived importance was positively associated with subjective happiness across cultures. It was also positively associated with prosocial intentions, although only in India. Perceived importance of gods and fate was mostly positively associated with prosocial intentions. Perceived importance of gods, but not fate, was positively associated with subjective happiness across cultures. Finally, perceived importance of chance and luck was mostly either negatively associated with prosocial intentions and subjective happiness or not at all. Our results highlight the importance of studying agency beliefs in different cultures and distinguishing different kinds of determination: not just internal and external but also teleological and non-teleological.

Evaluation of the possibility of chaos for doubly-fed induction generator in wind power generation system

<span lang="EN-US">The doubly-fed induction generator (DFIG) has the advantages of compactness and low cost, so it has been applied more and more in practice. However, the structure of the DFIG system is complex, multivariable, nonlinear, and difficult to control. Chaos is a phenomenon that only occurs with nonlinear dynamical systems, sensitive to initial conditions and aperiodic but it is governed by deterministic laws, unlike random perturbations. For most powertrain systems, chaos causes disadvantages, reduce performance, and even destruction of the system. By method of analysis based on theory and simulation, the paper will demonstrate the chaotic phenomenon for DFIG when the parameters of the system change into a certain value. From that set of parameters, the controller is designed to avoid or eliminate that chaotic behavior, so that the system works more reliably and with better quality.</span>

Dynamical and Probabilistic Approaches to Irreversibility

Boltzmann’s H-theorem is considered a great triumph of science. Though some modifications are necessary to adapt it to modern dynamical theories, it is well established that one of its main tenets remains widely accepted: the introduction of probability is a key element in achieving a transition from time-reversible, deterministic dynamical laws at the microscopic level to irreversible laws describing the approach to equilibrium of isolated macroscopic systems. Thus, it is somehow surprising that we still find instances where this subject is labeled as paradoxical and elusive. More remarkable is the fact that this often happens in texts that succeed in presenting Boltzmann’s ideas with clarity. In order to shed light on how probability allows us to go form microscopic reversibility to macroscopic irreversibility, we use numerical results from a two-dimensional lattice gas composed of distinguishable particles. We discuss the roles played by noise, coarse graining, and probability. The simplicity of our model might help the newcomer to this area in better grasping Boltzmann’s fundamental breakthrough.

Switch-Constrained Multiple-Model Algorithm for Maneuvering Target Tracking

In most of the existing state estimation algorithms for maneuvering target tracking, the formulation of the mode switching process fails to accurately capture the deterministic law that the target mode will persist for a period of time once it turns to be in effect. In this paper, two strategies are presented to describe this characteristic. First, a constraint that model switching occurs no more than once over three consecutive time steps is proposed to provide a deterministic description that mode does not switch continuously. Second, considering target mode always lasts for some time while mode switching is completed instantly, the transition probabilities from one model to itself are fixed at extremely large values to enhance the certainty in mode sojourn segments. Based on these strategies, two recursive multiple model (MM) filters are derived in the framework of generalized pseudo-Bayesian (GPB) estimation and interacting multiple model (IMM) estimation, respectively. In both algorithms, although the large probability of model staying unchanged causes high peak errors at mode switching instants, the introduction of the switching constraint prevents the input to the mode-matched filter from being affected by the model transition probability, thereby obtaining a near-optimal performance in mode sojourn segments. Additionally, in order to reduce the peak estimation errors, a mode switching detector based on likelihood function is presented to work in parallel with the recursive MM filters. Once the detector declares that a mode switch occurs, the final estimate is adjusted from the output of the recursive MM filters to the estimate of the corresponding elemental filter, performance of which is guaranteed by the switching constraint. Simulation results demonstrate the capability of the proposed recursive MM filters to obtain performance close to that of a filter without model uncertainty in mode sojourn segments and the effectiveness of the mode switching detector to reduce peak errors at the same time.

On the predictability of localization instabilities of quasibrittle materials from accelerating rates of acoustic emission

Forecasting quasibrittle failure in geomaterials is of paramount importance in the physics of fractures but rarely succeeds. To clarify the physics relating to the failure predictability in a quasibrittle regime, a combined AE (acoustic emission)-DIC (digital image correlation) technique is used in uniaxial compression experiments of flawed granite to trace its damage conditions in real time. The mechanistic correlations of the AE rate-process with the internal FPZ (fracture process zone) development are available. It is shown that the complete record of the AE activities does not meet a deterministic scaling law (e.g., typical time‐reversed Omori law), indicating a challenge in predicting ultimate failure via AE. Subsets of a power law acceleration registered much earlier than ultimate failure imply that the procedural sample-sized localization instability is predictable but still depends on the FPZ dynamic evolutions. More importantly, we find that the coexistence of FPZs and the intermittency of crack growth are the two main reasons for the difficulty of forecasting failure in flawed granite. This study sheds light on upcoming investigations in which the roles of FPZs, especially their spatiotemporal patterns, should be highlighted.

On relation between renormalized frequency and heat capacity for particles in an anharmonic potential

For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas in the anharmonic potential. The orbital motion and thermal motion depend on the same anharmonic parameters, but in different combinations. These two manners of combinations are fundamentally different, demonstrating that statistical law cannot emerge from the deterministic law for the many-body system.

Taming Pereboom’s Wild Coincidences

AbstractPereboom’s ‘wild coincidences’ argument against agent-causal libertarianism is based on the claim that in a world governed by statistical laws, the dovetailing of indeterministic physical happenings with the free actions of agent causes would be a coincidence too wild to be credible. In this paper it is shown that the conclusion is valid for deterministic laws, but that it fails for statistical laws. Therefore, the ‘wild coincidences’ argument does not provide the promised empirical refutation of agent-causal libertarianism.

Singularity, Observability and Statistical Independence in the Context of Chaotic Systems

Pseudorandom number generators (PRNGs) have always been a central research topic in data science, and chaotic dynamical systems are one of the means to obtain scientifically proven data. Chaotic dynamical systems have the property that they have a seemingly unpredictable and random behavior obtained by making use of deterministic laws. The current paper will show how several notions used in the study of chaotic systems—statistical independence, singularity, and observability—can be used together as a suite of test methods for chaotic systems with high potential of being used in the PRNG or cryptography fields. In order to address these topics, we relied on the adaptation of the observability coefficient used in previous papers of the authors, we calculated the singularity areas for the chaotic systems considered, and we evaluated the selected chaotic maps from a statistical independence point of view. By making use of the three notions above, we managed to find strong correlations between the methods proposed, thus supporting the idea that the resulting test procedure is consistent. Future research directions consist of applying the proposed test procedure to other chaotic systems in order to gather more data and formalize the approach in a test suite that can be used by the data scientist when selecting the best chaotic system for a specific use (PRNG, cryptography, etc.).

TARDYS Quantifiers: Extracting Temporal and Reversible DYnamical Symmetries

One of the great challenges in complex and chaotic dynamics is to reveal the details of its underlying determinism. This can be manifest in the form of temporal correlations or structured patterns in the dynamics of a measurable variable. These temporal dynamical structures are sometimes a consequence of hidden global symmetries. Here, we identify the temporal (approximate) symmetries of a semiconductor laser with external optical feedback, based on which we define the Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers to evaluate the relevance of specific temporal correlations in a time series. We show that these symmetries are also present in other complex dynamical systems, letting us extrapolate one system’s symmetries to characterize and distinguish chaotic regimes in other dynamical systems. These symmetries, natural of the dynamics of the laser with feedback, can also be used as indicators in forecasting regular-to-chaos transitions in mathematical iterative maps. We envision that this can be a useful tool in experimental data, as it can extract key features of the deterministic laws that govern the dynamics of a system despite the lack of knowledge of those specific quantitative descriptions.

Are we free to make the laws?

Humeans about laws maintain that laws of nature are nothing over and above the complete distribution of non-modal, categorical properties in spacetime. ‘Humean compatibilists’ argue that if Humeanism about laws is true, then agents in a deterministic world can do otherwise than they are lawfully determined to do because of the distinctive nature of Humean laws. More specifically, they reject a central premise of the Consequence argument by maintaining that deterministic laws of nature are ‘up to us’. In this paper, we present a new argument for Humean compatibilism. We argue that Humeans about laws indeed have resources for defending compatibilism that non-Humeans lack (though not for the reasons typically discussed in the literature). Moreover, we show that utilizing these resources does not lead to objectionable consequences. Humeans about laws should thus embrace Humean compatibilism.

One-dimensional telegraphic process with noninstantaneous stochastic resetting.

In this paper, we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting, meaning that at random times it is forced to return to the starting point. Here we consider a return mechanism governed by a deterministic law of motion, so that the time cost required to return is correlated to the position occupied at the time of the reset. We show that in such conditions the process reaches a stationary state which, for some kinds of deterministic return dynamics, is independent of the return phase. Furthermore, we investigate the first-passage properties of the system and provide explicit formulas for the mean first-hitting time. Our findings are supported by numerical simulations.

Quantum Legacies: Dispatches from an Uncertain World

Quantum Legacies: Dispatches from an Uncertain World

Macroscopic Limit of Quantum Systems

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.

New insight into subcritical rupture of SiC-based filaments at intermediate temperatures (400–900 °C) under air

The delayed failure of SiC fibrous reinforcement has continuously been investigated to warrant the long term performances of Ceramic Matrix Composite (CMC). Chiefly assessed on multifilament tow samples to alleviate some handling difficulties, subcritical crack growth (SCG) parameters are however ruled by structural artifacts which hinder the identification of intrinsic filament behavior. In this paper, we propose to estimate the true filament parameters for 5 fiber types from bundle behavior using a recently communicated Monte Carlo algorithm integrating flaw and stress distributions through a deterministic fracture mechanics law under Paris’ formulation. So computed tow lifetime are broadly dispersed, encompassing raw data, and show a structure-dependent scale effect, revealed by nfilament>ntow where n is the stress exponent. The relationship between SCG coefficient and chemical composition of the substrate is discussed and highlights the major effect of doping elements (Ti or Zr), oxygen or hydrogen content.

Ground Demonstration of the Use of Limnospira indica for Air Revitalization in a Bioregenerative Life-Support System Setup: Effect of Non-Nitrified Urine–Derived Nitrogen Sources

Long-duration human space missions require considerable amounts of water, oxygen, and nutritious biomass. Additionally, the space vehicles must be well equipped to deal with metabolic human waste. It is therefore important to develop life-support systems which make these missions self-sufficient in terms of water, food, and oxygen production as well as waste management. One such solution is the employment of regenerative life-support systems that use biological and chemical/physical processes to recycle crew waste, revitalize air, and produce water and food. Photosynthetic cyanobacteria Limnospira could play a significant role in meeting these objectives. Limnospira can metabolize CO2 and nitrogen-rich human waste to produce oxygen and edible biomass. So far, life-support system studies have mainly focused on using chemical/physical methods to recycle water, degrade human waste, and recycle CO2 into oxygen. Nowadays, additional microbial processes are considered, such as nitrification of urea–ammonium–rich human waste and then using the nitrate for cyanobacterial cultivation and air vitalization. This cascade of multiple processes tends to increase the complexity of the life-support systems. The possibility of using non-nitrified urine for Limnospira cultivation can partially solve these issues. Our previous studies have shown that it is possible to cultivate Limnospira with urea and ammonium, the prominent nitrogen forms present in non-nitrified urine. In this study, we investigated the possibility of cultivating Limnospira with the different nitrogen forms present in non-nitrified urine and also evaluated their effect on the oxygen production capacity of Limnospira. For this 35-day-long study, we worked on a simplified version of the European Space Agency’s MELiSSA. During this ground demonstration study, we monitored the effect of urea and ammonium (vs. nitrate) on the oxygen production capacity of Limnospira. A deterministic control law, developed and validated on the basis of a stochastic light-transfer model, modulated (increase/decrease) the incident light on the photobioreactor (with Limnospira) to control oxygen levels in the closed loop. The CO2 from the mouse compartment was recycled as a carbon source for Limnospira. We observed that while the system could meet the desired oxygen levels of 20.3% under the nitrate and urea regime, it could only reach a maximum O2 level of 19.5% under the ammonium regime.