Dynamics Of Physical Systems Research Articles

How Do We Move: Modeling Human Movement with System Dynamics

Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. The human movements can be viewed as a dynamic process that human transits between states (e.g., locations) over time. In the human world where intelligent agents like humans or vehicles with human drivers play an important role, the states of agents mostly describe human activities, and the state transition is influenced by both the human decisions and physical constraints from the real-world system (e.g., agents need to spend time to move over a certain distance). Therefore, the modeling of state transition should include the modeling of the agent's decision process and the physical system dynamics. In this paper, we propose MoveSD to model state transition in human movement from a novel perspective, by learning the decision model and integrating the system dynamics. MoveSD learns the human movement with Generative Adversarial Imitation Learning and integrates the stochastic constraints from system dynamics in the learning process. To the best of our knowledge, we are the first to learn to model the state transition of moving agents with system dynamics. In extensive experiments on real-world datasets, we demonstrate that the proposed method can generate trajectories similar to real-world ones, and outperform the state-of-the-art methods in predicting the next location and generating long-term future trajectories.

Simple Reservoir Computing Capitalizing on the Nonlinear Response of Materials: Theory and Physical Implementations

The potential of nonlinear dynamical systems serving as reservoirs has attracted much attention for the physical realization of reservoir computing (RC). Here, we propose a hardware system working as a reservoir with one simple form of nonlinearity that reflects the intrinsic characteristics of the materials. We show that insufficient dynamics in such physical systems can perform like complex dynamical systems with the assistance of external controls. Based on the idea of spatial multiplexing, this dynamical system is studied under two frameworks. The correlation between structural adjustments of the reservoir and system performance in processing various types of task is proposed. Our results are expected to enable the development of material-based devices for RC.

Real-time collision dynamics of vector solitons in a fiber laser

Particle-like structures of solitons, as a result of the balance between dispersion and nonlinearity, enable remarkable elastic and inelastic soliton collisions in many fields. Despite the experimental observation of temporal vector-soliton collisions in birefringent fibers, collision dynamics of vector solitons in fiber lasers have not been revealed before, to the best of our knowledge. Here, the real-time spectral evolutions of vector solitons during collisions in a dual-comb fiber laser, which generates vector solitons with slightly different repetition rates, are captured by a time-stretch dispersive Fourier transform technique. We record the whole process of vector-soliton collisions, including the formation of weak pulses induced by cross-polarization coupling, opposite central wavelength shifts of both vector solitons, distinct intensity redistribution and dissipative energy, and gradual recovery to initial states. Furthermore, extreme collisions with strong four-wave mixing sidebands are observed by virtue of coherent coupling between the orthogonal polarization components of vector solitons. Numerical simulations match well with the experimental observations. The experimental and numerical evidences of vector-soliton collision dynamics could give insight into the understanding of nonlinear dynamics in fiber lasers and other physical systems, as well as the improvement of laser performance for application in dual-comb spectroscopy.

Presence of Megastability and Infinitely Many Equilibria in a Periodically and Quasi-Periodically Excited Single-Link Manipulator

In the last two years, many chaotic or hyperchaotic systems with megastability have been reported in the literature. The reported systems with megastability are mostly developed from their dynamic equations without any reference to the physical systems. In this paper, the dynamics of a single-link manipulator is considered to observe the existence of interesting dynamical behaviors. When the considered dynamical system is excited with (a) periodically forced input or (b) quasi-periodically forced input, it indicates the existence of megastability. This paper reports megastability in a physical dynamical system with infinitely many equilibria. The considered system has other dynamical behaviors like chaotic, quasi-periodic and periodic. These behaviors are analyzed using Lyapunov spectrum, bifurcation diagram and phase plots. The simulation results reveal that the objectives of the paper are achieved successfully.

Reconstruction of few-fs XUV pulses with a perturbative approach

A precise temporal characterization of the pulses involved in pump-probe experiments is crucial for a proper investigation of the ultrafast dynamics in several physical systems. Indeed, it is required for the assessment of the dynamical properties under examination with sufficient temporal resolution. In the fewfs/attosecond domain, typical reconstruction procedures require time-consuming interative methods, which are also sensitive to the experimental noise and to the distortion of the measurement. We developed an approach, called Simplified Trace Reconstruction In the Perturbative regimE (STRIPE), which allows us for a precise characterization of the infrared (IR) and extreme ultraviolet (XUV) pulses, used in a pump-probe experiment. Our method is not based on a phase retrival algorithm, and for this it is typically much faster than the other ones currently known. Moreover, it allows for easily including in the reconstruction the experimental non-idealities that may affect the measurement, like possible distortion due to the measurement procedure itself.

Complex interplay between spectral harmonicity and different types of cross-frequency couplings in nonlinear oscillators and biologically plausible neural network models.

Cross-frequency coupling (CFC) refers to the nonlinear interaction between oscillations in different frequency bands, and it is a rather ubiquitous phenomenon that has been observed in a variety of physical and biophysical systems. In particular, the coupling between the phase of slow oscillations and the amplitude of fast oscillations, referred as phase-amplitude coupling (PAC), has been intensively explored in the brain activity recorded from animals and humans. However, the interpretation of these CFC patterns remains challenging since harmonic spectral correlations characterizing nonsinusoidal oscillatory dynamics can act as a confounding factor. Specialized signal processing techniques are proposed to address the complex interplay between spectral harmonicity and different types of CFC, not restricted only to PAC. For this, we provide an in-depth characterization of the time locked index (TLI) as a tool aimed to efficiently quantify the harmonic content of noisy time series. It is shown that the proposed TLI measure is more robust and outperforms traditional phase coherence metrics (e.g., phase locking value, pairwise phase consistency) in several aspects. We found that a nonlinear oscillator under the effect of additive noise can produce spurious CFC with low spectral harmonic content. On the other hand, two coupled oscillatory dynamics with independent fundamental frequencies can produce true CFC with high spectral harmonic content via a rectification mechanism or other post-interaction nonlinear processing mechanisms. These results reveal a complex interplay between CFC and harmonicity emerging in the dynamics of biologically plausible neural network models and more generic nonlinear and parametric oscillators. We show that, contrary to what is usually assumed in the literature, the high harmonic content observed in nonsinusoidal oscillatory dynamics is neither a sufficient nor necessary condition to interpret the associated CFC patterns as epiphenomenal. There is mounting evidence suggesting that the combination of multimodal recordings, specialized signal processing techniques, and theoretical modeling is becoming a required step to completely understand CFC patterns observed in oscillatory rich dynamics of physical and biophysical systems.

Erol Başar and the scientific revolution in nonlinear brain dynamics: A selective review

Erol Başar was one of the most significant neuroscientists of the past century. Two main threads of thought guided Başar's scientific labor: i) the study of brain oscillations and ii) its marriage to basic principles of physics. These two threads provided him with the crucial element to introduce nonlinear random theory into brain research. Until the decade of the seventies, the underling paradigm in studying the electrical activity of the brain was dominated by a simplistic linear systems model that entailed absolute separation between a determinist evoked responses to stimuli and a superimposed background electrical activity considered as “noise”. Başar questioned this simplistic linear model and its interpretation. Başar underscored the nonlinear dynamics of the brain, demonstrated for the first time the interaction between evoked and background activity, and widened the study of event-related activity from the time domain to the frequency and time-frequency domain, heralding a new understanding of the event-related dynamics. These advances were a consequence of Başar's fascination with the physics and mathematics of dynamical physical systems which he rightly believed to be the key to understanding the brain. Here we carry out a selected review, based on a scientometric analysis of Başar's scientific trajectory in the field of Brain Dynamics as embodied in 278 peer-reviewed papers. We also report the geographical distribution of Başar's collaborators, distribution of his citations, and his interaction with many international groups. This analysis illustrates the importance of his innovative contributions and the impact it had on our field. It underscores that he is one of the initiators of a “scientific revolution” in neurophysiology: from linear systems to random non-linear systems analysis and the new vision of the brain as a dynamical system.

Beating absorption in solid-state high harmonics

Since the new millennium coherent extreme ultra-violet and soft x-ray radiation has revolutionized the understanding of dynamical physical, chemical and biological systems at the electron’s natural timescale. Unfortunately, coherent laser-based upconversion of infrared photons to vacuum-ultraviolet and soft x-ray high-order harmonics in gaseous, liquid and solid targets is notoriously inefficient. In dense nonlinear media, the limiting factor is strong re-absorption of the generated high-energy photons. Here we overcome this limitation by generating high-order harmonics from a periodic array of thin one-dimensional crystalline silicon ridge waveguides. Adding vacuum gaps between the ridges avoids the high absorption loss of the bulk and results in a ~ 100-fold increase of the extraction depth. As the grating period is varied, each high harmonic shows a different and marked modulation, indicating their waveguiding in the vacuum slots with reduced absorption. Looking ahead, our results enable bright on-chip coherent short-wavelength sources and may extend the usable spectral range of traditional nonlinear crystals to their absorption windows. Potential applications include on-chip chemically-sensitive spectro-nanoscopy.

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. We present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

Understanding Ecosystem Complexity via Application of a Process-Based State Space rather than a Potential Surface

Ecosystems are complex objects, simultaneously combining biotic, abiotic, and human components and processes. Ecologists still struggle to understand ecosystems, and one main method for achieving an understanding consists in computing potential surfaces based on physical dynamical systems. We argue in this conceptual paper that the foundations of this analogy between physical and ecological systems are inappropriate and aim to propose a new method that better reflects the properties of ecosystems, especially complex, historical nonergodic systems, to which physical concepts are not well suited. As an alternative proposition, we have developed rigorous possibilistic, process-based models inspired by the discrete-event systems found in computer science and produced a panel of outputs and tools to analyze the system dynamics under examination. The state space computed by these kinds of discrete ecosystem models provides a relevant concept for a holistic understanding of the dynamics of an ecosystem and its abovementioned properties. Taking as a specific example an ecosystem simplified to its process interaction network, we show here how to proceed and why a state space is more appropriate than a corresponding potential surface.

Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological, and economic systems. By expressing the probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function of the intensities close to the critical point n=1 of the Hawkes process, with a nonuniversal exponent, function of the background intensity ν_{0} of the Hawkes intensity, the average timescale of the memory kernel and the branching ratio n. Our theoretical predictions are confirmed by numerical simulations.

Different Dynamic Formulations for a Mechanism using Bond Graph

For modeling dynamics of mechanisms, various classical formulations are available in the literature. The equations of dynamics given by various classical formulations can also be derived from the bond graph. The bond graph is a convenient graphical representation for modeling dynamics of physical systems in multi-energy domains.In this paper, various alternative causality assignment procedures in the bond graph are used to derive different classical formulations such as the Lagrange’s equations of the first kind (with multipliers), Lagrange’s formulation of the second kind, and Hamiltonian formulations. An example of the quick return mechanism has been modeled using the bond graph technique, and various alternative causality assignment procedures are applied to derive the various formulations. Simulation coding has been done using MATLAB and results have been analyzed and discussed. The purpose of this paper is to show how the various formulations can be obtained from bond graph using various alternative causality assignment procedures.

Digital Twins in Pharmaceutical and Biopharmaceutical Manufacturing: A Literature Review

The development and application of emerging technologies of Industry 4.0 enable the realization of digital twins (DT), which facilitates the transformation of the manufacturing sector to a more agile and intelligent one. DTs are virtual constructs of physical systems that mirror the behavior and dynamics of such physical systems. A fully developed DT consists of physical components, virtual components, and information communications between the two. Integrated DTs are being applied in various processes and product industries. Although the pharmaceutical industry has evolved recently to adopt Quality-by-Design (QbD) initiatives and is undergoing a paradigm shift of digitalization to embrace Industry 4.0, there has not been a full DT application in pharmaceutical manufacturing. Therefore, there is a critical need to examine the progress of the pharmaceutical industry towards implementing DT solutions. The aim of this narrative literature review is to give an overview of the current status of DT development and its application in pharmaceutical and biopharmaceutical manufacturing. State-of-the-art Process Analytical Technology (PAT) developments, process modeling approaches, and data integration studies are reviewed. Challenges and opportunities for future research in this field are also discussed.

Lean Manufacturing 4.0 - dynamic physical and cybernetic system for Industry 4.0

The intelligent manufacturing system is realized through fusion between the production system with information and communication technologies. This allows to build a digital twin of physical production system, the two being connected and communicate each other data in real time about production status and progress. The existing Industry 4.0 physical system identify the active production resources, who are directly involved in the production processes, and of the passive ones, who have supporting roles. In Industry 4.0 those resources are directly interconnected with the corresponding cyber elements in order to supervise the whole system and the corresponding processes. Into this architecture, the physical production passive and active resources will form a dynamic subsystem, through which one can manage the physical and cybernetic changeable manufacturing processes and various products, in different manufacturing stages. This paper presents a solution to change the cyber-physical system by replacing the production physical active elements with those elements who need to change on the production line and the corresponding digital resources, including the specific Lean 4.0 production system tools who supervises the manufacturing cell and controls the execution. This dynamic system allows achieving a higher level of the production system.

A New Look on Financial Markets Co-Movement through Cooperative Dynamics in Many-Body Physics.

One of the main contributions of the Capital Assets Pricing Model (CAPM) to portfolio theory was to explain the correlation between assets through its relationship with the market index. According to this approach, the market index is expected to explain the co-movement between two different stocks to a great extent. In this paper, we try to verify this hypothesis using a sample of 3.000 stocks of the USA market (attending to liquidity, capitalization, and free float criteria) by using some functions inspired by cooperative dynamics in physical particle systems. We will show that all of the co-movement among the stocks is completely explained by the market, even without considering the market beta of the stocks.

An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence

In the study of dynamics of physical systems an important role is played by symmetry principles. As an example in classical physics, symmetry plays a role in quantum physics, turbulence and similar theoretical models. We end up having to deal with an equation whose solution we desire to be in a closed form. But obtaining a solution in such form is achieved only in special cases. Hence, we resort to iterative schemes. There is where the novelty of our study lies, as well as our motivation for writing it. We have a very limited literature with eighth-order convergent iteration functions that can handle multiple zeros m≥1. Therefore, we suggest an eighth-order scheme for multiple zeros having optimal convergence along with fast convergence and uncomplicated structure. We develop an extensive convergence study in the main theorem that illustrates eighth-order convergence of our scheme. Finally, the applicability and comparison was illustrated on real life problems, e.g., Van der Waal’s equation of state, Chemical reactor with fractional conversion, continuous stirred reactor and multi-factor problems, etc., with existing schemes. These examples further show the superiority of our schemes over the earlier ones.

Early-Time Exponential Instabilities in Nonchaotic Quantum Systems

The majority of classical dynamical systems are chaotic and exhibit the butterfly effect: a minute change in initial conditions has exponentially large effects later on. But this phenomenon is difficult to reconcile with quantum mechanics. One of the main goals in the field of quantum chaos is to establish a correspondence between the dynamics of classical chaotic systems and their quantum counterparts. In isolated systems in the absence of decoherence, there is such a correspondence in dynamics, but it usually persists only over a short time window, after which quantum interference washes out classical chaos. We demonstrate that quantum mechanics can also play the opposite role and generate exponential instabilities in classically nonchaotic systems within this early-time window. Our calculations employ the out-of-time-ordered correlator (OTOC)-a diagnostic that reduces to the Lyapunov exponent in the classical limit but is well defined for general quantum systems. We show that certain classically nonchaotic models, such as polygonal billiards, demonstrate a Lyapunov-like exponential growth of the OTOC at early times with Planck's-constant-dependent rates. This behavior is sharply contrasted with the slow early-time growth of the analog of the OTOC in the systems' classical counterparts. These results suggest that classical-to-quantum correspondence in dynamics is violated in the OTOC even before quantum interference develops.

On Different Approaches for Integrals of Physical Dynamical Systems

For driven time dependent harmonic oscillator a detailed and systematic study of several methods for the building of Integrals is carried out. The central feature of the present discussion is the establishment of Integrals for the dynamical system. In spite of their different procedural details all the approaches lead to the same invariant for the given classical system. Advantage and limitations of different methods are briefly highlighted.

The X-Ray Emission Effectiveness of Plasma Mirrors: Reexamining Power-Law Scaling for Relativistic High-Order Harmonic Generation

Ultrashort pulsed lasers provide uniquely detailed access to the ultrafast dynamics of physical, chemical, and biological systems, but only a handful of wavelengths are directly produced by solid-state lasers, necessitating efficient high-power frequency conversion. Relativistic plasma mirrors generate broadband power-law spectra, that may span the gap between petawatt-class infrared laser facilities and x-ray free-electron lasers; despite substantial theoretical work the ultimate efficiency of this relativistic high-order-harmonic generation remains unclear. We show that the coherent radiation emitted by plasma mirrors follows a power-law distribution of energy over frequency with an exponent that, even in the ultrarelativistic limit, strongly depends on the ratio of laser intensity to plasma density and exceeds the frequently quoted value of −8/3 over a wide range of parameters. The coherent synchrotron emission model, when adequately corrected for the finite width of emitting electron bunches, is not just valid for p-polarized light and thin foil targets, but generally describes relativistic harmonic generation, including at normal incidence and with finite-gradient plasmas. Our numerical results support the ω−4/3 scaling of the synchrotron emission model as a limiting efficiency of the process under most conditions. The highest frequencies that can be generated with this scaling are usually restricted by the width of the emitting electron bunch rather than the Lorentz factor of the fastest electrons. The theoretical scaling relations developed here suggest, for example, that with a 20-PW 800-nm driving laser, 1 TW/harmonic can be produced for 1-keV photons.

A Novel Framework for Simultaneous Topology and Sizing Optimization of Complex, Multi-Domain Systems-of-Systems

Abstract This article presents a novel design framework for topology and component sizing optimization of multi-domain dynamic systems described by conservation laws. Multidisciplinary design optimization (MDO) is a powerful tool for minimizing metrics such as inefficiency and cost for these systems-of-systems (SoS). However, quality of the designs identified from the optimization procedure depends on model accuracy and ability to capture inter-system interactions. This work utilizes a conservation-based, graphical modeling approach to capture physical system dynamics and interactions, and expands it to be used in MDO techniques. This yields three contributions to the literature. First, an augmented graph-based model is provided, expressing continuous and discrete design variable values as changes to vertex size, edge size, and edge connections of the dynamic system graph. Second, a sizing and topology optimization framework is developed using the augmented graph-based model as a basis. Third, analytical and numerical sensitivity functions are derived for a cooling system design problem, stemming from application of the design framework. The design framework is applied to two case studies for cooling subsystem design and electric vehicle (EV) powertrain design, with the goal of optimizing thermal and electrical component sizes, as well as discrete choices in the topology of the system being designed. These case studies provide examples for how the design framework enables analysis of alternatives (AoA) during early design stages.