Large Dynamic Systems Research Articles

Molecular Dynamical and Quantum Mechanical Exploration of the Site-Specific Dynamics of Cy3 Dimers Internally Linked to dsDNA.

Performing spectroscopic measurements on biomolecules labeled with fluorescent probes is a powerful approach to locating the molecular behavior and dynamics of large systems at specific sites within their local environments. The indocarbocyanine dye Cy3 has emerged as one of the most commonly used chromophores. The incorporation of Cy3 dimers into DNA enhances experimental resolution owing to the spectral characteristics influenced by the geometric orientation of excitonically coupled monomeric units. Various theoretical models and simulations have been utilized to aid in the interpretation of the experimental spectra. In this study, we employ all-atom molecular dynamics simulations to study the structural dynamics of Cy3 dimers internally linked to the dsDNA backbone. We used quantum mechanical calculations to derive insights from both the linear absorption spectra and the circular dichroism data. Furthermore, we explore potential limitations within a commonly used force field for cyanine dyes. The molecular dynamics simulations suggest the presence of four possible Cy3 dimeric populations. The spectral simulations on the four populations show one of them to agree better with the experimental signatures, suggesting it to be the dominant population. The relative orientation of Cy3 in this population compares very well with previous predictions from the Holstein-Frenkel Hamiltonian model.

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods.

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

Large dynamic range stellar radiation simulation optical system

For the current stellar spectral simulation can not realize the stellar color temperature information with large dynamic range simulation, this paper proposes a broad spectrum high-resolution subdivision and spatial beam zoning modulation combined with a large dynamic range of stellar radiation information simulation method, designed a kind of imaging and non-imaging stellar radiation information simulation optical system, using an optical system to achieve multi-color temperature spectrum and large dynamic range stellar simulation. The experimental results show that the designed system can simultaneously achieve the spectral simulation accuracy (single point evaluation) better than ± 7% in the range of spectral 450–1000 nm and color temperature 3000–11,000 K; on the premise of ensuring the spectral simulation accuracy, the magnitude simulation range reaches 0 to + 12 Mv, and the magnitude simulation accuracy is better than ± 0.05 Mv; Accurate simulation of stellar spectral information and energy large dynamic range tuning is realized, and the system is extended. The system function has been extended to realize the switching of broadband and narrowband modes, The half-peak width of the narrowband output beam is better than 4.1 nm, which extends the application of the spectral simulation technology and provides the theoretical and technical basis for the ground calibration of the development of the high-precision stellar radiation information ground simulation system.

A novel non-intrusive ROM for randomly excited linear dynamical systems with high stochastic dimension using ANN

Analyzing large stochastic dynamical systems is computationally very expensive. A statistical simulation framework requires invoking the solver multiple times — ranging from thousands to millions. A non-intrusive reduced order model (ROM) serves as a computationally efficient alternative in this framework. Uncertainties in dynamical systems originate from two sources: system parameters and excitation. However, all the existing ROMs have been developed for uncertainty only in the system parameters. To the best of the authors’ knowledge, no ROM exists for dynamical systems under random excitation. A discretization of the input process increases the stochastic dimensionality, typically by a few hundred or thousand. This leads to a high dimensional interpolation or regression in the ROM, which is practically infeasible. This issue is addressed in this work by proposing a novel non-intrusive ROM that bypasses the need for such discretization. Accordingly, a regression is carried out directly on the random excitation using a neural network-based surrogate model. A principal component-based data compression is used in tandem to reduce the stochastic dimensionality of excitations. Detailed numerical studies are conducted to study the accuracy and efficiency of the proposed ROM using two examples: a mistuned bladed disk problem and a soil–structure interaction. The numerical results show that the proposed ROM is accurate and gains a significant speed-up of more than sixty for both examples. Using the proposed ROM, the cost of uncertainty quantification can be reduced significantly within the framework of Monte Carlo simulation.

Polynomial-chaos-based conditional statistics for probabilistic learning with heterogeneous data applied to atomic collisions of Helium on graphite substrate

A formulation and an algorithm are presented to construct a truncated polynomial chaos representation of a vector-valued random output. This representation depends on a vector-valued random input with a known probability measure and a vector-valued random latent variable with an unknown probability measure. The construction of this PCE representation relies solely on a training set comprising a small number of independent realizations of the non-Gaussian dependent random output and input vectors. The training set consists of heterogeneous data, which poses challenges in accurately estimating the chaos coefficients. Despite the heterogeneity of the data, the proposed formulation and algorithm allow for the construction of a highly accurate global surrogate model. Additionally, we propose an alternative approach by constructing a surrogate model based on prior separation of the heterogeneous dataset into subsets, each containing “quasi-homogeneous” data. The separation method is designed to account for a partial overlap of the probability measure supports associated with the subsets. The identification of the PCE is performed offline. By utilizing the PCE, a fast online surrogate model is obtained, enabling analysis of large dynamical systems beyond the computational capabilities currently available. An application to atomic collisions of Helium on a graphite substrate is presented, where the training set was generated by Molecular Dynamics simulations done in a previous paper. The obtained results demonstrate accuracy of the proposed approach.

Evolutionary dynamics of N-player sender-receiver game in networks with community structure.

Network typology largely affects the evolutionary dynamics of collective behaviors in many real-world complex systems. As a conventional transmission model, the sender-receiver game paves the way to explore the evolution of honest signals between senders and receivers. In practice, the utilities of an agent often depend not only on pairwise interactions, but also on the group influence of players around them, and thus there is an urgent need for deeper theoretical modeling and investigations on individuals' non-pairwise interactions. Considering the underlying evolutionary game dynamics and multiple community network structures, we explore the evolution of honest behaviors by extending the sender-receiver game to multiple communities. With the new dynamical model of the multi-community system, we perform a stability analysis of the system equilibrium state. Our results reveal the condition to promote the evolution of honest behaviors and provide an effective method for enhancing collaboration behaviors in distributed complex systems. Current results help us to deeply understand how collective decision-making behaviors evolve, influenced by the spread of true information and misinformation in large dynamic systems.

Optimal explicit stabilized postprocessed τ-leap method for the simulation of chemical kinetics

The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chains) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this paper, we propose a new discrete stochastic simulation algorithm: the postprocessed second kind stabilized orthogonal τ-leap Runge–Kutta method (PSK-τ-ROCK). In the context of chemical kinetics, this method can be seen as a stabilization of Gillespie's explicit τ-leap algorithm combined with a postprocessor. The stabilized procedure allows to simulate problems with multiple scales (stiff), while the postprocessing procedure allows to approximate the invariant measure (e.g. mean and variance) of ergodic stochastic dynamical systems. We prove stability and accuracy of the PSK-τ-ROCK for a reference system. Numerical experiments illustrate the high reliability and efficiency of the scheme when compared to other τ-leap methods.

Semiempirical Methods for Molecular Systems in Strong Magnetic Fields.

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, || ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, || > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Nonlinear Model Predictive Control using Neural ODE Replicas of Dynamic Simulators

We propose simulation-based nonlinear model predictive control as a first step towards autonomous decision-making for stable operation of large complex dynamical systems such as chemical plants. The effect of abrupt external disturbances should be quickly eliminated, taking into account such complex dynamic responses, to maintain stable production. In this paper, we propose a control system to eliminate these effects. The system uses engineering models, including dynamic simulators, based on chemical engineering knowledge. Dynamic simulators are generally not differentiable with respect to actions; however, differentiable models are advantageous for fast nonlinear optimization. To take advantage of both reliable dynamic simulators and differentiable models, we introduce neural ordinary differentiable equation models and clone the behaviour of simulators on them. The cloned differentiable neural replica model is then incorporated into a gradient-based nonlinear model predictive control. Evaluation of this method in a real methanol distillation plant confirms that it can significantly remove abrupt heavy rain disturbances compared to existing methods.

Automata Cascades: Expressivity and Sample Complexity

Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as complex systems made of many components, each implementing a specific functionality. Any automaton can serve as a component; using specific components allows for a fine-grained control of the expressivity of the resulting class of automata; using prime automata as components implies specific expressivity guarantees. Moreover, specifying automata as cascades allows for describing the sample complexity of automata in terms of their components. We show that the sample complexity is linear in the number of components and the maximum complexity of a single component, modulo logarithmic factors. This opens to the possibility of learning automata representing large dynamical systems consisting of many parts interacting with each other. It is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of states and input letters, which implies that it is only possible to learn automata where the number of states is linear in the amount of data available. Instead our results show that one can learn automata with a number of states that is exponential in the amount of data available.

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

SummaryThe proper orthogonal decomposition (POD) is successfully employed in a variety of projection‐based methods for parametric model order reduction (pMOR) of large dynamical systems. It extracts the most energetic modes describing the dynamics of a system from time snapshots of the solution. In practice, these snapshots are computed at user‐defined parameters of the system with a high fidelity model. Then either all the snapshots are concatenated to extract a global POD basis, or a different POD basis is extracted for each parameter value. In the latter case, for unseen target parameters, the POD bases need to be adapted with a dedicated technique. An established method addressing this task is the interpolation on the tangent space to the Grassmann manifold (ITSGM). It interpolates the linear subspaces spanned by the known POD bases, discarding by construction the knowledge on the modes ordering by energy levels. In this paper, we formalize an ordered reduced basis interpolation (ORBI) technique which preserves such ordering. This approach improves the adaptation accuracy of the resulting POD basis as more information is taken into account in the construction of the interpolation operator. Numerical investigations are conducted on the parametric reduced order model of a dynamical system representing a small‐scale gas‐bearings supported rotor. Results show that the proposed method is more accurate than the ITSGM method at a similar computation cost. Trained at only three points of the parameters space, the developed hyper reduced order model (h‐ROM) performs to faster simulations with satisfactory accuracy, even far from the training points.

Structural Dynamics of Bridges Under the Coupling Effect of Windmills and Bridges

To analyze the coupled dynamics effects of existing railroad frame bridge structures under the action of traffic, a coupled train-ballast track-suspension bridge girder-soil dynamics model is established based on railroad large system dynamics and finite element theory. The joint ABAQUS-MATLAB simulation, time-varying coupling, and multi-step dynamic iterative solution strategies are introduced to numerically simulate the mechanical properties of existing railroad structures under the coupled effects of wind loads and traffic action. Specifically, (1) a dichotomous method is proposed to investigate the static behavior of the bridge in the bridge-forming state, and the maximum upper arch of the stiffened girder is 3.67 cm, which occurs at about 1/4 and 3/4 positions of the main span, and the lower deflection of the side span is larger, and the maximum lower deflection occurs at 11.04 cm in the span of the 110 m side span. The vertical acceleration in the span increases immediately with the maximum peak of 30 cm/s2, while the lateral acceleration is maintained within 20 cm/s22. (2) The effects of the stiffness of the rail fasteners and the bridge plate support stiffness on the dynamics were studied. (3) The results of the time-domain analysis are in general agreement with the simulation data, except for the error of the ambient vibration background existing at the peak. The correctness of the simulation model is verified.

The shrinking target problem for matrix transformations of tori: Revisiting the standard problem

Let T be a d×d matrix with real coefficients. Then T determines a self-map of the d-dimensional torus Td=Rd/Zd. Let {En}n∈N be a sequence of subsets of Td and let W(T,{En}) be the set of points x∈Td such that Tn(x)∈En for infinitely many n∈N. For a large class of subsets (namely, those satisfying the so called bounded property (B) which includes balls, rectangles, and hyperboloids) we show that the d-dimensional Lebesgue measure of the shrinking target set W(T,{En}) is zero (resp. one) if a natural volume sum converges (resp. diverges). In fact, we prove a quantitative form of this zero-one criteria that describes the asymptotic behaviour of the counting function R(x,N):=#{1≤n≤N:Tn(x)∈En}. The counting result makes use of a general quantitative statement that holds for a large class measure-preserving dynamical systems (namely, those satisfying the so called summable-mixing property). We next turn our attention to the Hausdorff dimension of W(T,{En}). In the case the subsets En are balls, rectangles or hyperboloids we obtain precise formulae for the dimension. These shapes correspond, respectively, to the simultaneous, weighted and multiplicative theories of classical Diophantine approximation. The dimension results for balls generalises those obtained in [25] for integer matrices to real matrices. In the final section, we discuss various problems that stem from the results proved in the paper.

Editorial: Active particle models and methods in science and society

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward at new perspectives, with emphasis on the interaction of multiple social dynamics.

Stabilization through self-coupling in networks of small-world and scale-free topology

Mechanisms that ensure the stability of dynamical systems are of vital importance, in particular in our globalized and increasingly interconnected world. The so-called connectivity-stability dilemma denotes the theoretical finding that increased connectivity between the components of a large dynamical system drastically reduces its stability. This result has promoted controversies within ecology and other fields of biology, especially, because organisms as well as ecosystems constitute systems that are both highly connected and stable. Hence, it has been a major challenge to find ways to stabilize complex systems while preserving high connectivity at the same time. Investigating the stability of networks that exhibit small-world or scale-free topology is of particular interest, since these topologies have been found in many different types of real-world networks. Here, we use an approach to stabilize recurrent networks of small-world and scale-free topology by increasing the average self-coupling strength of the units of a network. For both topologies, we find that there is a sharp transition from instability to asymptotic stability. Then, most importantly, we find that the average self-coupling strength needed to stabilize a system increases much slower than its size. It appears that the qualitative shape of this relationship is the same for small-world and scale-free networks, while scale-free networks can require higher magnitudes of self-coupling. We further explore the stabilization of networks with Kronecker-Leskovec topology. Finally, we argue that our findings, in particular the stabilization of large recurrent networks through small increases in the unit self-regulation, are of practical importance for the stabilization of diverse types of complex systems.

Online joint optimization of pick order assignment and pick pod selection in robotic mobile fulfillment systems

Robotic mobile fulfillment systems is a large dynamic system where information such as backlog, inventory, pod location, and robot state will change with time during its operation. In this paper, we model the dynamic system for the online joint optimization of pick order assignment and pick pod selection considering multiple items and then propose a new MIP model to solve the decision-making in the key process. We design a heuristic based on alternate decision and order-driven to solve large-scale problems. We extend an open-source simulation framework to evaluate the results of proposed model and algorithm through different instances in the dynamic system. Experimental results show that the performance of the new MIP model is at least 13% higher than that of the different settings, and the performance of the designed heuristic is at least 57% higher than that of the state-of-the-art sequential method in the literature.

High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows

The magnetised spherical Couette (MSC) problem, a three dimensional magnetohydrodynamic paradigmatic model in geo- and astrophysics, is considered to investigate bifurcations to high-dimensional invariant tori and chaotic flows in large scale dissipative dynamical systems with symmetry. The main goal of the present study is to elucidate the origin of chaotic transients and intermittent behaviour from two different sequences of Hopf bifurcations involving invariant tori with four fundamental frequencies, which may be resonant. Numerical evidence of the existence of a crisis event destroying chaotic attractors and giving rise to the chaotic transients is provided. It is also shown that unstable invariant tori take part in the time evolution of these chaotic transients. For one sequence of bifurcations, the study demonstrates that chaotic transients display on–off intermittent behaviour. A possible explanatory mechanism is discussed.

Coexistence of localization and transport in many-body two-dimensional Aubry-André models

Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension substantial evidence for the existence of such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In two-dimensional disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed the avalanche instability. In quasiperiodic systems, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying the out-of-equilibrium dynamics of large systems, we find a long-lived MBL phase, in contrast to random systems. Furthermore, we show that deterministic lines of weak potential, which appear in investigated quasiperiodic models, support large-scale transport, while the system as a whole does not thermalize. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties - a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.

Efficient time-dependent orbital-free density functional theory: Semilocal adiabatic response

Orbital-free density functional theory and its time-dependent extension are efficient ab initio methods for calculating the electronic structure and dynamics of large systems. Through the calculation of the optical spectra of selected clusters, we reach three important conclusions: (1) The quality of the spectra is strongly affected by the quality of the corresponding ground-state electron density; (2) the adiabatic part of the electronic response to external perturbations can be safely evaluated at the semilocal level; and (3) the nonadiabatic, current-dependent part of the time-dependent Pauli potential is key to recover correct spectral envelopes.

A combined FD-HB approximation method for steady-state vibrations in large dynamical systems with localised nonlinearities

The approximation of steady-state vibrations within non-linear dynamical systems is well-established in academics and is becoming increasingly important in industry. However, the complexity and the number of degrees of freedom of application-oriented industrial models demand efficient approximation methods for steady-state solutions. One possible approach to that problem are hybrid approximation schemes, which combine advantages of standard methods from the literature. The common ground of these methods is their description of the steady-state dynamics of a system solely based on the degrees of freedom affected directly by non-linearity—the so-called non-linear degrees of freedom. This contribution proposes a new hybrid method for approximating periodic solutions of systems with localised non-linearities. The motion of the non-linear degrees of freedom is approximated using the Finite Difference method, whilst the motion of the linear degrees of freedom is treated with the Harmonic Balance method. An application to a chain of oscillators showing stick-slip oscillations is used to demonstrate the performance of the proposed hybrid framework. A comparison with both pure Finite Difference and Harmonic Balance method reveals a noticeable increase in efficiency for larger systems, whilst keeping an excellent approximation quality for the strongly non-linear solution parts.