Dynamical screening and ionic conductivity in water from ab initio simulations

We present a method to calculate ionic conductivities of complex fluids from ab initio simulations. This is achieved by combining density functional theory molecular dynamics simulations with polarization theory. Conductivities are then obtained via a Green-Kubo formula using time-dependent effective charges of electronically screened ions. The method is applied to two different phases of warm dense water. We observe large fluctuations in the effective charges; protons can transport effective charges greater than +e for ultrashort time scales. Furthermore, we compare our results with a simpler model of ionic conductivity in water that is based on diffusion coefficients. Our approach can be directly applied to study ionic conductivities of electronically insulating materials of arbitrary composition, e.g., complex molecular mixtures under such extreme conditions that occur deep inside giant planets.     

Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other approaches of frequency determination (e.g., based on Hilbert transform) fail. Using the method we characterize the effects of phase synchronization for systems with ill-defined phase by external forcing and due to mutual coupling.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

Dynamics of solitons under random perturbations

The dynamics of solitons is investigated in media with randomly inhomogeneous and fluctuating parameters. Some exact results of the theory of nonlinear stochastic waves are given. An analysis is made of various approximate approaches, e.g. of the mean field method and the Born approximation. Special attention is paid to the perturbation technique based on the inverse scattering transform and to the construction of the most adequate stochastic perturbation theory for solitons. The described formalism is used to investigate the evolution of nonlinear wave (soliton) parameters, and the statistical characteristics of radiation generated by solitons in fluctuating media are analysed also. The same approach makes it possible to take into account the simultaneous effect of random and regular (e.g., friction) perturbations on the dynamics of solitons. Examples are given of situations arising when one describes nonlinear waves in real physical systems.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.     

Binary Systems Around a Black Hole

We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. For this purpose, the motion equations are obtained in two different but equivalent ways. The particles can either be considered as a zeroth order (static) perturbation to the given metric or as an external Newtonian force in the geodesic equations. After obtaining the motion equations we perform simulations of two and three interacting particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and note differences in the stability, e.g., binary systems are found only in the general relativistic approach.     

Network reconstruction from binary-state time series in presence of time delay and hidden nodes

Complex networks with binary-state dynamics represent many meaningful behaviors in a variety of contexts. Reconstruction of networked systems hosting delayed binary processes with hidden nodes becomes an outstanding challenge in this field. To address this issue, we extend the statistical inference method to complex networked systems with distinct binary-state dynamics in presence of time delay and missing data. By exploiting the expectation-maximization (EM) algorithm, we implement the statistical inference based approach to different (i.e., random, small world, and scale-free) networks hosting delayed-binary processes. Our framework is completely data driven, and does not require any a prior knowledge about the detailed dynamical process on the network; especially, our method can independently infer each physical connectivity and estimate the time delay solely from the data of a pair of nodes in this link. We provide a physical understanding of the underlying mechanism; and extensive numerical simulations validate the robustness, efficiency, and accuracy of our method.     

Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications

Engineered and natural systems often involve irregular and self-similar geometric forms,which is called fractal geometry. For instance, precision machining produces a visuallyflat surface, while which looks like a rough mountain in the nanometer scale under themicroscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers,arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractalbehaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemicaletching on the surface of machined parts and electrical conduction in the heart, most ofexisting works modeled space-time dynamics (e.g., reaction, diffusion and propagation) onthe Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurateapproximation of real-world dynamics, due to sensitive dependence of nonlinear dynamicalsystems on initial conditions. In this paper, we developed novel methods and tools for thenumerical simulation and pattern recognition of spatiotemporal dynamics on fractalsurfaces of complex systems, which include (1) characterization and modeling of fractalgeometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3)recognizing and quantifying spatiotemporal patterns. Experimental results show that theproposed methods outperform traditional modeling approaches based on the Euclideangeometry, and provide effective tools to model and characterize space-time dynamics onfractal surfaces of complex systems.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Ab initio molecular dynamics with a classical pressure reservoir: simulation of pressure-induced amorphization in a Si35H36 cluster

We present a new constant-pressure ab initio molecular dynamics method suitable for studying, e.g., pressure-induced structural transformations in finite nonperiodic systems such as clusters. We immerse an ab initio treated cluster into a model classical liquid, described by a soft-sphere potential, which acts as a pressure reservoir. The pressure is varied by tuning the parameter of the liquid potential. We apply the method to a Si35H36 cluster, which undergoes a pressure-induced amorphization at approximately 35 GPa, and remains in a disordered state even upon pressure release.     

The Emergence of Temporal Structures in Dynamical Systems

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.     

Dynamical response to perturbation of critical Boolean networks

Boolean networks can be used as simple but general models for complex self-organizing systems. The freedom to choose different rules and structures of interactions makes this model applicable to a wide variety of complex phenomena. It is known that the damage dynamics in annealed Boolean systems should fall in the same universality class of the directed percolation model. In this work we present results about the behavior of this model at and near the critically ordered condition for both the annealed and the quenched versions of the model. Our study concentrates on the way the system responds to a small perturbation. We show that the characteristic correlation time, i.e., the time in which any memory of this perturbation is lost, diverges as one moves towards criticality. Exactly at the critical point, we observe that the time for returning to the natural state after the perturbation follows a power-law distribution. This indicates that most perturbations are quickly restored, while few events may have a global effect on the system, suggesting a mechanism that assures at the same time robustness and adaptability. The critical exponents obtained are in agreement with the values expected for the universality class of mean-field directed percolation both in the annealed and in the quenched Boolean network model. This gives further evidence that annealed Boolean networks may in certain conditions provide a good model for understanding the behavior of regulatory systems. Our results may give insight into the way real self-organizing systems respond to external stimuli, and why critically ordered systems are often observed in Nature.     

Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model

We investigate the quantum dynamics of repulsively bound atom pairs in an optical lattice described by the periodic Bose-Hubbard model both analytically and numerically. In the strongly repulsive limit, we analytically study the dynamical problem by the perturbation method with the hopping terms treated as a perturbation. For a finite-size system, we numerically solve the dynamic problem in the whole regime of interaction by the exact diagonalization method. Our results show that the initially prepared atom pairs are dynamically stable and the dissociation of atom pairs is greatly suppressed when the strength of the on-site interaction is much greater than the tunneling amplitude, i.e., the strongly repulsive interaction induces a self-localization phenomenon of the atom pairs.     

"Metric" complexity for weakly chaotic systems

We consider the number of Bowen sets necessary to cover a large measure subset of the phase space. This introduces some complexity indicator characterizing different kinds of (weakly) chaotic dynamics. Since in many systems its value is given by a sort of local entropy, this indicator is quite simple to calculate. We give some examples of calculations in nontrivial systems (e.g., interval exchanges and piecewise isometries) and a formula similar to that of Ruelle-Pesin, relating the complexity indicator to some initial condition sensitivity indicators playing the role of positive Lyapunov exponents.     

Isotope fractionation by thermal diffusion in silicate melts

Isotopes fractionate in thermal gradients, but there is little quantitative understanding of this effect in complex fluids. Here we present results of experiments and molecular dynamics simulations on silicate melts. We show that isotope fractionation arises from classical mechanical effects, and that a scaling relation based on Chapman-Enskog theory predicts the behavior seen in complex fluids without arbitrary fitting parameters. The scaling analysis reveals that network forming elements (Si and O) fractionate significantly less than network modifiers (e.g., Mg, Ca, Fe, Sr, Hf, and U).     

Solitons in condensed matter: A paradigm

For this new journal dealing with nonlinear phenomena we review the setting of several important current problems in the physics of condensed matter (solids, liquids). We show how the concepts embodied in the mathematical analysis of solitons provide systematic new insight (i.e., a paradigm) into a central question: what are the important physical configurations in nonlinear condensed systems? Following these general issues we summarize the analysis of the dynamics and equilibrium thermodynamics (i.e., statistical mechanics) of non-linear one-dimensional model systems, and we indicate how the solitonic configurational phenomenology provides a basis for dynamic effects which are seen both experimentally and in molecular dynamics computer simulations. Many problems in condensed matter differ from the more familiar nonlinear mechanical or hydrodynamic applications in that finite temperature thermal fluctuations must be considered along with systematic dynamics.     

Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

In this paper we discuss the control of complex spatio-temporal dynamics in a spatially extended nonlinear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A presented method is connected with stabilization of unstable homogeneous equilibrium state and the unstable spatio-temporal periodical states analogous to unstable periodic orbits of chaotic dynamics of the systems with few degrees of freedom. We show that this method is effective and allows to achieve desired regular dynamics chosen from a number of possible in the considered system.     

Shear flow pumping in open micro- and nanofluidic systems

Based on a novel interplay of wetting adhesion and concurrent flow concepts, we propose to drive open microfluidic systems by shear in a covering fluid layer, e.g., oil covering water-filled chemical channels. The advantages are simpler forcing and prevention of evaporation of volatile components. We calculate the expected throughput for straight channels and show that devices can be built with off-the-shelf technology. Molecular dynamics simulations suggest that this concept is scalable down to the nanoscale.     

Stochastic-dynamical thermostats for constraints and stiff restraints

A broad array of canonical sampling methods are available for molecular simulation based on stochastic-dynamical perturbation of Newtonian dynamics, including Langevin dynamics, Stochastic Velo- city Rescaling, and methods that combine Nosé-Hoover dynamics with stochastic perturbation. In this article we discuss several stochastic-dynamical thermostats in the setting of simulating systems with holonomic constraints. The approaches described are easily implemented and facilitate the recovery of correct canonical averages with minimal disturbance of the underlying dynamics. For the purpose of illustrating our results, we examine the numerical application of these methods to a simple atomic chain, where a Fixman term is required to correct the thermodynamic ensemble.     

Chaotic capture of vortices by a moving body. I. The single point vortex case

The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the chaotic dynamics and is similar to that of other chaotic scattering phenomena. We show numerically that cases exist where the vortex can be captured around an elliptic point external to (and possibly far from) the body, and the existence of other very complicated motions are also demonstrated. Finally, generalizations of the problem of the vortex-body interaction are indicated, and some possible applications are postulated such as the interaction of line vortices with aircraft wings.