Phase Space Dynamics Research Articles

Recent DIII-D advances in runaway electron measurement and model validation

Novel measurements and modeling of runaway electron (RE) dynamics in DIII-D have resolved experimental discrepancies and validated predictions for ITER, improving confidence that RE avoidance and mitigation can be predictably achieved. Considering RE formation, first experimental assessments of the RE seed current demonstrates that present hot-tail theories are not yet accurate and require improved treatment of the pellet dynamics. Novel measurements of kinetic instabilities in the MHz-range have been made in the RE formation phase, with the intensity of these modes correlated with previously unexplained empirical thresholds for RE generation. Controlled RE dissipation experiments in quiescent regimes have validated RE distribution function dependencies on collisional and synchrotron damping, both in terms of distribution function shape and dissipation rates. Measurements of RE bremsstrahlung and synchrotron emission are now used in tandem to resolve energy and pitch-angle effects. A resolution to long-standing dissipation anomalies in the quiescent regime is offered by taking into account kinetic instability effects on RE phase-space dynamics. Kinetic instabilities in the 100–200 MHz range are directly observed, though modeling finds the largest dissipation arises from GHz range instabilities that are beyond the reach of existing diagnostics. Kinetic instabilities are also observed in the mature post-disruption RE plateau phase, so long as the collisional damping rate is reduced with low-Z injection. Experiments with high-Z injection find that the dissipation rate saturates with injection quantity, likely due to neutral diffusion rates being slower than vertical instability rates in DIII-D. Considering the final loss, a 0D model for first-wall Joule heating is found to be in agreement with experiment, and controlled access to RE equilibria with edge safety factor of two identifies novel dynamics brought about by large-scale kink instabilities. These dynamics are typified by fast (tens of microseconds) RE loss rates without RE beam regeneration. The above measurements and comparison with theory represent significant advances in the understanding of RE dynamics and indicate possible new opportunities for RE avoidance or mitigation via kinetic instabilities.

Estimation of nonlinear surface pressure characteristics of aerofoil: A 0-1 test approach

We investigate the nonlinear behaviour of the surface flow over a two-dimensional NACA 2415 airfoil undergoing turbulent inflow having 8.46% TI at Re=3.01×105 using the 0-1 test for chaos. It clearly identifies the overall surface flow changes and also finds the transitions from regular to chaotic behaviour over the airfoil surfaces. 0-1 test for chaos has been successfully applied to study the subsequent transitions associated with the flow mechanisms like flow bifurcation at the leading-edge, acceleration of the flow that propagates from the curved surfaces, splitting, merging and rolling up of vortices near the vicinity of the trailing edge. In our present study, the 0-1 test for chaos just takes the input as a time series data, measured simultaneously over the airfoil surfaces to obtain the translational dynamics in phase space by using the variables p(n) and q(n) and the asymptotic growth rate (K) calculated from the translation behaviour of variables. The translational variables take a value 0 or 1, based on the underlying dynamics of the system as regular or chaotic. Our study states that, 0-1 test for chaos seems to be efficient in accurately predicting the underlying dynamics of the surface flow induced over the airfoil under aperiodic conditions.

Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

Although scaling relations of power law forms have been revealed in a wide variety of complex systems, the origin of scaling relations in real systems remains mostly unsolved. Based on a long tradition in physics, we here explore the phase space dynamics of business companies, whose different measures of size have been found to exhibit multiple scaling relations. Using a large scale dataset of Japanese companies covering over two million companies for over two decades (1994–2015), we compile the data of three measures of size, namely, annual sales, number of employee and number of trading partners. Tracking the historical time evolution of companies, we first show that there exists a stable region that attracts most of the data points in the long time scale, although the company dynamics in the three-dimensional phase space looks random in a shorter time scale. We then elaborate on ‘evolving flow diagrams’ of the averaged motion in the 3D space. Remarkably, the flow diagrams indicate that a 3D curve which represents the scaling relations between the three size measures can be regarded as an approximate attractor of the averaged flows. The results could serve for better modeling and understanding of companies dynamics and our method can be applied to other dynamics such as social and biological phenomena.

Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics

In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and thus remains valid beyond shell-crossing. Here, we present an exact reformulation of the KFT framework that allows to resum an infinite subset of terms appearing in the original perturbative expansion of KFT. We develop the general formalism of this resummed KFT, including a diagrammatic language for the resummed perturbation theory, and compute the lowest-order results for the power spectra of the dark matter density contrast and momentum density. This allows us to derive analytically how the linear growth of the largest structures emerges from Newtonian particle dynamics alone, which, to our knowledge, is the first time this has been achieved.

Emotion recognition through EEG phase space dynamics and Dempster-Shafer theory

Emotions play an important role in our life. Emotion recognition which is considered a subset of brain computer interface (BCI), has drawn a great deal of attention during recent years. Researchers from different fields have tried to classify emotions through physiological signals. Nonlinear analysis has been reported to be successful and effective in emotion classification due to the nonlinear and non-stationary behavior of biological signals. In this study, phase space reconstruction and Poincare planes are employed to describe the dynamics of electroencephalogram (EEG) in emotional states. EEG signals are taken from a reliable database and phase space is reconstructed. A new transformation is introduced in order to quantify the phase space. Dynamic characteristics of the new space are considered as features. Most significant features are selected and samples are classified into four groups including high arousal – high valence (HAHV), low arousal – high valence (LAHV), high arousal – low valence (HALV) and low arousal – low valence (LALV). Classification accuracy was about 90% on average. Results suggest that the proposed method is successful and classification performance is good in comparison with most studies in this field. Brain activity is also reported with respect to investigating brain function during emotion elicitation. We managed to introduce a new way to analyze EEG phase space. The proposed method is applied in a real world and challenging application (i.e. emotion classification). Not only does the proposed method describe EEG changes due to different emotional states but also it is able to represent new characteristics of complex systems. The suggested approach paves the way for researchers to analyze and understand more about chaotic signals and systems.

Explaining Homeopathy with Quantum Electrodynamics.

Every living organism is an open system operating far from thermodynamic equilibrium and exchanging energy, matter and information with an external environment. These exchanges are performed through non-linear interactions of billions of different biological components, at different levels, from the quantum to the macro-dimensional. The concept of quantum coherence is an inherent property of living cells, used for long-range interactions such as synchronization of cell division processes. There is support from recent advances in quantum biology, which demonstrate that coherence, as a state of order of matter coupled with electromagnetic (EM) fields, is one of the key quantum phenomena supporting life dynamics. Coherent phenomena are well explained by quantum field theory (QFT), a well-established theoretical framework in quantum physics. Water is essential for life, being the medium used by living organisms to carry out various biochemical reactions and playing a fundamental role in coherent phenomena. Quantum electrodynamics (QED), which is the relativistic QFT of electrodynamics, deals with the interactions between EM fields and matter. QED provides theoretical models and experimental frameworks for the emergence and dynamics of coherent structures, even in living organisms. This article provides a model of multi-level coherence for living organisms in which fractal phase oscillations of water are able to link and regulate a biochemical reaction. A mathematical approach, based on the eigenfunctions of Laplace operator in hyper-structures, is explored as a valuable framework to simulate and explain the oneness dynamics of multi-level coherence in life. The preparation process of a homeopathic medicine is analyzed according to QED principles, thus providing a scientific explanation for the theoretical model of "information transfer" from the substance to the water solution. A subsequent step explores the action of a homeopathic medicine in a living organism according to QED principles and the phase-space attractor's dynamics. According to the developed model, all levels of a living organism-organelles, cells, tissues, organs, organ systems, whole organism-are characterized by their own specific wave functions, whose phases are perfectly orchestrated in a multi-level coherence oneness. When this multi-level coherence is broken, a disease emerges. An example shows how a homeopathic medicine can bring back a patient from a disease state to a healthy one. In particular, by adopting QED, it is argued that in the preparation of homeopathic medicines, the progressive dilution/succussion processes create the conditions for the emergence of coherence domains (CDs) in the aqueous solution. Those domains code the original substance information (in terms of phase oscillations) and therefore they can transfer said information (by phase resonance) to the multi-level coherent structures of the living organism. We encourage that QED principles and explanations become embodied in the fundamental teachings of the homeopathic method, thus providing the homeopath with a firm grounding in the practice of rational medicine. Systematic efforts in this direction should include multiple disciplines, such as quantum physics, quantum biology, conventional and homeopathic medicine and psychology.

A novel EEG-based approach to classify emotions through phase space dynamics

Emotion recognition has drawn a great deal of attention in brain computer interface field. Researches have come to the conclusion that nonlinear features are more successful in emotion classification because of non-stationary and chaotic behavior of biological signals, especially electroencephalogram (EEG). In this study, a new method based on phase space dynamics and Poincare sections is introduced to classify emotions. This transformation quantifies the phase space and represents its characteristics in a new state space which can simply reflect the signal behavior. Not only are the proposed state space and quantifiers effective to appropriately describe nonlinear signal dynamics, but also this method successfully works in real-world applications like EEG-based emotion recognition. In this work, EEGs are transformed into the new state space and Poincare intersections are considered as features with the aim of classifying EEGs into four emotional groups based on arousal and valence values. A reliable dataset is used, and classification accuracy is about 82%. As results suggest, the proposed method and features are efficient in this task in comparison with previous studies employing the same dataset.

Constructing phase space distributions with internal symmetries

We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general extension of the Wigner phase space distribution to include color and spin degrees of freedom in terms of dynamical Grassmann variables. The corresponding Liouville distribution for colored particles, which obey Wong's equation, has only singlet and octet components, while higher moments are fully constrained by the Grassmann algebra. The extension of phase space dynamics to spin is represented by a generalization of the Pauli-Lubanski vector; its time evolution via the Bargmann-Michel-Telegdi equation also follows from the phase space trajectories of the underlying Grassmann coordinates. Our results for the Liouville phase space distribution in systems with both spin and color are of interest in fields as diverse as chiral fluids, finite temperature field theory and polarized parton distribution functions. We also comment on the role of the chiral anomaly in the phase space dynamics of spinning particles.

Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems.

Simulating electron-nucleus coupled dynamics poses a nontrivial challenge and an important problem in the investigation of ultrafast processes involving coupled electronic and vibrational dynamics. Because irreversibility of the system dynamics results from thermal activation and dissipation caused by the environment, in dynamical studies, it is necessary to include heat bath degrees of freedom in the total system. When the system dynamics involves high-energy electronic transitions, the environment is regarded to be in a low-temperature regime and we must treat it quantum mechanically. In this Article, we present rigorous and versatile approaches for investigating the dynamics of open systems with coupled electronic and vibrational degrees of freedom within a fully quantum mechanical framework. These approaches are based on a quantum Fokker-Planck equation and a quantum Smoluchowski equation employing a heat bath with an Ohmic spectral density, with non-Markovian low-temperature correction terms, and extensions of these equations to the case of multistate systems. The accuracy of these equations was numerically examined for a single-state Brownian system, while their applicability was examined for multistate double-well systems by comparing their results with those of the fewest-switch surface hopping and Ehrenfest methods with a classical Markovian Langevin force. Comparison of the transient absorption spectra obtained using these methods clearly reveals the importance of the quantum low-temperature correction terms. These equations allow us to treat nonadiabatic dynamics in an efficient way, while maintaining numerical accuracy. The C++ source codes that we developed, which allow for the treatment of the phase and coordinate space dynamics with any single-state or multistate potential forms, are provided as Supporting Information.

Dynamic Shear Suppression in Quantum Phase Space.

Classical phase space flow is inviscid. Here we show that in quantum phase space Wigner's probability current J can be effectively viscous. This results in shear suppression in quantum phase space dynamics which enforces Zurek's limit for the minimum size scale of spotty structures that develop dynamically. Quantum shear suppression is given by gradients of the quantum terms of J's vorticity. Used as a new measure of quantum dynamics applied to several evolving closed conservative 1D bound state systems, we find that shear suppression explains the saturation at Zurek's scale limit and additionally singles out special quantum states.

Traveling wave solutions to a neural field model with oscillatory synaptic coupling types.

In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay, and biologically motivated oscillatory coupling types. Neuronal tracing studies show that long-ranged excitatory connections form stripe-like patterns throughout the mammalian cortex; thus, we aim to generalize the notions of pure excitation, lateral inhibition, and lateral excitation by allowing coupling types to spatially oscillate between excitation and inhibition. With fronts as our main focus, we exploit Heaviside firing rate functions in order to establish existence and utilize speed index functions with at most one critical point as a tool for showing uniqueness of wave speed. We are able to construct Evans functions, the so-called stability index functions, in order to provide positive spectral stability results. Finally, we show that by incorporating slow linear feedback, we can compute fast pulses numerically with phase space dynamics that are similar to their corresponding singular homoclinical orbits.

Non-linear forecasting of the state of a socio-eco-oriented innovative economy in the conditions of systemic crises

The paper deals with the problem of sustainable development and innovative integral modeling and forecasting approach in the management of technogenic objects and processes (TOP) as a system of socio-eco-economic and humanitarian type (SEEH). Based on the use of information and innovation technologies in order to forecast the non-linear dynamics of eco-economic and socio-humanitarian systems, integrated stochastic models of objects and processes were developed and studied, suitable for the conditions of systemic crises. The paper handles the aspect of integration of 4 business and functioning areas of the modern complex systems. It proposes a general conceptual integrated model, generalized synergetic model of dynamics, considering different uncertainty (stochastic and chaotic components). The paper examines the aspects of integration of multiple business areas and sectors of the modern complex systems functioning and developing under the present conditions of non-linearity, instability and crises. An integrated stochastic non-linear phase-space growth dynamics model was developed and studied to forecast the development of the state of an innovative economy. The paper looks into the aspects of activity management of the modern complex systems functioning and developing under the present conditions of instability.

Phase-space quantum profile of Pöschl-Teller two-level systems

The quantum phase-space dynamics driven by hyperbolic P\"oschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited states exhibit some non-classical and non-linear patterns which are theoretically tested and quantified according to a non-gaussian continuous variable framework. It comprises the computation of quantifiers of non-classicality for an anharmonic two-level system where non-Liouvillian features are identified through the phase-space portrait of quantum fluctuations. In particular, the associated non-gaussian profiles are quantified by measures of {\em kurtosis} and {\em negative entropy}. As expected from the PT {\em quasi}-harmonic profile, our results suggest that quantum wells can work as an experimental platform that approaches the gaussian behavior in the investigation of the interplay between classical and quantum scenarios. Furthermore, it is also verified that the Wigner representation admits the construction of a two-particle bipartite quantum system of continuous variables, $A$ and $B$, identified by $\sum_{i,j=0,1}^{i\neq j}\vert i_{_A}\rangle\otimes\vert j_{_B}\rangle$, which are shown to be separable under gaussian and non-gaussian continuous variable criteria.

Phase-space dynamics of opposition control in wall-bounded turbulent flows

We investigate the nonlinear phase-space dynamics of plane Couette flow and plane Poiseuille flow under the action of opposition control at low Reynolds numbers in domains close to the minimal unit. In Couette flow, the effect of the control is analysed by focussing on a pair of non-trivial equilibrium solutions. It is found that the control only slightly modifies the statistics, turbulent skin friction and phase-space projection of the lower-branch equilibrium solution, which, in this case, is in fact identical to the edge state. On the other hand, the upper-branch equilibrium solution and mean turbulent state are modified considerably when the control is applied. In phase space, they gradually approach the lower-branch equilibrium solution on increasing the control amplitude, and this results in an elevation of the critical Reynolds number at which the equilibrium solutions first occur via a saddle-node bifurcation. It is also found that the upper-branch equilibrium solution is stabilised by the control. In Poiseuille flow, we study an unstable periodic orbit on the edge state and find that it, too, is modified very little by opposition control. We again observe that the turbulent state gradually approaches the edge state in phase space as the control amplitude is increased. In both flows, we find that the control significantly reduces the fluctuating strength of the turbulent state in phase space. However, the reduced distance between the turbulent trajectory and the edge state yields a significant reduction in turbulence lifetimes for both Couette and Poiseuille flow. This demonstrates that opposition control greatly increases the probability of the trajectory escaping from the turbulent state, which takes the form of a chaotic saddle.

Kinetic Model of Translational Autoregulation.

We investigate the dynamics of a kinetic model of inhibitory autoregulation as exemplified when a protein inhibits its own production by interfering with its mRNA, known in molecular biology as translational autoregulation. We first show how linear models without feedback set the stage with a nonequilibrium steady state that constitutes the target of the regulation. However, regulation in the simple linear model is far from optimal. The negative feedback mechanism whereby the protein "jams" the mRNA greatly enhances the effectiveness of the control, with response to perturbation that is targeted, rapid, and metabolically efficient. Understanding the full dynamics of the system phase space is essential to understanding the autoregulation process.

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

The Relation between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares

Abstract A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the acceleration and transport mechanisms at work. This Letter addresses this general problem, in particular in solar flares, where in addition to scattering by turbulence, the magnetic field convergence from the acceleration region toward its boundaries also influences the particle escape. We test an (approximate) analytic relation between escape and scattering times, and the field convergence rate, based on the work of Malyshkin & Kulsrud, valid for both strong and weak diffusion limits and isotropic pitch-angle distributions of the injected particles, with a numerical model of particle transport. To this end, a kinetic Fokker–Planck transport model of particles is solved with a stochastic differential equation scheme, assuming different initial pitch-angle distributions. This approach enables further insights into the phase-space dynamics of the transport process, which would otherwise not be accessible. We find that in general the numerical results agree well with the analytic equation for the isotropic case; however, there are significant differences in the weak diffusion regime for non-isotopic cases, especially for distributions beamed along the magnetic field lines. The results are important in the interpretation of observations of energetic particles in solar flares and other similar space and astrophysical acceleration sites, and for the determination of acceleration-transport coefficients, commonly used in Fokker–Planck–type kinetic equations.

Homoclinic chaos and its organization in a nonlinear optics model

We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary representations that lets one detect regions of simple and complex dynamics as well as fine organization structures of the latter in parameter space. Massively parallel simulations shorten the computational time to disclose highly detailed bifurcation diagrams to a few seconds.

Synchronous detection of longitudinal and transverse bunch signals at a storage ring

To understand and control the dynamics in the longitudinal phase space, time-resolved measurements of different bunch parameters are required. For a reconstruction of this phase space, the detector systems have to be synchronized. This reconstruction can be used e.g. for studies of the micro-bunching instability. It occurs if the interaction of the bunch with its own radiation leads to the formation of sub-structures on the longitudinal bunch profile. These sub-structures can grow rapidly -- leading to a sawtooth-like behaviour of the bunch. At KARA, we use a fast-gated intensified camera for energy spread studies, Schottky diodes for coherent synchrotron radiation studies as well as electro-optical spectral decoding for longitudinal bunch profile measurements. For a synchronization, a hardware synchronization scheme is used which compensates for eventual hardware delays. In this paper, the different experimental setups and their synchronization are discussed and first results of synchronous measurements are presented.

Propagation direction of geodesic acoustic modes driven by drift wave turbulence

Selection rule of the radial propagation direction of geodesic acoustic modes (GAMs) is investigated. Here, we study the influence of nonlinear coupling with drift wave turbulence on the propagation direction of GAMs. Based on wave-kinetic equation for the turbulence, the phase-space dynamics is numerically solved and the nonlinear saturated states are obtained, where the phase-space consists of the real space and the wavenumber space. A wave pattern of the GAM in a nonlinear saturated state varies to form a standing wave, outward and inward propagating waves, depending on the peak radial wavenumber of the turbulence. The impact of nonlinear coupling with turbulence is discussed by deriving the GAM dispersion relation that includes the effect of the turbulence.