arXiv subjects

Zhixin Lu

Publications and source records attributed to Zhixin Lu.

33 records · Page 2Linked to original sources

arXiv2022

Full $f$ and $δf$ gyrokinetic particle simulations of Alfvén waves and energetic particle physics

In this work, we focus on the development of the particle-in-cell scheme and the application to the studies of Alfvén waves and energetic particle physics in tokamak plasmas. The $δf$ and full $f$ schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code [Lu et al. J. Comput. Phys. 440 (2021) 110384] has been upgraded using cubic spline finite elements and full $f$ and $δf$ schemes. The EP-driven TAE has been simulated for the ITPA-TAE case featured by a small electron skin depth $\sim 1.18\times10^{-3}\;{\rm m}$, which is a challenging parameter regime of electromagnetic simulations, especially for the full $f$ model. The simulation results using the $δf$ scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full $f$ and $δf$ schemes. Simulations with mixed full $f$ EPs and $δf$ electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full $f$ scheme is a natural choice for EP physics studies which allows a large variation of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.

physics.plasm-ph↗

arXiv2022

One dimensional reduced model for ITER relevant energetic particle transport

We set up a mapping procedure able to translate the evolution of the radial profile of fast ions, interacting with Toroidal Alfvén Eigenmodes, into the dynamics of an equivalent one dimensional bump-on-tail system. We apply this mapping technique to reproduce ITER relevant simulations, which clearly outlined deviations from the diffusive quasi-linear (QL) model. Our analysis demonstrates the capability of the one-dimensional beam-plasma dynamics to predict the relevant features of the non-linear hybrid LIGKA/HAGIS simulations. In particular, we clearly identify how the deviation from the QL evolutive profiles is due to the presence of avalanche processes. A detailed analysis regarding the reduced dimensionality is also addressed, by means of phase-space slicing based on constants of motion. In the conclusions, we outline the main criticalities and outcomes of the procedure, which must be satisfactorily addressed to make quantitative prediction on the observed outgoing fluxes in a Tokamak device.

physics.plasm-ph↗

arXiv2021

An E & B Gyrokinetic Simulation Model for Kinetic Alfvén Waves inTokamak Plasmas

The gyrokinetic particle simulation serves as a powerful tool for the studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general and comprehensive form and has been implemented in simulating kinetic Alfvén waves in uniform plasma [Chen et al, Science China Phys. Mechanics & Astronomy 64 (2021)]. In our work, the Chen et al. GK-E&B model has been expressed in general tokamak geometry explicitly using specific coordinates. Its reduction to the uniform plasma is verified and the numerical results show good agreement with the work by Chen et al. The theoretical dispersion relation and numerical results in the local screw pinch model are in excellent agreement. Numerical results show excellent performance in a realistic parameter regime of burning plasmas in terms of high values of $β/( M_e k_\perp^2 ρ_i^2)$, which is challenging for traditional methods due to the ``cancellation' problem. As one application, the GK-E&B model is implemented with kinetic electrons in the local limit. With the matched ITPA-TAE parameters, numerical results show the capability of the GK-E&B in treating the parallel electron Landau damping for realistic tokamak plasma parameters. As another application, the global GK-E&B model is implemented with the dominant electron contribution to $E_\|$ in the cold electron limit. Its capability in simulating the finite $E_\|$ due to the finite electron mass is demonstrated.

physics.plasm-ph↗

arXiv2021

Gyrokinetic simulations of electric current generation in ion temperature gradient driven turbulence

Gyrokinetic simulations in the collisionless limit demonstrate the physical mechanisms and the amplitude of the current driven by turbulence. Simulation results show the spatio-temporal variation of the turbulence driven current and its connection to the divergence of the Reynolds stress and the turbulence acceleration. Fine structures (a few ion Larmor radii) of the turbulence induced current are observed near the rational surfaces with the arbitrary wavelength solver of the quasi-neutrality equation. The divergence of the Reynolds stress plays a major role in the generation of these fine structures. The so-called "spontaneous" current is featured with large local magnitude near the rational surfaces.

physics.plasm-ph↗

arXiv2021

Learning Continuous Chaotic Attractors with a Reservoir Computer

Neural systems are well known for their ability to learn and store information as memories. Even more impressive is their ability to abstract these memories to create complex internal representations, enabling advanced functions such as the spatial manipulation of mental representations. While recurrent neural networks (RNNs) are capable of representing complex information, the exact mechanisms of how dynamical neural systems perform abstraction are still not well-understood, thereby hindering the development of more advanced functions. Here, we train a 1000-neuron RNN -- a reservoir computer (RC) -- to abstract a continuous dynamical attractor memory from isolated examples of dynamical attractor memories. Further, we explain the abstraction mechanism with new theory. By training the RC on isolated and shifted examples of either stable limit cycles or chaotic Lorenz attractors, the RC learns a continuum of attractors, as quantified by an extra Lyapunov exponent equal to zero. We propose a theoretical mechanism of this abstraction by combining ideas from differentiable generalized synchronization and feedback dynamics. Our results quantify abstraction in simple neural systems, enabling us to design artificial RNNs for abstraction, and leading us towards a neural basis of abstraction.

cs.NE↗

arXiv2021

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of Reversed Shear Alfvén Eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with Energetic Particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression $A(s)=e^{- σ(s-s_0)^2}$ with complex parameters $σ$ and $s_0$, where $s$ is the normalized radial coordinate. The mode structure is distorted in opposite {manners} when the EP drive shifted from one side of $q_{min}$ to the other side, and specifically, a non-zero average radial wave number $\langle k_s\rangle$ with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number $\langle k_s\rangle$, corresponding to different initial EP density profiles with EP drive shifted away from the $q_{min}$.

physics.plasm-ph↗

arXiv2021

Effects of anisotropic energetic particles on zonal flow residual level

In tokamak plasmas, the interaction among the micro-turbulence, zonal flows (ZFs) and energetic particles (EPs) can affect the turbulence saturation level and the consequent confinement quality and thus, is important for future burning plasmas. In this work, the EP anisotropy effects on the ZF residual level are studied by using anisotropic EP distributions with dependence on pitch. Significant effects on the long wavelength ZFs have been found when small to moderate width around the dominant pitch in the EP distribution function is assumed. In addition, it is found that ZF residual level is enhanced by barely passing/trapped and/or deeply trapped EPs, but it is suppressed by well passing and/or intermediate trapped EPs. Numerical calculation shows that for ASDEX Upgrade plasmas, typical EP distribution functions can bring in -3%~+5.5% mitigation/enhancement in ZF residual level, depending on the EP distribution functions.

physics.plasm-ph↗

arXiv2020

Path-dependent Dynamics Induced by Rewiring Networks of Inertial Oscillators

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when network structure is time-varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain can exhibit these properties simultaneously. How does the rewiring of network connectivity affect synchronization in systems with multistability, where different paths of network evolution may differentially impact system dynamics? To address this question, we study the effects of time-evolving network topology on coupled Kuramoto oscillators with inertia. We show that hysteretic synchronization behavior occurs when the network density of coupled inertial oscillators is slowly varied as the dynamics evolve. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony, and that these changes remain after the network returns to its initial configuration and are robust to a wide range of network perturbations. Our findings suggest that the specific progression of network topology, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

nlin.AO↗

arXiv2020

Teaching Recurrent Neural Networks to Modify Chaotic Memories by Example

The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems perform analogous functions despite flexible organization and unstructured sensory input. Recent efforts have made progress in modeling the representation and recall of information in neural systems. However, precisely how neural systems learn to modify these representations remains far from understood. Here we demonstrate that a recurrent neural network (RNN) can learn to modify its representation of complex information using only examples, and we explain the associated learning mechanism with new theory. Specifically, we drive an RNN with examples of translated, linearly transformed, or pre-bifurcated time series from a chaotic Lorenz system, alongside an additional control signal that changes value for each example. By training the network to replicate the Lorenz inputs, it learns to autonomously evolve about a Lorenz-shaped manifold. Additionally, it learns to continuously interpolate and extrapolate the translation, transformation, and bifurcation of this representation far beyond the training data by changing the control signal. Finally, we provide a mechanism for how these computations are learned, and demonstrate that a single network can simultaneously learn multiple computations. Together, our results provide a simple but powerful mechanism by which an RNN can learn to manipulate internal representations of complex information, allowing for the principled study and precise design of RNNs.

cond-mat.dis-nn↗

arXiv2020

Supervised Chaotic Source Separation by a Tank of Water

Whether listening to overlapping conversations in a crowded room or recording the simultaneous electrical activity of millions of neurons, the natural world abounds with sparse measurements of complex overlapping signals that arise from dynamical processes. While tools that separate mixed signals into linear sources have proven necessary and useful, the underlying equational forms of most natural signals are unknown and nonlinear. Hence, there is a need for a framework that is general enough to extract sources without knowledge of their generating equations, and flexible enough to accommodate nonlinear, even chaotic, sources. Here we provide such a framework, where the sources are chaotic trajectories from independently evolving dynamical systems. We consider the mixture signal as the sum of two chaotic trajectories, and propose a supervised learning scheme that extracts the chaotic trajectories from their mixture. Specifically, we recruit a complex dynamical system as an intermediate processor that is constantly driven by the mixture. We then obtain the separated chaotic trajectories based on this intermediate system by training the proper output functions. To demonstrate the generalizability of this framework \emph{in silico}, we employ a tank of water as the intermediate system, and show its success in separating two-part mixtures of various chaotic trajectories. Finally, we relate the underlying mechanism of this method to the state-observer problem. This relation provides a quantitative theory that explains the performance of our method, such as why separation is difficult when two source signals are trajectories from the same chaotic system.

eess.SP↗

arXiv2019

Invertible generalized synchronization: A putative mechanism for implicit learning in biological and artificial neural systems

Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their governing equations. The brain is able to learn the dynamic nature of the physical world via experience; analogously, artificial neural systems can learn the long-term behavior of complex dynamical systems from data. Yet, precisely how this implicit learning occurs remains unknown. Here, we draw inspiration from human neuroscience and from reservoir computing to propose a first-principles framework explicating putative mechanisms of implicit learning. Specifically, we show that an arbitrary dynamical system implicitly learns other dynamical attractors by embedding them into its own phase space through invertible generalized synchronization. By sustaining the embedding through fine-tuned feedback loops, the arbitrary dynamical system can imitate the attractor dynamics it has learned. To evaluate the mechanism's relevance, we construct several distinct neural network models that adaptively learn and imitate multiple attractors. We observe and explain the emergence of 5 distinct phenomena reminiscent of cognitive functions: (i) imitating a dynamical system purely from learning the time series, (ii) learning multiple attractors by a single system, (iii) switching among the imitations of multiple attractors, either spontaneously or driven by external cues, (iv) filling-in missing variables from incomplete observations of a learned dynamical system, and (v) deciphering superimposed input from different dynamical systems. Collectively, our findings support the notion that artificial and biological neural networks can learn the dynamic nature of their environment, and systems within their environment, through the mechanism of invertible generalized synchronization.

q-bio.NC↗

arXiv2019

Design of Large Sequential Conformational Change in Mechanical Networks

From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the form of links that transmit forces between constituent elements. However, the principled design of specific movements is made difficult by the number and nonlinearity of interactions. Here, we model mechanical systems as linkages of rigid bonds (edges) connected by joints (nodes), and formulate a simple but powerful framework for designing full nonlinear coordinated motions using concepts from dynamical systems theory. We begin with principles for designing finite and infinitesimal motions in small modules, and show that each module is a one-dimensional map between distances across pairs of nodes. Next, we represent the act of combining modules as an iteration of this map, and design networks whose geometries reflect the map's fixed points, limit cycles, and chaos. We use this representation to design different folding sequences from a deployable network and a soliton, to a branched network acting as a mechanical AND gate. Finally, we design large changes in curvature of the entire network, and construct physical networks from laser-cut acrylic, origami, and 3D printed material to demonstrate the framework's potential and versatility for designing the full conformational trajectory of morphing metamaterials and structures.

cond-mat.soft↗

arXiv2018

Attractor Reconstruction by Machine Learning

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes conditions under which reservoir computing can create an empirical model capable of skillful short-term forecasts and accurate long-term ergodic behavior. We illustrate this theory through numerical experiments. We also argue that the theory applies to certain other machine learning methods for time series prediction.

nlin.CD↗

arXiv2018

Conformational Control of Mechanical Networks

Understanding conformational change is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes and tunable metamaterials. Of particular interest is the relationship between the network topology or geometry and the specific motions observed under controlling perturbations. We study this relationship in mechanical networks of 2-D and 3-D Maxwell frames composed of point masses connected by rigid rods rotating freely about the masses. We first develop simple principles that yield all bipartite network topologies and geometries that give rise to an arbitrarily specified instantaneous and finitely deformable motion in the masses as the sole non-rigid body zero mode. We then extend these principles to characterize networks that simultaneously yield multiple specified zero modes, and create large networks by coupling individual modules. These principles are then used to characterize and design networks with useful material (negative Poisson ratio) and mechanical (targeted allosteric response) functions.

physics.comp-ph↗

arXiv2017

Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data

We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a 'reservoir'. After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the 'output weights'. The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's 'climate'. Since the reservoir equations and output weights are known, we can compute derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system, and the Kuramoto-Sivashinsky (KS) equation. In particular, we use the Lorenz system to show that achieving climate reproduction may require tuning of the reservoir parameters. For the case of the KS equation, we note that as the system's spatial size is increased, the number of Lyapunov exponents increases, thus yielding a challenging test of our method, which we find the method successfully passes.

nlin.CD↗