Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110)

Imaging of ultrafast photoexcited electron dynamics in pentacene nanocrystals on a graphite substrate

Understanding molecular film growth on substrates and the ultrafast electron dynamics at their interface is crucial for advancing next-generation organic electronics. We have focused on studying the ultrafast photoexcited electron dynamics in nanoscale organic crystals of an aromatic molecule, pentacene, on a two-dimensional material of graphite substrate. Through the use of time-resolved two-photon photoelectron emission microscopy (2P-PEEM), we have visualized the ultrafast lateral evolution of photoexcited electrons. By resonantly tuning the incident photon to excite pentacene molecules, polarization-dependent 2P-PEEM has revealed that pentacene nanocrystals (sub- to several μm) on the substrate exhibit a preferential orientation, in which a molecular π-orbital contacts the substrate in a "lying flat" orientation, facilitating electron transfer to the substrate. The time-resolved 2P-PEEM captures the motion of excited electrons in a femto- to pico-second timescale, clearly imaging the ultrafast charge transfer and lateral expansion two-dimensionally on the graphite substrate. Moreover, we found that the lying-flat molecular orientation of pentacene nanocrystals is transformable into a "standing-up" one through gentle heating up to 50 °C. These experimental insights using time-resolved 2P-PEEM will be highly valuable in enhancing the photofunctionalities of organic electronic devices by controlled molecular deposition.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Production of Noble-Metal Nanohelices Based on Nonlinear Dynamics in Electrodeposition of Binary Copper Alloys

Spatiotemporal pattern formation is dynamic self-organization widely observed in nature and drives various functions. Among these functions, chirality plays a central role. The relationship between dynamic self-organization and chirality has been an open question; therefore, the production of chiral nanomaterials by dynamic self-organization has not been achieved. Here, we show that the confinement of a two-dimensional spatiotemporal micropattern via the electrodeposition of a binary Cu alloy into a nanopore induces mirror symmetry breaking to produce a helical nanostructure of the noble-metal component although it is still not yet possible to control the handedness at this stage. This result suggests that spatiotemporal symmetry breaking functions as a mirror symmetry breaking if cylindrical pores are given as the boundary condition. This study can be a model system of how spatiotemporal symmetry breaking plays a role in mirror symmetry breaking, and it proposes a new approach to producing helical nanomaterials through dynamic self-organization.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

Co Loading Adjustment for the Effective Obtention of a Sedative Drug Precursor through Efficient Continuous-Flow Chemoselective Hydrogenation of 2-Methyl-2-Pentenal

This work presents the effect of Co loading on the performance of CNR115 carbon-supported catalysts in the continuous-flow chemoselective hydrogenation of 2-methyl-2-pentenal for the obtention of 2-methylpentanal, an intermediate in the synthesis of the sedative drug meprobamate. The Co loading catalysts (2, 6, 10, and 14 wt.%) were characterized by Brunauer–Emmett–Teller (BET) surface area analysis, transmission electron microscopy (TEM), H2 temperature-programmed reduction (H2-TPR), temperature-programmed desorption of hydrogen (H2-TPD) analysis, X-ray diffraction (XRD), and X-ray photoelectron spectroscopy for selected samples, and have been studied as hydrogenation catalysts at different pressure and temperature ranges. The results reveal that a certain amount of Co is necessary to achieve significant conversion values. However, excessive loading affects the morphological parameters, such as the surface area available for hydrogen adsorption and the particle size, preventing an increase in conversion, despite the increased presence of Co. Moreover, the larger particle size, caused by increasing the loading, alters the chemoselectivity, favouring the formation of 2-methyl-2-pentenol and, thus, decreasing the selectivity towards the desired product. The 6 wt.% Co-loaded material demonstrates the best catalytic performance, which is related to the formation of NPs with optimum size. Almost 100% selectivity towards 2-methylpentanal was obtained for the catalysts with lower Co loading (2 and 6 wt.%).

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors: synchronization, desynchronization, and oscillation quenching. However, analyzing all of these transitions within a single theoretical framework is difficult, and thus the feedback effect is only partially understood in each framework. Herein, we analyze a model of globally coupled phase oscillators exposed to global feedback, which shows all of the typical macroscopic dynamical states. Analytical tractability of the model enables us to obtain detailed phase diagrams where transitions and bistabilities between different macroscopic states are identified. Additionally, we propose strategies to steer the oscillators into targeted states with minimal feedback strength. Our study provides a useful overview of the effect of global feedback and is expected to serve as a benchmark when more sophisticated feedback needs to be designed.

Continuous 2-Methyl-3-butyn-2-ol Selective Hydrogenation on Pd/γ-Al2O3 as a Green Pathway of Vitamin A Precursor Synthesis

In this work, the effect of pretreatment conditions (10% H2/Ar flow rate 25 mL/min and 400 °C, 3 h or 600 °C, 17 h) on the catalytic performance of 1 wt.% Pd/γ-Al2O3 has been evaluated for hydrogenation of 2-methyl-3-butyn-2-ol in continuous-flow mode. Two palladium catalysts have been tested under different conditions of pressure and temperature and characterized using various physicochemical techniques. The catalytic performance of red(400 °C)-Pd/γ-Al2O3 and red(600 °C)-Pd/γ-Al2O3 are affected by the coexistence of several related factors like the competition between PdH and PdCx formation during the reaction, structure sensitivity, hydrogen spillover to the alumina support and presence or absence of Pd–Al species. High-temperature reduction leads to formation of Pd–Al species in addition to pure Pd. The Pd–Al species which reveal unique electronic properties by decreasing the Pdδ− surface concentration via electron transfer from Pd to Al, leading to a weaker Pd–Alkyl bonding, additionally assisted by the hydrogen spillover, are the sites of improved semi-hydrogenation of 2-methyl-3-butyn-2-ol towards 2-methyl-3-buten-2-ol (97%)—an important intermediate for vitamin A synthesis.

How a Quantum Computer Could Solve a Microkinetic Model

A CO oxidation microkinetic model is set up for a quantum circuit. The CO oxidation microkinetic model, and microkinetic models in general, exhibit an advantage of not requiring an encoding step because of being a subclass of systems of equations. The microkinetic model is cast as a nonlinear set of equations at first. Then, a linearizing approximation is made, and the resulting linear set of equations may be iterated to converge to the solution to the nonlinear set of equations. In this CO oxidation, the linearized set of equations is realized to chemical accuracy with one iteration. Current limitations in executing the quantum circuit to obtain the solution are discussed.

Potassium-incorporated manganese oxide enhances the activity and durability of platinum catalysts for low-temperature CO oxidation

Potassium-incorporated manganese oxide is demonstrated as an efficient support for fabricating highly active and stable Pt catalysts for low-temperature CO oxidation.

Cancer: A turbulence problem

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Application of nonlinear dynamics to cancer ecosystems.

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Chemical turbulence and strange attractor models in tumor growth, invasion and pattern formation are investigated.

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Computational algorithms for detecting such structures are proposed.

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Complex systems applications to cancer dynamics.

Cancers are complex, adaptive ecosystems. They remain the leading cause of disease-related death among children in North America. As we approach computational oncology and Deep Learning Healthcare, our mathematical models of cancer dynamics must be revised. Recent findings support the perspective that cancer-microenvironment interactions may consist of chaotic gene expressions and turbulent protein flows during pattern formation. As such, cancer pattern formation, protein-folding and metastatic invasion are discussed herein as processes driven by chemical turbulence within the framework of complex systems theory. To conclude, cancer stem cells are presented as strange attractors of the Waddington landscape.

Delayed global feedback in the genesis and stability of spatiotemporal excitation patterns in paced biological excitable media

Biological excitable media, such as cardiac or neural cells and tissue, exhibit memory in which a change in the present excitation may affect the behaviors in the next excitation. For example, a change in calcium (Ca2+) concentration in a cell in the present excitation may affect the Ca2+ dynamics in the next excitation via bi-directional coupling between voltage and Ca2+, forming a delayed feedback loop. Since the Ca2+ dynamics inside the excitable cells are spatiotemporal while the membrane voltage is a global signal, the feedback loop is then a delayed global feedback (DGF) loop. In this study, we investigate the roles of DGF in the genesis and stability of spatiotemporal excitation patterns in periodically-paced excitable media using mathematical models with different levels of complexity: a model composed of coupled FitzHugh-Nagumo units, a 3-dimensional physiologically-detailed ventricular myocyte model, and a coupled map lattice model. We investigate the dynamics of excitation patterns that are temporal period-2 (P2) and spatially concordant or discordant, such as subcellular concordant or discordant Ca2+alternans in cardiac myocytes or spatially concordant or discordant Ca2+ and repolarization alternans in cardiac tissue. Our modeling approach allows both computer simulations and rigorous analytical treatments, which lead to the following results and conclusions. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions with the discordant P2 patterns being spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. The theoretical analyses of the coupled map lattice model reveal the underlying instabilities and bifurcations for the genesis, selection, and stability of spatiotemporal excitation patterns.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.

Cluster singularity: The unfolding of clustering behavior in globally coupled Stuart-Landau oscillators

The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle oscillators. In particular, we show how clustering occurs in minimal networks and elaborate how the observed 2-cluster states crowd when increasing the number of oscillators. Using persistence, we discuss how this crowding leads to a continuous transition from balanced cluster states to synchronized solutions via the intermediate unbalanced 2-cluster states. These cascade-like transitions emerge from what we call a cluster singularity. At this codimension-2 point, the bifurcations of all 2-cluster states collapse and the stable balanced cluster state bifurcates into the synchronized solution supercritically. We confirm our results using numerical simulations and discuss how our conclusions apply to spatially extended systems.

Spiral wave initiation in excitable media

Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Metal Catalysts for Heterogeneous Catalysis: From Single Atoms to Nanoclusters and Nanoparticles

Metal species with different size (single atoms, nanoclusters, and nanoparticles) show different catalytic behavior for various heterogeneous catalytic reactions. It has been shown in the literature that many factors including the particle size, shape, chemical composition, metal-support interaction, and metal-reactant/solvent interaction can have significant influences on the catalytic properties of metal catalysts. The recent developments of well-controlled synthesis methodologies and advanced characterization tools allow one to correlate the relationships at the molecular level. In this Review, the electronic and geometric structures of single atoms, nanoclusters, and nanoparticles will be discussed. Furthermore, we will summarize the catalytic applications of single atoms, nanoclusters, and nanoparticles for different types of reactions, including CO oxidation, selective oxidation, selective hydrogenation, organic reactions, electrocatalytic, and photocatalytic reactions. We will compare the results obtained from different systems and try to give a picture on how different types of metal species work in different reactions and give perspectives on the future directions toward better understanding of the catalytic behavior of different metal entities (single atoms, nanoclusters, and nanoparticles) in a unifying manner.

Synchronization of three electrochemical oscillators: From local to global coupling

We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.

Optical Control of a Biological Reaction-Diffusion System

Patterns formed by reaction and diffusion are the foundation for many phenomena in biology. However, the experimental study of reaction-diffusion (R-D) systems has so far been dominated by chemical oscillators, for which many tools are available. In this work, we developed a photoswitch for the Min system of Escherichia coli, a versatile biological in vitro R-D system consisting of the antagonistic proteins MinD and MinE. A MinE-derived peptide of 19 amino acids was covalently modified with a photoisomerizable crosslinker based on azobenzene to externally control peptide-mediated depletion of MinD from the membrane. In addition to providing an on-off switch for pattern formation, we achieve frequency-locked resonance with a precise 2D spatial memory, thus allowing new insights into Min protein action on the membrane. Taken together, we provide a tool to study phenomena in pattern formation using biological agents.

Surface Structures of Model Metal Catalysts in Reactant Gases

Atomic scale knowledge of the surface structure of a metal catalyst is essential for fundamentally understanding the catalytic reactions performed on it. A correlation between the true atomic surface structure of a metal catalyst under reaction conditions and the corresponding catalytic performance is the key in pursuing mechanistic insight at a molecular level. Here the surface structures of model, metal catalysts in both ultrahigh vacuum (UHV) and gaseous environments of CO at a wide range of pressures are discussed. The complexity of observed surface structures in CO is illustrated, driving the necessity for visualization of the catalytic metals under realistic reaction conditions. Technical barriers for visualization of metal surfaces in situ at high temperature and high pressure are discussed.

Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov–Zhabotinsky (BZ) reaction.

Selectively oxidized carbon nanocatalysts for the oxidation of cis-cyclooctene

Selectively oxidized multi-walled carbon nanotubes and graphene flakes showed superior performance in cis-cyclooctene epoxidation: 47% conversion and 79% selectivity for the best in class oxidized MWCNT, and 57% coversion and 85% selectivity for the best graphene flake material.

Mesoscale Structures in the Adlayer of A-B2 Heterogeneous Catalysis

This article explores the adsorbate distributions in the adlayer for a model A-B₂ system of heterogeneous catalysis, i.e., A + ¹/₂B₂ → AB, via kinetic Monte Carlo (KMC) simulations. In comparison with our previous work on the A-B model (Sun, F.; Huang, W.; Li, J. Structural characteristics of the adlayer in heterogeneous catalysis. Chem. Eng. Sci. 2016, 153, 87-92), species B₂ here brings about significant new features due to its special site requirement during adsorption and desorption and a different stoichiometric ratio in reactions. The effects of various kinetic processes on the adsorbate distribution are found to be similar to those in the A-B system; that is, both desorption and diffusion (besides adsorption) processes contribute to the adlayer uniformity while reactions account for clustering. However, desorption exhibits a stronger role than diffusion in homogenizing the adlayer, which is opposite to the finding in the previous A-B model. Under a fixed partial pressure, different reaction and desorption rate constants can lead to steady states with different dominant species, which has not been observed in the A-B system. The regime of species B poisoning shrinks as well, leading to the spreading of the coexisting regime, in comparison with the A-B model.

Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

Molecules at Solid Surfaces: A Personal Reminiscence

I was fortunate to start my career in physical chemistry at a time when the development of the ultrahigh vacuum technique and of novel physical methods enabled the study of processes on well-defined surfaces at an atomic scale. These investigations included the mechanisms of heterogeneously catalyzed reactions, such as CO oxidation and ammonia synthesis, and phenomena of spatio-temporal self-organization, as described by the concepts of nonlinear dynamics.

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatiotemporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatiotemporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Generic stabilizability for time-delayed feedback control

Time-delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current output and the output from a fixed time T ago. Thus, any periodic orbit of period T in the feedback-controlled system is also a periodic orbit of the uncontrolled system, independent of any modelling assumptions. It has been an open problem whether this approach can be successful in general, that is, under genericity conditions similar to those in linear control theory (controllability), or if there are fundamental restrictions to time-delayed feedback control. We show that, in principle, there are no restrictions. This paper proves the following: for every periodic orbit satisfying a genericity condition slightly stronger than classical linear controllability, one can find control gains that stabilize this orbit with extended time-delayed feedback control. While the paper's techniques are based on linear stability analysis, they exploit the specific properties of linearizations near autonomous periodic orbits in nonlinear systems, and are, thus, mostly relevant for the analysis of nonlinear experiments.

Flow-induced arrest of spatiotemporal chaos and transition to a stationary pattern in the Gray-Scott model

We examine the prototypical Gray-Scott model, which mimics cubic autocatalytic reaction with linear decay of the autocatalyst, to model the kinetics of a reaction-diffusion system subjected to advective streamline flow. For a proper choice of boundary conditions and parameter space, the system admits wave-induced spatiotemporal chaos in the absence of flow. We show that flow above a critical value leads to an arrest of the spatiotemporal chaos due to a change in the instability from absolute to convective type. Furthermore, stationary spatial structures are borne out of a second successive bifurcation for yet another critical flow value. The theoretical formulations are corroborated by extensive numerical simulation of the full reaction-diffusion-advection system in one dimension.

From chemical systems to systems chemistry: Patterns in space and time

We present a brief, idiosyncratic overview of the past quarter century of progress in nonlinear chemical dynamics and discuss what we view as the most exciting recent developments and some challenges and likely areas of progress in the next 25 years.

Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.

Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions

Detailed experimental and numerical results are presented about the pattern formation mechanism of spatially organized partially synchronized states in a networked chemical system with oscillatory metal dissolution. Numerical simulations of the reaction system are used to identify experimental conditions (heterogeneity, network topology, and coupling time-scale) under which the chemical reactions, which take place in a network, are split into coexisting coherent and incoherent domains through the chimera mechanism. Experiments are carried out with a network of twenty electrodes arranged in a ring with seven nearest neighbor couplings in both directions along the ring. The patterns are characterized by analyzing the oscillation frequencies and entrainments to the mean field of the phases of oscillations. The chimera state forms from two domains of elements: the chimera core in which the elements have identical frequencies and are entrained to their corresponding mean field and the chimera shell where the elements exhibit desynchrony with each other and the mean field. The experiments point out the importance of low level of heterogeneities (e.g., surface conditions) and optimal level of coupling strength and time-scale as necessary components for the realization of the chimera state. For systems with large heterogeneities, a 'remnant' chimera state is identified where the pattern is strongly affected by the presence of frequency clusters. The exploration of dynamical features with networked reactions could open up ways for identification of novel types of patterns that cannot be observed with reaction diffusion systems (with localized interactions) or with reactions under global constraints, coupling, or feedback.

Synthesis of heterocycles and fused heterocycles catalyzed by nanomaterials

The application of nanomaterials as heterogeneous catalyst for the synthesis of different heterocyclic systems is reviewed.

Insights into collective cell behaviour from populations of coupled chemical oscillators

Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Experiments with coupled chemical oscillators can provide insights into the collective behaviour.

Effect of delay mismatch in Pyragas feedback control

Pyragas time-delayed feedback is a control scheme designed to stabilize unstable periodic orbits, which occur naturally in many nonlinear dynamical systems. It has been successfully implemented in a number of applications, including lasers and chemical systems. The control scheme targets a specific unstable periodic orbit by adding a feedback term with a delay chosen as the period of the unstable periodic orbit. However, in an experimental or industrial environment, obtaining the exact period or setting the delay equal to the exact period of the target periodic orbit may be difficult. This could be due to a number of factors, such as incomplete information on the system or the delay being set by inaccurate equipment. In this paper, we evaluate the effect of Pyragas control on the prototypical generic subcritical Hopf normal form when the delay is close to but not equal to the period of the target periodic orbit. Specifically, we consider two cases: first, a constant, and second, a linear approximation of the period. We compare these two cases to the case where the delay is set exactly to the target period, which serves as the benchmark case. For this comparison, we construct bifurcation diagrams and determine any regions where a stable periodic orbit close to the target is stabilized by the control scheme. In this way, we find that at least a linear approximation of the period is required for successful stabilization by Pyragas control.

The ReactorSTM: atomically resolved scanning tunneling microscopy under high-pressure, high-temperature catalytic reaction conditions

To enable atomic-scale observations of model catalysts under conditions approaching those used by the chemical industry, we have developed a second generation, high-pressure, high-temperature scanning tunneling microscope (STM): the ReactorSTM. It consists of a compact STM scanner, of which the tip extends into a 0.5 ml reactor flow-cell, that is housed in a ultra-high vacuum (UHV) system. The STM can be operated from UHV to 6 bars and from room temperature up to 600 K. A gas mixing and analysis system optimized for fast response times allows us to directly correlate the surface structure observed by STM with reactivity measurements from a mass spectrometer. The in situ STM experiments can be combined with ex situ UHV sample preparation and analysis techniques, including ion bombardment, thin film deposition, low-energy electron diffraction and x-ray photoelectron spectroscopy. The performance of the instrument is demonstrated by atomically resolved images of Au(111) and atom-row resolution on Pt(110), both under high-pressure and high-temperature conditions.

Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

The deterministic chaos and random noise in turbulent jet

A turbulent flow is usually treated as a superposition of coherent structure and incoherent turbulence. In this paper, the largest Lyapunov exponent and the random noise in the near field of round jet and plane jet are estimated with our previously proposed method of chaotic time series analysis [T. L. Yao, et al., Chaos 22, 033102 (2012)]. The results show that the largest Lyapunov exponents of the round jet and plane jet are in direct proportion to the reciprocal of the integral time scale of turbulence, which is in accordance with the results of the dimensional analysis, and the proportionality coefficients are equal. In addition, the random noise of the round jet and plane jet has the same linear relation with the Kolmogorov velocity scale of turbulence. As a result, the random noise may well be from the incoherent disturbance in turbulence, and the coherent structure in turbulence may well follow the rule of chaotic motion.

Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection

A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady states of the model and numerical simulations of the model to show how the asymmetric nonlocal coupling controls and alters the steady states and the front dynamics in the system. In a second step, a third fast reaction-diffusion equation is included which induces the formation of more complex patterns. A linear stability analysis predicts traveling waves for asymmetric nonlocal coupling, in contrast to a stationary Turing patterns for a system with symmetric nonlocal coupling. These findings are verified by direct numerical integration of the full equations with nonlocal coupling.