Mercury Beating Heart Research Articles

Direct Current (DC) Electric Field-Enabled Beating Heart of Ga-Based Liquid Metal

Mercury beating heart (MBH) is a well-known demonstration of redox processes. However, the development and application of the MBH system are significantly restricted due to its safety issues. Here, a direct current electric field-enabled gallium-based liquid metal heartbeat in a salt solution or alkaline solution is introduced as a demonstration appropriate for undergraduate general chemistry. The former oscillation occurs on the cathode, the latter on the anode. The objective is to achieve a visually appealing effect in the classroom and motivate students to understand the underlying concepts. Students are encouraged to assemble the instrument and perform the demonstration under supervision. Apart from the gallium-based liquid metal and a helping-hand stand, the demonstration utilizes common laboratory apparatus, and the materials for the solutions can be obtained in an undergraduate general chemistry laboratory.

Entrainment of aperiodic and periodic oscillations in the Mercury Beating Heart system using external periodic forcing.

We report experimental results indicating entrainment of aperiodic and periodic oscillatory dynamics in the Mercury Beating Heart (MBH) system under the influence of superimposed periodic forcing. Aperiodic oscillations in MBH were controlled to generate stable topological modes, namely, circle, ellipse, and triangle, evolving in a periodic fashion at different parameters of the forcing signal. These periodic dynamics show 1:1 entrainment for circular and elliptical modes, and additionally the controlled system exhibits 1:2 entrainment for elliptical and triangular modes at a different set of parameters. The external periodic forcing of the periodic MBH system reveals the existence of domains of entrainment (1:1, 1:2, 1:3, and 1:4) represented in the Arnold tongue structures. Moreover, Devil's staircase is obtained when the amplitude-frequency space of parameters of the applied signal is scanned.

Oscillatory activity regulation in an ensemble of autonomous mercury beating heart oscillators.

Collective behavior of an ensemble of directly or indirectly coupled oscillators can be a function of population density. Experiments using autonomous mercury beating heart (MBH) oscillators coupled through their surroundings are employed, to study the existence of quorum-like (population dependent) phenomena. Two coupling mechanisms are used, namely, static and dynamic coupling. For the static coupling scheme, the transitions of a subset of the coupled oscillators occur from active (oscillatory) to inactive (quiescent) state and vice versa. A continuous variation of collective dynamics was observed as the population of the oscillators increased. For the dynamic coupling scheme, the time for which the coupled oscillators are active changes sharply as the population increases beyond a certain threshold.

Cessation of oscillations in a chemo-mechanical oscillator

In this paper, different methods for cessation of oscillations in a chemo-mechanical oscillator [mercury beating heart (MBH)] are presented. The first set of experiments were carried out on a single MBH oscillator. To achieve cessation of oscillations, two protocols, namely, inverted feedback and delayed feedback were employed. In the second set of experiments, two quasi-identical MBH oscillators are considered. They are first synchronized via a bidirectional attractive coupling. These two synchronized oscillators are thereafter coupled with a unidirectional repulsive coupling and the system dynamics were observed. Subsequently, in the next protocol, the effect of a unidirectional delay coupling on the two synchronized oscillators was explored. The cessation of oscillations in all the above experimental setups was observed as the feedback/coupling was switched on at a suitable strength. Oscillatory dynamics of the system were restored when the feedback/coupling was switched off.

Control, synchronization, and enhanced reliability of aperiodic oscillations in the Mercury Beating Heart system.

Experiments involving the Mercury Beating Heart (MBH) oscillator, exhibiting irregular (aperiodic) dynamics, are performed. In the first set of experiments, control over irregular dynamics of the MBH oscillator was obtained via a superimposed periodic voltage signal. These irregular (aperiodic) dynamics were recovered once the control was switched off. Subsequently, two MBH oscillators were coupled to attain synchronization of their aperiodic oscillations. Finally, two uncoupled MBH oscillators were subjected, repeatedly, to a common stochastic forcing, resulting in an enhancement of their mutual phase correlation.

Dependence of synchronization on frequency mismatch and network configuration in chemo-mechanical oscillators

In this paper, synchronization among the mercury beating heart (MBH) oscillators is studied. In the first set of experiments, two MBH oscillators were taken. Frequency of one oscillator is kept constant and that of the other is increased monotonically. These were then coupled using bidirectional and unidirectional coupling mechanisms separately. Dependence of synchronization on the frequency difference between the two oscillators is investigated. For the second set of experiments involving unidirectional coupling, an ensemble of fifteen oscillators was taken and different configurations of these oscillators were considered. These include an all-to-all network and fractionally distributed master slave configurations. The effect of both the extent of coupling and network configuration on synchronization among these oscillators was investigated.

Partially synchronized states in an ensemble of chemo-mechanical oscillators

Partially synchronized (clustered) states are defined as coexisting coherent (synchronized) and incoherent (unsynchronized) domains in an ensemble of interacting oscillators. We report these clustered states in experiments involving an ensemble of sixteen mercury beating heart (MBH) oscillators. These oscillators interact via resistors and are subjected to two different network schemes: 1) All to all and 2) Nonlocal. For the all to all network, the coupling strengths were inhomogeneously distributed, whereas for the nonlocal network scenario, each oscillator was coupled, with an identical coupling strength, with four of its nearest neighbors in either direction. For both of these network schemes, partially synchronized states results into grouping of these oscillators, wherein some oscillators are synchronized and rest are unsynchronized. For all to all network, the partially synchronized states are observed, for the intermediate inhomogeneities, when subjected to the power law and the ‘U’ shape profiles of coupling strengths. Irrespective of the coupling profile chosen, low inhomogeneities in the coupling strengths leaves all the oscillators in a single coherent state whereas for the high inhomogeneities scenarios oscillators are located in the incoherent domain. In comparison, for the nonlocal network partially synchronized states emerge when the coupling constant is appropriately chosen. The experimental results for both these network scenarios have been analyzed using the redox time series (chemical activity) and the time evolution of the normalized areas for the mercury drop (mechanical activity). The existence of partially synchronized states in the experiments was verified using different diagnostic tools such as time series plot, space–time plot and average frequency.

Synchronization using environmental coupling in mercury beating heart oscillators.

We report synchronization of Mercury Beating Heart (MBH) oscillators using the environmental coupling mechanism. This mechanism involves interaction of the oscillators with a common medium/environment such that the oscillators do not interact among themselves. In the present work, we chose a modified MBH system as the common environment. In the absence of coupling, this modified system does not exhibit self sustained oscillations. It was observed that, as a result of the coupling of the MBH oscillators with this common environment, the electrical and the mechanical activities of both the oscillators synchronized simultaneously. Experimental results indicate the emergence of both lag and the complete synchronization in the MBH oscillators. Simulations of the phase oscillators were carried out in order to better understand the experimental observations.

Experimental evidence of explosive synchronization in mercury beating-heart oscillators.

We report experimental evidence of explosive synchronization in coupled chemo-mechanical systems, namely in mercury beating-heart (MBH) oscillators. Connecting four MBH oscillators in a star network configuration and setting natural frequencies of each oscillator in proportion to the number of its links, a gradual increase of the coupling strength results in an abrupt and irreversible (first-order-like) transition from the system's unordered to ordered phase. On its turn, such a transition indicates the emergence of a bistable regime wherein coexisting states can be experimentally revealed. Finally, we prove how such a regime allows an experimental implementation of magneticlike states of synchronization, by the use of an external signal.

Kuramoto transition in an ensemble of mercury beating heart systems.

We have studied, experimentally, the collective behavior of the electrically coupled autonomous Mercury Beating Heart (MBH) systems exhibiting the breathing mode, by varying both the coupling strength and the population size (from N = 3 to N = 16). For a fixed N, the electrical and the mechanical activities of the MBH systems achieve complete synchronization at different coupling strengths. The electrical activity of each MBH system is measured by the corresponding electrode potential (Ei = Vi). Additionally, the mechanical activity of each MBH oscillator is visually observed (snapshots and video clips). Subsequently, this activity is quantified by calculating the temporal variation in the area (Ai) of the Hg drop. As a result, the synchronization of the electrical (Ei = Vi) and the mechanical (Ai) activities can be measured. The extent of synchronization was quantified by employing the order parameter (r). Our experimental results are found to be in agreement with the Kuramoto theory.

Extensive study of shape and surface structure formation in the mercury beating heart system.

A phenomenological study of the mercury beating heart system in a three electrode electrochemical cell configuration forced with a harmonic perturbation is presented. The system is controlled via a potentiostat, where the mercury drop is electrically connected to a platinum wire and acts as the working electrode. This configuration exhibits geometrical shapes and complex surface structures when a harmonic signal is superimposed to the working electrode potential. This study involves a wide range of frequencies and amplitudes of the forcing signal. Differents levels of structure complexity are observed as a function of the parameters of the applied perturbation. At certain amplitudes and frequencies, rotational behavior is also observed.

Pattern Formation in the Mercury Beating Heart System

In this work is presented a phenomenological study of the mercury beating heart (MBH) in a configuration of three electrode electrochemical cell, where the mercury drop is the working electrode. We report the occurrence of a traveling wave on the MBH system as result of the chemo-mechanical processes taking place. Under fixed potential conditions the drop changes its shape and rotates simultaneously. Using image processing, it was possible to gain information about angular velocities, changes in perimeter of the drop and periodicities in the spatiotemporal changes observed. Furthermore when a sinusoidal potential is applied, the mercury drop exhibit geometrical shapes and complex surface structures. Here the characterization study was realized by observing a wide range of frequencies and amplitudes of a sinusoidal wave potential signal. As frequency increases, shapes with higher number of peaks and more complex surface structures appear. A possible resonant coupling of some traveling waves, originated by the electrochemical process and shaped by the mercury hydrodynamic, results in these complexes surface structures.

Synchronization in autonomous mercury beating heart systems.

The ability of the mercury beating heart (MBH) system to exhibit sustained mechanical and electrochemical activities simultaneously without any external agent (fluctuating or constant), has attracted researchers for decades. The interplay of these activities could mimic the biological phenomena such as a pulsating heart that occurs due to the coupled tissues exhibiting mechanical as well as electrical dynamics. In the present work, we have studied experimentally the dynamics of electrically coupled two and three autonomous MBH systems. A dynamical triangular (heart) shape, in the traditional watch glass geometry, has been chosen for the experiments. It is found that the redox potentials (electrical behavior) of the quasi-identical (due to the inherent heterogeneities in the setup) MBH systems get synchronized at the intermediate coupling strengths whereas coherence in their mechanical activities occur only at large coupling strengths. To the best of our knowledge, this synchronization phenomenon involving two distinct activities (electrical and mechanical) and different coupling thresholds has not been reported, so far. The coherent mechanical activities means the simultaneous occurrence of compressions and expansions in the coupled Hg drops, which are shown using snapshots. In addition to this, the redox time series have also been provided to demonstrate the synchronization in the electrical behavior of MBH systems. Moreover, a mathematical framework considering only electrical and mechanical components of the MBH systems is presented to validate the experimental findings that the strong synchrony in the redox potentials of the MBH systems is a prerequisite for the synchrony in their mechanical activities.

Potential-Dependent Topological Modes in the Mercury Beating Heart System

We study the dynamics of the mercury beating heart (MBH) system in an acidic solution in the absence of a strong oxidant. Furthermore, the system is subjected to an external square wave potential. It was observed that different shapes (circular, elliptical, triangular, and multilobed stars) of the mercury drop could be stabilized as the frequency of the external potential and the volume of the mercury were varied. The redox potential time series for this forced MBH system, corresponding to the different stabilized topological configurations, were also recorded, and their power spectra were analyzed. The obtained results, involving the different topological modes, were fairly reproducible and sustainable. A possible oxidation-reduction mechanism for these experimental observations is provided.

Mercury Beating Heart: Modifications to the Classical Demonstration

By analogy with the classical variant of the mercury beating heart (MBH), we propose several demonstrations of the MBH with various solutions of electrolytes, where the beating is generated by external power supply. Details for performing the experiments of MBH are given in this article. Video clips are offered in addition to classical demonstrations with an overhead projector or video camera. Mercury oscillations were observed without physical contact of mercury with the electrodes. When an aqueous solution of sodium sulfate or alkali hydroxide was used as electrolyte, an amalgam formed (even without direct contact between the electrode and mercury drop) and a mechanism is proposed for this phenomenon.

Complex Oscillatory Behavior of the Mercury Beating Heart System

We show the dynamics of the oscillatory Mercury Beating Heart (MBH) reaction in acid aqueous solution with [CeIV(SO4)3]2− as oxidizing agent. The rich dynamics is appropriate to introduce students to oscillatory chemical reactions and nonlinear concepts. These oscillations display different modes of oscillations with geometric structures similar to heart, circle, and pointed stars. We consider oxidation-reduction reactions to explain the different periods of oscillations due mainly to the formation of mercury(I) species and plot the socalled reconstruction attractors from the variation of the Hg electrode potential in time.

Study of the Extinction Dynamics of the Mercury Beating Heart Reaction in Acid Solution and in the Presence of γ-Radiation

The dynamics of the oscillatory mercury beating heart (MBH) reaction in acid aqueous solution with CeIV as the oxidizing agent was investigated. The reaction slowly runs down over a period of a few hours, until all oscillatory activity eventually ceases. During this period the dynamics slowly evolves, showing qualitatively different forms of oscillations. These oscillations display different modes of oscillations with geometric structures similar to heart, circle, pentagon, hexagon, and 8- and 16-pointed stars. As time proceeds, limit-cycle oscillations of period-1, period-3, and period-2 appear successively. However, these oscillations are damped and could be interpreted in terms of a subcritical Hopf bifurcation. We propose different oxidation−reduction reactions to explain the appearance of these cycles based on the formation of mercury(I) species, in the form of free Hg22+ ion or, in molecular form, as a soluble mercurous sulfate or a mercurous sulfate film. The theoretical potential values calculated for these reactions agree well with our experimental values. An experiment was performed also without adding the CeIV oxidant, generating in situ species of Hg(I) by γ-irradiating the metallic Hg in the same acid solution as before. It is shown that 60Co γ-rays induce the generation of oscillations. In this way we support our claim that oscillations are due to the formation of chemical species of Hg(I) be it ionic or molecular and that extinction occurs when [Hg(II)] ≫ [Hg(I)].