Bistable Elements Research Articles

Protective role of the half-center oscillator connectivity against external perturbations

Central pattern generators (CPGs) are neuronal circuits that control rhythmic movements in animals. The heartbeat of the medicinal leech is controlled by a CPG that is distributed over several ganglia. In ganglia 3 and 4, there are half-center oscillators (HCOs): pairs of reciprocally inhibitory heart interneurons (HNs). These HCOs form the kernel of the heartbeat CPG, and each HCO is composed of a pair of endogenously bursting heart interneurons [1]. A canonical model of the HN accurately reproduces experimental results [1,2]. It also exhibits bistability of bursting and silence in single HNs and the HCO [1,3]. The single HN and HCO model have been expanded into a family of models that satisfy biological constraints [2]. Multistability is highly prevalent in this database [4]. The coexistence of bursting and silent regimes could present a life threatening condition for the animal. If a perturbation were able to trigger a switch in the activity of the CPG to a silent state, circulation of blood in the leech would be crippled. Our hypothesis is that the HCO connectivity protects functional pattern of activity against an external perturbation. Here, we investigated the perturbations that switch the activity of the HN and the HCO from bursting to silence. Over a series of simulations, we applied a 30 ms pulse of current with various amplitudes and phases of application in the period of bursting activity. This protocol provided a set of pulse parameters in the (phase, amplitude) parameter space for which a switch was triggered. In the canonical model of a single HN for which the leak conductance was 9.59 nS, both depolarizing and hyperpolarizing pulses could trigger switches (Figure ​(Figure1).1). We observed contiguous sets of pulse parameters where triggered switches occurred, but there were also fine structures in the parameter space (Figure ​(Figure1).1). We estimated the susceptibility of bursting activity in the HN to perturbations by the proportion of pulse parameter sets that would trigger a switch to the total number of trials. We found that 20.84% of pulses triggered a switch (Figure ​(Figure1).1). We repeated this pulse protocol in the HCO for the same parameter values of the ionic conductances, and found that no pulses elicited a switch from bursting to silence. Our results suggest that in a network consisting of bistable elements, the half-center oscillator connectivity protects the functional regime against external perturbations. Figure 1 Properties of pulses triggering a switch from bursting to silence. Red or blue points indicate a switch or failure to switch. The yellow trajectory is the bursting waveform that defines the phase. The green dashed line indicates 0 nA.

Verification of scalable ultra-sensitive detection of heterogeneity in an electronic circuit

We study the impact of small heterogeneity in signals applied to globally coupled nonlinear bistable elements. In the absence of coupling, the collective response is simply the average of all the uncorrelated signals. When the elements are coupled and a bias is applied, we find that even a very small number of different inputs are able to drag the collective response towards the stable state of the minority inputs. In our explicit demonstration we have taken Schmitt triggers as the basic nonlinear bistable elements, and the inputs are encoded as voltages applied to them. The average of output voltages of all the Schmitt triggers corresponds to the global output of the system. We also observe that the minimum heterogeneity that can be detected scales with ratio of threshold voltage to source voltage of the Schmitt triggers, and can be be brought down to the limit of single bit detection.

Memory element based on ferroelectric field-effect transistor with use of ZnO:Li/LaB6 heterostructures

Ferroelectric field-effect transistors using ZnO:Li films simultaneously as a transistor channel and as a ferroelectric active element have been prepared and studied. We show an opportunity of using the ferroelectric field-effect transistor based on ZnO:Li films in ZnO:Li'LaB6 heterostructure as a bistable memory element for information recording. The proposed structure of a ferroelectric memory cell does not possess the fatigue under repeated readout of single recorded information that will allow increasing the resource of storage devices essentially. DOI: 10.3103/S1068337213030067

Fabrication of Al/MgO/C and C/MgO/InSe/C tunneling barriers for tunable negative resistance and negative capacitance applications

Abstract In this work, the design and characterization of magnesium oxide based tunneling diodes which are produced on Al and InSe films as rectifying substrates are investigated. It was found that when Al thin films are used, the device exhibit tunneling diode behavior of sharp valley at 0.15 V and peak to valley current ratio (PVCR) of 11.4. In addition, the capacitance spectra of the Al/MgO/C device show a resonance peak of negative capacitance (NC) values at 44.7 MHz. The capacitance and resistance–voltage characteristics handled at an ac signal frequency of 100 MHz reflected a build in voltage ( V bi ) of 1.29 V and a negative resistance (NR) effect above 2.05 V. This device quality factor ( Q )–voltage response is ~10 4 . When the Al substrate is replaced by InSe thin film, the tunneling diode valley appeared at 1.1 V. In addition, the PVCR, NR range, NC resonance peak, Q and V bi are found to be 135, 0.94–2.24 and 39.0 MHz, ~10 5 and 1.34 V, respectively. Due to the wide differential negative resistance and capacitance voltage ranges and due to the response of the C/MgO/InSe/C device at 1.0 GHz, these devices appear to be suitable for applications as frequency mixers, amplifiers, and monostable–bistable circuit elements (MOBILE).

Feedback-induced stationary localized patterns in networks of diffusively coupled bistable elements

Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in different parts of the parameter space are discussed. Numerical investigations are performed for large random Erdös-Rényi and scale-free networks. In both kinds of systems, localized stationary activation patterns have been observed. The active nodes in such a pattern form a subnetwork, whose size decreases as the feedback intensity is increased. For strong feedbacks, active subnetworks are organized as trees. Additionally, local feedbacks affecting only the nodes with high degrees (i.e., hubs) or the periphery nodes are considered.

Nonlinear channelizer

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

Traveling and pinned fronts in bistable reaction-diffusion systems on networks.

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed.

Structures undergoing discrete phase transformation

Discrete phase transformations occur in a wide range of structures and systems, from proteins and sub-cellular components in biological systems to micro-scale structures of standard materials. In this paper we study theoretically the mechanical behavior of these intriguing structures. We reexamine the conventional model of a bi-stable chain by introducing the concept of an ideal bi-stable element, and show that any bi-stable element can be conceptually separated into an ideal bi-stable element connected in series with an elastic spring. This new approach allows relatively simple calculations, important insights, and meaningful results. Emphasis is put on consequences of the discrete nature of these structures, and in particular on finite size effects, non-trivial stability, dissipation ratchets, and escape rates. We also consider the inverse problem of finding micro-level properties from experiments, and propose a novel method which provides “sub-pixel” resolution that is not subjected to the sampling rule of the Nyquist frequency. Simple experiments are performed in order to demonstrate some of the theoretical concepts.

General solution to the Hertz–Mindlin problem via Preisach formalism

In this paper we analyze the contact problem for two elastic spheres with friction (the Hertz–Mindlin or HM problem) and present an original solution expressed in terms of the Preisach description. The major obstacle for an efficient use of the HM mechanics in the case of general loading histories lies in the complex memory-dependent and hysteretic behavior of the shear stress (traction) caused by the presence of irreversible slip in the contact zone. On the other hand, the Preisach formalism provides a versatile and powerful tool that is applicable to a wide class of systems with rate-independent hysteresis of any nature. The approach consists in a representation of a hysteretic system as a collection of bi-stable elements which can be switched from one state to another by an external action. An ensemble of the states of the elements determines all memory information contained in the system. Switching of elements is governed by a simple and easy-to-program procedure applicable to any kind of external action (protocol). We show that the two crucially identifying criterions of a generic Preisach system are verified within the HM mechanics and we calculate the characteristic parameters of the Preisach description. As a result, we obtain a compact and efficient analytical solution that allows to compute the hysteretic response in a direct way, i.e. without consideration of cumbersome traction distribution expressions.

Shape Memory Alloy Expandable Pedicle Screw to Enhance Fixation in Osteoporotic Bone: Primary Design and Finite Element Simulation

The properties of shape memory alloys, specifically the equiatomic intermetallic NiTi, are unique and significant in that they offer simple and effective solutions for some of the biomechanical issues encountered in orthopedics. Pedicle screws, used as an anchoring point for the implantation of spinal instrumentations in the spinal fracture and deformity treatments, entail the major drawback of loosening and backing out in osteoporotic bone. The strength of the screw contact with the surrounding bone diminishes as the bone degrades due to osteoporosis. The SMArtTM pedicle screw design is developed to address the existing issue in degraded bone. It is based on the interaction of bi-stable shape memory-superelastic elements. The bi-stable assembly acts antagonistically and consists of an external superelastic tube that expands the design protrusions when body temperature is attained; also an internal shape memory wire, inserted into the tube, retracts the assembly while locally heated to above the body temperature. This innovative bi-stable solution augments the pull-out resistance while still allowing for screw removal. The antagonistic wire-tube assembly was evaluated and parametrically analyzed as for the interaction of the superelastic tube and shape memory wire using a finite element model developed in COMSOL Multiphysics®. The outcomes of the simulation suggest that shape memory NiTi inserts on the SMArtTM pedicle screw can achieve the desired antagonistic functionality of expansion and retraction. Consequently, a parametric analysis was conducted over the effect of different sizes of wires and tubes. The dimensions for the first sample of this innovative pedicle screw were determined based on the results of this analysis.

Minimal energy control of a nanoelectromechanical memory element

The Pontryagin minimal energy control approach has been applied to minimise the switching energy in a nanoelectromechanical memory system and to characterise global stability of the oscillatory states of the bistable memory element. A comparison of two previously experimentally determined pulse-type control signals with Pontryagin control function has been performed, and the superiority of the Pontryagin approach with regard to power consumption has been demonstrated. An analysis of global stability shows how values of minimal energy can be utilized in order to specify equally stable states.

Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics

We demonstrate how the collective response of N globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large network of otherwise identical elements. Counter-intuitively, when there are a small number of elements with natural stable state different from the bulk of the elements, all the elements of the system evolve to the stable state of the minority due to strong coupling. The critical fraction of distinct elements needed to produce this swing shows a sharp transition with increasing N, scaling as . Furthermore, one can find a global bias that allows robust one-bit sensitivity to heterogeneity. Importantly, the time needed to reach the attracting state does not increase with the system size. We indicate the relevance of this ultra-sensitive generic phenomenon for massively parallelized applications, such as the determination of the existence of a “needle in a haystack” by one measurement.

Design, fabrication, and evaluation of negative stiffness elements using SLS

PurposeRecent research has shown that constrained bistable structures can display negative stiffness behavior and provide extremal vibrational and acoustical absorptive capacity. These bistable structures are therefore compelling candidates for constructing new meta‐materials for noise reduction, anechoic coatings, and backing materials for broadband imaging transducers. To date, demonstrations of these capabilities have been primarily theoretical because the geometry of bistable elements is difficult to construct and refine with conventional manufacturing methods and materials. The purpose of this paper is to leverage the geometric design freedoms provided by selective laser sintering (SLS) technology to design and construct constrained bistable structures with negative stiffness behavior.Design/methodology/approachA meso‐scale negative stiffness system is designed and fabricated with SLS technology. The system includes a bistable structure in the form of a pre‐compressed/pre‐buckled beam. The dynamic transmissibility of the system is measured, and its behavior is compared to the predictions of analytical models.FindingsExperimental results demonstrate that pre‐compression and pre‐buckling can be used to induce negative stiffness behavior and thereby increase the damping and shift the resonant frequency of an unconstrained beam.Originality/valueThe results support the usefulness of SLS and other additive manufacturing technologies for acoustic and dynamic applications. Specifically, the demonstrated advantages of SLS include the ability to rapidly redesign, functionally 2 prototype, and tune physical models for acoustic and dynamic experimentation. Of significant importance is the ability of SLS to enable consolidation of parts that are traditionally separate, thereby reducing vibrational noise in these systems. In this specific application, SLS enables a proof‐of‐concept comparison of the theoretical and experimental behavior of a meso‐scale negative stiffness system. The demonstrated acoustical and vibrational absorptive capacity of these systems is expected to lead to designs for new structures and materials that offer significantly improved energy absorbing capabilities over a broad range of tunable frequencies without compromising structural stiffness.

Photoinduced Memory Effect in a Redox Controllable Bistable Mechanical Molecular Switch

Something to remember: A rotaxane could be operated as a bistable memory element under kinetic control (see picture). Data was written on the molecule by an oxidation stimulus and locked by UV light irradiation. After the writing session, the oxidized species was reduced back to the original form without losing the written data for a few hours. Light irradiation also protects nonoxidized rotaxanes from accidental writing.

Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction–diffusion–convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.

Spatiotemporal stochastic resonance in a bistable FitzHugh-Nagumo ring with phase-repulsive coupling

In this paper, we numerically study a ring of bistable FitzHugh-Nagumo elements coupled in a phase-repulsive way, which are externally driven by a weak periodic signal and noises, and focus on the system’s response. A novel type of spatiotemporal stochastic resonance of antiphase state is uncovered, namely, for an intermediate strength of individual noise, the elements can form an “...-upper-lower-upper-lower-...” antiphase structure along the ring, and the global activation oscillates nearly synchronously with the weak periodic signal. Meanwhile, the system response undergoes a resonant behavior with the intensity of noise. It is shown that the combinative effects of the periodic signal, noise, and coupling are of importance for its appearance. The influences of common and individual noises are also investigated.

Design considerations of a large-displacement multistable micro actuator with serially connected bistable elements

In this work we report on a finite element modeling and design methodology, fabrication and characterization of a large-displacement low voltage multistable micro actuator with an integrated electrostatic comb drive transducer. The compliant suspension of the device incorporates multiple serially connected bistable arch-shaped beams and exhibits controllable sequential snap-through buckling under an increasing actuation force. The device can be considered therefore as an example of a compliant multistep structure. The device is also distinguished by its ability to remain in several different stable configurations at the same actuation voltage while the force–displacement characteristic of the suspension can be tailored by changing the geometry parameters of the flexures. A model built using the shallow arch approximation along with a nonlinear finite element analysis were used in order to study the influence of the suspension architecture on the stability limits of the structure and for evaluation of design parameters of the actuator. Bistable and multistable devices were fabricated by a Deep Reactive Ion Etching (DRIE) based process using silicon-on-insulator (SOI) wafers. Experimental results, which are consistent with the model predictions, demonstrate that the compliant multistep devices exhibit improved lateral stability and consequently larger stable displacements compared to the conventional comb drive actuators. Stable displacements up to 80 μm at a voltage of 30 V were registered in the experiments while three snap-through and snap-back events took place during loading and unloading, respectively. Our computational and experimental results show that the suggested device has clear functional advantages and can be efficiently used in applications including switches, threshold inertial sensors, variable optical attenuators as well as in micro-and nanomechanical logical elements.

Mechanical behaviour of bistable struts

The mechanical behaviour of a bistable structural element, which is based on the snap-through and bifurcation properties of the von Mises truss, has been investigated in this article. By assuming the joint behaviour as ideal hinges and using the large deformation theory based on a linear elastic material, a simple analytical model for the stability of the von Mises truss was formulated. The governing set of non-linear equilibrium equations was obtained by applying the principle of stationary total potential energy. Then, the formulae of the snap-through and bifurcation buckling loads and the equilibrium path were given. In addition to the well-known cases of primary and secondary branches, a third type that the bifurcation buckling point lying on the descending branch of the load versus displacement curve was discussed. In this case, although its upper bifurcation load is lower than its upper snap-through buckling load, the truss experiences a symmetric snap-through mode first, and hence the bifurcation point is not physically relevant. Finally, the assumptions of the classical von Mises truss analysis are discussed.

Coherence resonance and stochastic resonance in directionally coupled rings

In coupled systems, symmetry plays an important role for the collective dynamics. We investigate the dynamical response to noise with and without weak periodic modulation for two classes of ring systems. Each ring system consists of unidirectionally coupled bistable elements but in one class, the number of elements is even while in the other class the number is odd. Consequently, the rings without forcing show at a certain coupling strength, either ordering (similar to anti-ferromagnetic chains) or auto-oscillations. Analysing the bifurcations and fixed points of the two ring classes enables us to explain the dynamical response measured to noise and weak modulation. Moreover, by analysing a simplified model, we demonstrate that the response is universal for systems having a directional component in their stochastic dynamics in phase space around the origin.

A minimal model of C. elegans forward locomotion: the larval L1 circuit

The nematode Caernohabditis elegans possesses one of the simplest central nervous systems, and by far the best characterized. In the adult, the nervous system consists of a mere 302 neurons, of which the majority are located in the head, and the rest are distributed in the pharynx, along the ventral cord or in small ganglia. In particular, the local control (along the body) of the worm’s sinuous undulations is instantiated by 8 classes of ventral cord motor neurons. But of those, only 3 classes exist as the larva hatches out of the egg (the so called L1 stage in development). This appears quite remarkable, given the similar repertoire of behaviors in the larva, as compared to the fully developed adult. Here, we ask what minimal design principles must apply for the L1 circuit to generate robust forward locomotion. Robustness is taken to mean effective locomotion in different physical environments (e.g. high viscosity agar gels versus water) [1,2]. To address this challenge, we adopt an integrated neuromechanical model of forward locomotion in the adult that consists of the ventral cord nervous system, muscles, a body and a physical environment [2], and adapt the model nervous system and muscles to match the L1. In particular, we assume the forward locomotion control in the L1 consists of repeating units, each consisting only of a pair of neurons: one excitatory DB and one inhibitory DD. DB neurons are modeled as bistable elements [2] innervating dorsal muscles, and DD neurons are modeled as linear elements inhibiting ventral muscles. High level control is modeled with an on/off AVB unit that drive all B-neurons. The rhythm is generated entirely on the dorsal side and is achieved by a closed-loop proprioceptive feedback (via postulated stretch sensitivity of DB neurons). Inhibitory neurons receive synaptic inputs from the local DB neuron and are therefore enslaved to its oscillations. The integrated model successfully generates and propagates coordinated undulations on agar and liquid model environments. In the model, both of these behaviors are achieved by a single (i.e., fixedparameter) model worm. The model makes a number of relatively easily testable predictions: 1) L1 larva have a minimal, reflex-driven mechanism to control body undulations. 2) Inhibitory D-neurons are essential for forward locomotion in the L1. 3) Muscle properties must differ substantially between the ventral and dorsal side (specifically, ventral but not dorsal muscles must be spontaneously active).