Bistable Transition Research Articles

Magneto‐Responsive Bistable Structures with Rate‐Dependent Actuation Modes

AbstractStructural instabilities can be used to provide rapid responses activated by mechanical force or displacement thresholds. The emergence of responsive materials has opened the door for adapting such structural instabilities to actuators that will abruptly deform guided by external stimuli. However, fast configurational transitions between equilibrium states imply important viscoelastic roles at the material level that inevitably scale up to the structural level. A comprehensive understanding of viscoelastic effects is provided on bistable structural transitions combining a new experimental perspective and a thorough modeling analysis. The insights from these results are here translated to magneto‐responsive bistable structures offering a route‐map to design effective actuation conditions. The bistable transition functionally depends on the combination of magnetic field amplitude and application rate. The understanding of the viscoelastic and magneto‐mechanical coupling provides efficient actuation via temporal magnetic pulses, removing the need of generating continued magnetic fields. Finally, these insights are combined to develop a responsive structure whose transient and steady bistable transitions can be modulated by the application rate of external magnetic stimuli.

Thermally active programmable metamaterials with holey tilted struts

Bistable transition is often applied in the design of microstructures in metamaterials. In this study, we introduce a series of strategically placed holes in the tilted struts, and observe, through numerical and experimental analysis, an effect of the perforation on the snap-through buckling behavior of the structure. By infilling the holes with thermal-sensitive polymer bars, we realize actively tuning the local stiffness of the holey struts, thereby enabling a means to switch the metamaterial between bistable and monostable states. Furthermore, we propose a multi-stable metamaterial by stacking bistable units with different arrange of infilled and empty holes. The designed metamaterial demonstrates a progressive restoration from the deformed shape to its original shape as the environment temperature reaches up to certain values. These findings highlight the potential of holey-type bistable metamaterials in the design of actuators, deployable structures, and reusable energy absorbers.

Macrophage phenotype transitions in a stochastic gene-regulatory network model

Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

MULTISTABILITY IN A CHIRAL SEMICONDUCTOR MICROCAVITY

The features of the bi- and multistability effects in the semiconductor Bragg microcavity with chiral photonic crystal slab on the upper mirror are investigated theoretically. It is shown that the response of such a chiral structure under a linearly polarized coherent resonant pump demonstrates sharp multistable transitions with abrupt jumps of the exciton intensity and degree of circular polarization. It is shown that of the thresholds of bistable transitions in the system with different sense of circular polarization differ slightly, i.e. in case of a non-optimized structure, we can expect to obtain even a larger amplitude of the jumps of the degree of circular polarization of the excitonic response due to the multistability than in a specially optimized chiral structure with a high degree of circular polarization at low pump intensity.

Bi-stability and critical transitions in mental health care systems: a model-based analysis

BackgroundDelayed initiation and early discontinuation of treatment due to limited availability and accessibility of services may often result in people with mild or moderate mental disorders developing more severe disorders, leading to an increase in demand for specialised care that would be expected to further restrict service availability and accessibility (due to increased waiting times, higher out-of-pocket costs, etc.).MethodsWe developed a simple system dynamics model of the interaction of specialised services capacity and disease progression to examine the impact of service availability and accessibility on the effectiveness and efficiency of mental health care systems.ResultsModel analysis indicates that, under certain conditions, increasing services capacity can precipitate an abrupt, step-like transition from a state of persistently high unmet need for specialised services to an alternative, stable state in which people presenting for care receive immediate and effective treatment. This qualitative shift in services system functioning results from a ‘virtuous cycle’ in which increasing treatment-dependent recovery among patients with mild to moderate disorders reduces the number of severely ill patients requiring intensive and/or prolonged treatment, effectively ‘releasing’ services capacity that can be used to further reduce the disease progression rate. We present an empirical case study of tertiary-level child and adolescent mental health services in the Australian state of South Australia demonstrating that the conditions under which such critical transitions can occur apply in real-world services systems.ConclusionsPolicy and planning decisions aimed at increasing specialised services capacity have the potential to dramatically increase the effectiveness and efficiency of mental health care systems, promoting long-term sustainability and resilience in the face of future threats to population mental health (e.g., economic crises, natural disasters, global pandemics).

Synchronization of phase oscillators on complex hypergraphs.

We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for the system's order parameters. We illustrate our framework with the example of a hypergraph with hyperedges of sizes 2 (links) and 3 (triangles). For this case, we obtain a set of two coupled nonlinear algebraic equations for the order parameters. For strong values of coupling via triangles, the system exhibits bistability and explosive synchronization transitions. We find conditions that lead to bistability in terms of hypergraph properties and validate our predictions with numerical simulations. Our results provide a general framework to study the synchronization of phase oscillators in hypergraphs, and they can be extended to hypergraphs with hyperedges of arbitrary sizes, dynamic-structural correlations, and other features.

A Complexity Science Account of Humor

A common assumption of psychological theories of humor is that experienced funniness results from an incongruity between stimuli provided by a verbal joke or visual pun, followed by a sudden, surprising resolution of incongruity. In the perspective of complexity science, this characteristic incongruity-resolution sequence is modeled by a phase transition, where an initial attractor-like script, suggested by the initial joke information, is suddenly destructed, and in the course of resolution replaced by a less probable novel script. The transition from the initial to the enforced final script was modeled as a succession of two attractors with different minimum potentials, during which free energy becomes available to the joke recipient. Hypotheses derived from the model were tested in an empirical study where participants rated the funniness of visual puns. It was found, consistent with the model, that the extent of incongruity and the abruptness of resolution were associated with reported funniness, and with social factors, such as disparagement (Schadenfreude) added to humor responses. The model suggests explanations as to why bistable puns and phase transitions in conventional problem solving, albeit also based on phase transitions, are generally less funny. We proposed that findings from the model can be transferred to decision processes and mental change dynamics in psychotherapy.

Data-driven approximation for extracting the transition dynamics of a genetic regulatory network with non-Gaussian Lévy noise

In the study of biological systems, several methods based on statistical physics or machine learning have been developed for inference or prediction in the presence of complicated nonlinear interactions and random noise perturbations. However, there have been few studies dealing with the stochastic non-Gaussian perturbation case, which is more natural and universal than Gaussian white noise. In this manuscript, for a two-dimensional biological model (the MeKS network) perturbed by non-Gaussian stable Lévy noise, we use a data-driven approach with theoretical probabilistic foundation to extract the rare transition dynamics representing gene expression. This involves theories of non-local Kramers–Moyal formulas and the non-local Fokker–Planck equation, as well as the corresponding numerical algorithms, aimed at extracting the maximum likelihood transition path. The feasibility and accuracy of the method are checked. Furthermore, several dynamical behaviors and indicators are investigated. In detail, the investigation shows a bistable transition probability state of the ComK protein concentration and bifurcations in the learned transition paths from vegetative state to competence state. Analysis of the tipping time illustrates the difficulty of the gene expression. This method will serve as an example in the study of stochastic systems with non-Gaussian perturbations from biological data, and provides some insights into the extraction of other dynamical indicators, such as the mean first exit time and the first escape probability with respect to their own biological interpretations.

Exacerbated drought accelerates catastrophic transitions of groundwater-dependent ecosystems in arid endorheic basins

• Two Haloxylon species exhibited distinct water use strategies but analogous bistable transitions. • Drought accelerates catastrophic shifts in both Haloxylon ecosystems by reducing resilience. • Natural and anthropogenic forcings are aggravating drought in groundwater-dependent ecosystems. • Drought adaptation strategies for such ecosystems must account for maintaining resilience. Drought has become a major threat to regional sustainable development in drylands. Ecological drought, emphasizing the process of drought impacts on ecosystems in coupled human-natural systems, has been posing large risks to the stability of groundwater-dependent ecosystems (GDEs) in drylands. Yet, the interconnected avenues via which ecological drought drives vegetation transition, ecological resilience and ecosystem services in GDEs with species-specific traits remain elusive, especially in arid endorheic basins. Here, we combine comprehensive field measurements derived from representative groundwater depth transects in Central Asia and simulations obtained from the stochastic eco-hydrological models and the Langevin approach, we find that two groundwater-dependent species, the salt-tolerant Haloxylon ammodendron and salt-sensitive Haloxylon persicum , exhibit contrasting water use strategies being driven by variations in eco-physiological traits and environmental regimes. Nonetheless, both the low-resilient H. ammodendron and high-resilient H. persicum vegetation tend to show bistable transition corresponding to vegetated and bare soils under drought stress with stochastic noises and time delays. Alarmingly, ecological drought is accelerating catastrophic transitions in both Haloxylon ecosystems induced by diminishing ecological flows, depleting soil moisture, and aggravating salinization, together with climate forcing. In particular, exacerbated drought stress reduces ecological resilience, enhances the likelihood of catastrophic shifts, and reduces ecosystem services of GDEs in arid endorheic basins. Our results highlight that ecological drought adaptation strategies must account for resilience maintenance by balancing water scarcity, water overuse, and water/soil quality to avoid accelerating regime shifts in dryland ecosystems.

Quantifying cell transitions in C. elegans with data-fitted landscape models.

Increasing interest has emerged in new mathematical approaches that simplify the study of complex differentiation processes by formalizing Waddington's landscape metaphor. However, a rational method to build these landscape models remains an open problem. Here we study vulval development in C. elegans by developing a framework based on Catastrophe Theory (CT) and approximate Bayesian computation (ABC) to build data-fitted landscape models. We first identify the candidate qualitative landscapes, and then use CT to build the simplest model consistent with the data, which we quantitatively fit using ABC. The resulting model suggests that the underlying mechanism is a quantifiable two-step decision controlled by EGF and Notch-Delta signals, where a non-vulval/vulval decision is followed by a bistable transition to the two vulval states. This new model fits a broad set of data and makes several novel predictions.

Pneumatically Actuated Soft Gripper with Bistable Structures.

This study presents the design and test of a novel self-adaptive soft gripper, integrating pneumatic actuators and bistable carbon-fiber reinforced polymer laminates. The morphology was designed using the distinct structural characteristics of bistable structures; and the stable gripping configuration of the gripper was maintained through the bistability without continuous pressure application. The sufficient compliance of bistable structures makes the gripper versatile and adaptable to gripping deformable objects. First, a pneumatic-actuated method was introduced to achieve the reversible shape transition of the bistable structure. Next, three arrangement methods for actuators were analyzed with respect to the bistable transition and curvature, where it was found that the cross-arrangement is optimal. The effects of pneumatic actuators with different geometrical parameters on the response times are discussed, and the results show that the bistable structure can achieve shape transition within milliseconds under low pressure. Furthermore, the numerical and experimental results show good agreement between critical pressures and out-of-plane deformation. Furthermore, the shape retention function of the soft gripper was studied by using it to grasp objects of various sizes even when the pressure was reduced to the initial state. The bistable laminates exhibit sufficient compliance, and the deformed laminates can automatically accommodate the deformation of objects. The relationship between the weight and size of available gripping objects was studied; functional tests confirmed that the proposed soft gripper is versatile and adaptable for gripping objects of various shapes, sizes, and weights. This gripper has immense potential to reduce energy consumption in vacuum environments such as underwater and space.

Movie viewing elicits rich and reliable brain state dynamics

Adaptive brain function requires that sensory impressions of the social and natural milieu are dynamically incorporated into intrinsic brain activity. While dynamic switches between brain states have been well characterised in resting state acquisitions, the remodelling of these state transitions by engagement in naturalistic stimuli remains poorly understood. Here, we show that the temporal dynamics of brain states, as measured in fMRI, are reshaped from predominantly bistable transitions between two relatively indistinct states at rest, toward a sequence of well-defined functional states during movie viewing whose transitions are temporally aligned to specific features of the movie. The expression of these brain states covaries with different physiological states and reflects subjectively rated engagement in the movie. In sum, a data-driven decoding of brain states reveals the distinct reshaping of functional network expression and reliable state transitions that accompany the switch from resting state to perceptual immersion in an ecologically valid sensory experience.

The effect of heterogeneity on hypergraph contagion models.

The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes. Previous results have shown that these higher-order interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. In this paper, we present and analyze a hyperdegree-based mean-field description of the dynamics of the susceptible–infected–susceptible model on hypergraphs, i.e., networks with higher-order interactions, and illustrate its applicability with the example of a hypergraph where contagion is mediated by both links (pairwise interactions) and triangles (three-way interactions). We consider various models for the organization of link and triangle structures and different mechanisms of higher-order contagion and healing. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently or when link and triangle connections are positively correlated when compared to the uncorrelated case. We verify these results with microscopic simulations of the contagion process and with analytic predictions derived from the mean-field model. Our results show that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs.

A Promising Phase Change Material with Record High Ionic Conductivity over a Wide Temperature Range of a Plastic Crystal Phase and Magnetic Thermal Memory Effect.

The emerging organic ion plastic crystals (OIPCs) are the most promising candidates used as solid-state electrolytes in a range of ionic devices. To endow an OIPC with additional functionality may create a new type of material for multifunctional devices. Herein, we present an ion plastic crystal, [EMIm][Ni(mnt)2] (1; [EMIm]+ = 1-ethyl-3-methylimidazolium and mnt2- = maleonitriledithiolate), and its crystal consists of twin dimeric chains of [Ni(mnt)2]- anions, embraced by [EMIm]+ cations. A crystal-to-plastic crystal transformation with a large latent heat that occurred at ∼367/337 K on heating/cooling is confirmed by the differential scanning calorimetry (DSC) technique. The plastic crystal phase in 1, characterized by variable temperature powder X-ray diffraction (PXRD) and optical microscopy images, spans a broad temperature range with ΔT ∼123/153 K on heating/cooling (DSC measurement), and the wide ΔT is relevant to an extra stable anion chain owing to the strong antiferromagnetic (AFM) interactions protecting the chain from collapse in the plastic crystal state. 1 is a single-component ion plastic crystal with a record high ion conductivity, 0.21 S·cm-1, at 453 K. The crystal-to-plastic crystal transformation in 1 is coupled to a bistable magnetic transition to give a multi-in-one multifunctional material. This study provides a creative thought for the design of OIPCs with striking thermal, electrical, and magnetic multifunctionality.

A unifying model for the propagation of prion proteins in yeast brings insight into the [PSI+] prion.

The use of yeast systems to study the propagation of prions and amyloids has emerged as a crucial aspect of the global endeavor to understand those mechanisms. Yeast prion systems are intrinsically multi-scale: the molecular chemical processes are indeed coupled to the cellular processes of cell growth and division to influence phenotypical traits, observable at the scale of colonies. We introduce a novel modeling framework to tackle this difficulty using impulsive differential equations. We apply this approach to the [PSI+] yeast prion, which is associated with the misconformation and aggregation of Sup35. We build a model that reproduces and unifies previously conflicting experimental observations on [PSI+] and thus sheds light onto characteristics of the intracellular molecular processes driving aggregate replication. In particular our model uncovers a kinetic barrier for aggregate replication at low densities, meaning the change between prion or prion-free phenotype is a bi-stable transition. This result is based on the study of prion curing experiments, as well as the phenomenon of colony sectoring, a phenotype which is often ignored in experimental assays and has never been modeled. Furthermore, our results provide further insight into the effect of guanidine hydrochloride (GdnHCl) on Sup35 aggregates. To qualitatively reproduce the GdnHCl curing experiment, aggregate replication must not be completely inhibited, which suggests the existence of a mechanism different than Hsp104-mediated fragmentation. Those results are promising for further development of the [PSI+] model, but also for extending the use of this novel framework to other yeast prion or amyloid systems.

On the mean speed of bistable transition fronts in unbounded domains

This paper is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior domains we show that all transition fronts propagate with the same global mean speed, which turns out to be equal to the uniquely defined planar speed. In domains with multiple cylindrical branches, we show that the solutions emanating from some branches and propagating completely are transition fronts propagating with the unique planar speed. We also give some geometrical and scaling conditions on the domain, either exterior or with multiple cylindrical branches, which guarantee that any transition front has a global mean speed.

Harnessing transition waves to realize deployable structures

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Theoretical analysis of pressure induced spin crossover phenomenon in a di-nuclear Fe(II) molecular complex

We have studied a Fe-based di-nuclear molecular complex having the chemical formula [{Fe(bpp)(NCS)2}2(’-bipy)]·2MeOH (where bpp = -bis(pyrazol-3-yl) pyridine and ’-bipy = ’-bipyridine, 1) using density functional theory and model Hamiltonian approach. Our study provides insight to the pressure driven spin-crossover (SCO) phenomena observed experimentally in these systems. Upon increasing the pressure, the spin state of Fe(II) cation gradually changes from a high spin state (S =2) to a low spin (LS) state (S =0) accompanied by volume contraction. The gradual increase in pressure shrinks Fe–N bond length and also causes angular deviation of the FeN6 octahedron leading to full conversion to the LS state without global structural phase transition. We have carried out exact diagonalization study of an effective single site Hamiltonian and confirmed the importance of intramolecular interaction for SCO phenomena. We have investigated the cooperativity of the observed SCO phenomena. We have also studied the effect of Co doping on the spin state of Fe and find that the spin state of Fe has a subtle dependency on the concentration of dopant atoms. Excess Co doping pave the way towards the possibility of an intermediate spin state for Fe and can give rise to a bistable spin transition process.

Atmospheric Bistability and Abrupt Transitions to Superrotation: Wave–Jet Resonance and Hadley Cell Feedbacks

AbstractStrong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with easterlies or weak westerlies in the tropics, to such a superrotating state remains unclear. Is it abrupt or continuous? This question may have far-reaching consequences, as it may provide a mechanism for abrupt climate change in a planetary atmosphere, both through the loss of stability of the conventional circulation and through potential noise-induced transitions in the bistability range. We study two previously suggested feedbacks that may lead to bistability between a conventional and a superrotating state: the Hadley cell feedback and a wave–jet resonance feedback. We delineate the regime of applicability of these two mechanisms in a simple model of zonal acceleration budget at the equator. Then we show using numerical simulations of the axisymmetric primitive equations that the wave–jet resonance feedback indeed leads to robust bistability, while the bistability governed by the Hadley cell feedback, although observed in our numerical simulations, is much more fragile in a multilevel model.

Stability of bistable transition fronts in [formula omitted

This paper is concerned with the Lyapunov stability of bistable transition fronts for reaction–diffusion equations in RN with N≥2. By constructing appropriate super–sub solutions, we show that any transition fronts of bistable reaction–diffusion equations is Lyapunov stable under spatial decaying initial perturbations.