Spatial Bistability Research Articles

Evolution of UAV Landing Structures in the Bistable Space of Kresling Origami Structures

Landing gear plays an important role in enabling unmanned aerial vehicles to engage in complex missions and protect expensive airborne sensors. Most existing landing gears are designed to satisfy only specific maneuvers in predefined scenarios. Although effective in predefined scenarios, these landing gears cannot guarantee the adaptiveness in multiple scenarios. A promising solution is to build a model automatically generated based on the actual requirements, so that the expected model structure can be obtained through a constraint generation process. However, translating the actual requirements into reasonable design constraints is complex. For this purpose, we propose a landing structure design process in the bistable space of the Kresling tube. Furthermore, we use a combination of graph search and controller to optimize the landing structure. We validate the bistatic and graph search combined design structure in a realistic environment and test the mechanisms flexibility and assisted landing capability. Experiments show that the structure combining spatial bistability with a graph search approach can safely and successfully land a quadrotor under various conditions while enhancing the UAV's shock absorption during landing.

Spatial Nonreciprocal Transmission and Optical Bistability Based on Millimeter‐Scale Suspended Metasurface

AbstractWhen light interacts with microscopic objects at the micro‐ and nano‐scale, the momentum exchange between photons and objects can be very significant. While the optical radiation pressure at the same level is usually too weak to change the mechanical state of macro‐scale objects at millimeter scale or beyond. Suspended metasurfaces with excellent mechanical and optical properties are ideal candidates for light‐matter interactions. Here, without sound insulation conditions, the spatial optical nonreciprocity based on an optomechanical system with a 2 mm × 2 mm × 110 nm Si3N4 suspended metasurface at the telecom wavelength is demonstrated, with peak wavelength shift up to 1.1 pm, which is about 4.0 times of the full width at half maximum, together with optical bistability at only about 10 W cm−2 input intensities, which is more than 4 orders of magnitude lower than traditional nonlinear optical mechanism. This work may pave new avenues for spatially nonreciprocal devices and bistable devices, and benefit the applications such as precision sensing, cavity quantum optomechanics, and all‐optical switching.

Pattern Formation in the Bromate-Sulfite-Ferrocyanide Reaction.

Mixed Landolt-type pH oscillators are versatile systems that allow the experimental study of a wide range of nonlinear phenomena including multistability, oscillations, and spatiotemporal patterns. We report on the dynamics of the bromate-sulfite-ferrocyanide reaction operated in a open one-side-fed reactor, where spatial bistability, spatiotemporal oscillations, front and Turing-type patterns have been observed. The role of different experimental parameters, like the input flow concentrations of the hydrogen and the ferrocyanide ions, the temperature and the thickness of the gel medium (which affects the rate of the diffusive feed) have been investigated. We point out that all these parameters can be efficiently used to control the spatiotemporal dynamics. We show that the increase of ionic strength stabilizes the uniform states at the expense of the patterned one. Some general aspects of the spatiotemporal dynamics of mixed Landolt type systems, which are based on the oxidation of sulfite ions by strong oxidants, are emphasized.

Spatiotemporal behavior induced by differential diffusion in Landolt systems.

The spatiotemporal dynamics of Landolt type reactions, for instance reactions between sulfite ions and strong oxidants, performed in a medium fed by the diffusion from a boundary is investigated numerically by using a simple general reaction scheme. In these conditions, the model can generate various spatiotemporal phenomena, e.g., spatial bistability, simple and complex oscillations, birhythmicity, and chaos, even though in a spatially homogeneous open reactor only steady-state bistability can develop. The model consists of two reactions, a protonation equilibrium of the reductant and an oxidation step that is autoactivated by hydrogen ions. The rich dynamics is the result of two factors: (i) long-range activation, through the rapidly diffusing hydrogen ions, (ii) the presence of two parallel autocatalytic pathways. Long range activation provides the necessary negative feedback, whereas the dual nature of the autocatalysis leads to the appearance of two different oscillatory modes. The presence of a second-order term in the rate law of the autocatalytic reaction is linked to a large amplitude oscillations that affect the system as a whole, whereas the third-order one gives rise to localized front oscillations. The complex phenomena, like mixed mode and chaotic oscillations are observed at the meeting of these different oscillatory modes.

Pattern formation of Rho GTPases in single cell wound healing

The Rho GTPases-Rho, Rac, and Cdc42-control an enormous variety of processes, many of which reflect activation of these GTPases in spatially confined and mutually exclusive zones. By using mathematical models and experimental results to establish model parameters, we analyze the formation and segregation of Rho and Cdc42 zones during Xenopus oocyte wound repair and the role played by Abr, a dual guanine nucleotide exchange factor-GTPase-activating protein, in this process. The Rho and Cdc42 zones are found to be best represented as manifestations of spatially modulated bistability, and local positive feedback between Abr and Rho can account for the maintenance and dynamic properties of the Rho zone. In contrast, the invocation of an Abr-independent positive feedback loop is required to account for Cdc42 spatial bistability. In addition, the model replicates the results of previous in vivo experiments in which Abr activity is manipulated. Further, simulating the model with two closely spaced wounds made nonintuitive predictions about the Rho and Cdc42 patterns; these predictions were confirmed by experiment. We conclude that the model is a useful tool for analysis of Rho GTPase signaling and that the Rho GTPases can be fruitfully considered as components of intracellular pattern formation systems.

Precision of Hunchback Expression in the Drosophila Embryo

Activation of the gap gene hunchback (hb) by the maternal Bicoid gradient is one of the most intensively studied gene regulatory interactions in animal development. Most efforts to understand this process have focused on the classical Bicoid target enhancer located immediately upstream of the P2 promoter. However, hb is also regulated by a recently identified distal shadow enhancer as well as a neglected "stripe" enhancer, which mediates expression in both central and posterior regions of cellularizing embryos. Here, we employ BAC transgenesis and quantitative imaging methods to investigate the individual contributions of these different enhancers to the dynamic hb expression pattern. These studies reveal that the stripe enhancer is crucial for establishing the definitive border of the anterior Hb expression pattern, just beyond the initial border delineated by Bicoid. Removal of this enhancer impairs dynamic expansion of hb expression and results in variable cuticular defects in the mesothorax (T2) due to abnormal patterns of segmentation gene expression. The stripe enhancer is subject to extensive regulation by gap repressors, including Kruppel, Knirps, and Hb itself. We propose that this repression helps ensure precision of the anterior Hb border in response to variations in the Bicoid gradient.

Mechano-chemical dynamics of active gels: interplay between spatial bistability and volume variations

AbstractThe mechano-chemical dynamics of a spherical bead of gel immersed in an autocatalytic bistable chemical reaction are examined. The spheres exhibit autonomous volume self-oscillation dynamics. We present a multi-diffusional approach to a hydrodynamic theory of gels, and also evolution equations incorporating chemical processes.

Multiple types of spatio-temporal oscillations induced by differential diffusion in the Landolt reaction

The acid autoactivated iodate-sulfite redox reaction (Landolt reaction) exhibits bistability but no oscillatory dynamics when operated in a continuous stirred tank reactor (CSTR). However, it has been previously found experimentally that this reaction can exhibit both spatial bistability and oscillations when carried out in a one side diffusely fed spatial reactor. The precise origin of the oscillatory instability remained mainly elusive. We unambiguously show, in numerical simulations based of a kinetic model recently proposed by Csekõet al., J. Phys. Chem., 2008, 112, 5954), that the observed oscillations are due to the faster diffusion of the proton relative to the other feed species (long range activation instability). Furthermore, our calculations account for the previous experimental observation of two different oscillatory modes. The first one is associated to localized front oscillations, as already reported in another reaction. The other one is a periodic switch between the two states of the spatial bistability and affects the system as a whole. This oscillatory mode was undocumented in the previous studies of long range activation instabilities. More complex dynamical behaviors that mix these two types of oscillations are also reported.

An effective design method to produce stationary chemical reaction-diffusion patterns

We present a semi-empirical experimental design method to produce nontrivial chemical reaction-diffusion patterns in open reactors. We specially focus on the development of stationary patterns. The method is based on autoactivated reactions that produces spatial bistability, the addition of an independent antagonist reaction to produce spatio-temporal oscillations, and the introduction of a low mobility complexing agent that rapidly and reversibly binds the main autoactivatory species. The method is presented in formal way. Actual experimental results are used for illustration. We point out the open problems of the mathematical description: they relate to the boundary conditions, to the dimensionality of the system, and to the coupled time- and space-scale changes induced by the complexing agent.

Simulation of interaction of oriented J aggregates with resonance laser radiation

The interaction of laser radiation with single J aggregates of cyanine dyes is theoretically analyzed and numerically simulated. The quantum-mechanical calculations of the equilibrium geometry and the energies and intensities of the lowest singlet electronic transitions in pseudoisocyanine chloride and its linear (chain) oligomers are fulfilled. The data of these calculations can serve as parameters of the analyzed model of interaction of J aggregates with radiation in the one-particle density matrix approximation. This model takes into account relaxation processes, the annihilation of excitations at neighboring molecules, and inhomogeneous broadening. Assuming that the inhomogeneous broadening is absent, calculations demonstrate the existence of spatial bistability, molecular switching waves, and dissipative solitons. The effect of the inhomogeneous broadening and the radiation intensity on the effective coherence length in linear (chain) J aggregates is analyzed.

Extracellular regulation of BMP signaling

In the developing organism, cells differentiate, divide and die as part of groups of hundreds or thousands of cells called 'morphogenetic fields'. Fields have the remarkable property of self-regulation: for example, if the forelimb field is bisected, each half can give rise to a complete limb after transplantation, as discovered by Ross Harrison in 1918. Therefore, cells in the morphogenetic field are capable of long-range communication with each other in order to ascertain their position [1]. This positional information is relayed in the extracellular space in the form of concentration gradients of specific classes of extracellular molecules called 'morphogens' that trigger cellular responses by binding and activating cell surface receptors. Here, we focus on a family of morphogens called 'Bone Morphogenetic Proteins' (BMPs), which has provided a new paradigm for signaling regulation in the extracellular space.

Pattern formation in the thiourea–iodate–sulfite system: Spatial bistability, waves, and stationary patterns

We present a detailed study of the reaction–diffusion patterns observed in the thiourea–iodate–sulfite (TuIS) reaction, operated in open one-side-fed reactors. Besides spatial bistability and spatio-temporal oscillatory dynamics, this proton autoactivated reaction shows stationary patterns, as a result of two back-to-back Turing bifurcations, in the presence of a low-mobility proton binding agent (sodium polyacrylate). This is the third aqueous solution system to produce stationary patterns and the second to do this through a Turing bifurcation. The stationary pattern forming capacities of the reaction are explored through a systematic design method, which is applicable to other bistable and oscillatory reactions. The spatio-temporal dynamics of this reaction is compared with that of the previous ferrocyanide–iodate–sulfite mixed Landolt system.

Adding a Turing Pattern Reaction

![Figure][1] CREDIT: HORVATH ET AL. Two chemical-reaction systems can form sustained stationary patterns (Turing patterns) in solution as the result of the movement of a diffusible species and the formation of negative feedback loops—the chlorite-iodide–malonic acid reaction and the ferrocyanide-iodate-sulfite reaction. Horvath et al. (p. [772][2]) set out to find other examples based on three criteria—that the reaction can develop spatial bistability, that independent control of the negative feedback reaction can be achieved, and the activating and inhibiting processes can be decoupled by slowing down the diffusing species with a complexing agent. The thiourea-iodate-sulfite (TuIS) reaction could be developed into a system that produced different stationary patterns, including stripes and hexagonal arrays of spots. Thus, such Turing pattern–generating reactions are not necessarily uncommon. [1]: pending:yes [2]: /lookup/doi/10.1126/science.1169973

An Experimental Design Method Leading to Chemical Turing Patterns

Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information.

Pattern formation in the ferrocyanide-iodate-sulfite reaction: The control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.

Sustained Spatiotemporal Patterns in the Bromate−Sulfite Reaction

The acid autoactivated bromate-sulfite reaction exhibits spatial bistability, travelling acid-base fronts, and spatiotemporal oscillations when operated in an unstirred one-side-fed spatial reactor. We show that a skeleton kinetic model, recently proposed by Szántó and Rábai, in which we take into account the charge and the actual diffusivity of solvated ions, provides theoretical results in good agreement with experimental observations. The differences with previous observations made with the homologous iodate-sulfite reaction are discussed. Despite the analogies in the phase diagram of these two systems, it is concluded that the relevant kinetic mechanism of the iodate-sulfite system cannot be just a homologous transcription of that presently working well for the bromate-sulfite system, even in excess sulfite conditions.

Spatiotemporal Dynamics of the Landolt Reaction in an Open Spatial Reactor with Conical Geometry

In a previous study, the iodate-sulfite proton autoactivated reaction (Landolt reaction) was shown to exhibit spatial bistability and spatiotemporal oscillations when operated in an open spatial reactor with fixed "thickness", i.e., feed boundary to core distance. Here, we show that the spatial reactors with conical geometry enable one to rapidly probe the sensitivity of the above phenomena over a large range of the "thickness" parameter. This often-neglected parameter in chemical pattern studies plays an important role on the selection and stability of states. We reveal that the quenching capacity of slow diffusing polyacrylate ions on the spatiotemporal oscillations depends on this "thickness". The presented results should be useful for further research on reaction diffusion patterns and chemomechanical structures.

Spatial bistability: A source of complex dynamics. From spatiotemporal reaction-diffusion patterns to chemomechanical structures

We show experimentally and theoretically that reaction systems characterized by a slow induction period followed by a fast evolution to equilibrium can readily generate "spatial bistability" when operated in thin gel reactors diffusively fed from one side. This phenomenon which corresponds to the coexistence of two different stable steady states, not breaking the symmetry of the boundary conditions, can be at the origin of diverse reaction-diffusion instabilities. Using different chemical reactions, we show how stationary pulses, labyrinthine patterns or spatiotemporal oscillations can be generated. Beyond simple reaction-diffusion instabilities, we also demonstrate that the cross coupling of spatial bistability with the size responsiveness of a chemosensitive gel can give rise to autonomous spatiotemporal shape patterns, referred to as chemomechanical structures.

Spatial bistability, oscillations and excitability in the Landolt reaction

The spatio-temporal dynamics of the iodate–sulfite reaction (Landolt reaction) is investigated in a one-side-fed gel reactor. In these conditions, the system can generate spatial bistability, oscillations and excitability, even though in a well-stirred open reactor only steady-state bistability can be observed. Different experiments to probe the origin of the observed spatio-temporal instabilities are discussed. The reaction is mainly auto-activated by protons. The different observations globally support that the oscillatory behaviors are the result of long-range activation, through the rapidly diffusing protons. Such a source of temporal instability has only been recently discovered. This is the second experimental example for such a mechanism. Phase diagrams are established as a function of the ratio and the value of the input concentrations of iodate and sulfite. Remarkably, the stability limits of the steady spatial states and the spatio-temporal oscillatory state organize in a cross-shaped phase diagram, a topology commonly observed in open well stirred systems.