Range Of Bistability Research Articles

Reversible Solubility Switching of a Polymer Triggered by Visible-Light Responsive Azobenzene Photochromism with Negligible Thermal Relaxation.

This study reports the reversible solubility switching of a polymer triggered by non-phototoxic visible light. A photochromic polymerizable azobenzene monomer with four methoxy groups at the ortho-position (mAzoA) was synthesized, exhibiting reversible photoisomerization between trans- and cis-states using green (546 nm) and blue light (436 nm). Free radical copolymerization of hydrophilic dimethylacrylamide (DMAAm) with mAzoA produced a light-responsive random copolymer (P(mAzoA-r-DMAAm)) that shows a reversible photochromic reaction to visible light. Optimizing mAzoA content resulted in P(mAzoA10.7-r-DMAAm)3.0kDa exhibiting LCST-type phase separation in PBS (pH 7.4) with trans- and cis-states at 39.2°C and 32.9°C, respectively. The bistable temperature range of 6.3°C covers 37°C, suitable for mammalian cell culture. Reversible solubility changes were demonstrated under alternating green and blue light at 37°C. 1H NMR indicated significant retardation of thermal relaxation from cis- to trans-states, preventing undesired thermal mechanical degradation. Madin Darby Canine Kidney (MDCK) cells adhered to the P(mAzoA-r-DMAAm) hydrogel, confirming its non-cytotoxicity and potential for biocompatible interfaces. This principle is useful for developing hydrogels that can reversibly stimulate cells mechanically or chemically in response to visible light.

Experimental bifurcation analysis of a clamped beam with designed mechanical nonlinearity

We use control-based continuation (CBC) to perform an experimental bifurcation study of a periodically forced dual-beam. The nonlinearity is of geometric nature, provided by a thin, clamped beam. The overall system exhibits hysteresis and bistability in its open-loop frequency response due to a hardening, Duffing-like nonlinear stiffness, which can be designed or adjusted by choosing the properties of the thin beam. We employ local stabilising feedback control to implement CBC and track stable periodic solutions past the fold points. Thus obtained continuous solution branches are used to generate the solution surface over the plane of excitation amplitude and frequency. This surface features two curves of fold bifurcations that meet at a cusp point, and they delimit the experimentally observed bistability range of this nonlinear beam.

Effect of Tunable Dielectric Core on Optical Bistability in Cylindrical Core–Shell Nanocomposites

In this paper, the effect of a tunable dielectric core on local field enhancement, induced optical bistability, and the optical bistability domain in cylindrical core–shell nanoparticle composites are studied. The local field enhancement factor increases significantly at two resonant frequencies. The results demonstrate that the local field enhancement factor in the cylindrical core–shell nanoparticle increases when the natural attribute of the dielectric function of the dielectric core is varied by adding a dielectric function to it. Furthermore, we demonstrated that the magnitude of the imaginary part of the active dielectric core increases as the onset and offset input intensities increase. This indicates that the optical bistability or threshold width range widens as the imaginary part of the dielectric function of the dielectric core increases, thereby enlarging the threshold domain to improve system activation.

From thin plates to Ahmed bodies: linear and weakly nonlinear stability of rectangular prisms

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$ , while the length-to-height ratio $1/6< L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$ , two stationary modes, $A$ and $B$ , become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$ , two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ values of these four modes increase with $L/H$ , reproducing qualitatively the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly nonlinear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases, state $(A,0)$ appears first, followed by state $(0,B)$ . While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$ , similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully nonlinear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies.

Exploring the mono-/bistability range of positively autoregulated signaling systems in the presence of competing transcription factor binding sites.

Binding of transcription factor (TF) proteins to regulatory DNA sites is key to accurate control of gene expression in response to environmental stimuli. Theoretical modeling of transcription regulation is often focused on a limited set of genes of interest, while binding of the TF to other genomic sites is seldom considered. The total number of TF binding sites (TFBSs) affects the availability of TF protein molecules and sequestration of a TF by TFBSs can promote bistability. For many signaling systems where a graded response is desirable for continuous control over the input range, biochemical parameters of the regulatory proteins need be tuned to avoid bistability. Here we analyze the mono-/bistable parameter range for positively autoregulated two-component systems (TCSs) in the presence of different numbers of competing TFBSs. TCS signaling, one of the major bacterial signaling strategies, couples signal perception with output responses via protein phosphorylation. For bistability, competition for TF proteins by TFBSs lowers the requirement for high fold change of the autoregulated transcription but demands high phosphorylation activities of TCS proteins. We show that bistability can be avoided with a low phosphorylation capacity of TCSs, a high TF affinity for the autoregulated promoter or a low fold change in signaling protein levels upon induction. These may represent general design rules for TCSs to ensure uniform graded responses. Examining the mono-/bistability parameter range allows qualitative prediction of steady-state responses, which are experimentally validated in the E. coli CusRS system.

Invasion reversal by front transitions and their implications for ecosystem management

Alien species often become invasive by triggering the growth of pathogens that exert a strong negative effect on the native species. Using an extended Lotka–Volterra plant competition model that includes pathogen dynamics with a strong Allee effect we identify a bistability range of counter-propagating fronts representing invasion and recovery dynamics. The fronts differ in the levels of the pathogen in the front zone; high, beyond the Allee threshold for the invasion front and low, below that threshold for the recovery front. Invasion reversal is then studied as induced transitions from invasion fronts to recovery fronts. The study suggests managing invasion by local manipulations in the front zone that increase the Allee threshold and thereby reverse the front from invasion to recovery. We demonstrate numerically direct and indirect manipulations of this kind.

Lamella-rod pattern transition and confinement effects during eutectic growth

We present an in situ experimental study of the lamellar-to-rod transition during directional solidification of a model eutectic transparent alloy –the succinonitrile-(d)camphor (SCN-DC) system. Coupled-growth patterns, and their morphological transformations upon changes of the pulling velocity V (3.5−70.0nms−1) were observed in real time in a series of flat-wall samples with different thicknesses δ from 15 (thin samples) to 350 µm (thick samples). At relatively large velocity, rod-like patterns formed systematically. In contrast, stable lamellae were observed at sufficiently low velocity, regardless of the sample thickness in the investigated range. In confined-geometry samples (δ=30−140 µm), lamellar patterns were stable over a large range of the interphase spacing λ at low V. The lamella in contact with the sample walls were stabilized against a propagative breakup, and the formation of rods was mediated by secondary instabilities such as a zigzag mode and a spatial-oscillation mode. In the bistable range, a hysteresis upon increasing or decreasing V was observed, as well as complex phenomena involving oscillatory, mixed and hybrid patterns. The (reverse) transition from rods to lamellae involved a rod elongation instability. A discussion on the elementary mechanisms that determine the lamellar-rod transition, and their dependence on λ and V is initiated.

Theoretical investigation of the nonreciprocal bistable absorption of electromagnetic waves in one-dimensional photonic crystals combined with the nonlinear magnetized plasma defect layer

In this paper, we investigate the nonreciprocity bistable absorption of a one-dimensional photonic crystals combined with a novel nonlinear magnetized plasma defect layer. It is figured out that the structure has apparent nonreciprocity, bistable positive and negative absorption of the forward and backward incidences under the nonlinear magneto-optical effect. In addition, the tuning effects of the external magnetic fields and angles are studied. The consequences indicate that the two have significantly opposite working modulation effects on the bistable working range and absorptance. Specifically, the external magnetic field leads to individually controlling the bistability switch-down threshold, and the angle can affect the switch-up and switch-down thresholds concurrently. In the simulation of the electric field diagrams of the proposed structure, the incident side is larger than the transmitted to verify these negative absorption properties. The external magnetic fields and angles will form an alternating conversion between positive and negative absorption with different transmitted intensities. Considering the significance of theoretical experimental verification, concise and feasible experimental schemes are given. This work provides a constructive proposal for the design of magnetization modulated isolators for the nonlinear magnetized plasma materials.

Theoretical analysis of optical bistability in a CW-pumped erbium-doped fiber laser

A theoretical model that allows numerical simulations of optical bistability phenomena in CW-pumped erbium-doped fiber lasers is presented. Results of the simulations match correctly with previous experimental data. In order to simulate this phenomenon, the population inversion and optical powers longitudinal distributions along the active fiber have been considered. If this fiber is long enough, it has been found that the transition between the non-lasing and the lasing states involves a dramatic redistribution of the population inversion along the active medium. This fact makes that non-lasing and lasing states constitute different enough initial conditions which determine different final responses to the same control parameter, that is to say, bistability. On the other hand, a theoretical justification is found for a previous experimental result which pointed out that the bistability range becomes reduced if an external signal is launched to the cavity. Finally, the bistability range width dependence on the active fiber length is analyzed.

Advances in biophysical feedbacks and the resulting stable states in tidal flat systems

<p indent="0mm">As an integral part of the coastal wetland system, tidal flats play an important role in maintaining the health of coastal ecosystems, resisting natural coastal disasters, and blue carbon sequestration. Tidal flats can provide suitable habitats for a variety of organisms; simultaneously, such organisms mediate hydrodynamic and sediment processes, hence affecting the geomorphic evolution and stability of tidal flat systems. In recent years, tidal flat systems have faced the comprehensive impacts of rapid human activities, frequent storm surges, and reduced sediment availabilities, which have aggravated tidal flat erosion. Severe erosion is accompanied by a critical biomass loss, especially under complex biological-physical interactions. Tidal flat degradation is often amplified, threatening the stability of tidal flat systems. The ultimate goal of ecological protection and restoration of tidal flat systems is to establish a self-sustaining method with less artificial assistance. To date, only a few ecological restoration projects in China have considered the integration of biological and physical processes in tidal flats. The most important reason is the lack of understanding of the basic laws of natural construction and operation of the systems. Therefore, understanding and giving way to the self-organization process driven by the biophysical interactions in tidal flat systems have become an important scientific and technical necessity in the ecological protection and restoration of tidal flats. First, we summarized the biophysical effects of salt marsh vegetation and benthic microalgae on the hydrodynamic and sediment movement process of tidal flats. Salt marsh plants and benthic microalgae change the hydrodynamic and sediment processes through wave dissipation and sediment stabilization. Conversely, the changing physical conditions affect the growth and development of salt marsh and benthic microalgae. Second, we qualitatively analyzed the bistability and catastrophic shift of a tidal flat system driven by the salt marsh-sediment and benthic microalgae-sediment feedback, both containing some similarities and differences. Specifically, driven by biophysical feedbacks, both the salt marsh- and benthic microalgae-sediment systems have alternative stable states; with the increased bottom shear stress, both systems shift from a state characterized by high biomass and sediment deposition to that with low biomass and sediment deposition; the bistable range of the salt marsh-sediment system is wider, and the system has a greater hysteresis, indicating that once degraded, it is more difficult for the salt marsh system to be restored to its original state. Third, we discussed the self-organized bio-geomorphic characteristics. The scale-dependent feedback between organisms and physical environments results in spatial patterns. The self-organized patterns have been widely found in a tidal flat ecosystem, for example, circular salt marsh clusters, salt marsh cliffs, and patterned mudflats characterized by the microalgae-covered hummocks alternating with water-filled hollows. Self-organized patterns can improve the primary productivity and sediment deposition of tidal flats, thereby enhancing the stability of ecosystems, which is of great significance for the ecosystem function of tidal flats. Finally, this paper proposed the critical scientific problems that still need to be solved in the future, such as the continuous field observation at the system level, the regulation of biological interspecific interactions under physical conditions, and the quantitative simulation of catastrophic shift thresholds in the tidal flat bio-geomorphic system.

Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe

This paper analyzes the properties of the nonequilibrium singular point in one-dimensional elementary catastrophe. For this analysis, the Kosambi–Cartan–Chern (KCC) theory is applied to characterize the dynamical system based on differential geometrical quantities. When both the nonlinear connection and deviation curvature are zero, that is, when the geometric stability of the KCC theory is neutral, two bifurcation curves are obtained: one is the known curve with an equilibrium singular point, and the other is a new curve with a nonequilibrium singular point. The two singular points are distinguished based on the vanishing condition of the Berwald connection. Applied to the ecosystem described by the Hill function, the absolute value of the cuspidal curvature of the nonequilibrium singular point is larger than that of the equilibrium singular point. The ecological interpretation of this result is that the range of bistability of the ecosystem in the nonequilibrium state is greater than that in the equilibrium state. The type of singular points in equilibrium and nonequilibrium bifurcation curves are not necessarily the same. For instance, there is a combination in which even if the former has one cusp, the latter may show various types, depending on the parametric space. These results demonstrate that there are cases where simply shifting the system from the equilibrium to nonequilibrium state expands the range of bistability and changes the type of singularity. Although singularity analysis is often performed near the equilibrium point, nonequilibrium analysis, i.e. analysis based on the KCC theory, provides a useful perspective for analyzing singularity theory according to the bifurcation phenomenon.

Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number$Re$are increased, showing that the bistability is neither a finite-size nor a finite-$Re$effect. We furthermore predict a cross-over from a bimodal regime at low box size, low$Re$to a regime of pure hysteresis at high box size, high$Re$, in which any transition from one state to the other is prohibited at any finite time scale.

Network modeling-based identification of the switching targets between pyroptosis and secondary pyroptosis

The newly identified cell death type, pyroptosis plays crucial roles in various diseases. Most recently, mounting evidence accumulates that pyroptotic signaling is highly correlated with coronavirus disease 2019 (COVID-19). Thus, understanding the induction of the pyroptotic signaling and dissecting the detail molecular control mechanisms are urgently needed. Based on recent experimental studies, a core regulatory model of the pyroptotic signaling is constructed to investigate the intricate crosstalk dynamics between the two cell death types, i.e., pyroptosis and secondary pyroptosis. The model well reproduces the experimental observations under different conditions. Sensitivity analysis determines that only the expression level of caspase-1 or GSDMD has the potential to individually change death modes. The decrease of caspase-1 or GSDMD level switches cell death from pyroptosis to secondary pyroptosis. Besides, eight biochemical reactions are identified that can efficiently switch death modes. While from the viewpoint of bifurcation analysis, the expression level of caspase-3 is further identified and twelve biochemical reactions are obtained. The coexistence of pyroptosis and secondary pyroptosis is predicted to be observed not only within the bistable range, but also within proper monostable range, presenting two potential different control mechanisms. Combined with the landscape theory, we further explore the stochastic dynamic and global stability of the pyroptotic system, accurately quantifying how each component mediates the individual occurrence probability of pyroptosis and secondary pyroptosis. Overall, this study sheds new light on the intricate crosstalk of the pyroptotic signaling and uncovers the regulatory mechanisms of various stable state transitions, providing potential clues to guide the development for prevention and treatment of pyroptosis-related diseases.

Thermal Bistability of an Ultrathin Film of Iron(II) Spin-Crossover Molecules Directly Adsorbed on a Metal Surface.

Spin-crossover molecules are very attractive compounds to realize multifunctional spintronic devices. Understanding their properties when deposited on metals is therefore crucial for their future rational implementation as ultrathin films in such devices. Using X-ray absorption spectroscopy, we study the thermal transition of the spin-crossover compound FeII((3,5-(CH3)2Pz)3BH)2 from submonolayer to multilayers on a Cu(111) substrate. We determine how the residual fraction of high spin molecules at low temperature, as well as the bistability range and the temperature of switching, depends on the layer thickness. The most spectacular effect is the clear opening of a 35 ± 9 K thermal hysteresis loop for a 3.0 ± 0.7 monolayers thick film. To better understand the role played by the substrate and the dimensionality on the thermal bistability, we have performed Monte Carlo Arrhenius simulations in the framework of a mechanoelastic model that include a molecule-substrate interaction. This model reproduces well the main features observed experimentally and can predict how the spin-crossover transition is modified by the thickness and the substrate interaction.

Effects of degree distributions in random networks of type-I neurons.

We consider large networks of theta neurons and use the Ott-Antonsen ansatz to derive degree-based mean-field equations governing the expected dynamics of the networks. Assuming random connectivity, we investigate the effects of varying the widths of the in- and out-degree distributions on the dynamics of excitatory or inhibitory synaptically coupled networks and gap junction coupled networks. For synaptically coupled networks, the dynamics are independent of the out-degree distribution. Broadening the in-degree distribution destroys oscillations in inhibitory networks and decreases the range of bistability in excitatory networks. For gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations. Many of the results are shown to also occur in networks of more realistic neurons.

Model-based robustness and bistability analysis for methylation-based, epigenetic memory systems.

In recent years, epigenetic memory systems have been developed based on DNA methylation and positive feedback systems. Achieving a robust design for these systems is generally a challenging and multifactorial task. We developed and validated a novel mathematical model to describe methylation-based epigenetic memory systems that capture switching dynamics of methylation levels and methyltransferase amounts induced by different inputs. A bifurcation analysis shows that the system operates in the bistable range, but in its current setup is not robust to changes in parameters. An expansion of the model captures heterogeneity of cell populations by accounting for distributed cell division rates. Simulations predict that the system is highly sensitive to variations in temperature, which affects cell division and the efficiency of the zinc finger repressor. A moderate decrease in temperature leads to a highly heterogeneous response to input signals and bistability on a single-cell level. The predictions of our model were confirmed by flow cytometry experiments conducted in this study. Overall, the results of our study give insights into the functional mechanisms of methylation-based memory systems and demonstrate that the switching dynamics can be highly sensitive to experimental conditions.

Stationary states and instabilities of a Möbius fiber resonator

We examine the steady state and dynamic behaviour of an optical resonator comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibres over a single roundtrip. We find this supports a range of rich multi-dimensional bistability in the continuous wave regime, as well as previously unseen cavity soliton states. Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fibre resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fibre loops. Parametric instability gives birth to train of pulses with a peculiar period-doubling behavior.

Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

Abstract

Dynamics of Ultrathin Vanadium Oxide Layers on Rh(111) and Rh(110) Surfaces During Catalytic Reactions

Over the past 35 years rate oscillations and chemical wave patterns have been extensively studied on metal surfaces, while little is known about the dynamics of catalytic oxide surfaces under reaction conditions. Here we report on the behavior of ultrathin V oxide layers epitaxially grown on Rh(111) and Rh(110) single crystal surfaces during catalytic methanol oxidation. We use photoemission electron microscopy and low-energy electron microscopy to study the surface dynamics in the 10−6 to 10−2 mbar range. On VOx/Rh(111) we find a ripening mechanism in which VOx islands of macroscopic size move toward each other and coalesce under reaction conditions. A polymerization/depolymerization mechanism of VOx that is sensitive to gradients in the oxygen coverage explains this behavior. The existence of a substructure in VOx islands gives rise to an instability, in which a VOx island shrinks and expands around a critical radius in an oscillatory manner. At 10−2 mbar the VOx islands are no longer stable but they disintegrate, leading to turbulent redistribution dynamics of VOx. On the more open and thermodynamically less stable Rh(110) surface the behavior of VOx is much more complex than on Rh(111), as V can also populate subsurface sites. At low V coverage, one finds traveling interface pulses in the bistable range. A state-dependent anisotropy of the surface is presumably responsible for intriguing chemical wave patterns: wave fragments traveling along certain crystallographic directions, and coexisting different front geometries in the range of dynamic bistability. Annealing to 1000 K causes the formation of macroscopic VOx islands. Under more reducing conditions dendritic growth of a VOx overlayer is observed.

Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability.

The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully understood, and current models often assume a long-range infectionlike process for the dynamics of marks, due to the polymeric nature of the chromatin fiber which allows looping between distant sites. While these existing models typically consider antagonizing marks, here we propose a qualitatively different scenario which analyses the spreading of a single mark. We define a one-dimensional stochastic model in which mark spreading/infection occurs as a long-range process whereas mark erasure/recovery is a local process, with an enhanced rate at boundaries of infected domains. In the limiting case where our model exhibits absorbing states, we find a first-order-like transition separating the marked/infected phase from the unmarked/recovered phase. This suggests that our model, in this limit, belongs to the long-range compact directed percolation universality class. The abrupt nature of the transition is retained in a more biophysically realistic situation when a basal infection/recovery rate is introduced (thereby removing absorbing states). Close to the transition there is a range of bistability where both the marked/infected and unmarked/recovered states are metastable and long lived, which provides a possible avenue for controlling fate decisions in cells. Increasing the basal infection/recovery rate, we find a second transition between a coherent (marked or unmarked) phase, and a mixed, or random, one.