Edge Of Instability Research Articles

Rapid screening of creep resistance in additive manufactured Ti-6Al-4V alloy

In this study, rapid screening of creep resistance for additively manufactured (AM) materials is enabled using an accelerated creep test (ACT) called the dynamic negative stepped test (DNST). Additively manufactured components are on the rise in aerospace systems, particularly turbine engine parts. It can be challenging to identify the AM process parameters that correspond to high-temperature strength and creep resistance. Tests are needed that rapidly screen and qualify creep resistance. In DNST, the temperature is held constant, and the specimen is taken through a series of load holds from high to low. The DNST contains two distinct characteristics: (1) the hold duration for each step is “dynamically” controlled to ensure the minimum-creep-strain-rate is achieved at every step, and (2) the “descending” profile maximizes damage accumulation while remaining on the edge of instability. The DNST assesses a material's ability to resist creep damage accumulated across multiple deformation mechanisms. In this study, electron beam melted Ti–6Al–4V, built at six (6) directions: 0°, 30°, 45°, 60°, 90°, and V, is tested using a four-step DNST at 650 °C. Analysis of the minimum-creep-strain-rate (at each step), creep ductility, and rupture were performed. A strain energy density (SED) benchmark metric was established to rapidly screen and classify creep resistance using an “Ashby-like” plot that balanced energy dissipated and energy dissipation rate. The creep resistance was found to be ranked from V, 60, 45, 30, 90, and 0 in descending order. Microstructural and crystallographic characterization revealed grain refinement progressing from the strain-free to the high-strain regions, indicative of dynamic recrystallization (DRX). Further observations revealed that the material's energy capacity increased with the alignment of the grains' long axis and tensile direction.

Intermittency Scaling for Mixing and Dissipation in Rotating Stratified Turbulence at the Edge of Instability

Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape atmospheric dynamics. In this context, we analyze new direct numerical simulations of rotating stratified flows with a large-scale forcing, which is either random or quasi-geostrophic (QG). Runs were performed at a moderate Reynolds number Re and up to 1646 turn-over times in one case. We found intermittent fluctuations of the vertical velocity w and temperature θ in a narrow domain of parameters as for decaying flows. Preliminary results indicate that parabolic relations between normalized third- and fourth-order moments of the buoyancy flux ∝wθ and of the energy dissipation emerge in this domain, including for passive and active scalars, with or without rotation. These are reminiscent of (but not identical to) previous findings for other variables and systems such as oceanic and atmospheric flows, climate re-analysis data, fusion plasmas, the Solar Wind, or galaxies. For QG forcing, sharp scaling transitions take place once the Ozmidov length scale ℓOz is resolved—ℓOz being the scale after which a turbulent Kolmogorov energy spectrum likely recovers at high Re.

Quasiuniversal scaling in mouse-brain neuronal activity stems from edge-of-instability critical dynamics

The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the brain transmits, processes, and stores information. An inspiring, albeit controversial, conjecture proposes that some statistical characteristics of empirically observed neuronal activity can be understood by assuming that brain networks operate in a dynamical regime with features, including the emergence of scale invariance, resembling those seen typically near phase transitions. Here, we present a data-driven analysis based on simultaneous high-throughput recordings of the activity of thousands of individual neurons in various regions of the mouse brain. To analyze these data, we construct a unified theoretical framework that synergistically combines a phenomenological renormalization group approach and techniques that infer the general dynamical state of a neural population, while designing complementary tools. This strategy allows us to uncover strong signatures of scale invariance that are "quasiuniversal" across brain regions and experiments, revealing that all the analyzed areas operate, to a greater or lesser extent, near the edge of instability.

Strange Properties of Linear Reservoirs in the Infinitely Large Limit for Prediction of Continuous-Time Signals

Large linear reservoirs, while not necessarily of practical utility, might provide insight to large nonlinear reservoirs. Our study of large linear reservoirs in the context of improving predictive capabilities suggests that: one desires to be near the edge of instability; and random matrix theory guarantees that the performance of large linear random matrices is only dependent on how weights in the weight matrix are chosen and not the individual weights. It also seems as though dynamic and static weights are quite different in performance. We comment on how these lessons may or may not apply to the large nonlinear reservoirs that are typically used for prediction applications.

Asymmetrical performance of a laser-based reservoir computer with optoelectronic feedback.

We numerically quantify the performance of a photonic reservoir computer based on a semiconductor laser subject to high-pass filtered optoelectronic feedback. We assess its memory capacity, computational ability, and performance in solving a multi-step prediction task. By analyzing the complex bifurcation landscape of the corresponding delay-differential equation model, we observe that optimal performance occurs at the edge of instability, at the onset of periodic regimes, and unveil a parity asymmetry in the performance with a slight advantage for positive over negative feedback.

Endogenous liquidity crises

Empirical data reveals that the liquidity flow into the order book (limit orders, cancellations and market orders) is influenced by past price changes. In particular, we show that liquidity tends to decrease with the amplitude of past volatility and price trends. Such a feedback mechanism in turn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects within a stylized order book model, we demonstrate numerically that there exists a second order phase transition between a stable regime for weak feedback to an unstable regime for strong feedback, in which liquidity crises arise with probability one. We characterize the critical exponents, which appear to belong to a new universality class. We then propose a simpler model for spread dynamics that maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for the real markets, such a phase transition scenario requires the system to sit below, but very close to the instability threshold (self-organised criticality), or else that the feedback intensity is itself time dependent and occasionally visits the unstable region. An alternative scenario is provided by a class of non-linear Hawkes process that show occasional ‘activated’ liquidity crises, without having to be poised at the edge of instability.

Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance.

Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). The intermittent control paradigm is based on the alternation of on-phases, driven by a proportional/derivative delayed feedback controller, and off-phases, where the feedback is switched off and the motion evolves according to the intrinsic dynamics of the CIP. In its standard formulation, the switching mechanism consists of a simple threshold operator: the feedback control is switched off if the current (delayed) state vector is closer to the stable than to the unstable manifold of the off-phase and is switched on in the opposite case. Although this simple formulation is effective for explaining upright standing as well as CIP balancing, it fails in the most challenging configuration of the CIP. In this work we propose a modification of the standard intermittent control policy that focuses on the explicit selection of switching times and is based on the phase reset of the estimated state vector at each switching time and on the simulation of an approximated internal model of CIP dynamics. We demonstrate, by simulating the modified intermittent control policy, that it can match the limits of human performance, while operating near the edge of instability.

Endogenous Liquidity Crises

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations and market orders) is influenced by past price changes. In particular, we show that liquidity tends to decrease with the amplitude of past volatility and price trends. Such a feedback mechanism in turn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects within a stylized order book model, we demonstrate numerically that there exists a second order phase transition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, which appear to belong to a new universality class. We then propose a simpler model for spread dynamics that maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for the real markets, such a phase transition scenario requires the system to sit below, but very close to the instability threshold (self-organised criticality), or else that the feedback intensity is itself time dependent and occasionally visits the unstable region. An alternative scenario is provided by a class of non-linear Hawkes process that show occasional “activated” liquidity crises, without having to be poised at the edge of instability.

Colloquium: Criticality and dynamical scaling in living systems

A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e. in the vicinity of the critical point of a phase transition. Criticality has been argued to provide biological systems with an optimal balance between robustness against perturbations and flexibility to adapt to changing conditions, as well as to confer on them optimal computational capabilities, huge dynamical repertoires, unparalleled sensitivity to stimuli, etc. Criticality, with its concomitant scale invariance, can be conjectured to emerge in living systems as the result of adaptive and evolutionary processes that, for reasons to be fully elucidated, select for it as a template upon which higher layers of complexity can rest. This hypothesis is very suggestive as it proposes that criticality could constitute a general and common organizing strategy in biology stemming from the physics of phase transitions. However, despite its thrilling implications, this is still in its embryonic state as a well-founded theory and, as such, it has elicited some healthy skepticism. From the experimental side, the advent of high-throughput technologies has created new prospects in the exploration of biological systems, and empirical evidence in favor of criticality has proliferated, with examples ranging from endogenous brain activity and gene-expression patterns, to flocks of birds and insect-colony foraging, to name but a few...

Dynamical criticality during induction of anesthesia in human ECoG recordings.

In this work we analyze electro-corticography (ECoG) recordings in human subjects during induction of anesthesia with propofol. We hypothesize that the decrease in responsiveness that defines the anesthetized state is concomitant with the stabilization of neuronal dynamics. To test this hypothesis, we performed a moving vector autoregressive analysis and quantified stability of neuronal dynamics using eigenmode decomposition of the autoregressive matrices, independently fitted to short sliding temporal windows. Consistent with the hypothesis we show that while the subject is awake, many modes of neuronal activity oscillations are found at the edge of instability. As the subject becomes anesthetized, we observe statistically significant increase in the stability of neuronal dynamics, most prominently observed for high frequency oscillations. Stabilization was not observed in phase randomized surrogates constructed to preserve the spectral signatures of each channel of neuronal activity. Thus, stability analysis offers a novel way of quantifying changes in neuronal activity that characterize loss of consciousness induced by general anesthetics.

Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors

The ongoing activity of the brain at rest, i.e., under no stimulation and in absence of any task, is astonishingly highly structured into spatiotemporal patterns. These spatiotemporal patterns, called resting state networks, display low-frequency characteristics (<0.1 Hz) observed typically in the BOLD-fMRI signal of human subjects. We aim here to understand the origins of resting state activity through modeling via a global spiking attractor network of the brain. This approach offers a realistic mechanistic model at the level of each single brain area based on spiking neurons and realistic AMPA, NMDA, and GABA synapses. Integrating the biologically realistic diffusion tensor imaging/diffusion spectrum imaging-based neuroanatomical connectivity into the brain model, the resultant emerging resting state functional connectivity of the brain network fits quantitatively best the experimentally observed functional connectivity in humans when the brain network operates at the edge of instability. Under these conditions, the slow fluctuating (<0.1 Hz) resting state networks emerge as structured noise fluctuations around a stable low firing activity equilibrium state in the presence of latent "ghost" multistable attractors. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity.

Cationic Lipids: from Membrane Destabilization to Cell Signaling

Cationic liposomes have been used over the past decades with gene therapy or vaccination trials in mind, considering them primarily as the smart Trojan horse allowing to go trough the cell walls. Fusion-promoting lipids such as DOPE were thus added with some success to try to enhance the destabilizing properties of some cationic lipids, while others were intrinsically destabilizing. It is difficult to conceive that lipids that destabilize membranes would act innocently on the cell physiology. After all, lipids are not only the backbone of membranes, they also act as facilitators of membrane functions such as endocytosis, budding, curving; they regulate protein membrane activity and can even serve as signal transmitters (bioactive lipids). Rather than being considered as responsible for harmful side-effects that should be minimized, cationic lipids could be considered as a potential immunostimulating or pharmacological agents. We illustrate these aspects with diC14-amidine, which forms liposomes with a bilayer at the edge of instability. DiC14-amidine fuses easily with cell membranes, modifies cell signaling and activates immune responses through destabilization and/or activation of specific membrane receptors, like TLR4 [1,2]. Like it was shown for natural lipids, this demonstrates that cationic lipids are not only membrane destabilizing agents but might affect cell membrane components function. 1. Lonez C, Vandenbranden M, Ruysschaert JM. Prog Lipid Res. 2008. 47(5):340-7. 2. Tanaka T et al. Eur J Immunol. 2008. 38(5):1351-7.

Motor prediction at the edge of instability: Alteration of grip force control during changes in bimanual coordination.

Predicting the consequences of actions is fundamental for skilled motor behavior. We investigated whether motor prediction is influenced by the fact that some movements are easier to perform and stabilize than others. Twelve subjects performed a bimanual rhythmical task either symmetrically or asymmetrically (the latter being more difficult and less stable) while oscillating in each hand an object attached to an elastic cord. Motor prediction was monitored through the adequacy of anticipatory grip force adjustments with respect to the elastic resisting force. Results showed less adequate predictive control during asymmetrical movements (compared with symmetrical ones). Furthermore, switching between modes of coordination induced even larger alterations. An interesting finding was that grip force control did not always stabilize around the expected value after voluntary transition. We conclude that motor prediction is affected by the degree of coordination between the upper limbs and by phase transitions and is prone to carryover effects.

Manipulating the edge of instability

We investigate the integration of visual and tactile sensory input for dynamic manipulation. Our experimental data and computational modeling reveal that time-delays are as critical to task-optimal multisensory integration as sensorimotor noise. Our focus is a dynamic manipulation task “at the edge of instability.” Mathematical bifurcation theory predicts that this system will exhibit well-classified low-dimensional dynamics in this regime. The task was using the thumbpad to compress a slender spring prone to buckling as far as possible, just shy of slipping. As expected from bifurcation theory, principal components analysis gives a projection of the data onto a low dimensional subspace that captures 91–97% of its variance. In this subspace, we formulate a low-order model for the brain+hand+spring dynamics based on known mechanical and neurophysiological properties of the system. By systematically occluding vision and anesthetically blocking thumbpad sensation in 12 consenting subjects, we found that vision contributed to dynamic manipulation only when thumbpad sensation was absent. The reduced ability of the model system to compress the spring with absent sensory channels closely resembled the experimental results. Moreover, we found that the model reproduced the contextual usefulness of vision only if we took account of time-delays. Our results shed light on critical features of dynamic manipulation distinct from those of static pinch, as well as the mechanism likely responsible for loss of manual dexterity and increased reliance on vision when age or neuromuscular disease increase noisiness and/or time-delays during sensorimotor integration.

Superconductivity on the verge of catastrophe

A new study suggests that the highest transition temperatures in cuprate superconductors occur when the materials are on the edge of instability to another, non-superconducting, ordered 'stripe' phase.

Biological properties of hyaluronan in aqueous solution are controlled and sequestered by reversible tertiary structures, defined by NMR spectroscopy.

Hyaluronan (HA) is a ubiquitous polysaccharide of (predominantly) animal origin that has important medical applications in joint, skin, and eye conditions. Biological activities shown by HA fragments in angiogenesis, inflammation, etc. are absent from highly polymerized HA. We propose that HA physiological properties are controlled by molecular mass dependent transitions between tertiary structures (e.g., beta sheets) and 2-fold helices, - reversible "denaturation", which is central to HA solution behavior. We demonstrate this phenomenon by 13C NMR. Four different acetamido C=O resonances, assigned to secondary, tertiary, and disordered HA structures, monitored "denaturation" by (a) warming, (b) alkalinizing to pH >12.0, (c) hyaluronidase digestion, and (d) methylation of carboxylates. (a) and (b) acted reversibly but (c) and (d) are irreversible. 1H NMR implicated H-bonded acetamido NH in (b). Temperature dependencies of other 13C chemical shifts were small and unspecific. Arrhenius plots indicate that hyaluronan tertiary structures are on the edge of instability under physiological conditions. The results help to explain the appearance of biological activities on "denaturation" or degradation of HA.

Colloidal Properties of Crude Oils Studied by Dynamic Light-Scattering

Colloidal properties and kinetics of asphaltene aggregation in three crude oils using a dynamic light-scattering method adapted to opaque fluids were investigated. The technique makes it possible to measure the size of particles suspended in nearly nontransparent liquid media. The studied native crude oils were found to have persisting colloidal particles. The observed particles are assumed to be asphaltene/resin aggregates. Using n-heptane as a precipitant, asphaltene aggregation kinetics in crude oils was studied. Experimental measurements of the particle size as a function of time in solutions with different oil/precipitant ratios are reported. The aggregation kinetics accelerates with increasing precipitant concentration. The oil sample with a large amount of paraffins is on the edge of instability and exhibits a slow asphaltene aggregation process without precipitant. Aggregation in the two other oils starts only at some threshold concentration of the precipitant, lasts a short time, and results in the formation of stable-in-size particles. The results obtained prove that dynamic light scattering is an effective method to test petroleum colloid stability.

Nonlinear Cepheid Pulsation Calculations and Comparison with Linear Theory

Linear and nonlinear pulsation calculations have been carried out on a number of purely radiative classical Cepheid models, using identical input physics and models as nearly identical as is feasible. The models chosen for the companson all had the composition X=0.602, Z=O.044, but some of the linearized calculations were performed using different compositions. Two main mass- luminosity relations have been assumed, one based on evolution calculations with conventional masses, the other with masses reduced by a factor of about 2 for given luminosity. The linear blue instability edges are discussed, and it is concluded that uncertainties in both theory and observation preclude a clear distinction between the above two mass-luminosity relations on the basis of the blue edges alone, although the larger ( evolutionary'') masses are very wealdy favored. Comparison of the two sets of calculations show that, overall, the nonlinear results are consistent with the linear results. In particular, no well- established cases of hard'' self-excited oscillations have been found. The nonlinear calculations suggest that some models which according to the linear theory are simultaneously unstable in both F and 1H moles, can attain an apparently stable finite limiting amplitude in either mede, depending on initial conditions (e.g., directionmore » of evolution). The portion of the instability strip where this kind of behavior is expected to be most likely, is found to correspond, for the adopted composition, to periods around 6-11 days (including both F and 1H periods) if Cepheids have the evolutionary'' mases, and around 2- 4 days if their masses are half as large. Stars lying well above (below) these peried ranges in the instability strip are expected to be predominantly F(1H) pulsators. It is likely that these period ranges would occur at shorter periods with a smaller helium abundance. For example, for Y=0.20 it is estimated that the above period range would be around 2.5-5 days for the evolutionary'' masses. Finally, it is concluded that the large-amplitude mede behavior is predictable from linear theory in certain cases, but not in all. (auth)« less