Onset Of Bursting Research Articles

Effects of the Reynolds number and reduced frequency on the aerodynamic performance and dynamic stall behaviors of a vertical axis wind turbine

Dynamic stall is the main reason for the low power efficiency of vertical axis wind turbines (VAWTs) at low tip speed ratios, where the utilizable wind kinetic energy is also high. However, the determining factors behind VAWT dynamic stall have not been adequately investigated. Therefore, we carefully investigated VAWT dynamic stall under the different Reynolds numbers (Re) and reduced frequencies (k). The unsteady flow characteristics are identified using transitional URANS simulations. Although the blade undergoes significant vortex movements during each revolution, the output power is primarily determined by the aerodynamic responses close to the onset of dynamic stall. Increasing Re and k can impact dynamic stall behaviors significantly and also improve VAWT performance effectively. As both Re and k increase, the onset of dynamic stall is progressively postponed to a higher angle of attack, effectively suppressing the separated flow. Dynamic stall behaviors are therefore changed from abrupt stall to moderate stall with attenuated laminar separation bubble (LSB) bursting and dynamic stall vortex (DSV) shedding. An increase in Re hardens the LSB and prevents the DSV formation due to strong inertial forces, particularly at low Re. On the other hand, increasing k slows the flow-field transitions and delays the onset of LSB bursting and DSV shedding, particularly at high k.

The Role of Inertia in the Onset of Turbulence in a Vortex Filament

The decay of the kinetic energy of a turbulent flow with time is not necessarily monotonic. This is revealed by simulations performed in the framework of discrete mechanics, where the kinetic energy can be transformed into pressure energy or vice versa; this persistent phenomenon is also observed for inviscid fluids. Different types of viscous vortex filaments generated by initial velocity conditions show that vortex stretching phenomena precede an abrupt onset of vortex bursting in high-shear regions. In all cases, the kinetic energy starts to grow by borrowing energy from the pressure before the transfer phase to the small turbulent structures. The result observed on the vortex filament is also found for the Taylor–Green vortex, which significantly differs from the previous results on this same case simulated from the Navier–Stokes equations. This disagreement is attributed to the physical model used, that of discrete mechanics, where the formulation is based on the conservation of acceleration. The reasons for this divergence are analyzed in depth; however, a spectral analysis allows finding the established laws on the decay of kinetic energy as a function of the wave number.

Mechanisms ruling the lifetimes of films of liquid mixtures

Foams and bubbles formed in liquid mixtures have lifetimes longer by several orders of magnitude than in pure liquids of similar viscosities. We have shown recently that this effect results from slight differences in molecular concentrations between bulk and surfaces, which give rise to a thickness-dependent surface tension of liquid films. We present a quantitative description of the enhanced stability of liquid films in binary mixtures, based on experimental data and theoretical analysis. Experiments were performed with mixtures of different natures and compositions: foams of stationary heights were obtained by continuous injection of gas, on one hand, and single bubbles were swollen under the surface of a liquid bath, on the other hand. Remarkably, the lifetimes measured in both experiments exhibit the same variations with mixture composition, and follow a power law with the microscopic length that characterises the amplitude of the thickness-dependent surface tension. In addition, the lifetimes vary with the squared film thicknesses at the onset of bursting. We suggest that two stages occur between the birth of liquid films and their rupture. We show how the thickness-dependent surface tension allows an equilibrium shape to be reached at the end of a first stretching stage. We give an analytical description of this shape, which is fully consistent with experimental findings. We suggest a possible mechanism for final rupture of the film, and discuss it in light of existing theoretical predictions. Finally, we compare the properties of liquid mixtures and surfactant solutions, and in particular their surface rheology.

Effects of immiscible interface and particle channelization on particle dynamics of oblique oily sand jets

This paper investigates the evolution of oblique sand jets passing through a thin layer of oil and entering stagnant water known as oily sand jets. The jet evolution parameters include the frontal position, the trajectory of particle clusters, the frontal width, the area of oily sand clusters, cloud velocities, and bursting times. Two scaling parameters, known as aspect ratio and particle to nozzle size ratio, were found to control the evolution of oily sand jets. The results show that the ratio of a nozzle to sand particle size can cause particle channelization, which can significantly alter the motion of particle clusters in stagnant water. Moreover, the aspect ratio indicating the correlation between sand mass and nozzle diameter describes the dispersion of particle clusters during the evolution of oily sand jets. The frontal width of the oily sand jet was measured during the experiment, and the results were compared with the width of vertical sand jets in water. The results show that the width of the oblique oily sand jets increased as oily sand jets descended into water. In addition, the frontal width of oily sand jets was found to be greater than the frontal width of vertical sand jets without an oil layer. Experimental observations indicated that the channelization effect is initiated when the nozzle diameter is more than 36 times of mean particle size. The centroid of oily sand jets in the vertical direction increased by 50% due to the channelization effect. A two-stage cluster bursting was observed due to the excess shear stress between the outer boundary of clusters and the ambient water. The bursting stages were called the primary and secondary bursting, and the onset of cluster bursting was extracted for both stages. It was found that the primary and secondary bursting times were longer in experiments without particle channelization. The mean shear stress acting on the oil layer was calculated based on the forces acting on the control volume. Particle channelization was found as the main factor affecting the magnitude of shear stress at the boundary of sand clusters.

Bursting in a next generation neural mass model with synaptic dynamics: a slow–fast approach

We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that includes short-term synaptic plasticity. Neural mass models can mimic the collective dynamics of large-scale neuronal populations in terms of a few macroscopic variables like mean membrane potential and firing rate. The present one is particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate and fire (QIF) neurons. Without synaptic dynamics, a periodic external current with slow frequency varepsilon can lead to burst-like dynamics. The firing patterns can be understood using singular perturbation theory, specifically slow–fast dissection. With synaptic dynamics, timescale separation leads to a variety of slow–fast phenomena and their role for bursting becomes inordinately more intricate. Canards are crucial to understand the route to bursting. They describe trajectories evolving nearby repelling locally invariant sets of the system and exist at the transition between subthreshold dynamics and bursting. Near the singular limit varepsilon = 0, we report peculiar jump-on canards, which block a continuous transition to bursting. In the biologically more plausible varepsilon -regime, this transition becomes continuous and bursts emerge via consecutive spike-adding transitions. The onset of bursting is complex and involves mixed-type-like torus canards, which form the very first spikes of the burst and follow fast-subsystem repelling limit cycles. We numerically evidence the same mechanisms to be responsible for bursting emergence in the QIF network with plastic synapses. The main conclusions apply for the network, owing to the exactness of the meanfield limit.

Helium flux effects on bubble growth and surface morphology in plasma-facing tungsten from large-scale molecular dynamics simulations

We investigate helium flux effects on helium transport and surface evolution in plasma-facing tungsten using molecular dynamics. The simulations span two orders of magnitude, from ITER-relevant levels to those more typical of simulations published to date. Simulation times of up to 2.5 µs (corresponding to actual fluences of m−2) are achieved, revealing concerted bubble-bursting events that are responsible for significant and very sudden changes in surface morphology. The depth distribution of helium depends very strongly on helium flux: helium self-trapping becomes more probable near the surface at high flux, and a layer of near-surface bubbles forms. Helium retention prior to the onset of bubble bursting is also substantially lower at low flux than it is at high flux. Surface features at low fluence are correlated with the positions of bubbles, but at high fluence, bubbles tend to coalesce, venting to the surface at one or more locations and leaving large interconnected cavities below the surface. Ruptured bubbles may serve as pathways deeper into the material, allowing helium to bypass the layer of near-surface bubbles and fill deeper, potentially much larger, bubbles that can produce more substantial surface features. Deeper bubbles also emit prismatic dislocation loops that can fill in cavities closer to the surface. Our results suggest that nearly all molecular dynamics simulations published to date are hampered by finite-size effects, and that helium flux is a very important parameter in determining the behavior of helium in plasma-facing components.

Modulation of glycinergic inhibition on respiratory rhythmic hypoglossal bursting in the rat.

The hypoglossal nerve displays respiratory rhythmic bursting and is composed of preinspiratory and inspiratory activity which is important in maintaining upper airway patency. The present study was designed to examine the modulatory role of glycinergic inhibition in respiratory rhythmic hypoglossal bursting. The activity of the phrenic nerve, as well as the medial and lateral branches of the hypoglossal nerve, was recorded simultaneously in urethane-anesthetized and mechanically ventilated adult rats in response to moderate and high levels of sustained lung inflation. The results demonstrated that inspiratory activity of the phrenic nerve gradually reduced with increasing lung inflation. The burst amplitude and discharge onset of the hypoglossal nerve branches were enhanced during moderate lung inflation but inhibited by high levels of lung inflation. These lung volume-mediated respiratory reflexes were abolished following a bilateral cervical vagotomy. In addition, intravenous administration of a glycine receptor antagonist (strychnine, 1 μmole/kg) attenuated preceding onset of rhythmic hypoglossal bursting but enhanced inspiratory hypoglossal burst amplitude during the baseline. Moreover, both excitatory and inhibitory effects of lung inflation on hypoglossal nerve activity were attenuated following a glycine transmission blockade. These results suggest that glycinergic inhibition modulated rhythmic hypoglossal bursting and was involved in mediating lung volume-induced respiratory reflexes.

LES study on the shape effect of ground obstacles on wake vortex dissipation

The lingering wake vortex following a landing aircraft has long been a hazard to aviation safety. Previous studies at the German Aerospace Center (DLR) confirmed the effectiveness of applying ground-based obstacles to improve the dissipation of the wake vortex pair by triggering the onset of the vortex bursting by the artificial introduction of shortwave instability. Following the design of the plate line obstacles as proposed by DLR for vortex dissipation, we further investigate the influence of the shape of the ground obstacles on dissipating wake vortex in the present work. The secondary vortex structure, resulting from the interaction between the vortical flow and the obstacle plate, stems from the location of the obstacle and travels outward along the vortex axis, thus spreading instability to the vortex structure along the way. 3D numerical simulations were conducted using Large Eddy Simulation with OpenFOAM solver. The numerical solutions were first compared to the experimental vortex measurement performed in DLR's Wasser Schleppkanal Göttingen tow-tank. In addition to the baseline setup three different shaped obstacles were numerically tested and compared in the simulation. The numerical results reveal that 50% reduction of the wake dissipation, measured with the circulation of the vortex, was achieved within t⁎=1.5 compared to t⁎>4.0 in the absence of ground obstacle. The present study showed that the shape of the obstacles affects the pattern of the secondary vortex structure created, and the resulting drag force acting on the obstacle has a more direct effect on wake dissipation.

Mapping Connectivity of Network Bursting Neurons

Synchronized neuronal activity is an emergent phenomenon found in many neural systems. In cultured neurons, this phenomenon is known as network bursting and involves the simultaneous firing of hundreds of neurons. Bursting occurs only after the network is sufficiently mature (typically 8-12 days in vitro). Afterwards, bursting activity increases both in intensity and frequency (usually 2-4 bursts per minute). Using a technique developed in our lab, we mapped the connectivity structure of neuronal cultures before and after the onset of network bursting. From the measured connectivity maps, we determined various network properties, such as topology, clustering, and efficiency; and show how these properties correlate with busting onset.

Differential Inhibition of Bilateral Phrenic Bursting following Pulmonary Chemoreflex in Rats with Chronic Cervical Spinal Hemisection

High cervical spinal injury usually interrupts bulbospinal pathways and results in inactivation of phrenic bursting ipsilateral to the lesion. The ipsilateral phrenic activity can partially recover over weeks to months post‐injury due to activation of the latent crossed phrenic pathway. Ipsilateral phrenic nerve exhibits a greater capacity to increase activity during respiratory challenges than the contralateral phrenic nerve. However, whether bilateral phrenic nerves show a differential response to respiratory inhibitory inputs is unclear. Accordingly, present study was designed to examine bilateral phrenic bursting in response to capsaicin‐induced pulmonary chemoreflex, a robust respiratory inhibitory stimulus. Bilateral phrenic nerve activity were recorded in anesthetized and mechanically‐ventilated adult rats at 8‐9 weeks post‐C2 hemisection (C2Hx) or C2 laminectomy. Intra‐jugular capsaicin (1.5 µg/kg) injection was used to activate pulmonary C‐fibers to evoke the pulmonary chemoreflex. Present results showed capsaicin‐induced prolongation of expiratory duration (i.e., apnea) was significantly attenuated in C2Hx animals. However, ipsilateral phrenic activity was robustly inhibited after capsaicin treatment compared to contralateral phrenic nerve of C2Hx animals or ipsilateral phrenic nerve of uninjured animals. In addition, discharge onset of ipsilateral phrenic bursting of C2Hx animals is significantly delayed after capsaicin delivery. These results suggest that phrenic motor output is more susceptible to inhibitory inputs after cervical hemisection. Moreover, central (i.e., apnea) and spinal (i.e., inhibition of phrenic bursting) component of the pulmonary chemoreflex were differentially modulated during chronic injury phase.

Stochastic Phenomena in One-Dimensional Rulkov Model of Neuronal Dynamics

We study the nonlinear Rulkov map-based neuron model forced by random disturbances. For this model, an overview of the variety of stochastic regimes is given. For the parametric analysis of these regimes, the stochastic sensitivity functions technique is used. In a period-doubling zone, we analyze backward stochastic bifurcations modelling changes of modality of noisy neuron spiking. Noise-induced transitions in a zone of bistability are considered. It is shown how such random transitions can generate a new neuronal regime of the stochastic bursting and transfer the system from order to chaos. A transient zone of values of noise intensity corresponding to the onset of noise-induced bursting and chaotization is localized by the stochastic sensitivity functions technique.

Numerically induced bursting in a set of coupled neuronal oscillators

We present our numerical observations on dynamics in the system of two linearly coupled FitzHugh–Nagumo oscillators close to the destabilization of the state of rest. Under the considered parameter values the system, if integrated sufficiently accurately, converges to small-scale periodic oscillations. However, minor numerical inaccuracies, which occur already at the default precision of the standard Runge–Kutta solver, lead to a breakup of periodicity and an onset of large-scale aperiodic bursting.

P.2.013 Effects of melatonin on diurnal variations of spontaneous seizures and behavioural changes in kainate model of temporal lobe epilepsy

Hyperexcitability in the medial entorhinal cortex-hippocampal (mEC-HC) circuit in the initial weeks after prolonged seizure activity may contribute to the epileptogenic process in animal models of temporal lobe epilepsy (TLE). The present study examined combined mEC-HC slices (400 μm) using field potential recordings 1–2 weeks following the multiple administration, low-dose kainic acid (KA) model of TLE [Hellier, J.L., Patrylo, P.R., Buckmaster, P.S., Dudek, F.E., 1998. Recurrent spontaneous motor seizures after repeated low-dose systemic treatment with kainate: assessment of a rat model of temporal lobe epilepsy. Epilepsy Res. 31, 73–84]. Field potential recordings in slices from KA-treated rats demonstrated hallmarks of hyperexcitability in the mEC and in the CA1 and CA3 cell body regions of the HC. Spontaneous burst (SB) activity was observed under baseline recording conditions in the mEC of several slices from KA-treated rats, but not in the slices from saline-treated control rats. Elevating ACSF [K+]o (6 mM) in the presence of picrotoxin (50 μM) increased SB rates in all slices tested. However, there was a significantly shorter latency to onset of bursting and prolonged evoked response durations in layer II of the mEC of slices from KA-treated rats versus those from controls. Neither carbamazepine (CBZ) nor phenytoin (PHT) abolished SB activity in slices from KA-treated rats; whereas, SB activity in slices from control rats was dose-dependently reduced at 100 μM CBZ. In contrast, the novel anticonvulsant retigabine (RGB) dramatically reduced SB frequency in both control and KA-treated groups. The hyperexcitability observed in combined mEC-HC brain slices from KA-treated rats suggests that the mEC, as well as the HC, may contribute to the epileptogenic process after KA-induced seizure activity. This model may provide an efficient, flexible in vitro paradigm for differentiating novel AEDs in a model of pharmacoresistant bursting.

Calcium Involvement in Regulation of Neuronal Bursting in Disinhibited Neuronal Networks: Insights from Calcium Studies in a Spherical Cell Model

Cytosolic calcium is involved in the regulation of many intracellular processes. Intracellular calcium may therefore potentially affect the behavior of both single neurons and synaptically connected neuronal assemblies. In computer model studies, we investigated calcium dynamics in spherical neurons during periods of recurrent neuronal bursting that were simulated in a disinhibited neuronal network. The model takes into account calcium influx via voltage-gated calcium channels, extrusion through the cell membrane, and binding to two different buffers representing fixed and mobile endogenous calcium buffers. Throughout the duration of the simulated recurrent neuronal bursting, the concentration of free fixed buffers shows a hyperbolic decrease in time at a rate that is not uniform inside a neuron. Recurrent calcium influxes associated with bursting lead to the formation of gradients in the concentration of the fixed buffer in the radial direction, and are accompanied by the redistribution of mobile buffers acting to compensate for these gradients. Simulated intracellular calcium transients have a slow component characterized by a gradual increase in the calcium baseline level that reaches a plateau 120–200 s after the onset of recurrent bursting. Using this model, we demonstrate what we believe is a novel mechanism of regulation of network excitability that occurs in conditions of prolonged and recurrent neuronal bursting in disinhibited networks. This mechanism is expressed via interaction of calcium clearance systems inside neurons with calcium-dependent potassium regulation of neuronal excitability in membranes. This is a network phenomenon because it arises largely by synaptic interactions. Therefore, it can serve as a network safety mechanism to prevent excessive and uncontrolled neuronal firing resulting from the lack of inhibition or after acute suppression of the inhibitory drive.

Development of a Simplified Theoretical Model for Dynamic Burst Time And Pressure of a Cylindrical Shell

The object of this study is to determine the short-term burst pressure and time of metal cylinders under short- term dynamic loading conditions. A simplified theoretical model to calculate these dynamic burst time and pressure of cy- lindrical shells has been developed and the results are compared with finite element analysis (FEA) results via the use of the LS-DYNA code (1). Based on the agreement between the two results, it can be concluded that a properly formulated simplified theoretical model can be employed with sufficient accuracy to determine the short-term dynamic burst pres- sures of metal cylinders. In the 1950's, Cooper (2) developed an analytical equa- tion to predict the static burst pressure for cylinders made of an isotropic ductile material. This equation provided the de- sired relationship between the burst pressure, material char- acteristics, original dimensions, and ultimate tensile strength of the material. At the same time, Svensson (3) derived a solution of the burst pressure for an arbitrary thick end- capped pipe based on the von-Mises yield criterion. Tadmor et al. (4) developed an analytical expression of the burst pressure of multilayered cylinders. They performed a large strain analysis, taking into consideration the elastic-plastic deformation with the Hill yield function and arbitrary hard- ening. An overall effective modulus was used to determine the onset of bursting, and they then derived the relations for thin-walled cylinders with the neglect of the elastic strains. Klever (5) presented an analytical model to determine the burst strength of the thin-wall uncorroded and corroded pipe- lines. The model results compared well with those of an un- corroded pipe test. Stewart et al. (6) re-examined the funda- mental relationships that govern the equilibrium and stability

Slow acceleration and deacceleration through a Hopf bifurcation: Power ramps, target nucleation, and elliptic bursting

From the periodicity of regional climate change to sustained oscillations in living cells, the transition between stationary and oscillatory behavior is often through a Hopf bifurcation. When a parameter slowly passes or ramps through a Hopf bifurcation there is a delayed transition to sustained oscillations and an associated memory effect where onset is dependent on the initial state of the system. Most theoretical studies of the delay and memory effect assume constant ramp speeds, overlooking the problem of slow parameter acceleration or deacceleration through the Hopf bifurcation. Using both numerical and analytic methods, we show that slow nonlinear ramps can significantly increase or decrease the onset threshold, changing profoundly our understanding of the associated memory effect. We found that slow parameter acceleration increases the threshold, whereas slow deacceleration decreases the threshold. The theory is applied to the formation of pacemakers in the unstirred Belousov-Zhabotinsky reaction and the onset of elliptic bursting in the context of nerve membrane excitability. We show that our results generalize to all systems where slow passage through a Hopf bifurcation is the underlying mechanism for onset.

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This article studies tubular hydroforming of high strength low alloy (HSLA) and dual phase (DP600) straight tubes under the action of end feeding loads. Experiments demonstrate that higher end feed loads enhance the formability of the tubes and increase the internal fluid pressure for onset of necking and bursting. Because of the action of the internal pressure and the axial compressive load, the onset of localization (necking) is due to a complex three-dimensional state of stress. Using free expansion experiments, approximate upper and lower bound strain-based forming limit curves are determined for the tube materials. These limit curves, in turn, are used to derive upper and lower bound extended stress-based forming limit curves [Simha et al., Prediction of necking in tubular hydroforming using an extended stress-based FLC. Transactions of the ASME Journal of Engineering Materials and Technology 2007;129(1): 36–47]. In conjunction with finite element computations that use solid elements to model the tube, these stress-based limit curves are used to predict upper and lower bound necking pressures under the action of end feed loading. These predictions of necking pressures, when an appropriate coefficient of tube-die friction is used, are found to bracket the experimentally measured necking pressures. Computations using plane stress shell elements to model the tubes are shown to give erroneous results, since the plane stress approximation is not valid when tubes are hydroformed in a die.

Phenytoin- and carbamazepine-resistant spontaneous bursting in rat entorhinal cortex is blocked by retigabine in vitro

Hyperexcitability in the medial entorhinal cortex-hippocampal (mEC-HC) circuit in the initial weeks after prolonged seizure activity may contribute to the epileptogenic process in animal models of temporal lobe epilepsy (TLE). The present study examined combined mEC-HC slices (400 microm) using field potential recordings 1-2 weeks following the multiple administration, low-dose kainic acid (KA) model of TLE [Hellier, J.L., Patrylo, P.R., Buckmaster, P.S., Dudek, F.E., 1998. Recurrent spontaneous motor seizures after repeated low-dose systemic treatment with kainate: assessment of a rat model of temporal lobe epilepsy. Epilepsy Res. 31, 73-84]. Field potential recordings in slices from KA-treated rats demonstrated hallmarks of hyperexcitability in the mEC and in the CA1 and CA3 cell body regions of the HC. Spontaneous burst (SB) activity was observed under baseline recording conditions in the mEC of several slices from KA-treated rats, but not in the slices from saline-treated control rats. Elevating ACSF [K(+)](o) (6mM) in the presence of picrotoxin (50 microM) increased SB rates in all slices tested. However, there was a significantly shorter latency to onset of bursting and prolonged evoked response durations in layer II of the mEC of slices from KA-treated rats versus those from controls. Neither carbamazepine (CBZ) nor phenytoin (PHT) abolished SB activity in slices from KA-treated rats; whereas, SB activity in slices from control rats was dose-dependently reduced at 100 microM CBZ. In contrast, the novel anticonvulsant retigabine (RGB) dramatically reduced SB frequency in both control and KA-treated groups. The hyperexcitability observed in combined mEC-HC brain slices from KA-treated rats suggests that the mEC, as well as the HC, may contribute to the epileptogenic process after KA-induced seizure activity. This model may provide an efficient, flexible in vitro paradigm for differentiating novel AEDs in a model of pharmacoresistant bursting.

Emergent epileptiform activity in neural networks with weak excitatory synapses

Brain electrical activity recorded during an epileptic seizure is frequently associated with rhythmic discharges in cortical networks. Current opinion in clinical neurophysiology is that strongly coupled networks and cellular bursting are prerequisites for the generation of epileptiform activity. Contrary to expectations, we found that weakly coupled cortical networks can create synchronized cellular activity and seizure-like bursting. Evaluation of a range of synaptic parameters in a detailed computational model revealed that seizure-like activity occurs when the excitatory synapses are weakened. Guided by this observation, we confirmed experimentally that, in mouse neocortical slices, a pharmacological reduction of excitatory synaptic transmission elicited sudden onset of repetitive network bursting. Our finding provides powerful evidence that onset of seizures can be associated with a reduction in synaptic transmission. These results open a new avenue to explore network synchrony and may ultimately lead to a rational approach to treatment of network pathology in epilepsy.

Chaotic bursting at the onset of unstable dimension variability.

Dynamical systems possessing symmetries have invariant manifolds. According to the transversal stability properties of this invariant manifold, nearby trajectories may spend long stretches of time in its vicinity before being repelled from it as a chaotic burst, after which the trajectories return to their original laminar behavior. The onset of chaotic bursting is determined by the loss of transversal stability of low-period periodic orbits embedded in the invariant manifold, in such a way that the shadowability of chaotic orbits is broken due to unstable dimension variability, characterized by finite-time Lyapunov exponents fluctuating about zero. We use a two-dimensional map with an invariant subspace to estimate shadowing distances and times from the statistical properties of the bursts in the transversal direction. A stochastic model (biased random walk with reflecting barrier) is used to relate the shadowability properties to the distribution of the finite-time Lyapunov exponents.