Low-amplitude Oscillations Research Articles

High Frequency Microrheology of Living Cells

The viscoelastic nature of living cells is crucial for their biological function. Experiments using various techniques have shown that cells present solid- and liquid-like behavior. Over a wide frequency range (0.1Hz-100Hz), elastic and viscous moduli are coupled and follow a weak power law of exponent 0.05-0.035, with elastic stresses dominating over viscous stresses (1-4). This response is incompatible with one typical relaxation time and has been explained in terms of soft glassy rheology with a spectrum of relaxation times (1). At higher frequencies, semiflexible polymer theory and experiments suggest an exponent of ∼0.75 (5, 6). However, experimental data on cells at high rates is still limited due to experimental limitations. The aim of this work was to overcome this limitation by adapting a high-speed atomic force microscope to extend the frequency range up to 120 kHz, about two orders of magnitude faster than previous studies. Applying low amplitude oscillations over five decades (1Hz-120kHz), we probe the microrheology of living fibroblasts under different cytoskeletal interventions. Unlike previous studies, our results suggest that the weak power law extends to frequencies up to ∼10kHz. At higher frequencies, the data suggest a power law of exponent between 0.5 and 0.85, modulated upon intervention of the cytoskeleton activity.

Numerical investigations on shock oscillations ahead of a hemispherical shell in supersonic flow

A clear understanding of the mechanism responsible for large amplitude shock pulsations ahead of a hemispherical cavity in supersonic flow is presented for the first time in this article. This has applications in supersonic parachute decelerators during the atmospheric descent stage of aerospace vehicles. A cell-centered finite volume code FaSTAR is used to solve the full Navier–Stokes equations on a hemispherical shell facing a Mach 4.0 supersonic free stream. The numerical method is validated against earlier experimental results. First, Flow Configuration A appears consisting of an axisymmetric shock that undergoes low-amplitude oscillations. This flow transitions to Flow Configuration B that has an asymmetric shock structure and undergoes large-amplitude non-stationary shock pulsations. The shock stand-off distance in Flow Configuration B is 1.65 times that in Flow Configuration A. The generation of vortices from the curved shock, amplification of vortices of one kind due to the dynamics of the cavity flow, and further interaction of these amplified vortices with the shock in a loop causes the large-amplitude shock pulsations. The oscillation frequencies as determined from cavity pressure and shock stand-off distance signals extracted from the unsteady results are 1.26 kHz during Flow Configuration A, and 859 and 863 Hz during the non-stationary pulsations of Flow Configuration B. The Helmholtz resonator model predicts quite accurately the frequency of Flow Configuration A (1.27 kHz), and to a good extent the frequency in Flow Configuration B (916.7 Hz).

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes.

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

Brain state dependent stimulus information in the auditory thalamocortical system

Activity in the absence of stimuli is ubiquitous across the thalamocortical system (TS), with patterns of spontaneous activity reflecting ongoing behavioural state. Under anaesthesia and during deep sleep the TS operates in an inactivated state (characterised by low frequency high amplitude oscillations in local field potential (LFP)) in which neurons collectively alternate between periods of local silence and high synaptic activity. During wakefulness and REM sleep, however, the TS operates in an activated state (characterised by high frequency low amplitude oscillations in LFP) in which neurons fire in a sustained desynchronised manner. Such brain states may be indicative of different modes of neural processing, but the effect of brain state on neural processing remains unclear. Here we analyse data recorded in the auditory TS of urethane anaesthetised rats subjected to single-click acoustic stimulation over a range of intensities, presented in both the inactivated state (natural under the anaesthesia) and the activated state (induced through electrical stimulation of the basal forebrain). Evoked spike trains were identified for single units in the auditory thalamus and across depths of the primary auditory cortex. Mutual information (MI) between stimulus and response was then computed for spike probability, counts and timing. Evoked spiking activity was observed to last around 300ms, consisting of distinct initial and secondary (rebound) activity. Analysis of responses of single units over a full 300ms window showed that spike count and timing measures gave little more MI than response probability, suggesting that stimulus intensity is primarily encoded probabilistically, at least at the level of the single unit. Moreover, whilst many single units are uninformative of stimulus intensity, the most informative thalamorecipient (TC) and infragranular (IF) single units show increased MI in the activated state. Additionally, upon temporally partitioning data according to initial or rebound activity, we see that TC units are more informative in the activated state during initial activity whereas IF units are more informative in the activated state during rebound activity, suggesting that information loss in the inactivated state may be cumulative in time as sensory signals propagate through neural circuits.

Decayless low-amplitude kink oscillations: a common phenomenon in the solar corona?

We investigate the decayless regime of coronal kink oscillations recently discovered in the Solar Dynamics Observatory (SDO)/AIA data. In contrast to decaying kink oscillations that are excited by impulsive dynamical processes, this type of transverse oscillations is not connected to any external impulsive impact, such as a flare or CME, and does not show any significant decay. Moreover the amplitude of these decayless oscillations is typically lower than that of decaying oscillations. The aim of this research is to estimate the prevalence of this phenomenon and its characteristic signatures. We analysed 21 active regions (NOAA 11637--11657) observed in January 2013 in the 171 A channel of SDO/AIA. For each active region we inspected six hours of observations, constructing time-distance plots for the slits positioned across pronounced bright loops. The oscillatory patterns in time-distance plots were visually identified and the oscillation periods and amplitudes were measured. We also estimated the length of each oscillating loop. Low-amplitude decayless kink oscillations are found to be present in the majority of the analysed active regions. The oscillation periods lie in the range from 1.5 to 10~minutes. In two active regions with insufficient observation conditions we did not identify any oscillation patterns. The oscillation periods are found to increase with the length of the oscillating loop. The considered type of coronal oscillations is a common phenomenon in the corona. The established dependence of the oscillation period on the loop length is consistent with their interpretation in terms of standing kink waves.

Intermittency Route to Combustion Instability in a Laboratory Spray Combustor

In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one-dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high-amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behavior from low-amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of high-amplitude bursts of periodic oscillations separated by low-amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high-amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low-amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz., stable, intermittency, and limit cycle) is studied in three-dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot (RP) techniques are employed to confirm the type of intermittency.

Intermittent Burst Oscillations: Signature Prior to Flame Blowout in a Turbulent Swirl-Stabilized Combustor

This experimental study focuses on characterizing the nonlinear combustion dynamics prior to blowout in a partially premixed combustor with a swirl-stabilized burner. Experiments were performed by varying the global equivalence ratio from 0.92 to 0.33. The acquired time-series data of pressure fluctuations were analyzed using nonlinear time-series analysis. When the combustor was operated at an equivalence ratio of 0.92, broadband low-amplitude pressure oscillations called combustion noise were observed. As the equivalence ratio is decreased to 0.62, the oscillations change their characteristics from low-amplitude broadband oscillations to high-amplitude discrete tones, and the combustor undergoes limit-cycle oscillations. A sharp peak is observed in the amplitude spectra of the acoustic pressure oscillations at this stage. On reducing the equivalence ratio to 0.42 and lower, the periodic motion is interrupted by occasional irregular bursts and the system switches back and forth between the noisy (periodic) and quiet (aperiodic) zones. In the dynamical systems theory parlance, this irregular switching between periodic and aperiodic behaviors is termed intermittency. On reducing the equivalence ratio further, the system reaches blowout condition. Intermittency can be used as the signature prior to flame blowout. The dynamical patterns and inherent nonlinearity during the transition from chaotic behavior to intermittent burst oscillations prior to blowout are shown qualitatively by drawing phase portraits, return maps, and recurrence plots.

Highly Efficient Genome Editing via CRISPR/Cas9 to Create Clock Gene Knockout Cells.

Targeted genome editing using CRISPR/Cas9 is a relatively new, revolutionary technology allowing for efficient and directed alterations of the genome. It has been widely used for loss-of-function studies in animals and cell lines but has not yet been used to study circadian rhythms. Here, we describe the application of CRISPR/Cas9 genome editing for the generation of an F-box and leucine-rich repeat protein 3 (Fbxl3) knockout in a human cell line. Genomic alterations at the Fbxl3 locus occurred with very high efficiency (70%-100%) and specificity at both alleles, resulting in insertions and deletions that led to premature stop codons and hence FBXL3 knockout. Fbxl3 knockout cells displayed low amplitude and long period oscillations of Bmal1-luciferase reporter activity as well as increased CRY1 protein stability in line with previously published phenotypes for Fbxl3 knockout in mice. Thus, CRISPR/Cas9 genome editing should be highly valuable for studying circadian rhythms not only in human cells but also in classic model systems as well as nonmodel organisms.

The M-current contributes to high threshold membrane potential oscillations in a cell type-specific way in the pedunculopontine nucleus of mice.

The pedunculopontine nucleus is known as a cholinergic nucleus of the reticular activating system, participating in regulation of sleep and wakefulness. Besides cholinergic neurons, it consists of GABAergic and glutamatergic neurons as well. According to classical and recent studies, more subgroups of neurons were defined. Groups based on the neurotransmitter released by a neuron are not homogenous, but can be further subdivided. The PPN neurons do not only provide cholinergic and non-cholinergic inputs to several subcortical brain areas but they are also targets of cholinergic and other different neuromodulatory actions. Although cholinergic neuromodulation has been already investigated in the nucleus, one of its characteristic targets, the M-type potassium current has not been described yet. Using slice electrophysiology, we provide evidence in the present work that cholinergic neurons possess M-current, whereas GABAergic neurons lack it. The M-current contributes to certain functional differences of cholinergic and GABAergic neurons, as spike frequency adaptation, action potential firing frequency or the amplitude difference of medium afterhyperpolarizations (AHPs). Furthermore, we showed that high threshold membrane potential oscillation with high power, around 20 Hz frequency is a functional property of almost all cholinergic cells, whereas GABAergic neurons have only low amplitude oscillations. Blockade of the M-current abolished the oscillatory activity at 20 Hz, and largely diminished it at other frequencies. Taken together, the M-current seems to be characteristic for PPN cholinergic neurons. It provides a possibility for modulating gamma band activity of these cells, thus contributing to neuromodulatory regulation of the reticular activating system.

DISCOVERY OF MULTIPLE PULSATIONS IN THE NEWδSCUTI STAR HD 92277: ASTEROSEISMOLOGY FROM DOME A, ANTARCTICA

We report the discovery of low-amplitude oscillations in the star HD 92277 from long, continuous observations in the r and g bands using the CSTAR telescopes in Antarctica. A total of more than 1950 hours of high-quality light curves were used to categorize HD 92277 as a new member of the delta Scuti class. We have detected 21 (20 frequencies are independent and one is the linear combination) and 14 (13 frequencies are independent and one is the linear combination) pulsation frequencies in the r and g bands, respectively, indicating a multi-periodic pulsation behavior. The primary frequency f(1) = 10.810 days(-1) corresponds to a period of 0.0925 days and is an l = 1 mode. We estimate a B - V index of 0.39 and derive an effective temperature of 6800 K for HD 92277. We conclude that long, continuous and uninterrupted time-series photometry can be performed from Dome A, Antarctica, and that this is especially valuable for asteroseismology where multi-color observations (often not available from space-based telescopes) assist with mode identification.

Using Extrapolation Techniques in VOF Methodology to Model Expanding Bubbles

A numerical method is presented to study cavity and bubble dynamics. The liquid phase is assumed to be inviscid and incompressible and separated from the gas or vacuum phase by a free surface. On the free surface the stress tensor reduces to a spatially constant pressure. The flow in the bulk of the liquid is computed using a second-order-in-time projection method. The interface is advected and reconstructed using a Volume-of-Fluid (VOF) method. Setting the pressure on the free surface to the prescribed value involves a modified stencil on nodes close to the interface. This modifed stencil contains interpolated pressures on branches that are cut by the interface. Capillary e_ects are taken into account by adding the Laplace law pressure increment to these prescribed pressures. The curvature that appears in the Laplace law is computed using the height-function method. The VOF advection and momentum advection schemes both require an extension of the velocity in a two-layer wide ghost cell region on the grid across the free surface. This ghost layer is computed in two stages. In the preliminary stage a first-order velocity extrapolation of the liquid velocity field to the ghost layers is performed. In the second stage the ghost layer velocities are projected on the space of divergence free velocities using an auxiliary projection step. The whole procedure is implemented in a free code developed with the help of Gretar Tryggvason and Yue (Stanley) Ling and is available at http://parissimulator.sf.net. Tests are perfomed on radial flows with spherical symmetry except for boundary conditions far from the bubble in a cubic box. In such a geometry the flow is predicted by solutions of the Rayleigh-Plesset equation. Good comparison to the Rayleigh-Plesset solution for a single bubble with low and moderate amplitude oscillations is shown. Perspectives for parallel simulations involving very large numbers of bubbles are given.

Wavelet-analysis of skin temperature oscillations during local heating for revealing endothelial dysfunction

Skin microvessels have proven to be a model to investigate the mechanisms of vascular disease; in particular, endothelial dysfunction. To analyze skin blood flow, high-resolution thermometry can be used because low-amplitude skin temperature oscillations are caused by changes in the tone of skin vessels. The aim of our study was to test the possibilities of wavelet analysis of skin temperature (WAST) for the diagnosis of impaired regulation of microvascular tone in patients with type 2 diabetes. A local heating functional test was used for the assessment of microvascular tone regulation. A control group consisted of healthy male and female volunteers (n=5 each), aged 39.1±5.3years. A group of patients with type 2 diabetes comprised thirteen people, seven men and six women, aged 36 to 51years old (43.2±3.4years). The diagnosis of diabetes was made according to the criteria of the World Health Organization (WHO). The mean disease duration was 7.36±0.88years. Skin temperature oscillations, reflecting intrinsic myogenic activity (0.05–0.14Hz), neurogenic factors (0.02–0.05Hz) and endothelial activity (0.0095–0.02Hz) increase greatly during local heating for healthy subjects. In the group of patients with type 2 diabetes, no statistically significant differences in the amplitudes in the endothelial range were observed. Relative changes in the oscillation amplitudes in patients with type 2 diabetes were markedly lower compared to the control group. The latter indicates that the WAST method enables assessment of the state of vascular tone and the effects of mechanisms responsible for regulation of blood flow in the microvasculature.

Rheometric Monitoring of the Formation of Milk–Protein Blob

This paper presents the results of the theoretical and experimental studies of newly designed devices, namely, the VRSh-1 ball rheometer and the Sgustok-1S dual-range rotary viscometer, for the continuous automatic monitoring of structure formation processes in milk–protein blobs. Each type of rheometers is studied to substantiate and select their geometric and kinematic parameters and the shape of measuring elements. It has been shown that the mechanical actions on the structure of milk–protein blobs during the rheometric monitoring of their formation must be minimal to obtain reliable data on their readiness. It has been proven that the monitoring of the formation of blobs by the method of the low-amplitude dynamic oscillations of a ball does not necessitate the measurement of the phase shift of its oscillations, and the total force of the resistance of a strengthening clot to the displacements of a ball inside it should be selected as a control parameter, which is in direct proportion to the amplitude of linear displacements of a ball in a viscoelastic medium (blob). Such a solution simplifies the design of a rheometer and makes it possible to obtain a similar rheogram, which precisely and reliably describes the coagulation of a milk mixture. The possibility of switching the rigidity ranges of force indicators without stopping the electrical drive, the design of which prevents a formed blob from dynamic impacts, thus providing the precision of monitoring and the preservation of the structure of a blob, has been designed for the method a cylinder rotating in a formed blob. The algorithm of the computer approximation of rheometric monitoring results for the formation of milk–protein blobs with the possibility of correcting its consistence at the terminal stage of coagulation is described.

Oscillatory processes in lymph microcirculation in the human skin

This study was the first to use laser Doppler flowmetry followed by wavelet analysis in order to estimate oscillations in lymph microcirculation in 30 subjects with (n = 13) or without (n = 17) edema of the distal part of the upper limb. Lymph flow in the human skin exhibited clear dominance of pacemaker phase oscillations in the frequency ranges of 0.021–0.042 and 0.016–0.035 Hz in the skin of the palm surface of the finger nail bone and in the skin of the forearm, respectively. Edema was associated with an increase in the peak frequencies and normalized maximum amplitudes (Al/Ml, where Al is the mean value of the maximum amplitude of phase oscillations, and Ml is the value of the averaged lymph flow expressed in perfusion units). Low-amplitude oscillations were recorded rarer in the myogenic, endothelial, and respiratory ranges. We did not find any cardiac pulse rhythm in the wavelet spectrum of the lymph flow. We did not find any interaction between the Al/Ml value and the skin temperature. In the group of subjects without edema, under physiological conditions only, we found a negative correlation between the Al/Ml value and the amplitudes of myogenous proper blood flow oscillations, which reflected the number of functional capillaries and activity of oxidative metabolism in the tissue. In the group with edema, we did not find any correlations between the indices of lymph flow and blood flow. The values of normalized amplitude and frequency of phase oscillations may be used as efficient diagnostic tools in the studies on lymph microcirculation.

Intrinsic coherence resonance in the chloride-induced temporal dynamics of the iron electrodissolution-passivation in sulfuric acid solutions

The existence of intrinsic coherence resonance (ICR) is demonstrated experimentally for the Fe|0.75M H2SO4 electrochemical system in which the presence of chlorides induces current oscillations. Chlorides, destroying locally the passive oxide film of Fe, lead to pitting corrosion. It is shown that the intensity of the system internal noise, stemming perhaps from fluctuations of ionic concentrations, may be regulated upon changing the applied at the Fe electrode potential (E). Within a certain chloride concentration range (20≤cCl-/mM<50), the ICR occurs within two oscillatory regions. One is located at lower potentials, where the passive-active state dissolution (early stages of pitting) occurs, while the other takes over at higher potentials where the electropolishing state dissolution (late stages of pitting) of the Fe electrode arises. At sufficiently high chloride concentrations (≥50mM) only the electropolishing state dissolution of Fe emerges out of its passive state. To quantify the ICR, the coefficient of variation R and the effective diffusion coefficient Deff were calculated as a function of E for the chloride-induced spiking dynamics of the current, which is the characteristic response of the passive-active state dissolution of Fe. The ICR for the electropolishing state dissolution of Fe was quantified by calculating the coherence factor β as a function of E for the low-amplitude current oscillations established over a limiting current region. The coherence of chloride-induced current oscillations becomes maximal at a certain value of the potential applied at the Fe electrode as a result of an optimal level of the internal noise.

Daily variation in the electrophysiological activity of mouse medial habenula neurones

Intrinsic daily or circadian rhythms arise through the outputs of the master circadian clock in the brain's suprachiasmatic nuclei (SCN) as well as circadian oscillators in other brain sites and peripheral tissues. SCN neurones contain an intracellular molecular clock that drives these neurones to exhibit pronounced day–night differences in their electrical properties. The epithalamic medial habenula (MHb) expresses clock genes, but little is known about the bioelectric properties of mouse MHb neurones and their potential circadian characteristics. Therefore, in this study we used a brain slice preparation containing the MHb to determine the basic electrical properties of mouse MHb neurones with whole-cell patch clamp electrophysiology, and investigated whether these vary across the day–night cycle. MHb neurones (n = 230) showed heterogeneity in electrophysiological state, ranging from highly depolarised cells (∼ −25 to −30 mV) that are silent with no membrane activity or display depolarised low-amplitude membrane oscillations, to neurones that were moderately hyperpolarised (∼40 mV) and spontaneously discharging action potentials. These electrical states were largely intrinsically regulated and were influenced by the activation of small-conductance calcium-activated potassium channels. When considered as one population, MHb neurones showed significant circadian variation in their spontaneous firing rate and resting membrane potential. However, in recordings of MHb neurones from mice lacking the core molecular circadian clock, these temporal differences in MHb activity were absent, indicating that circadian clock signals actively regulate the timing of MHb neuronal states. These observations add to the extracellularly recorded rhythms seen in other brain areas and establish that circadian mechanisms can influence the membrane properties of neurones in extra-SCN sites. Collectively, the results of this study indicate that the MHb may function as an intrinsic secondary circadian oscillator in the brain, which can shape daily information flow in key brain processes, such as reward and addiction.

Decay-less kink oscillations in coronal loops

Context: Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 A. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force.

Frequency bands of strongly nonlinear homogeneous granular systems

Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB.

High frequency oscillations: The new EEG frontier

Electroencephalography has traditionally included frequencies up to 80 or 100Hz. In the last decade, EEG activity between 100 and 500Hz (High Frequency Oscillations or HFOs) consisting primarily of low-amplitude short oscillations has been recorded in the intracranial EEG of patients with epilepsy. HFOs often, but not always, coincide with spikes. They appear to be a good surrogate marker of epileptic activity for several reasons: (1) they are most frequent in the seizure onset zone, (2) they seem to reflect disease activity as they follow the fluctuations of seizure occurrence when medication levels are changed (unlike spikes), and (3) they appear to be a good indicator of the epileptogenic region as they are a better predictor of post-surgical outcome than spikes or the seizure onset zone.

Microrheology of complex systems and living cells using AFM

Biological cells display viscoelastic mechanical properties that are a key factor in the regulation of cell processes, such as migration, adhesion and deformability. One interesting tool to probe the mechanical properties of living cells and other complex systems is the Atomic Force Microscopy (AFM). Rheological properties of the sample are obtained usually from the force-indentation (F-δ) measurements and by fitting with the Sneddon's modification of the Hertz model. This model describes the relationship between the force applied by a stiff cone, a purely elastic indentation in a flat and soft sample and the Young's modulus E. AFM uses a flexible cantilever with a pyramidal tip (or sphere) at the end that will locally indent the viscoelastic material. Another approach is to superpose low-amplitude sinusoidal oscillations to an initial identation δ0 (polyacrylamide gel or cells). Then one can determine the complex shear modulus G*...