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Frequency as a function of Reynolds number. ... h-dependence of the frequency, Re=350, Stage II. ... Oscillating flow... h-dependence of the frequency, Re=350, Stage I.
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Emitted light intensity relative to mean intensity versus time. (a) Stable limit cycle; (b) Pulsation with rapid growth in amplitude leading to extinction. (c) Intermittent pulsations close to the marginal stability. (d) Pulsation with two competing frequencies. ... (a) Non-dimensional pulsation frequency versus relative Damköhler number. Open and solid symbols correspond to cases at constant inert composition and constant velocity, respectively. Symbol size is proportional to the amplitude ϵ. —-, f Dth/U2 =Da1/2. (b) Eq. (4) and data of Fig. 17a with C0=0.05. ... Measured cell size λc as a function diffusion length lD, determined with the thermal diffusivity and bulk velocity at the flame. (□, - - - corresponding to σ∗=1.75), variable inert composition at constant bulk velocity (average ϕ=0.45); (∘, — corresponding to σ∗=1.5, •), variable bulk velocity with pure CO2 as inert (average ϕ=0.62), the solid points representing oscillating cells. The error bars represent only the quantization error due to integer number of cells forming around the periphery of the inner quartz cylinder. ... Simultaneous traces of flame intensity (⊙) and position (□). (a) High frequency pulsations at 7.21Hz. (b) Low frequency pulsations at 0.86Hz.
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Evolution with time of the inclination angle θ. Thick and thin lines for sliding and rolling, respectively. After a transitory state in which θ rises with large oscillations, it goes to a quasi-stationary oscillations state with decreasing frequencies (bottom left) and amplitudes (bottom right). ... Evolution with time for different initial conditions of the inclination angle θ with (gray (red in the online version)) and without (black (blue in the online version)) Kutta–Joukowski airflow effect. In all the cases we see that after a transitory state in which θ rises with large oscillations, it goes to a quasi-stationary oscillations state. Thick and thin lines for sliding and rolling, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
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Bidirectional higher frequency intraburst epileptiform activities have different onset locations compared to lower frequency activity. (A) Four field electrodes (Ch1–Ch4) placed along the septotemporal axis of the hippocampus (left inset) record two consecutive epileptiform bursts. The initial burst begins at the temporal region (dashed vertical line), while higher frequency oscillations emerge from the septal region (solid vertical lines). (B) Four field electrodes (Ch1–Ch4) placed along the septotemporal axis of the hippocampus (left inset) record two consecutive epileptiform bursts. The initial burst begins at the septal region (dashed vertical line), while higher frequency oscillations emerge from the temporal region (solid vertical lines). (C) Latency graph (single seizure) plotting the differences in the relative times of the higher frequency epileptiform activity across the four channels shows bidirectional activity of the intraburst activity. The origin of the lower frequency depolarization was superpositioned on the latency graph near their respective region of onset (solid horizontal line) and it can be seen that at certain timepoints during the seizure, the lower frequency burst originates at a different location than their corresponding higher frequency components (arrows). ... Optical visualization of late seizure bidirectionality. (A1) In a different preparation, the orientation of the hippocampus and the recording electrode in the imaging chamber are shown. The area visualized is in the boxed region. (A2) Field recording (E) of two late seizure bursts and their corresponding optical traces (O) extracted from six locations in the photodiode array (location color-coded in A1) lying along the septotemporal axis. (A3) Analysis of the event initiation as seen by the optical traces reveals that the first burst has a septal origin (○, expanded from panel A2) while the consequent burst has a temporal origin (⋄). (A4) Pseudo-colored multiframe display of the beginning of the epileptic bursts. Each row represents a consecutive event (right inset; start time = 0 to 6 ms, Δt = 3 ms). Silent time between events omitted for visualization. Bursts initiated at septal (○) and temporal (⋄) locations along the septotemporal axis (dashed region). (B1) In a different preparation, the orientation of the hippocampus and the recording electrode in the imaging chamber. Area visualized in boxed region. (B2) Field recording (E) of the imaged burst and its corresponding optical traces (O) extracted from six locations in the photodiode array lying along the septotemporal axis (location color-coded in panel B1). Peak detection analysis of the optical traces reveals a separate site of onset of the higher and lower frequency components. (B3) Pseudo-colored multiframe display of the lower (1) and higher (2, 3) frequency epileptic activity. The lower frequency depolarization (⋄) originates at a more temporal location than the consequent higher frequency intraburst activity (○). Each row represents a consecutive time period (right inset; start time = 0 to 4 ms, Δt = 2 ms). ... Disconnection experiments. (A) The septal half of the hippocampus disconnected from the temporal half demonstrates epileptogenicity, as shown by recurrent, spontaneous seizures. Two channels (S1, S2) recorded seizures from the septal pole, and the mid-tissue region. Epileptiform activity seen after 10 min in low-Mg2+ ACSF. (B) The temporal half of the hippocampus disconnected from the septal half demonstrates epileptogenicity, as shown by recurrent, spontaneous seizures. Two channels (T1, T2) recorded seizures from the temporal pole, and the mid-tissue region. After five recurrent seizures, LRDs evolve in both channels. (C and D) Latency graphs (S1–S2; T1–T2) of three seizures from the septal (C, from boxed region in A) and temporal (D, from boxed region in B) regions reveal bidirectional epileptiform activity in the tissue. (E and F) Overlay of the latency graphs of the initial lower frequency component (●) of the burst and the subsequent higher frequency activity (□) reveals different sites of onset within the same bursts from the isolated septal (E) and temporal half (F). Expanded graph (inset) illustrates more clearly the differential sites of onset between these events.... Optical imaging of the origin of both the higher and lower frequency events of an epileptic burst. The initial lower-frequency component of the burst originates near the temporal region (lower region), while the subsequent higher-frequency events originate near the septal region (upper region). The septal hippocampus is located at the top of the window. The time lapse covers a period of about 500 ms (QuickTime; 3.3 MB). ... Network oscillators
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Longitudinal flame oscillations for a 10vol.% H2 experiment, re-interpreted with the theoretical considerations given in previous sections. The white arrow indicates the moment when strong external noise affects the flame. ... Stability graphs for a 10vol.% H2–air mixture at normal conditions and an excitation frequency of 110Hz corresponding to the auto excitation of the flame (left) and 1000Hz corresponding to the major frequency of the horn (right). ... Longitudinal flame oscillations for the 10% H2 experiment. Time and distance along horizontal and vertical directions respectively. The white arrow indicates the moment when the strong external noise was turned on and subsequently started affecting the flame propagation. ... Stability graphs for H2–air mixtures at normal conditions. From left to right and from top to bottom: (a) 10, (b) 10.5, (c) 11, (d) 12, (e) 13 and (f) 14vol.% H2. Excitation frequencies are 110, 122, 121, 130, 145 and 170Hz respectively. ... Positions and average velocity of the flame for 12% vol. H2 experiment. For clarity, the origin of coordinates for time and space was selected as the instant in which oscillations appear for the first time.
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The following is the Supplementary material related to this article Video 1.Video 1Video clip showing the variation of wall shear stress (WSS) vector in four featured points located on the walls (see text for details) of the patient-specific side-to-end AVF model. Left: plot of WSS distribution (magnitude) on the whole surface of the AVF. Middle: the variation of WSS vector in the four featured points throughout the cardiac cycle; note that points P1 and P4 are behind the walls, which were set transparent, and that the WSS vectors are coloured by their magnitude (colour scale on the left panel). Right: zoomed view of P2–P4 WSS unit vectors; note that in this case the WSS vector was normalized (its length is always 1) and the colour scale of the oscillatory shear index (OSI) was changed respect to Figure 2 to distinct it from the WSS scale in the left side. The waveform of inflow blood velocity (U) in the proximal artery (PA) is shown in the upper right panel. Time unit is ms to capture the high frequency oscillations of the WSS vectors and the whole video duration is one cycle period (1s). Of note, respect to the point (P2) on DA where the WSS vector oscillates with low frequency (i.e., of the heart rate), the oscillations of the WSS vector at point (P3) on the inner side of SS have a very high frequency.... Video clip showing the variation of wall shear stress (WSS) vector in four featured points located on the walls (see text for details) of the patient-specific side-to-end AVF model. Left: plot of WSS distribution (magnitude) on the whole surface of the AVF. Middle: the variation of WSS vector in the four featured points throughout the cardiac cycle; note that points P1 and P4 are behind the walls, which were set transparent, and that the WSS vectors are coloured by their magnitude (colour scale on the left panel). Right: zoomed view of P2–P4 WSS unit vectors; note that in this case the WSS vector was normalized (its length is always 1) and the colour scale of the oscillatory shear index (OSI) was changed respect to Figure 2 to distinct it from the WSS scale in the left side. The waveform of inflow blood velocity (U) in the proximal artery (PA) is shown in the upper right panel. Time unit is ms to capture the high frequency oscillations of the WSS vectors and the whole video duration is one cycle period (1s). Of note, respect to the point (P2) on DA where the WSS vector oscillates with low frequency (i.e., of the heart rate), the oscillations of the WSS vector at point (P3) on the inner side of SS have a very high frequency.
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Gamma-oscillations elicited by a sentence-cue visuomotor task in a 17-year-old male with focal epilepsy (patient #10). Gamma-augmentation involved the lateral-polar occipital region 500msec prior to the onset of button-press, the inferior occipital-temporal region, and the Rolandic area immediately prior to the onset of button-press. The magnitude of gamma-augmentation was greater when the right hand (i.e.: contralateral hand) was used for motor responses, compared to when the left hand (i.e.: ipsilateral hand) was used. The lateral portion of the inferior occipital-temporal region had greater gamma-augmentation elicited by a sentence-cue, whereas the medial portion had greater gamma-augmentation elicited by a gesture-cue. ... Gamma-oscillations elicited by a gesture-cue visuomotor task in a 17-year-old male with focal epilepsy (patient #10). Gamma-augmentation involved the lateral-polar occipital region 500msec prior to the onset of button-press, the inferior occipital-temporal region, and the Rolandic area immediately prior to the onset of button-press. The magnitude of gamma-augmentation was greater when the right hand (i.e.: contralateral hand) was used for motor responses, compared to when the left hand (i.e.: ipsilateral hand) was used. The medial portion of the inferior occipital-temporal region had greater gamma-augmentation elicited by a gesture-cue, whereas the lateral portion had greater gamma-augmentation elicited by a sentence-cue. ... Differential gamma-augmentation elicited by sentence- and gesture-cues in patient 10. Time-frequency ECoG matrixes relative to the onset of visual-cues revealed a functional double dissociation in patient 10. The sentence-cue visuomotor task resulted in gamma-augmentation in the lateral portion but not in the medial portion of the inferior occipital-temporal area (upper row). The gesture-cue visuomotor task resulted in gamma-augmentation in the medial and lateral portions of the inferior occipital-temporal area with greater intensity in the medial portion (middle row). Comparison of amplitudes between sentence- and gesture-cues revealed that the relatively lateral portion of inferior occipital-temporal area had significantly greater gamma-augmentation elicited by a sentence-cue (denoted by red areas in the bottom row), whereas the relatively medial portion had significantly greater gamma-augmentation elicited by a gesture-cue (denoted by blue areas in the bottom row). Please also see Videos S1 and S2 on the website.
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cell oscillations
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a) Colloidal particle (black point adherent to bubbles) with different bubble development states: no bubble (plate used here is 10μm in diameter), bubble growth and maximum bubble size; b) Simulation (increased by factor 10 for presentation reasons) (for equation see theoretical section) of colloidal particle propulsion speed (red) upon bubble growth, maximum size and after bubble de-pining (acceleration, maximum speed, and deceleration) and real measurement (black) (error bars from five bubble life cycles measurements of two different particles with same frequency). The bubble radius used in the simulations is also shown (green and right Y axis). Please note that a) and b) are from different plates. A is from a plate with a slightly lower bubbling frequency than b) and frequency differences up to factor 10 were found. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Ca2+ oscillations... Effect of ACh on endothelial cell [Ca2+]i in isolated sheets of cells. (A) Confocal brightfield (top) and fluorescence (bottom) images of an isolated endothelial cell sheet loaded with fluo-4. (B andC) The time course of endothelial cell fluorescence changes in response to 1μM ACh added at the time indicated (by ▴). (B) The average whole-cellular fluorescence intensity over time. The coloured lines correspond to the individual cells marked in (A). Note that the oscillations in fluorescence are partially synchronized. (C) The average multi-cellular relative fluorescence (F/F0) over time. The region of interest for measuring fluorescence intensity was increased to include all the cells depicted in (A). (D) Time course of increases in membrane potential (Em) in response to 3μM ACh added at the time indicated (by ▾). The average resting membrane potential was −16.7±2.4mV (n=3 cells), which was increased to −28.8±3.9mV (n=3 cells) by current injection (to cell 1: black trace; and cell 3: red trace). ACh hyperpolarized these cells to a peak of −67.1±2.1mV (n=3 cells). The response to ACh was reproducible (cell 2: green and blue traces correspond to first and second additions), and in two of the three cells, the membrane potential oscillated (frequency: 0.14±0.02Hz, n=3 responses). (E) The cell marked with the arrow in (A) was used to illustrate the time course of sub-cellular fluorescence changes in response to 1μM ACh (added at ▴). Top panel: Changes in F/F0 in the regions corresponding to the coloured boxes shown over the cell below. Note that the increases in F/F0 were synchronous. Bottom panels: The difference in fluorescence intensity (F−F0) across the length of the cell (white line over image) over time (single oscillation indicated by the bar in the top panel). The dotted line in each panel corresponds to the x-coordinate in the image above (white line), and t=0s. There was no evidence for a Ca2+ wave. Note that the longitudinal axis of the artery was horizontally orientated, as in Fig. 1A. A movie of this experiment is available online (Movie 2, Supplementary material). ... Effect of ACh on endothelial cell [Ca2+]i in pressurized arteries. (A) Confocal fluorescence image of arterial endothelial cells loaded with fluo-4. (B and C) The time course of endothelial cell fluorescence changes in response to 0.3μM ACh added at the time indicated (by ▴). (B) The average whole-cellular fluorescence intensity over time. The coloured lines correspond to the individual cells marked in (A), note that the oscillations in fluorescence were asynchronous. (C) The average multi-cellular relative fluorescence (F/F0) over time. The region of interest for measuring fluorescence intensity was increased to include all the cells in the field of view (>50 cells). Note that the pattern of oscillations was markedly dampened compared to the individual cells, reflecting the asynchronous signals. (D) Summarized data showing the time course of increases in F/F0 in response to 0.3μM ACh (n=10) or 3μM ACh (added at t=0s, n=3). (E) The cell marked with an arrow in (A) was enlarged (image below) and used to illustrate the time course of sub-cellular fluorescence changes in response to 0.3μM ACh (added at ▴). Top panel: changes in F/F0 in the regions corresponding to the coloured boxes shown over the cell below. Note that the increases in F/F0 started moving from right to left, were not uniform, and changed direction. Bottom five panels: The difference in fluorescence intensity (F−F0) across the length of the cell (white line in image) over time (a single oscillation indicated by the bar in the top panel). The dotted line in each panel corresponds to the x-coordinate in the image above (white line), and t=0s. The wave travelled from right to left at a speed of approximately 30μm/s, and appeared to quench at the position of the nucleus. A movie of this experiment is available online (Movie 1, Supplementary material). ... Effect of treatments on the oscillations in endothelial cell [Ca2+]i in pressurized arteries. The effect of the various treatments on the oscillations in endothelial cell [Ca2+]i in response to ACh in pressurized arteries. The values were obtained from the experiments presented in Figs. 1, 3 and 4. The time course following the addition of 0.3μM ACh to the bath was divided into two phases, initial: t=0–30s; and sustained: t=30–100s. The percentage of cells oscillating (A) was calculated from the 16 cells analyzed per artery, and the frequency of oscillations (B) calculated using cells that oscillated in (A).
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