### 181 results for qubit oscillator frequency

Contributors: João Casaleiro, Luís B. Oliveira, Igor M. Filanovsky

Date: 2016-01-01

(a) S...Capacitive coupled RC-**oscillators**.
...RC-**oscillators**...Coupled **oscillators**...In this paper the capacitive coupling in quadrature RC-**oscillators** is investigated. The capacitive coupling has the advantages of being noiseless with a small area penalty and without increasing the power dissipation. The results show that a phase error below 1° and an amplitude mismatch lower than 1% are obtained with a coupling capacitance about 20% of the **oscillator**׳s capacitance value. Due to this kind of coupling, the phase-noise improves by 3dB (to −115.1 dBc/Hz @ 10MHz) and the increase of power requirement is only marginal leading to a figure-of-merit of −154.8dBc/Hz. This is comparable to the best state-of-the-art RC-**oscillators**, yet the dissipated power is about four times less. We present calculations of **frequency**, phase error and amplitude mismatch that are validated by simulations. The theory shows that phase error is proportional to the amplitude mismatch, indicating that an automatic phase error minimization based on the amplitude mismatches is possible. The measurements on a 2.4GHz voltage-controlled quadrature RC-**oscillator** with capacitive coupling fabricated in 130nm CMOS circuit prototypes validate the theory....Quadrature **oscillator**...Simulated **frequency**.
...A quadrature RC-**oscillator** with capacitive coupling...**Frequency** of **oscillation** with the **oscillators** uncoupled and coupled (CX=20fF).
...Capacitive coupled incremental circuit.
...Relation between the **oscillation** **frequency** and the coupling strength.
...Capacitive coupled RC-oscillators.
...Coupled VDPOs.
...(a) Single RC **oscillator** and (b) small-signal equivalent circuit.
...Relation between the oscillation frequency and the coupling strength.
...Van der Pol **oscillators**...Frequency of oscillation with the oscillators uncoupled and coupled (CX=20fF).
... In this paper the capacitive coupling in quadrature RC-**oscillators** is investigated. The capacitive coupling has the advantages of being noiseless with a small area penalty and without increasing the power dissipation. The results show that a phase error below 1° and an amplitude mismatch lower than 1% are obtained with a coupling capacitance about 20% of the **oscillator**׳s capacitance value. Due to this kind of coupling, the phase-noise improves by 3dB (to −115.1 dBc/Hz @ 10MHz) and the increase of power requirement is only marginal leading to a figure-of-merit of −154.8dBc/Hz. This is comparable to the best state-of-the-art RC-**oscillators**, yet the dissipated power is about four times less. We present calculations of **frequency**, phase error and amplitude mismatch that are validated by simulations. The theory shows that phase error is proportional to the amplitude mismatch, indicating that an automatic phase error minimization based on the amplitude mismatches is possible. The measurements on a 2.4GHz voltage-controlled quadrature RC-**oscillator** with capacitive coupling fabricated in 130nm CMOS circuit prototypes validate the theory.

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Contributors: Shuai Zeng, Bing Li, Shaoqun Zeng, Shangbin Chen

Date: 2009-11-04

The purpose of this computational study was to investigate the possible role of voltage-gated Ca2+ channels in spontaneous Ca2+ **oscillations** of astrocytes. By incorporating different types of voltage-gated Ca2+ channels and a previous model, this study reproduced typical Ca2+ **oscillations** in silico. Our model could mimic the oscillatory phenomenon under a wide range of experimental conditions, including resting membrane potential (−75 to −60 mV), extracellular Ca2+ concentration (0.1 to 1500 μM), temperature (20 to 37°C), and blocking specific Ca2+ channels. By varying the experimental conditions, the amplitude and duration of Ca2+ **oscillations** changed slightly (both **frequency** changed significantly (∼400%). This indicates that spontaneous Ca2+ **oscillations** in astrocytes might be an all-or-none process, which might be **frequency**-encoded in signaling. Moreover, the properties of Ca2+ **oscillations** were found to be related to the dynamics of Ca2+ influx, and not only to a constant influx. Therefore, calcium channels dynamics should be used in studying Ca2+ **oscillations**. This work provides a platform to explore the still unclear mechanism of spontaneous Ca2+ **oscillations** in astrocytes....The occurrence of Ca2+ oscillation depends on the membrane potential. When the membrane potential is −64.9 mV, there is no Ca2+ oscillation. Within −70**.0 to −64**.9 mV, the frequency and amplitude of Ca2+ oscillations change with the membrane potential.
...Dependence of Ca2+ oscillations on extracellular Ca2+ concentration. Ca2+ oscillations stopped when the extracellular Ca2+ concentration was too low or too high. From 0.1 to 1500 μM, the frequency of Ca2+ oscillations increased with a rise in extracellular Ca2+ concentration.
...Typical spontaneous Ca2+ **oscillations** from the computational study. From top to bottom, the three plots correspond to **oscillations** in cytoplasmic Ca2+, ER Ca2+, and cytoplasmic IP3. All three variables have the same **frequency** but different peak times (details are shown in Fig. 4).
...(A) Bifurcation diagram of Ca2+ **oscillations** as a function of membrane potential. Sustained Ca2+ **oscillations** occurred in the potential range of −70.0 to −64.9 mV, where the maximum and minimum of Ca2+ **oscillations** were plotted. The dashed line refers to the unstable steady state. Out of the oscillatory domain, the system evolved into a stable steady state. (B) **Frequency** of Ca2+ **oscillations** versus membrane potential.
...The purpose of this computational study was to investigate the possible role of voltage-gated Ca2+ channels in spontaneous Ca2+ oscillations of astrocytes. By incorporating different types of voltage-gated Ca2+ channels and a previous model, this study reproduced typical Ca2+ oscillations in silico. Our model could mimic the oscillatory phenomenon under a wide range of experimental conditions, including resting membrane potential (−75 to −60 mV), extracellular Ca2+ concentration (0.1 to 1500 μM), temperature (20 to 37°C), and blocking specific Ca2+ channels. By varying the experimental conditions, the amplitude and duration of Ca2+ oscillations changed slightly (both **frequency** changed significantly (∼400%). This indicates that spontaneous Ca2+ oscillations in astrocytes might be an all-or-none process, which might be **frequency**-encoded in signaling. Moreover, the properties of Ca2+ oscillations were found to be related to the dynamics of Ca2+ influx, and not only to a constant influx. Therefore, calcium channels dynamics should be used in studying Ca2+ oscillations. This work provides a platform to explore the still unclear mechanism of spontaneous Ca2+ oscillations in astrocytes....Amplitude and frequency of Ca2+ oscillations versus temperature. In the temperature range of 20–37°C, both the amplitude (indicated as an asterisk) and frequency (dotted line) decreased with temperature.
...(A) Bifurcation diagram of Ca2+ oscillations as a function of membrane potential. Sustained Ca2+ oscillations occurred in the potential range of −70**.0 to −64**.9 mV, where the maximum and minimum of Ca2+ oscillations were plotted. The dashed line refers to the unstable steady state. Out of the oscillatory domain, the system evolved into a stable steady state. (B) **Frequency** of Ca2+ oscillations versus membrane potential.
...Typical spontaneous Ca2+ oscillations from the computational study. From top to bottom, the three plots correspond to oscillations in cytoplasmic Ca2+, ER Ca2+, and cytoplasmic IP3. All three variables have the same frequency but different peak times (details are shown in Fig. 4).
...Dependence of Ca2+ **oscillations** on extracellular Ca2+ concentration. Ca2+ **oscillations** stopped when the extracellular Ca2+ concentration was too low or too high. From 0.1 to 1500 μM, the **frequency** of Ca2+ **oscillations** increased with a rise in extracellular Ca2+ concentration.
...Amplitude and **frequency** of Ca2+ **oscillations** versus temperature. In the temperature range of 20–37°C, both the amplitude (indicated as an asterisk) and **frequency** (dotted line) decreased with temperature.
...The occurrence of Ca2+ **oscillation** depends on the membrane potential. When the membrane potential is −64.9 mV, there is no Ca2+ **oscillation**. Within −70.0 to −64.9 mV, the **frequency** and amplitude of Ca2+ **oscillations** change with the membrane potential.
... The purpose of this computational study was to investigate the possible role of voltage-gated Ca2+ channels in spontaneous Ca2+ **oscillations** of astrocytes. By incorporating different types of voltage-gated Ca2+ channels and a previous model, this study reproduced typical Ca2+ **oscillations** in silico. Our model could mimic the oscillatory phenomenon under a wide range of experimental conditions, including resting membrane potential (−75 to −60 mV), extracellular Ca2+ concentration (0.1 to 1500 μM), temperature (20 to 37°C), and blocking specific Ca2+ channels. By varying the experimental conditions, the amplitude and duration of Ca2+ **oscillations** changed slightly (both <25%), while the **frequency** changed significantly (∼400%). This indicates that spontaneous Ca2+ **oscillations** in astrocytes might be an all-or-none process, which might be **frequency**-encoded in signaling. Moreover, the properties of Ca2+ **oscillations** were found to be related to the dynamics of Ca2+ influx, and not only to a constant influx. Therefore, calcium channels dynamics should be used in studying Ca2+ **oscillations**. This work provides a platform to explore the still unclear mechanism of spontaneous Ca2+ **oscillations** in astrocytes.

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Contributors: Tara A. Whitten, Adam M. Hughes, Clayton T. Dickson, Jeremy B. Caplan

Date: 2011-01-15

Oscillatory activity is a principal mode of operation in the brain. Despite an intense resurgence of interest in the mechanisms and functions of brain rhythms, methods for the detection and analysis of oscillatory activity in neurophysiological recordings are still highly variable across studies. We recently proposed a method for detecting oscillatory activity from time series data, which we call the BOSC (Better **OSCillation** detection) method. This method produces systematic, objective, and consistent results across **frequencies**, brain regions and tasks. It does so by modeling the functional form of the background spectrum by fitting the empirically observed spectrum at the recording site. This minimizes bias in **oscillation** detection across **frequency**, region and task. Here we show that the method is also robust to dramatic changes in state that are known to influence the shape of the power spectrum, namely, the presence versus absence of the alpha rhythm, and can be applied to independent components, which are thought to reflect underlying sources, in addition to individual raw signals. This suggests that the BOSC method is an effective tool for measuring changes in rhythmic activity in the more common research scenario wherein state is unknown....Temporal independence of two alpha components. (A) An 8-s epoch from the alpha component shown in Fig. 2, with detected alpha-**frequency** **oscillations** highlighted in red. (B) The same time segment as in A, from the alpha component in Fig. 6. Note the alpha **oscillation** is maximal in B when the **oscillation** is at a minimum in A, demonstrating why these were extracted as temporally independent components.
...Lateralized alpha component. From the same subject as Figs. 2 and 4–5. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) **Oscillations** detected across all **frequencies** by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that **oscillations** were detected at each **frequency**. (E) The time-domain representation of the chosen component, with detected **oscillations** at the peak alpha **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E.
...**Oscillation**...Oscillatory activity is a principal mode of operation in the brain. Despite an intense resurgence of interest in the mechanisms and functions of brain rhythms, methods for the detection and analysis of oscillatory activity in neurophysiological recordings are still highly variable across studies. We recently proposed a method for detecting oscillatory activity from time series data, which we call the BOSC (Better OSCillation detection) method. This method produces systematic, objective, and consistent results across **frequencies**, brain regions and tasks. It does so by modeling the functional form of the background spectrum by fitting the empirically observed spectrum at the recording site. This minimizes bias in oscillation detection across **frequency**, region and task. Here we show that the method is also robust to dramatic changes in state that are known to influence the shape of the power spectrum, namely, the presence versus absence of the alpha rhythm, and can be applied to independent components, which are thought to reflect underlying sources, in addition to individual raw signals. This suggests that the BOSC method is an effective tool for measuring changes in rhythmic activity in the more common research scenario wherein state is unknown....**Oscillation** detection in a single electrode with weak alpha. The electrode was selected from the same subject as in Figs. 2 and 4. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) **Oscillations** detected across all **frequencies** by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes -closed condition (red) and eyes-open condition (black) that **oscillations** were detected at each **frequency**. (E) The raw signal from the chosen electrode, with detected **oscillations** at the peak alpha **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha **oscillation**.
...Lateralized **alpha** component. From the same subject as Figs. 2 and 4–5. (A) The spline-interpolated scalp distribution of an **alpha** component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across **all** frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at **each** **frequency**. (E) The time-domain representation of the chosen component, with detected oscillations at the peak **alpha** **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E.
...Distribution of power values. For **all** panels, the blue bars represent the empirical probability distribution function of power values** from** the signal used to estimate the background spectrum (signal** from** the entire recording) in 25 equally spaced bins for a given **frequency**. The red line represents the theoretical χ2(2) probability distribution function based on the estimated mean power at the same **frequency** derived** from** the linear-regression fit. Vertical lines represent the 90th, 95th and 99th percentile thresholds (left to right). Note that for **alpha** frequencies, a great proportion of the power values are far beyond the range plotted here; those are summed in the right-most bin. A–C are for the bilateral **alpha** component** from** ICA; D–F are for the individual electrode analysed in Fig. 4. A and D are** from** the peak **alpha** **frequency** of 9.5 Hz. B and E are** from** a lower **frequency** (5.4 Hz) and C and F are** from** a higher **frequency** (16.0 Hz).
...Alpha harmonic in an independent component. This is** from** a different subject** from** Figs. 2, 4–5 and 9–10. (A) The spline-interpolated scalp distribution of an **alpha** component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across **all** frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at **each** **frequency**. (E) The time-domain representation of the chosen component, with detected oscillations at the **alpha** harmonic **frequency** (19.0Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E.
...**Oscillation** detection in an ICA alpha component. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue) and the linear regression fit to the background (green). (C) **Oscillations** detected across all **frequencies** by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that **oscillations** were detected at each **frequency**. (E) The time-domain representation of the chosen component, with detected **oscillations** at the peak alpha **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha **oscillation**.
...Oscillation detection in a single electrode with strong **alpha**. The electrode was selected** from** the same subject as in Fig. 2. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across **all** frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at **each** **frequency**. (E) The raw signal** from** the chosen electrode, with detected oscillations at the peak **alpha** **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E to show the spindle-like appearance of the **alpha** oscillation.
...**Oscillation** detection in a single electrode with strong alpha. The electrode was selected from the same subject as in Fig. 2. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) **Oscillations** detected across all **frequencies** by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that **oscillations** were detected at each **frequency**. (E) The raw signal from the chosen electrode, with detected **oscillations** at the peak alpha **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E to show the spindle-like appearance of the alpha **oscillation**.
...Oscillation detection in an ICA **alpha** component. (A) The spline-interpolated scalp distribution of an **alpha** component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue) and the linear regression fit to the background (green). (C) Oscillations detected across **all** frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at **each** **frequency**. (E) The time-domain representation of the chosen component, with detected oscillations at the peak **alpha** **frequency** (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the **alpha** oscillation.
... Oscillatory activity is a principal mode of operation in the brain. Despite an intense resurgence of interest in the mechanisms and functions of brain rhythms, methods for the detection and analysis of oscillatory activity in neurophysiological recordings are still highly variable across studies. We recently proposed a method for detecting oscillatory activity from time series data, which we call the BOSC (Better **OSCillation** detection) method. This method produces systematic, objective, and consistent results across **frequencies**, brain regions and tasks. It does so by modeling the functional form of the background spectrum by fitting the empirically observed spectrum at the recording site. This minimizes bias in **oscillation** detection across **frequency**, region and task. Here we show that the method is also robust to dramatic changes in state that are known to influence the shape of the power spectrum, namely, the presence versus absence of the alpha rhythm, and can be applied to independent components, which are thought to reflect underlying sources, in addition to individual raw signals. This suggests that the BOSC method is an effective tool for measuring changes in rhythmic activity in the more common research scenario wherein state is unknown.

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Contributors: Tolga Esat Özkurt, Alfons Schnitzler

Cross-**frequency** coupling...Simulation results. Coupling portraits for simulated data for (A) clean (SNR=20dB) and (B) noisy cases (SNR=−10dB). PAC was generated to be at 60–80Hz (amplitude **frequency**) and 15Hz (phase **frequency**). The simulated signal contained also **oscillations** (at 20, 25, 30, 40 and 100Hz) having no coupling relation. These portraits show the mean PAC estimates over 100 repetitions for each method. Only methods robust enough were presented: direct PAC estimate, GLM with spurious term removed, MI with statistics and raw MI without statistics (ordered from left to right). Notice that the first two methods yield very similar outputs identifying PAC correctly and they are robust to both non-coupled **oscillations** and noise.
...Simulation results. Coupling portraits for simulated data for (A) clean (SNR=20dB) and (B) noisy cases (SNR=−10dB). PAC was generated to be at 60–80Hz (amplitude **frequency**) and 15Hz (phase **frequency**). The simulated signal contained also oscillations (at 20, 25, 30, 40 and 100Hz) having no coupling relation. These portraits show the mean PAC estimates over 100 repetitions for each method. Only methods robust enough were presented: direct PAC estimate, GLM with spurious term removed, MI with statistics and raw MI without statistics (ordered from left to right). Notice that the first two methods yield very similar outputs identifying PAC correctly and they are robust to both non-coupled oscillations and noise.
...Short communication - A critical note on the definition of phase–amplitude cross-**frequency** coupling...**Oscillations** ... Recent studies have observed the ubiquity of phase–amplitude coupling (PAC) phenomenon in human and animal brain recordings. While various methods were performed to quantify it, a rigorous analytical definition of PAC is lacking. This paper yields an analytical definition and accordingly offers theoretical insights into some of the current methods. A direct PAC estimator based on the given definition is presented and shown theoretically to be superior to some of the previous methods such as general linear model (GLM) estimator. It is also shown that the proposed PAC estimator is equivalent to GLM estimator when a constant term is removed from its formulation. The validity of the derivations is demonstrated with simulated data of varying noise levels and local field potentials recorded from the subthalamic nucleus of a Parkinson's disease patient.

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Contributors: S. Sutradhar, R. Paul

Date: 2014-03-07

Chromosomes move towards and away from the centrosomes during the mitosis. This **oscillation** is observed when the kinetochore, a specific protein structure on the chromosome is captured by centrosome-nucleated polymer called microtubules. We present a computational model, incorporating activities of various molecular motors and microtubule dynamics, to demonstrate the observed **oscillation**. The model is robust and is not restricted to any particular cell type. Quantifying the average velocity, amplitude and periodicity of the chromosomal **oscillation**, we compare numerical results with the available experimental data. Our analysis supports a tug-of-war like mechanism between opposing motors that changes the course of chromosomal **oscillation**. It turns out that, various modes of **oscillation** can be fully understood by assembling the dynamics of molecular motors. Near the stall regime, when opposing motors are engaged in a tug-of-war, sufficiently large kinetochore–microtubule generated force may prolong the stall durations....Simulation results obtained with stochastic switching approach. (a) The number of bound motors plotted with time show that, unlike the deterministic approach, here the number of motors (in particular, dynein) does not rise sharply. Note that maximum dynein number is less than value observed in the deterministic approach, (b) total force plotted against time is similar to the deterministic case, (c) mono-oriented chromosomal velocity as a function of time shows a rather smooth transition from P to AP and vice versa. In addition, multiple stall regimes during the switchover between AP & P motion are abundant and (d) unlike the deterministic scenario, the temporal evolution of the bioriented chromosomal velocity shows a frustrated behavior. Subplot (e) shows the chromosomal distance from the pole with respect to time. The curve from the early to late time regime corresponds to the **oscillation** of the mono-oriented chromosome, monotonic migration of the chromosome toward the spindle equator upon capture of the uncaptured KT and bioriented chromosomal **oscillation** (as in 2(e). Note that the onset of the biorientation (~1200s) is done manually).
...Simulation results obtained with deterministic switching approach. (a) The number of bound motors plotted as a function of time. The sharp rise in the number of motors is due to their rapid attachment after the winning motor species is selected deterministically, (b) total force is plotted against time. The asymmetry in the slope between the positive and the negative half of the force curve arises due to the difference of the stall forces between chromokinesin and dynein, (c) mono-oriented chromosomal velocity derived from the 14. Data shows that chromosome moves slower in P direction (−ve velocity) compared to the AP direction (+ve velocity), (d) chromosomal velocity after biorientation: symmetry between the positive and the negative halves of the curve suggests that the chromosome is driven by a single motor species, which is dynein in the present case. Note that the onset of the biorientation (~1200s) is done manually. Subplot (e) shows the distance of chromosome from the pole plotted with respect to time. The trajectory consists of a regular **oscillation**, a monotonic increase followed by an irregular **oscillation**. Regular **oscillation** corresponds to a mono-oriented chromosome, monotonic displacement represents the capture of the uncaptured sister KT and irregular **oscillation** is the signature of a bioriented chromosome.
...Schematic representation of a mono-oriented and a bioriented chromosome showing **oscillations** triggered by the capture of an uncaptured kinetochore by a randomly searching MT. (a) A mono-oriented chromosome is attached to a single pole by kinetochore MTs. The model consists of a pole, an MT aster and a chromosome. Dark green rods represent astral MTs, whereas, light green rods represent kinetochore MTs. Impingement on the chromosome arm and subsequent polymerization of MTs generate forces Fpoly in the AP direction. Dyneins and chromokinesins bind at their respective rates with the MTs and walk in opposite directions generating forces FDyn and FCK respectively. Vanishing net force stalls the chromosome, (b) a bioriented chromosome is attached to two poles by kinetochore MTs interacting with the opposite sister kinetochores. The model is described by twice the sets of parameters as mentioned in (a), (c) deterministic switching leads to two distinct stall regimes (near the pole and away from the pole). Exit from the stall near the pole and away from the pole are deterministically driven by chromokinesins and dyneins respectively. Hence, the motion of the chromosome is always directed and monotonous and (d) stochastic switching gives rise to more than two stall regimes. Exit from the stall is probabilistically driven by both types of motors. The winning motor directs the instantaneous chromosomal movement. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
...Effect of KMT polymerization and depolymerization force on mono-oriented chromosomal **oscillation**. Distance of the mono-oriented chromosome from the capturing pole is plotted against time for various KMT forces (0 pN/KMT, 5 pN/KMT and 25 pN/KMT). The stall-width increase (as visible in the gray and black curves) with the increasing KMT polymerization and depolymerization forces.
...Chromosomal distance from the left pole is plotted against time for the deterministic and the stochastic approach. The **oscillation** up to ~1000s is mono-oriented and from ~1200s onwards it is bioriented. Note that the onset of the biorientation is done manually. During the time span between 1000s and 1200s the chromosome moves monotonically toward the spindle equator as a result of the biorientation. In the deterministic approach, the average amplitude (distance traveled from P to AP) and the excursion period of each phase (P to AP or AP to P) for the mono-oriented chromosome are ~4μm and ~120s respectively; corresponding values after the biorientation are ~2μm and ~100s respectively. For the stochastic case, the average values of amplitude and excursion period for the mono-oriented chromosome are ~3.7μm and ~110s respectively; whereas these values for the bioriented case are ~1.5μm and ~90s. In the inset, we show the pole-to-chromosome distance against time using the stochastic switching scenario for a (a) bioriented and a (b) mono-oriented chromosome. The arrows show the intermediate stall events (N phase).
... Chromosomes move towards and away from the centrosomes during the mitosis. This **oscillation** is observed when the kinetochore, a specific protein structure on the chromosome is captured by centrosome-nucleated polymer called microtubules. We present a computational model, incorporating activities of various molecular motors and microtubule dynamics, to demonstrate the observed **oscillation**. The model is robust and is not restricted to any particular cell type. Quantifying the average velocity, amplitude and periodicity of the chromosomal **oscillation**, we compare numerical results with the available experimental data. Our analysis supports a tug-of-war like mechanism between opposing motors that changes the course of chromosomal **oscillation**. It turns out that, various modes of **oscillation** can be fully understood by assembling the dynamics of molecular motors. Near the stall regime, when opposing motors are engaged in a tug-of-war, sufficiently large kinetochore–microtubule generated force may prolong the stall durations.

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Contributors: Andrada Ianuş, Bernard Siow, Ivana Drobnjak, Hui Zhang, Daniel C. Alexander

Date: 2013-02-01

**Oscillating** gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal **oscillations** have been popular for some time, recent work suggests additional benefits of square or trapezoidal **oscillating** waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square **oscillating** gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan’s matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the **oscillation** **frequency** and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients....(a) Diffusion signal for different waveforms: square with 90° phase, apodised cosine and apodised trapezoid as a function of **oscillation** **frequency** for four different sizes of the restricted compartment; (b) corresponding extracted ADC values. The diffusion signal and ADC for apodised trapezoid and square wave are very similar and are plotted on top of each other.
...(a) Diffusion signal for different waveforms: square with 90° phase, apodised cosine and apodised trapezoid as a function of oscillation **frequency** for four different sizes of the restricted compartment; (b) corresponding extracted ADC values. The diffusion signal and ADC for apodised trapezoid and square wave are very similar and are plotted on top of each other.
...**Oscillating** gradient...(a) Average signal difference between square and sine approximations and the full trapezoidal expressions as a function of α for R=2μm and 10μm. (b) Diffusion signal for R=5μm for the three waveforms with gradient strength G=60mT/m and 200mT/m as a function of **oscillation** **frequency**.
...(a) Average signal difference between square and sine approximations and the full trapezoidal expression considering: I – same amplitude, II – same area under the curves, III – same area under the squared curves and IV – same b value per **oscillation**. (b) Difference between square and sine approximations and the full trapezoidal expressions with SR=200T/m/s as a function of n for all data points with R=5μm.
...Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan’s matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation **frequency** and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients....Restricted diffusion signal as a function of oscillation **frequency** for (a) several values of Δ, R=5μm and G=0.1T/m; (b) several gradient strengths, R=5μm and Δ=25ms. In (a) and (b) the filled markers indicate waveforms with integer number of oscillations. Restricted diffusion as a function of (c) gradient strength for several frequencies, R=5μm and Δ=45ms; (d) cylinder radius for several frequencies, G=0.1T/m and Δ=45ms. The markers show the MC simulation and the solid lines are the GPD approximations. The vertical bar separates different scales on the x-axis.
...Restricted diffusion signal as a function of **oscillation** **frequency** for (a) several values of Δ, R=5μm and G=0.1T/m; (b) several gradient strengths, R=5μm and Δ=25ms. In (a) and (b) the filled markers indicate waveforms with integer number of **oscillations**. Restricted diffusion as a function of (c) gradient strength for several **frequencies**, R=5μm and Δ=45ms; (d) cylinder radius for several **frequencies**, G=0.1T/m and Δ=45ms. The markers show the MC simulation and the solid lines are the GPD approximations. The vertical bar separates different scales on the x-axis.
...Square wave **oscillations**...(a) Average signal difference between square and sine approximations and the full trapezoidal expressions as a function of α for R=2μm and 10μm. (b) Diffusion signal for R=5μm for the three waveforms with gradient strength G=60mT/m and 200mT/m as a function of oscillation **frequency**.
... **Oscillating** gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal **oscillations** have been popular for some time, recent work suggests additional benefits of square or trapezoidal **oscillating** waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square **oscillating** gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan’s matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the **oscillation** **frequency** and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients.

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Contributors: R. Kalter, M.J. Tummers, S. Kenjereš, B.W. Righolt, C.R. Kleijn

Date: 2014-01-01

The effect of Lorentz forcing on self-sustained oscillations of turbulent jets (Re=3.1×103) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (FL0), to weaken or strengthen the self-sustained jet oscillations. The low **frequency** self-sustained jet oscillations induce a free surface oscillation. When FL0 the free surface oscillation amplitude is enhanced by a factor of 1.5....Amplitude A and frequency fTS of the free surface oscillation at a monitoring point at x=0.175m for the three different forcings (Rein=3.1×103, N=0.02). Dominant frequency fPOD from the power spectrum of the first chrono mode of the POD.
...(a) Time series for the first chrono-mode of the POD, a1(t), for the three different forcings with vin=0.4m/s (Re=3.1in×103, N=0.02). (b) Power spectra of the chrono-modes a1(t). **Frequency** peaks are found at fPOD=0.027Hz (FL0). The values of the **frequency** peaks are in reasonable agreement with the **frequencies** found for the free surface fluctuations, fTS.
...(a) Time series for the first chrono-mode of the POD, a1(t), for the three different forcings with vin=0.4m/s (Re=3.1in×103, N=0.02). (b) Power spectra of the chrono-modes a1(t). Frequency peaks are found at fPOD=0.027Hz (FLL>0). The values of the frequency peaks are in reasonable agreement with the frequencies found for the free surface fluctuations, fTS.
...(a–c) Profiles of the turbulence kinetic energy kturb,2D. (d–f) Profiles of the kinetic energy associated with the large-scale **oscillations** kosc,2D. The inlet velocity is vin=0.4m/s (Rein=3.1×103, N=0.02).
...Amplitude A and **frequency** fTS of the free surface **oscillation** at a monitoring point at x=0.175m for the three different forcings (Rein=3.1×103, N=0.02). Dominant **frequency** fPOD from the power spectrum of the first chrono mode of the POD.
...The effect of Lorentz forcing on self-sustained **oscillations** of turbulent jets (Re=3.1×103) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (FL0), to weaken or strengthen the self-sustained jet **oscillations**. The low **frequency** self-sustained jet **oscillations** induce a free surface **oscillation**. When FLoscillation is reduced by a factor of 6 and when FL>0 the free surface **oscillation** amplitude is enhanced by a factor of 1.5....Self-sustained **oscillations** ... The effect of Lorentz forcing on self-sustained **oscillations** of turbulent jets (Re=3.1×103) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (FL0), to weaken or strengthen the self-sustained jet **oscillations**. The low **frequency** self-sustained jet **oscillations** induce a free surface **oscillation**. When FL0 the free surface **oscillation** amplitude is enhanced by a factor of 1.5.

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Contributors: N. Mykytenko, D. Fink, A. Kiv

Date: 2015-01-01

Current spikes in conditions of real experiment [32]. Region I corresponds to regular **oscillations**, region II corresponds to current spikes (a). Illustration of model spikes in the model experiment. At the horizontal axis is the average amplitude of MP **oscillations** (b).
...The model for explanation of current **oscillation** effect in the track structure: **oscillations** of the model particles in the upper plane simulate current **oscillations** in tracks (see text).
...Illustration to the model: in the plane that intersects tracks we have a system of currents that **oscillate** depending on the appropriate conditions.
...Dependence of the maximum value, Amax of spike height on the **frequency** of FR.
...Dependence of the maximum value, Amax of spike height on the frequency of FR.
...(a) Dependence of the average amplitude, A¯ of MP **oscillations** on the **frequency** of FR. (b) Dependence of the average spike height on the **frequency** of applied voltage; Points: measurements, the curve is drown by the method of least squares [34].
...A phenomenological model for description of ion current pulsations in track-containing foils is proposed. Such structures belong to artificial porous materials having diverse applications. Typically pulsations of the ion current are observed in experiments in which the track-containing polymer foils are embedded in electrolytes, and AC voltage is applied. The proposed model is designed on the base of classical molecular dynamics. The interacting currents in tracks are simulated by two-dimensional system of **oscillating** model particles located in the nodes of a plane lattice. In the model external discontinuous forces are introduced to simulate an application of AC voltage. Interaction between model particles is varied to clarify its influence on pulsation effect. It is assumed that the average amplitude of **oscillations** of model particles is proportional to the average amplitude of current **oscillations** in real track structure. The model describes adequately the main features of the pulsation effect that were found experimentally. The obtained results can be useful for creation and improvement of sensors and other devices of track electronics....(a) Dependence of the average amplitude, A¯ of MP oscillations on the frequency of FR. (b) Dependence of the average spike height on the frequency of applied voltage; Points: measurements, the curve is drown by the method of least squares [34].
... A phenomenological model for description of ion current pulsations in track-containing foils is proposed. Such structures belong to artificial porous materials having diverse applications. Typically pulsations of the ion current are observed in experiments in which the track-containing polymer foils are embedded in electrolytes, and AC voltage is applied. The proposed model is designed on the base of classical molecular dynamics. The interacting currents in tracks are simulated by two-dimensional system of **oscillating** model particles located in the nodes of a plane lattice. In the model external discontinuous forces are introduced to simulate an application of AC voltage. Interaction between model particles is varied to clarify its influence on pulsation effect. It is assumed that the average amplitude of **oscillations** of model particles is proportional to the average amplitude of current **oscillations** in real track structure. The model describes adequately the main features of the pulsation effect that were found experimentally. The obtained results can be useful for creation and improvement of sensors and other devices of track electronics.

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Contributors: G. Catanzaro, F. Leone, I. Busá, P. Romano

Date: 2008-02-01

In this figure we report as a function of optical depth the computed **frequencies**, center of mass (γ0), amplitudes and phases derived from the fit of velocities for each of the selected lines. Meaning of the symbols is: circles (red) carbon lines, stars (magenta) silicon lines, triangles (blues) oxygen lines and boxes (green) nitrogen lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
...In this figure we report as a function of optical depth the computed frequencies, center of mass (γ0), amplitudes and phases derived from the fit of velocities for each of the selected lines. Meaning of the symbols is: circles (red) carbon lines, stars (magenta) silicon lines, triangles (blues) oxygen lines and boxes (green) nitrogen lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
...Pulsations, **oscillations**, and stellar seismology...**Frequencies** in oscillating β Cephei stars are usually inferred by means of radial velocities measured from the Siiii triplet λλ 4552–4574Å. These lines, relatively insensitive to the variation of Teff through a pulsation cycle, show small equivalent width variations....**Frequencies** in **oscillating** β Cephei stars are usually inferred by means of radial velocities measured from the Siiii triplet λλ 4552–4574Å. These lines, relatively insensitive to the variation of Teff through a pulsation cycle, show small equivalent width variations. ... **Frequencies** in **oscillating** β Cephei stars are usually inferred by means of radial velocities measured from the Siiii triplet λλ 4552–4574Å. These lines, relatively insensitive to the variation of Teff through a pulsation cycle, show small equivalent width variations.

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Contributors: Banafsheh Seyed-Aghazadeh, Collin Budz, Yahya Modarres-Sadeghi

Date: 2015-09-29

Flow forces acting on an **oscillating** cylinder.
...Vortex-induced vibration (VIV) of a curved circular cylinder (a quarter of a ring, with no extension added to either end) free to **oscillate** in the crossflow direction was studied experimentally. Both the concave and the convex orientations (with respect to the oncoming flow direction) were considered. As expected, the amplitude of **oscillations** in both configurations was decreased compared to a vertical cylinder with the same mass ratio. Flow visualizations showed that the vortices were shed in parallel to the curved cylinder, when the cylinder was free to **oscillate**. The sudden jump in the phase difference between the flow forces and the cylinder displacement observed in the VIV of vertical cylinders was not observed in the curved cylinders. Higher harmonic force components at **frequencies** twice and three times the **frequency** of **oscillations** were observed in flow forces acting on the vertical cylinder, as well as the curved cylinder. Asymmetry in the wake was responsible for the 2nd harmonic force component and the relative velocity of the structure with respect to the oncoming flow was responsible for the 3rd harmonic force component. The lock-in occurred over the same range of reduced velocities for the curved cylinder in the convex orientation as for a vertical cylinder, but it was extended to higher reduced velocities for a curved cylinder in the concave orientation. Higher harmonic force components were found to be responsible for the extended lock-in range in the concave orientation. Within this range, the higher harmonic forces were even larger than the first harmonic force and the structure was being excited mainly by these higher harmonic forces....Dimensionless (a) amplitude (A*=A/D) and (b) **frequency** (f*=fos/fna) of the crossflow **oscillations** versus the reduced velocity for a curved cylinder in the convex configuration (■) and a vertical cylinder (○).
...Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the convex configuration (■) and a vertical cylinder (○).
...Vortex-induced vibration (VIV) of a curved circular cylinder (a quarter of a ring, with no extension added to either end) free to oscillate in the crossflow direction was studied experimentally. Both the concave and the convex orientations (with respect to the oncoming flow direction) were considered. As expected, the amplitude of oscillations in both configurations was decreased compared to a vertical cylinder with the same mass ratio. Flow visualizations showed that the vortices were shed in parallel to the curved cylinder, when the cylinder was free to oscillate. The sudden jump in the phase difference between the flow forces and the cylinder displacement observed in the VIV of vertical cylinders was not observed in the curved cylinders. Higher harmonic force components at **frequencies** twice and three times the **frequency** of oscillations were observed in flow forces acting on the vertical cylinder, as well as the curved cylinder. Asymmetry in the wake was responsible for the 2nd harmonic force component and the relative velocity of the structure with respect to the oncoming flow was responsible for the 3rd harmonic force component. The lock-in occurred over the same range of reduced velocities for the curved cylinder in the convex orientation as for a vertical cylinder, but it was extended to higher reduced velocities for a curved cylinder in the concave orientation. Higher harmonic force components were found to be responsible for the extended lock-in range in the concave orientation. Within this range, the higher harmonic forces were even larger than the first harmonic force and the structure was being excited mainly by these higher harmonic forces....Flow visualizations in the wake of a curved cylinder for the fixed (a) convex and (b) concave configurations, and free-to-**oscillate** (c) convex and (d) concave configurations. Flow is from left to right.
...Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the concave configuration (▲) and a vertical cylinder (○).
...Dimensionless (a) amplitude (A*=A/D) and (b) **frequency** (f*=fos/fna) of the crossflow **oscillations** versus the reduced velocity for a curved cylinder in the concave configuration (▲) and a vertical cylinder (○).
... Vortex-induced vibration (VIV) of a curved circular cylinder (a quarter of a ring, with no extension added to either end) free to **oscillate** in the crossflow direction was studied experimentally. Both the concave and the convex orientations (with respect to the oncoming flow direction) were considered. As expected, the amplitude of **oscillations** in both configurations was decreased compared to a vertical cylinder with the same mass ratio. Flow visualizations showed that the vortices were shed in parallel to the curved cylinder, when the cylinder was free to **oscillate**. The sudden jump in the phase difference between the flow forces and the cylinder displacement observed in the VIV of vertical cylinders was not observed in the curved cylinders. Higher harmonic force components at **frequencies** twice and three times the **frequency** of **oscillations** were observed in flow forces acting on the vertical cylinder, as well as the curved cylinder. Asymmetry in the wake was responsible for the 2nd harmonic force component and the relative velocity of the structure with respect to the oncoming flow was responsible for the 3rd harmonic force component. The lock-in occurred over the same range of reduced velocities for the curved cylinder in the convex orientation as for a vertical cylinder, but it was extended to higher reduced velocities for a curved cylinder in the concave orientation. Higher harmonic force components were found to be responsible for the extended lock-in range in the concave orientation. Within this range, the higher harmonic forces were even larger than the first harmonic force and the structure was being excited mainly by these higher harmonic forces.

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