Current-frequency Curves Research Articles

A nonlinear analysis of electrically forced vibrations of piezoelectric plates with viscous damping near the thickness-shear mode

Based on the theory of nonlinear piezoelectricity, an approximate solution for electrically forced nonlinear thickness-shear vibrations of piezoelectric plates is introduced. The model considers an infinite piezoelectric plate subjected to an alternative voltage, incorporating 3rd-order and 4th-order elastic constants and viscous damping under finite deformation. The system's differential equations for steady-state forced vibrations are derived from the nonlinear pure thickness-shear vibration problem, and transformed so that the new electrical boundary conditions are free. After the application of Galerkin's method, the transformed differential equations lead to a cubic equation, capturing the nonlinear current-frequency curves of AT-cut quartz plates without the need of the quality factor Q, due to the introduced viscous damping. When the damping effect is ignored, the frequency response curves of the AT-cut quartz plate under a specific voltage are confirmed with the existing literature. The study emphasizes the presence of the critical voltage and the importance of the fourth-order elastic constant (c6666) in the stability, revealing lower c6666 values correspond to improved stability. Additionally, a proposed algorithm efficiently determines critical voltages for resonator stability.

Improved Design via Simulation of Micro-Modified PVDF and its Copolymer Energy Harvester with High Electrical Outputs.

In this work, micro-modified polyvinylidene fluoride (PVDF) and its copolymer poly(vinylidene-trifluoroethylene) (P(VDF-TrFE)) with salient enhancement in current output are demonstrated. The influence of surface-modified structure characteristics on electrical properties of energy harvester is systematically analyzed based on the finite element method. For vertical load mode, eight structures consisting of banded and disjunctive groups are compared to evaluate the voltage performance. The cylinder is proved to be the best structure of 3.25 V, compared to the pristine structure of 0.99 V (P(VDF-TrFE)). The relevant experiment has been done to verify the simulation. The relationship between radius, height, force and distance to the voltage output of the cylinder allocation is discussed. For periodical changing load mode, the cylinder modified structure shows a conspicuous enhancement in current output. The suitable resistance, current–voltage and frequency, the relationship between loading speed and current, and the ductility of current loading are studied. For 30 kHz, the peak current is 20 times larger than the flat plate structure. Tip shape mode and fusiform shape mode are found, which show the different shapes of the peak current-frequency curves. Four electrical loading circuit properties are also discussed: the suitable resistance of the system, synchronism of current and voltage, time delay nature of energy harvester and current-loading relationship. The simulation results can provide some theoretical basis for designing the energy harvester and piezoelectric nanogenerator (PENG).

Orexin enhances firing activities in the gigantocellular reticular nucleus through the activation of non-selective cationic conductance

Orexin/hypocretin has been implicated in central motor control. The gigantocellular reticular nucleus (Gi), a key element of the brainstem motor inhibitory system, also receives orexinergic innervations. However, the modulations of orexin on the neuronal activities and the underlying cellular mechanisms in Gi neurons remain unknown. Here, through whole-cell patch-clamp recordings, we first observed that orexin increased the firing frequency in Gi neurons. Interestingly, a postsynaptic depolarization elicited by orexin was observed in the presence of tetrodotoxin, without altering the input resistance of Gi neurons at around −60 mV. Moreover, through comparing the current-frequency curves constructed by identical current injections from equal membrane potentials, we found that orexin also increased the repetitive firing ability of Gi neurons. This action appeared to be caused by the shortening of inter-spike intervals, without altering the waveform of individual action potentials. We finally revealed that activation of the non-selective cationic conductance contributed to the orexin-elicited excitation in Gi neurons. Together, these results suggest that orexin may facilitate Gi-mediated motor functions through enhancing the neuronal activities of Gi neurons.

Probing nonlinear mechanical effects through electronic currents: The case of a nanomechanical resonator acting as an electronic transistor

We study a general model describing a self-detecting single electron transistor realized by a suspended carbon nanotube actuated by a nearby antenna. The main features of the device, recently observed in a number of experiments, are accurately reproduced. When the device is in a low current-carrying state, a peak in the current signals a mechanical resonance. On the contrary, a dip in the current is found in high current-carrying states. In the nonlinear vibration regime of the resonator, we are able to reproduce quantitatively the characteristic asymmetric shape of the current-frequency curves. We show that the nonlinear effects coming out at high values of the antenna amplitude are related to the effective nonlinear force induced by the electronic flow. The interplay between electronic and mechanical degrees of freedom is understood in terms of a unifying model, including in an intrinsic way the nonlinear effects driven by the external probe.

Photon-assistant Fano resonance in serially coupled triple quantum dots

Based on calculations of the electronic structure of serially coupled triplequantum dots (left, middle, right dots) (STQDs), we study the transportproperties of the system driven by an ac electric field. It is found that theΛ-type energy level of STQDs has great impact on the transport properties. For anasymmetric (between left and right dots) configuration, there is a symmetric peak in thecurrent-AC frequency curve due to resonant photon induced mixing between the left/rightdot and the middle dot. In the symmetric (between left and right dots) configuration, aFano asymmetric line shape appears in the current-frequency curve with the help of a‘trapping dark state’. Here the interesting coherent trapping phenomena, which usualappear in quantum optics, play an essential role in quantum electronic transport. Weprovide a clear physics picture for the Fano resonance and convenient ways to tune theFano effects.

How Membrane Properties Shape the Discharge of Motoneurons: A Detailed Analytical Study

Electrophysiological experiments and modeling studies have shown that afterhyperpolarization regulates the discharge of lumbar motoneurons in anesthetized cats and is an important determinant of their firing properties. However, it is still unclear how firing properties depend on slow afterhyperpolarization, input conductance, and the fast currents responsible for spike generation. We study a single-compartment integrate-and-fire model with a slow potassium conductance that exponentially decays between spikes. We show that this model is analytically solvable, and we investigate how passive and active membrane properties control the discharge. We show that the model exhibits three distinct firing ranges (primary, secondary, and high frequency), and we explain the origin of these three ranges. Explicit expressions are established for the gain of the steady-state current-frequency (I-f) curve in the primary range and for the gain of the I-f curve for the first interspike interval. They show how the gain is controlled by the maximal conductance and the kinetic parameters of the afterhyperpolarization conductance. The gain also depends on the spike voltage threshold, and we compute how it is decreased by threshold accommodation (i.e., the increase of the threshold with the injected current). In contrast, the gain is not very sensitive to the input conductance. This implies that tonic synaptic activity shifts the current-frequency curve in its primary range, in agreement with experiments. Taking into account the absolute refractory period associated with spikes somewhat reduces the gain in the primary range. More importantly, it accounts for the approximately linear and steep secondary range observed in many motoneurons. In the nonphysiological high-frequency range, the behavior of the I-f curve is determined by the fast voltage-dependent currents, via the amplitude of the fast repolarization afterspike, the duration of the refractory period, and voltage threshold accommodation, if present.

How shunting inhibition affects the discharge of lumbar motoneurones: a dynamic clamp study in anaesthetized cats.

In the present work, dynamic clamp was used to inject a current that mimicked tonic synaptic activity in the soma of cat lumbar motoneurones with a microelectrode. The reversal potential of this current could be set at the resting potential so as to prevent membrane depolarization or hyperpolarization. The only effect of the dynamic clamp was then to elicit a constant and calibrated increase of the motoneurone input conductance. The effect of the resulting shunt was investigated on repetitive discharges elicited by current pulses. Shunting inhibition reduced very substantially the firing frequency in the primary range without changing the slope of the current-frequency curves. The shift of the I-f curve was proportional to the conductance increase imposed by the dynamic clamp and depended on an intrinsic property of the motoneurone that we called the shunt potential. The shunt potential ranged between 11 and 37 mV above the resting potential, indicating that the sensitivity of motoneurones to shunting inhibition was quite variable. The shunt potential was always near or above the action potential voltage threshold. A theoretical model allowed us to interpret these experimental results. The shunt potential was shown to be a weighted time average of membrane voltage. The weighting factor is the phase response function of the neurone that peaks at the end of the interspike interval. The shunt potential indicates whether mixed synaptic inputs have an excitatory or inhibitory effect on the ongoing discharge of the motoneurone.

Generation of dc substrate current in metal-oxide-semiconductor structures under an oscillating gate voltage

The present letter reports the results of the experimental measurements of the dc substrate current in metal-oxide-semiconductor (MOS) structures operated under a gate-voltage signal oscillating under depletion limits. A new component has been detected in this current whose direction of flow is independent of the polarity of the applied gate voltage as well as the nature of the MOS structure. Its magnitude shows strong dependence on the frequency of the applied gate voltage, giving rise in general to three prominent peaks in the current-frequency curve. Arguments are given in support of the view that this current has its origin from the charging and discharging of the surface-states existing on the Si-SiO2 interface under non-steady-state emission.

Input‐output relations in the pathway of recurrent inhibition to motoneurones in the cat.

1. The output from Renshaw cells caused by a phasic motor volley was investigated when these neurones were submitted to a background firing secondary to a tonic motor discharge elicited by a repetitive stimulation of muscle group I afferents. It was invariably found in individual Renshaw cells that tonic excitation produced an increase in the additional ouput caused by the phasic motor volley. The curves displaying this increase exhibited a significant 'jump' when the output resulting from the combined tonic and phasic motor discharges ranged between 2 and 5 spikes during the first 10 msec following the phasic volley. 2. The whole pool of Renshaw cells was also considered by assessing the amount of recurrent inhibition in motoneurones following a phasic motor volley. Similarly it was found that additional recurrent inhibition elicited by a phasic motor volley was enhanced when the Renshaw cells received a tonic excitatory input. 3. The Renshaw cell discharges elicited by stimulation of two different nerves were compared when a conditioning stimulus was previously applied to only one of them. The results strongly suggest that a preceding volley caused a decrease in synaptic efficacy at the terminals of the recurrent collaterals. 4. The firing produced by current injected through the recording micro-electrode was investigated in one intracellularly recorded Renshaw cell. It was found that the current-frequency curve was linear for 'steady-state' firing but displayed a clearcut sigmoid shape for the earliest intervals before the final adaptation. 5. It is demonstrated that this sigmoid input-output relation in individual Renshaw cells is sufficient to explain how the controls acting on these neurones may change the gain in the recurrent pathway when Renshaw cells are fired by a phasic motor discharge. When Renshaw cells are fired by a longlasting tonic motor discharge the linear input-output relation in individual cells should not cause any modifications of the gain in the recurrent pathway. A change in this gain secondary to the effects of segmental and supraspinal control systems is, however, possible if the motor discharge creates a subliminal fringe within the pool of Renshaw cells.

Comparison of membrane properties of the cell body and the initial part of the axon of phasic motoneurones in the spinal cord of the cat.

Membrane properties of the cell body and the initial part of the axon of cat phasic motoneurones were analyzed. The mean input resistance was 9.1 MΩ in the axon and 2.0 MΩ in the cell body. A great scattering of values, however, was observed in the axons. The passive membrane time constants were 0.35 msec (τ m) in the axon and 3.2 msec (τ m) and 0.63 msec (τ 1) in the soma. A close electrotonic coupling between the soma and the axon was shown by means of synaptic potentials. In the cell body the threshold for excitation was 1.46 times higher than in the axon (14.2 mV and 9.7 mV respectively). Stimulating with current pulses an S-shaped spike inactivation curve was found in the axon. At threshold current intensity, spike inactivation reached 37.2%. In the cell body either no or only slight inactivation (7%) occurred at rheobase. During suprathreshold current stimulation the axon discharged only a few spikes, whereas the soma fired steadily. The current-frequency curve of the soma consisted of two linear ranges and, in addition, a logarithmic range quite similar to the logarithmic frequency curve of the axon was observed. The differences of the discharge behaviour of the cell body and the axon were discussed.

THE MECHANISM OF DISCHARGE PATTERN FORMATION IN CRAYFISH INTERNEURONS.

Excitatory and inhibitory processes which result in the generation of output impulses were analyzed in single crayfish interneurons by using intracellular recording and membrane polarizing techniques. Individual spikes which are initiated orthodromically in axon branches summate temporally and spatially to generate a main axon spike; temporally dispersed branch spikes often pace repetitive discharge of the main axon. Hyperpolarizing IPSP's sometimes suppress axonal discharge to most of these inputs, but in other cases may interact selectively with some of them. The IPSP's reverse their polarity at a hyperpolarized level of membrane potential; they sometimes exhibit two discrete time courses indicating two different input sources. Outward direct current at the main axon near branches causes repetitive discharges which may last, with optimal current intensities, for 1 to 15 seconds. The relation of discharge frequency to current intensity is linear for an early spike interval, but above 100 to 200 impulses/sec. it begins to show saturation. In one unit the current-frequency curve exhibited two linear portions, suggesting the presence of two spike-generating sites in the axon. Current threshold measurements, using test stimuli of different durations, showed that both accommodation and "early" or "residual" refractoriness contribute to the determination of discharge rate at different frequencies.

The mobility of positive ions in helium. Part I.―Helium ions

In a previous paper we gave an account of some experiments on the mobility of positive ions in helium gas. It was shown that minute traces of impurity profoundly affect the speed at which the charge is carried through the gas, so that very little significance can be attached to the values of the mobility of ions recorded in the literature. In particular we studied the behaviour of carefully purified helium gas when admitted at a pressure of 360 mm. of mercury into a baked-out apparatus. In our method of determining the mobility, a single group of ions gives rise to a peak in a current frequency curve, and it is easy to follow the changes produced by an impurity. Initially the ions in the helium had a high mobility and in one case we obtained a group with a mobility of the order of 17 cm./sec./volt/cm. at 760 mm. As the gas became contaminated by impurities gradually evolved from the glass walls and metal parts of the apparatus, peaks corresponding to groups of smaller mobility appeared, and eventually the charge was all carried by a group with mobility rather less than 8. The ions in these experiments were produced by means of α-particles from polonium. Traces of impurity in helium may affect the results in several ways. Firstly, they may lead to the formation of ionic clusters, particularly if the molecules of the impurity have a permanent dipole. In our experiments it seemed unlikely that molecules capable of forming clusters were present. Secondly, although with small concentrations of an impurity a negligible number of its ions will be produced by the direct action of the α-rays, they may be formed indirectly in either of the two following ways:—

Resonance in Alternating Currents Containing a Single Harmonic

Current-frequency relations in alternating current circuits as affected by harmonics.---Series circuit. The form of a current-frequency curve depends only upon the ratio $K=\frac{{R}^{2}C}{L}$ (herein designated as the "resonance factor"), and the ratio $a$ of the harmonic to the fundamental e.m.f. amplitude. Special cases are considered, particular attention being given to the third harmonic, and a method for plotting generalized current-frequency curves is outlined. As $K$ increases, the value of $a$, below which the $I\ensuremath{-}f$ curve can have only one maximum, increases from zero to unity; for each harmonic $n$, there is a definite value of $K$ given by ${K}_{E}=\frac{{(n\ensuremath{-}1)}^{2}({n}^{2}+4n+1)}{n({n}^{2}+1)}$, above which there can be only one peak to the curve no matter what the value of $a$. Parallel circuit. The current-frequency curve has only one minimum, regardless of the number of harmonics, but the position of the minimum point is dependent upon the number and amplitude of any harmonics present. A simple method of plotting generalized current-frequency curves is given, and the inductive and condensive currents briefly discussed. For each circuit, utilizing the relations obtained analytically, there is given an experimental method for determining the amplitudes of fundamental and harmonic in an e.m.f. wave.