• Ocean Systems Engineering
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• v.2 no.3
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• pp.229-238
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• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Physical Therapy Korea
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• v.8 no.4
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• pp.81-89
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• 2001

There are two independent mechanisms to control the segmental reflex gain in humans during gait. They are presynaptic inhibition and homosynaptic depression. Through the mechanism of the presynaptic inhibition, the muscle spindle afferent feedback can be properly gated during eccentric phase of gait. The modulation of the presynaptic inhibition is reflected in the level of H-reflex at a constant EMG level. During the eccentric muscle activation presynaptic inhibition should increase to account for the lower amplitude level of H-reflex at a constant level of EMG. Homosynaptic depression is another mechanism responsible for regulating the effectiveness of the muscle spindle afferent feedback. Both the presynaptic inhibition and the monosynaptic depression are responsible for modulating reflex gain during gait initiation. Reflex modulation is influenced not only as a passive consequence of the alpha motor neuron excitation level, but also through supraspinal mechanisms. Spastic paretic patients show the impaired soleus H-reflex modulation either during the initial stance phase, or during the swing phase. This abnormal modulatory mechanism can partially and artificially be restored by the application of peripheral stimulus to the sole of the foot, provided that the segmental circuitry remains functional.

• The Korean Journal of Physiology
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• v.18 no.1
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• pp.37-50
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• 1984

The effects of $Ca^{++}$ and its antagonists (verapamil and $La^{+++}$) upon the spontaneous contraction and the contracture induced by 60 mM K-Tyrode solution were studied in the isolated uterine muscle. Longitudinal muscle strips were prepared from the rat uteri at estrous stage. All experiments were performed in tris-buffered Tyrode solution which was aerated with 100% $O_2$ and kept at 35^{\circ}$. The results obtained were as follows: 1) In the uterine strips contracting spontaneously, both the amplitude of peak tension and the area of contraction curve increased dose-dependently in the range of $0.5${\sim}8$ mM $Ca^{++}$. The frequency of contraction increased as the concentration of $Ca^{++}$ increased up to 2 mM, but above this concentration the frequency decreased. In $Ca^{++}-free$ media, however, contraction did not develop. In the contracture induced by 60 mM K-Tyrode solution, the developed tension increased dose-dependently as the concentration of external $Ca^{++}$ increased to 8 mM. In the absence of external $Ca^{++}$ K-contracture appeared, but it was not sustained. 2) The spontaneous contraction of rat uterus was suppressed by verapamil in proportion to an increase of its concentration and totally abolished at the concentration of $3{\times}10^{-4}\;g/l$, but the spontaneous contraction re-appeared by addition of $Ca^{++}$. The amplitude of peak tension recovered completely but the recovery of frequency was incomplete. K-contracture decreased in a dose-dependent manner after the treatment with verapamil and totally disappeared at its concentration of $3{\times}10^{-4}\;g/l$. Even in this case contracture developed again by extra $Ca^{++}$. 3) The spontaneous contractile activity was inhibited by $La^{+++}$. At the concentration of $10^{-4}$M $La^{+++}$, fibrillation appeared. In the strip inhibited by $10^{-5}M\;La^{+++}$, contractility recovered completely by extra $Ca^{++}$ while in the $10^{-4}M\;La^{+++}$ treated preparation, the rhythmic spontaneous contraction did not develop even at the concentration of 16 mM $Ca^{++}$. After the initial transient depression of contracture tension by $10^{-3}M$ of $La^{+++}$, the strip stowed considerably large size of contracture, hardly influenced by external $Ca^{++}$ or verapamil. The results obtained in this experiment suggest that in the rat uterine muscle there would be some competitive actions between $Ca^{++}$ and its antagonists. It is speculated that $Ca^{++}$ plays an important role in the conduction of excitation, and $La^{+++}$ influences upon cellular $Ca^{++}$ mobilization and re-uptake process as well as transmembrane $Ca^{++}$ transport in a K-depolarized state.