scholarly journals High-Order Terms in the Asymptotic Expansions of the Steady-State Voltage Potentials in the Presence of Conductivity Inhomogeneities of Small Diameter

2003 ◽  
Vol 34 (5) ◽  
pp. 1152-1166 ◽  
Author(s):  
Habib Ammari ◽  
Hyeonbae Kang
1991 ◽  
pp. 27-32 ◽  
Author(s):  
Emad Fatemi ◽  
Carl L. Gardner ◽  
Joseph W. Jerome ◽  
Stanley Osher ◽  
Donald J. Rose

Author(s):  
D. D. Do ◽  
R. H. Weiland

AbstractSlow catalyst poisoning can result in the sudden failure of a chemical reactor operating isothermally with substrate-inhibited kinetics. At failure, a satisfactory steady state is exchanged for one of low conversion. The method of matched asymptotic expansions is used to give a detailed description of the exchange process in the phase plane. The structure of the jump is ascertained by separate asymptotic expansions across two adjoining transition regions in which the independent variables contain unknown shifts.


2004 ◽  
Vol 2004 (62) ◽  
pp. 3321-3332 ◽  
Author(s):  
Nejib Smaoui

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e.,ut=νuxx−unux+mu+h(x)). We show existence of an absorbing ball inL2[0,1]and uniqueness of steady state solutions for all integern≥1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability in time and convergence of the solution to the trivial solution. Numerical results using Chebychev collocation method with backward Euler time stepping scheme are presented for both the controlled and the uncontrolled equations illustrating the performance of the controller and supporting the analytical results.


2007 ◽  
Vol 97 (5) ◽  
pp. 3713-3721 ◽  
Author(s):  
Dmitry V. Vasilyev ◽  
Qin Shan ◽  
Yan Lee ◽  
Scott C. Mayer ◽  
Mark R. Bowlby ◽  
...  

Hyperpolarization-activated cyclic nucleotide–gated (HCN) channels are responsible for the functional hyperpolarization-activated current ( Ih) in dorsal root ganglion (DRG) neurons, playing an important role in pain processing. We found that the known analgesic loperamide inhibited Ih channels in rat DRG neurons. Loperamide blocked Ih in a concentration-dependent manner, with an IC50 = 4.9 ± 0.6 and 11.0 ± 0.5 μM for large- and small-diameter neurons, respectively. Loperamide-induced Ih inhibition was unrelated to the activation of opioid receptors and was reversible, voltage-dependent, use-independent, and was associated with a negative shift of V1/2 for Ih steady-state activation. Loperamide block of Ih was voltage-dependent, gradually decreasing at more hyperpolarized membrane voltages from 89% at –60 mV to 4% at –120 mV in the presence of 3.7 μM loperamide. The voltage sensitivity of block can be explained by a loperamide-induced shift in the steady-state activation of Ih. Inclusion of 10 μM loperamide into the recording pipette did not affect Ih voltage for half-maximal activation, activation kinetics, and the peak current amplitude, whereas concurrent application of equimolar external loperamide produced a rapid, reversible Ih inhibition. The observed loperamide-induced Ih inhibition was not caused by the activation of peripheral opioid receptors because the broad-spectrum opioid receptor antagonist naloxone did not reverse Ih inhibition. Therefore we suggest that loperamide inhibits Ih by direct binding to the extracellular region of the channel. Because Ih channels are involved in pain processing, loperamide-induced inhibition of Ih channels could provide an additional molecular mechanism for its analgesic action.


Author(s):  
Xiaoai Jiang ◽  
Alexander F. Vakakis

The nonlinear energy sinks (NESs) with strong essential stiffness nonlinearities have been shown to result in vibration isolation in the studied system. In comparison, we also studied the steady-state dynamic response of a system with its smooth high-order odd nonlinearity replaced with the best fitted nonsmooth “clearance nonlinearity”. The analysis was based on the complexification technique and the separation of the dynamic terms into the “slow-varying” and the “fast-varying” components. We found that the steady-state behavior of a system with the non-smooth NES resembles that of the system with the smooth high-order nonlinearity, preserving the nonlinear energy-pumping feature. This finding paves the way for constructing practical NESs and applying them to practical vibration-isolation problems.


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