scholarly journals ON THE LOCAL RESPONSE OF A SINGLE NODE OF RANVIER UNDER VARIOUS CONDITIONS

1960 ◽  
Vol 10 (3) ◽  
pp. 235-245 ◽  
Author(s):  
MASAMICHI ICHIOKA ◽  
YOKO UEHARA ◽  
SEIKICHI KITAMURA
Keyword(s):  
Node Of Ranvier ◽  
Local Response ◽  
Single Node

scholarly journals THE PARALLELISM BETWEEN THE ACTION POTENTIAL, ACTION CURRENT, AND MEMBRANE RESISTANCE AT A NODE OF RANVIER

1955 ◽  
Vol 39 (2) ◽  
pp. 211-223 ◽  
Author(s):  
I. Tasaki ◽  
W. H. Freygang
Keyword(s):  
Action Potential ◽  
Node Of Ranvier ◽  
Giant Axon ◽  
Membrane Resistance ◽  
Squid Giant Axon ◽  
Impedance Change ◽  
Action Current ◽  
Single Node ◽  
Resistance Change ◽  
Simultaneous Measurements

1. Simultaneous measurements of action potential and resistance and of action current and impedance change have been made at a single node of Ranvier. 2. There is a parallelism between action potential, action current, and resistance change measured at a node of Ranvier. 3. Some implications of these results have been discussed in relation to the corresponding data obtained from the squid giant axon.

scholarly journals INITIATION AND ABOLITION OF THE ACTION POTENTIAL OF A SINGLE NODE OF RANVIER

1956 ◽  
Vol 39 (3) ◽  
pp. 377-395 ◽  
Author(s):  
I. Tasaki
Keyword(s):  
Action Potential ◽  
Node Of Ranvier ◽  
Threshold Level ◽  
Rectangular Pulse ◽  
Membrane Voltage ◽  
Equilibrium Potential ◽  
Experimental Conditions ◽  
Single Node ◽  
Applied Pulse ◽  
Linear Behavior

1. Using single node preparations of the bull frog or the toad, observations were made on the variation of the voltage across the nodal membrane under various experimental conditions. 2. The time constant of the variation in the membrane voltage caused by a long subthreshold rectangular pulse was of the order of 0.1 msec. 3. The action potential was initiated when the potential inside the node was raised stimulating pulses above a threshold level of approximately 15 mv. for a node in normal Ringer; it was greater in a relatively refractory node and in a partially narcotized node. 4. The variation of the membrane voltage caused by long stimulating pulses of subrheobasic strengths was in general proportional to the strength of the applied pulse. A non-linear behavior of the membrane voltage was observed with barely subthreshold stimulating pulses. 5. The early portion of the action potential of a node was not modified by a direct current which was strong enough to produce measurable potential changes (IR drops) across the resting membrane. 6. A strong pulse of inward current applied to the node during activity abolished the portion of the action potential following the pulse in all-or-none manner. 7. There was no refractory period after a response abolished in its early phase. Following a response abolished later, the recovery in the spike height started from the level of the action potential at the time of abolition. 8. Initiation and abolition of action potentials at a single node are interpreted as "transitions" between the two "equilibrium potential levels" at the node.

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

2019 ◽  
Vol 31 (01) ◽  
pp. 2050017
Author(s):  
Liang Wang ◽  
Xuhui Meng ◽  
Hao-Chi Wu ◽  
Tian-Hu Wang ◽  
Gui Lu
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Distance Ratio ◽  
Single Node ◽  
Convection Diffusion ◽  
Velocity Models ◽  
Discrete Effect

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

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