Gap Junction Dynamics Induces Localized Conductance Bistability in Cardiac Tissue

2019 ◽  
Vol 29 (08) ◽  
pp. 1930021
Author(s):  
C. Hawks ◽  
J. Elorza ◽  
A. Witt ◽  
D. Laroze ◽  
I. R. Cantalapiedra ◽  
...  
Keyword(s):  
Gap Junction ◽  
Spatial Organization ◽  
Cardiac Tissue ◽  
Large Time ◽  
Ionic Channels ◽  
Final States ◽  
One Dimensional ◽  
The One ◽  
Junction Conductance ◽  
Large Time Scale

Connexins are specialized ionic channels that control the action potential propagation between cardiac myocytes. In this paper, we study the connexin dynamics in a one-dimensional model of cardiac tissue. We show that the connexin dynamics may lead to a spatial organization of the gap junction conductance. In the numerical simulations presented in this paper we have found two different regimes for the spatial organization of the conductances: (a) a spatially uniform conductance; (b) a spatially complex pattern of local values of high and low conductances. In addition, we have observed that, locally, the two final states are limit cycles with a period equal to the period associated with the external excitation of the tissue strand. The conductance dispersion usually takes place on a very large time scale, i.e. thousands of heart beats, and on a very short spatial scale. Due to its simplicity, the one-dimensional setting allows a detailed study of the emerging structure and in particular very long simulations. We have studied the transition between the two aforementioned states as a function of the gap junction conductance characteristics. Furthermore, we have studied the effect of initially added noises on the outcome of the system. Finally, using spatial autocorrelation functions we have characterized the spatial dispersion in conductance values.

Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Miguel Yangari
Keyword(s):  
Anomalous Diffusion ◽  
Large Time ◽  
Mild Solutions ◽  
Reaction Diffusion ◽  
Cooperative Systems ◽  
Initial Condition ◽  
Time Behaviour ◽  
One Dimensional ◽  
Infinitesimal Generators ◽  
The One

AbstractThe aim of this paper is to study the large-time behaviour of mild solutions to the one-dimensional cooperative systems with anomalous diffusion when at least one entry of the initial condition decays slower than a power. We prove that the solution moves at least exponentially fast as time goes to infinity. Moreover, the exponent of propagation depends on the decay of the initial condition and of the reaction term.

scholarly journals A Sharp Estimate of Entropy Solution to Euler-Poisson System for Semiconductors in the Whole Domain

2019 ◽  
pp. 1-12
Author(s):  
Yanqiu Cheng ◽  
Xixi Fang ◽  
Huimin Yu
Keyword(s):  
Large Time ◽  
Approximate Solutions ◽  
Entropy Inequality ◽  
Large Time Behavior ◽  
Doping Profile ◽  
Entropy Solutions ◽  
Time Behavior ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

In this paper, we are concerned with the global existence, large time behavior, and timeincreasing-rate of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. When the adiabatic index γ > 2, the L∞ estimates of artificial viscosity approximate solutions are obtained by using entropy inequality and maximum principle. Then the L∞ compensated compactness framework demonstrates theconvergence of approximate solutions. Finally, the global entropy solutions are proved to decay exponentially fast to the stationary solution, without any assumption on the smallness of initial data and doping profile.

Optimal decay rates on the solution to the compressible gas–liquid drift-flux model with slip

2017 ◽  
Vol 28 (02) ◽  
pp. 337-386 ◽  
Author(s):  
Guangyi Hong ◽  
Changjiang Zhu
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Decay Rates ◽  
Time Behavior ◽  
One Dimensional ◽  
Drift Flux Model ◽  
Drift Flux ◽  
Flux Model ◽  
The One ◽  
Compressible Gas

In this paper, the large time behavior of the solution to the initial-boundary problems for the one-dimensional compressible gas–liquid drift-flux model with slip is studied. Under some suitable smallness conditions upon the initial data, the optimal pointwise upper and lower decay estimates on masses as well as the sharpest decay rates for the norms in terms of the velocity function are obtained. This result generalizes the one in [On the large time behavior of the compressible gas–liquid drift-flux model with slip, Math. Models Methods Appl. Sci. 25 (2015) 2175–2215] by Evje and Wen. The key of the proof is to derive some new global-in-time weighted estimates. Our method can also be easily adopted to the study on the large time behavior of the solution to the one-dimensional compressible Naiver–Stokes equations.

Large-time dynamics for the one-dimensional Schrödinger equation

2011 ◽  
Vol 141 (2) ◽  
pp. 227-251 ◽  
Author(s):  
Nicolas Burq
Keyword(s):  
Initial Data ◽  
Harmonic Oscillator ◽  
Large Time ◽  
Natural Extension ◽  
Large Set ◽  
Deterministic Theory ◽  
One Dimensional ◽  
Time Dynamics ◽  
The One ◽  
Well Posed

Famous results by Rademacher, Kolmogorov and Paley and Zygmund state that random series on the torus enjoy better Lp bounds that the deterministic bounds. We present a natural extension of these harmonic analysis results to a partial-differential-equations setting. Specifically, we consider the one-dimensional nonlinear harmonic oscillator i∂tu + Δu − |x|2u = |u|r−1u, and exhibit examples for which the solutions are better behaved for randomly chosen initial data than would be predicted by the deterministic theory. In particular, on a deterministic point of view, the nonlinear harmonic oscillator equation is well posed in L2(ℝ) if and only if r ≤ 5. However, we shall prove that, for all nonlinearities |u|r−1u, r > 1, not only is the equation well posed for a large set of initial data whose Sobolev regularity is below L2, but also the flows enjoy very nice large-time probabilistic behaviour.These results are joint work with Laurent Thomann and Nikolay Tzvetkov.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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