Näherungslösung einer verallgemeinerten Nernst-Planck-Gleichung für ein eindimensionales Membranmodell / Approximative Solution of a Generalized Nernst-Planck-equation for a one Dimensional Membran-model

1976 ◽  
Vol 31 (7) ◽  
pp. 815-822
Author(s):  
J. Schröter ◽  
H.-P. Stormberg
Keyword(s):  
External Field ◽  
Planck Equation ◽  
Zeroth Approximation ◽  
Perturbation Approach ◽  
One Dimensional ◽  
Low Concentration ◽  
Fixed Charges ◽  
First Approximation ◽  
Starting Point ◽  
Approximative Solution

AbstractThe starting-point of this paper are generalized Nernst Planck equations, which are deduced microscopically. Using a perturbation approach a result of this equation is given for a constant external field and a membran, which has a low concentration of fixed charges. The used conditions give a zeroth approximation which describes the homogeneous electrolyte. The first approximation shows the influence of the fixed charges, the friction between ions and membran and the influence of the correlations. The flows and the concentrations are then calculated for a system with equal concentrations on both sides of the membran.

Nonequilibrium Properties of Weak Ion Exchange Membranes

1977 ◽  
Vol 32 (12) ◽  
pp. 1344-1352
Author(s):  
H.-P. Stormberg
Keyword(s):  
Ion Exchange ◽  
Electric Field ◽  
External Electric Field ◽  
Perturbation Approach ◽  
Ion Exchange Membranes ◽  
Stationary Flows ◽  
Fixed Charges ◽  
Starting Point ◽  
The Difference ◽  
Concentration Curves

Abstract The behaviour of a membrane with a low concentration of fixed charges in a constant external electric field is considered. The stationary flows, the concentration curves and the electric field are calculated for a system which has different concentrations on both sides of the membrane. The starting point of the calculation are the generalized Nernst-Planck equations which are deduced microscopically. Using a perturbation approach a solution to these equations is given. With this result the influence of fixed charges, of friction between the ions and the membrane and of the difference in concentrations can be discussed.

scholarly journals Recognition of Abnormal Chest Compression Depth Using One-Dimensional Convolutional Neural Networks

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 846
Author(s):  
Liang Zhao ◽  
Yu Bao ◽  
Yu Zhang ◽  
Ruidong Ye ◽  
Aijuan Zhang
Keyword(s):  
Chest Compression ◽  
Sensor Data ◽  
Evaluation Procedure ◽  
Support Vector ◽  
Portable Devices ◽  
Sensor Signal ◽  
Distance Measurements ◽  
Compression Depth ◽  
One Dimensional ◽  
Starting Point

When the displacement of an object is evaluated using sensor data, its movement back to the starting point can be used to correct the measurement error of the sensor. In medicine, the movements of chest compressions also involve a reciprocating movement back to the starting point. The traditional method of evaluating the effects of chest compression depth (CCD) is to use an acceleration sensor or gyroscope to obtain chest compression movement data; from these data, the displacement value can be calculated and the CCD effect evaluated. However, this evaluation procedure suffers from sensor errors and environmental interference, limiting its applicability. Our objective is to reduce the auxiliary computing devices employed for CCD effectiveness evaluation and improve the accuracy of the evaluation results. To this end, we propose a one-dimensional convolutional neural network (1D-CNN) classification method. First, we use the chest compression evaluation criterion to classify the pre-collected sensor signal data, from which the proposed 1D-CNN model learns classification features. After training, the model is used to classify and evaluate sensor signal data instead of distance measurements; this effectively avoids the influence of pressure occlusion and electromagnetic waves. We collect and label 937 valid CCD results from an emergency care simulator. In addition, the proposed 1D-CNN structure is experimentally evaluated and compared against other CNN models and support vector machines. The results show that after sufficient training, the proposed 1D-CNN model can recognize the CCD results with an accuracy rate of more than 95%. The execution time suggests that the model balances accuracy and hardware requirements and can be embedded in portable devices.

Dynamics of Spinning Disc Parametrically Excited by Noise

1999 ◽  
Author(s):  
Narayanan Ramakrishnan ◽  
N. Sri Namachchivaya
Keyword(s):  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Averaging ◽  
Transverse Motion ◽  
Probability Density Distribution ◽  
Integral Of Motion ◽  
Parametrically Excited ◽  
One Dimensional ◽  
Small Intensity ◽  
Spinning Disc

Abstract The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

Asymptotic behavior of velocity process in the Smoluchowski–Kramers approximation for stochastic differential equations

1991 ◽  
Vol 23 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Kiyomasa Narita
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Equation Of Motion ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Large Parameter ◽  
Uhlenbeck Process ◽  
One Dimensional ◽  
Kramers Equation ◽  
Non Linear Oscillator

Here a response of a non-linear oscillator of the Liénard type with a large parameter α ≥ 0 is formulated as a solution of a two-dimensional stochastic differential equation with mean-field of the McKean type. This solution is governed by a special form of the Fokker–Planck equation such as the Smoluchowski–Kramers equation, which is an equation of motion for distribution functions in position and velocity space describing the Brownian motion of particles in an external field. By a change of time and displacement we find that the velocity process converges to a one-dimensional Ornstein–Uhlenbeck process as α →∞.

On the solution of the Fokker–Planck equation for a Feller process

1990 ◽  
Vol 22 (01) ◽  
pp. 101-110
Author(s):  
L. Sacerdote
Keyword(s):  
Diffusion Processes ◽  
Planck Equation ◽  
Hyperbolic Type ◽  
Diffusion Equations ◽  
Time Varying ◽  
Feller Process ◽  
Parameter Group ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Type Boundary

Use of one-parameter group transformations is made to obtain the transition p.d.f. of a Feller process confined between the origin and a hyperbolic-type boundary. Such a procedure, previously used by Bluman and Cole (cf., for instance, [4]), although useful for dealing with one-dimensional diffusion processes restricted between time-varying boundaries, does not appear to have been sufficiently exploited to obtain solutions to the diffusion equations associated to continuous Markov processes.

scholarly journals Atomic Layer Deposition of SnO2-Coated Anodic One-Dimensional TiO2 Nanotube Layers for Low Concentration NO2 Sensing

2020 ◽  
Vol 12 (29) ◽  
pp. 33386-33396 ◽  
Author(s):  
Siowwoon Ng ◽  
Jan Prášek ◽  
Raul Zazpe ◽  
Zdeněk Pytlíček ◽  
Zdeněk Spotz ◽  
...  
Keyword(s):  
Atomic Layer Deposition ◽  
Atomic Layer ◽  
Tio2 Nanotube ◽  
One Dimensional ◽  
Low Concentration ◽  
Layer Deposition

scholarly journals The stark ladder and other one-dimensional external field problems

1981 ◽  
Vol 80 (1) ◽  
pp. 23-42 ◽  
Author(s):  
I. W. Herbst ◽  
J. S. Howland
Keyword(s):  
External Field ◽  
One Dimensional
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