scholarly journals ON THE INTENSITY-TIME RELATIONS FOR STIMULATION BY ELECTRIC CURRENTS. I

1932 ◽  
Vol 15 (6) ◽  
pp. 709-729 ◽  
Author(s):  
H. A. Blair
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Normal State ◽  
Applied Voltage ◽  
Electric Currents ◽  
Excitatory Effect ◽  
Rate Of Growth

Formulae are derived for the time-intensity relations for stimulation by direct currents using the following hypotheses: first, the current produces an excitatory effect whose rate of growth is proportional to the voltage; and second, the tissue reacts toward the normal state at a rate proportional to the amount of excitation. If p represents the local excitatory process numerically, the hypotheses are represented by the differential equation See PDF for Structure. where K and k are constants and V the applied voltage. For the stimulus to be adequate it is assumed that p must be built up to a certain liminal value. It appears as a deduction from the data that this liminal value is a function of the voltage of the form h ± αV where h and α are constants. α is zero or negligible for certain electrodes. αV is a measure of electrotonus or a similar phenomenon. Experimental data are discussed and are shown to agree satisfactorily with the derived formulae for stimulation both at the anode and cathode.

scholarly journals A critical statistical study of experimental data on the effect of minute electric currents on the growth rate of the coleoptile of barley

1926 ◽  
Vol 99 (695) ◽  
pp. 122-130 ◽  
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Statistical Study ◽  
Pure Line ◽  
Similar Data ◽  
Electric Currents ◽  
Rate Of Growth ◽  
The Mean ◽  
Positive Results ◽  
Case Based

A study of the effect of very minute electric currents on the rate of growth of the coleoptile of barley was published recently by one of us (F. G. G.) in collaboration. In this paper the mean rate of a number of control coleoptiles was compared with the mean rate of a number exposed to a minute electric discharge. The growth rate of individual coleoptiles showed, naturally, considerable divergences, so the mean result was in each case based on the observation of a large number of coleoptiles, the increments of growth of individual coleoptiles being stated as percentages of the rate of growth during the first hour of observation. It was assumed that the distribution of growth rates in a comparatively large sample of a pure-line barley would conform with the normal distribution; the probable errors of the mean results were therefore calculated in the ordinary way. During the continuation of this work positive results have been obtained in further experimental sets, but a number of these, though significant in the mass, were individually without significance. This suggested that a careful statistical study of the data on which the results were based might show how the accuracy of the method could be increased. Such a study has accordingly been undertaken, and it seems probable that methods employed are likely to be of use in the treatment of similar data.

scholarly journals Comparative analysis of methods to determine deflection in steel beams: theoretical analysis, finite element and experimental

2020 ◽  
pp. 32-37
Author(s):  
Gabriela Alor-Saavedra ◽  
Francisco Alejandro Alaffita-Hernández ◽  
Beatris Adriana Escobedo-Trujillo ◽  
Oscar Fernando Silva-Aguilar
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Finite Element ◽  
Comparative Analysis ◽  
Theoretical Analysis ◽  
Comparative Study ◽  
Steel Beams ◽  
Physical Systems ◽  
Theoretical Part ◽  
Made In

This work makes a comparative study of two methods to determine deflection in steel beams: (a) Theoretical and (b) Finite element. For method (a) the solution of the differential equation associated with the modeling of the deflection of a beam is found, while for method (b) a simulation is made in Solidworks. Both methods are compared with experimental data in order to analyze which of the methods presents less uncertainty and show the usefulness of the theoretical part in the modeling of physical systems.

scholarly journals Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture

2021 ◽  
Author(s):  
Benjamin P Holder ◽  
Catherine A. A. Beauchemin
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Influenza Infection ◽  
Biologically Relevant ◽  
Differential Equation Models ◽  
Viral Yield ◽  
Infection Parameters ◽  
Delay Differential

Background For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. Results We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. Conclusions By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.

scholarly journals Fractional-Derivative Approximation of Relaxation in Complex Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Kin M. Li ◽  
Mihir Sen ◽  
Arturo Pacheco-Vega
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
System Identification ◽  
Complex Systems ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Initial Conditions ◽  
Time Dependent ◽  
Fractional Order Differential Equation

In this paper, we present a system identification (SI) procedure that enables building linear time-dependent fractional-order differential equation (FDE) models able to accurately describe time-dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell-and-tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional-order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.

Study of Fuel Rod and Grid Supports Interaction

2003 ◽  
Author(s):  
Pablo R. Rubiolo ◽  
Dmitry V. Paramonov
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Ordinary Differential Equation ◽  
Laplace Transformation ◽  
Natural Frequencies ◽  
Work Rate ◽  
Fuel Rod ◽  
Impact Forces ◽  
Model Predictions ◽  
Normal Work

In order to predict the dynamic response of a nuclear fuel rod and its supports (spring and dimples) a non-linear model has been developed. The non-linearities arising from the supports are defined as a function of the rod motion and incorporated in the differential equation as generalized pseudoforces. This approach allows the use of modal analysis and preserves the physical understanding of rod frequencies and modes. The modal equations were written with the help of the Laplace transformation and integrated using an Ordinary Differential Equation (ODE) solver. The model determines the rod natural frequencies and motion, the support impact forces and the normal work rate. The paper describes the model predictions for a single span rod and compares them to experimental data.

Tunnelströme durch Al2O3-Schichten bei Kontakten verschiedener Austrittsarbeiten

1964 ◽  
Vol 19 (5) ◽  
pp. 573-579 ◽  
Author(s):  
H. G. Hurst ◽  
W. Ruppel
Keyword(s):  
Experimental Data ◽  
Work Function ◽  
Applied Voltage ◽  
Tunneling Current ◽  
Insulating Films ◽  
Tunneling Currents ◽  
Analytical Expressions

The tunneling current through Al2O3-layers of a thickness varying between 30 and 100 Å was measured for In-Al2O3-Al, Al-Al2O3-Al, and Au-Al2O3-Al layer cells. The dependence of the observed current on the applied voltage, the thickness of the Al2O03-layer, and temperature is in agreement with an analysis of tunneling currents through insulating films by STRATTON. By comparing the experimental data with the analytical expressions the following values are derived for the metal-Al2O3 work function: In: 0.55 eV; Al: 0.77 eV; Au: 1.6 eV.

Transport Phenomena in the Mixed and Normal State of (Bi1.6Pb0.4)Sr2Ca2(Cu1-xFex)3Oy Epitaxial Thin Films

1998 ◽  
Vol 12 (25n26) ◽  
pp. 1081-1088 ◽  
Author(s):  
G. Ilonca ◽  
A. V. Pop ◽  
D. Benea ◽  
C. Lung ◽  
M. Lachescu ◽  
...  
Keyword(s):  
Experimental Data ◽  
Thin Films ◽  
Normal State ◽  
Landau Theory ◽  
Upper Critical Field ◽  
Time Dependent ◽  
Epitaxial Thin Films ◽  
Critical Temperatures ◽  
Seebeck Coefficients ◽  
Hall Effects

We had performed a study on magnetoresistivity, Seebeck, Nernst and Hall effects in the mixed and normal state for Bi2223 thin films in magnetic fields between 0 and 5 T and in the temperature range 5–300 K. The critical temperatures, the Hall concentration, the Nernst and Seebeck coefficients depend strongly on the iron content in the samples. From our experimental data in the mixed state and fluctuation regime, the upper critical field slope (dBc2/dT )=-2:55 T/K was obtained, corresponding to ab-plane coherence length ξab=14 Å. The experimental data are in agreement with the predictions of the time-dependent Ginsburg–Landau theory.

Study on the Mechanics State of Concrete under Penetration and the Deceleration of Projectile

2011 ◽  
Vol 413 ◽  
pp. 1-6
Author(s):  
Tao Deng ◽  
Tao Ge
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Mass Conservation ◽  
Conservation Of Mass ◽  
Conservation Of Momentum ◽  
Coulomb Criterion ◽  
The Continuum

The concrete under penetration has a restricted deform and is in intrinsic friction state. By used conservation of mass, conservation of momentum and velocity expression on wave front, the velocity field of the pulverized zone near penetration is obtained. The boundary conditions and the continuum conditions were also considered for the obtained velocity field. The pulverized concrete near the penetration is described by Mohr-Coulomb criterion. Based on the conclusions above, cavity expand theory and the expand equation of inconsistent deform, the resistance of projectile is gained in intrinsic friction state. In according to movement differential equation, the deceleration model is built which can describe different phases for penetration and perforation. The decelerations of different size projectiles with different velocity were calculated and were contrasted with experimental data.

A Stability Algorithm for a Special Case of the Milling Process: Contribution to Machine Tool Chatter Research—6

1968 ◽  
Vol 90 (2) ◽  
pp. 325-329 ◽  
Author(s):  
R. E. Hohn ◽  
R. Sridhar ◽  
G. W. Long
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Machine Tool ◽  
Linear Differential Equation ◽  
Mathieu Equation ◽  
Milling Process ◽  
Machine Tool Chatter ◽  
Linear Differential ◽  
The Stability ◽  
Special Case

In an effort to determine the stability of the milling process, and due to the complexity of its describing equation, a special case of this equation is considered. In this way, it is possible to isolate and study its salient characteristics. Moreover, the simplified equation is representative of a machining operation on which experimental data can be obtained. This special case is described by a linear differential equation with periodic coefficients. A computer algorithm is developed for determining the stability of this equation. To demonstrate the use of the algorithm on an example whose solution is known, the classical Mathieu equation is studied. Also, experimental results on an actual machining operation described by this type of equation are compared to the results found using the stability algorithm. As a result of this work, some knowledge about the stability solution of the general milling process is obtained.

Sign in / Sign up

Export Citation Format

Share Document