The time-dependent electric current from a flame

1984 ◽  
Vol 393 (1805) ◽  
pp. 297-308 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Electric Current ◽  
Diffusion Flame ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Dependent Potential ◽  
Ionization Detectors

An earlier static treatment of the electric current from the diffusion flame in a flame ionization detector has been extended to include time-dependent currents. The nonlinear differential equation describing the electric field in the space outside the flame has been solved analytically for a class of problems in which a time-dependent potential difference is switched on after a static current has been established. Both one- and two-dimensional geometrical configurations are considered. The results could be useful in suggesting new experiments on flame ionization detectors.

The time-dependent electric current from a flame II. Theoretical solutions controlled by ionic diffusion

1993 ◽  
Vol 441 (1912) ◽  
pp. 387-398
Keyword(s):  
Diffusion Equation ◽  
Electric Field ◽  
Electric Current ◽  
Heat Propagation ◽  
Flame Ionization Detector ◽  
Three Dimensions ◽  
Time Dependent ◽  
Ionic Diffusion ◽  
Ionization Detector ◽  
Flame Ionization

Solutions are presented in one, two and three dimensions for the time-dependent electric field and current in a flame ionization detector dominated by ionic diffusion. The solutions are expressed in terms of ‘flame polynomials’ similar to the ‘heat polynomials’ of the heat propagation or diffusion equation. The conditions needed to define the solution are given by a physical argument.

scholarly journals Inverse reconstruction technique based on time-dependent Petschek-type reconnection model: first application to THEMIS magnetotail observations

2009 ◽  
Vol 27 (12) ◽  
pp. 4369-4377
Author(s):  
V. Ivanova ◽  
J. Liu ◽  
S. Kiehas ◽  
V. Semenov ◽  
H. Biernat
Keyword(s):  
Electric Field ◽  
Total Duration ◽  
Time Dependent ◽  
Reconstruction Technique ◽  
Field Variation ◽  
Magnetic Field Variation ◽  
Two Dimensional ◽  
Line Position ◽  
Inverse Reconstruction ◽  
Reconnection Model

Abstract. We apply the inverse reconstruction technique based on the two-dimensional time-dependent Petschek-type reconnection model to a dual bipolar magnetic structure observed by THEMIS B probe in the Earth's magnetotail during a substorm on 22 February 2008 around 04:35 UT. The technique exploits the recorded bipolar magnetic field variation as an input and provides the reconnection electric field and the location of the X-line as an output. As a result of the technique application, we get (1) the electric field, reaching ~1.1 mV/m at the maximum and consisting of two successive pulses with total duration of ~6 min, and (2) the approximate X-line position located in the magnetotail between 18 and 20 RE.

scholarly journals Computer simulation of the pulse-periodic electric field effect on the 2D director orientation of nematic liquid crystal. Experimental research of multimode nematic liquid crystal waveguides.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A.S. Ayriyan ◽  
◽  
E.A. Ayryan ◽  
A.A. Egorov ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Experimental Research ◽  
Point Of View ◽  
Dynamic Processes ◽  
Theoretical Point ◽  
Two Dimensional

In this paper, we numerically investigate a two-dimensional differential equation describing the motion of a director of a nematic liquid crystal for the case of an alternating external electric field. The presence of the previously discovered accumulation effect has been confirmed by numerical modeling. A comparison is made with the case of a constant electric field, and also a qualitative comparison with an experiment is given. Incomplete agreement with experimental data indicates the need for further research. However, it should be noted that the constructed mathematical model of the phenomenon allows at this stage to obtain estimates that are sufficiently acceptable for experiment and correctly predict the dynamics of processes in liquid crystals. An analysis of the features of the propagation of quasi-waveguide modes in a liquid crystal waveguide showed that, in the case of dynamic processes, such effects as power exchange between coupled modes, leakage of modes, re-emission of modes into modes of a different order, etc., can be observed. The programs for numerical solution and computer modeling of two-dimensional parabolic partial differential equation were developed both in FORTRAN and C/C++. The results obtained are important for further investigation of dynamic processes inside non-stationary liquid crystal layers, both from a theoretical point of view for understanding kinetic processes in liquid crystals and from a practical point of view when organizing and conducting different experimental research.

Development of a micro-flame ionization detector using a diffusion flame

2012 ◽  
Vol 168 ◽  
pp. 111-117 ◽  
Author(s):  
Jihyung Kim ◽  
Byunghoon Bae ◽  
James Hammonds ◽  
Taekyu Kang ◽  
Mark A. Shannon
Keyword(s):  
Diffusion Flame ◽  
Flame Ionization Detector ◽  
Ionization Detector ◽  
Flame Ionization

The symmetry group of the quantum harmonic oscillator in an electric field

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Juan Lejarreta ◽  
Jose Cerveró
Keyword(s):  
Schrödinger Equation ◽  
Electric Field ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Group Structure ◽  
Time Dependent ◽  
Frequency Function ◽  
General Group ◽  
Dependent Potential ◽  
The Relationship

AbstractIn this paper we present two results. First, we derive the most general group of infinitesimal transformations for the Schrödinger Equation of the general time-dependent Harmonic Oscillator in an electric field. The infinitesimal generators and the commutation rules of this group are presented and the group structure is identified. From here it is easy to construct a set of unitary operators that transform the general Hamiltonian to a much simpler form. The relationship between squeezing and dynamical symmetries is also stressed. The second result concerns the application of these group transformations to obtain solutions of the Schrödinger equation in a time-dependent potential. These solutions are believed to be useful for describing particles confined in boxes with moving boundaries. The motion of the walls is indeed governed by the time-dependent frequency function. The applications of these results to non-rigid quantum dots and tunnelling through fluctuating barriers is also discussed, both in the presence and in the absence of a time-dependent electric field. The differences and similarities between both cases are pointed out.

Calculations on the Time-Dependent Potential Flow in a Centrifugal Pump

1992 ◽  
Author(s):  
R. Badie ◽  
J. B. Jonker ◽  
T. G. van Essen
Keyword(s):  
Finite Element ◽  
Time Derivative ◽  
Time Dependent ◽  
Maximum Deviation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Fluid Forces ◽  
Potential Flows ◽  
Axial Moment ◽  
Dependent Potential

In this paper a finite element based method is presented for the calculation of two-dimensional time-dependent potential flows through a rotor/stator configuration. An algorithm was developed that numerically evaluates the time derivative of all relevant field quantities. For that purpose the computational domain was split into a region containing the rotor and one containing the stationary parts, each region being treated in a different coordinate system. The corresponding finite element grids are matched by an interface consisting of connect-elements which move in time. The pressure field was then obtained from the unsteady Bernoulli equation. The Kutta condition was imposed by a method using the linear property of the operators. The algorithm was in particular applied to calculate the two-dimensional quasi-steady flow through a volute laboratory pump which made an experimental verification possible. For various mass flows the lateral fluid forces, the axial moment, the total head of the pump were computed and analyzed. The agreement with the experimental data, with respect to the quantities in the volute, was reasonable. The deviation was quantitatively greatest at low mass flow, the maximum deviation in the velocity being 10%. The overall behavior of the pump could be well predicted.

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