scholarly journals Time-domain numerical modeling of wave propagation in poroelastic media with rational approximation of the fractional attenuation

2021 ◽  
Author(s):  
Jiangming Xie ◽  
Maojun Li ◽  
Miao-Jung Ou
Keyword(s):  
Time Domain ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Local System ◽  
Square Root ◽  
Permeability Model ◽  
Poroelastic Media ◽  
Interface Boundary Conditions ◽  
The Time Domain ◽  
Relative Approximation

n this work, we investigate the poroelastic waves by solving the time-domain Biot-JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson-Koplik-Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time-domain Biot-JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative approximation of the square-root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge-Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach.

scholarly journals Induced capacitance in the squid giant axon. Lipophilic ion displacement currents.

1983 ◽  
Vol 82 (3) ◽  
pp. 331-346 ◽  
Author(s):  
J M Fernández ◽  
R E Taylor ◽  
F Bezanilla
Keyword(s):  
Action Potential ◽  
Frequency Domain ◽  
Time Domain ◽  
Numerical Solutions ◽  
Ionic Current ◽  
Induced Polarization ◽  
Resting Potential ◽  
Axonal Membrane ◽  
Cable Properties ◽  
The Time Domain

Voltage-clamped squid giant axons, perfused internally and externally with solutions containing 10(-5) M dipicrylamine (DpA-), show very large polarization currents (greater than or equal to 1 mA/cm2) in response to voltage steps. The induced polarization currents are shown in the frequency domain as a very large voltage-and frequency-dependent capacitance that can be fit by single Debye-type relaxations. In the time domain, the decay phase of the induced currents can be fit by single exponentials. The induced polarization currents can also be observed in the presence of large sodium and potassium currents. The presence of the DpA- molecules does not affect the resting potential of the axons, but the action potentials appear graded, with a much-reduced rate of rise. The data in the time domain as well as the frequency domain can be explained by a single-barrier model where the DpA- molecules translocate for an equivalent fraction of the electric field of 0.63, and the forward and backward rate constants are equal at -15 mV. When the induced polarization currents described here are added to the total ionic current expression given by Hodgkin and Huxley (1952), numerical solutions of the membrane action potential reproduce qualitatively our experimental data. Numerical solutions of the propagated action potential predict that large changes in the speed of conduction are possible when polarization currents are induced in the axonal membrane. We speculate that either naturally occurring substances or drugs could alter the cable properties of cells in a similar manner.

Quasi-analytical method for frequency-to-time conversion in CSEM applications

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. E357-E363 ◽  
Author(s):  
Ali Moradi Tehrani ◽  
Evert Slob ◽  
Wim Mulder
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Diffusion Time ◽  
Basis Functions ◽  
Time Range ◽  
Late Time ◽  
Square Root ◽  
Domain Modeling ◽  
The Time Domain ◽  
Exponential Part

Frequency-to-time transformations are of interest to controlled-source electromagnetic methods when time-domain data are inverted for a subsurface resistivity model by numerical frequency-domain modeling at a selected, small number of frequencies whereas the data misfit is determined in the time domain. We propose an efficient, Prony-type method using frequency-domain diffusive-field basis functions for which the time-domain equivalents are known. Diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency. Data at a limited number of frequencies suffice for the transformation back to the time. In the exponential part, several diffusion-time values must be chosen. Once a suitable range of diffusion-time values are found, the method is quite robust in the number of values used. The highest power in the polynomial part can be determined from the source and receiver type. When the frequency-domain data are accurately approximated by the basis functions, the time-domain result is also accurate. This method is accurate over a wider time range than other methods and has the correct late-time asymptotic behavior. The method works well for data computed for layered and 3D subsurface models.

The Analysis of a Transmission Line Crosstalk in the Time Domain Based on First-Order Upwind

2014 ◽  
Vol 543-547 ◽  
pp. 813-816
Author(s):  
Yin Han Gao ◽  
Tian Hao Wang ◽  
Jun Dong Zhang ◽  
Kai Yu Yang ◽  
Yu Zhu
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Time Domain ◽  
Splitting Method ◽  
Discontinuous Solution ◽  
Characteristic Line ◽  
First Order ◽  
The Difference ◽  
Leapfrog Scheme ◽  
The Time Domain

This article will combine the difference scheme of first-order upwind with the multi-conductor transmission lines equation to analysis the multi-conductor transmission lines crosstalk in the time domain. First-order upwind is a finite difference algorithm in the time domain; it has a first order accuracy, in the discontinuous solution there is no non-physics-oscillation, when simulate the signal. The flux splitting method which is applied to the first-order upwind solved the problem that the characteristic line direction of the wind type make plus or minus transformation along with the coefficient, make the programming simple. In this paper, simulation results of transmission line crosstalk in this algorithm will be compared with the traditional leapfrog scheme, to verify its effectiveness.

Mixed Convolved Action Variational Methods for Poroelasticity

2016 ◽  
Vol 83 (9) ◽  
Author(s):  
Bradley T. Darrall ◽  
Gary F. Dargush
Keyword(s):  
Time Domain ◽  
Inner Product ◽  
Analytical Mechanics ◽  
Convolution Operators ◽  
Dissipative Processes ◽  
Poroelastic Media ◽  
Time Domain Response ◽  
Mixed Approach ◽  
Definition Of ◽  
The Time Domain

Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes, and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on the time-domain response of poroelastic media extends the recent formulations of the mixed convolved action (MCA). The action in this proposed approach is formed by replacing the inner product in Hamilton's principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulation developed here employs temporal impulses of velocity, effective stress, pore pressure, and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting MCA is formulated directly in the time domain to develop a new stationary principle for poroelasticity, which applies to dynamic poroelastic and quasi-static consolidation problems alike. By discretizing the MCA using the finite element method over both space and time, new computational mechanics formulations are developed. Here, this formulation is implemented for the two-dimensional case, and several numerical examples of dynamic poroelasticity are presented to validate the approach.

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Broadband spectroscopy of astrophysical ice analogues

2019 ◽  
Vol 629 ◽  
pp. A112 ◽  
Author(s):  
B. M. Giuliano ◽  
A. A. Gavdush ◽  
B. Müller ◽  
K. I. Zaytsev ◽  
T. Grassi ◽  
...  
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Time Domain ◽  
Complex Refractive Index ◽  
Far Infrared ◽  
Infrared Region ◽  
Thz Radiation ◽  
The Real ◽  
Thz Range ◽  
The Time Domain

Context. Reliable, directly measured optical properties of astrophysical ice analogues in the infrared and terahertz (THz) range are missing from the literature. These parameters are of great importance to model the dust continuum radiative transfer in dense and cold regions, where thick ice mantles are present, and are necessary for the interpretation of future observations planned in the far-infrared region. Aims. Coherent THz radiation allows for direct measurement of the complex dielectric function (refractive index) of astrophysically relevant ice species in the THz range. Methods. We recorded the time-domain waveforms and the frequency-domain spectra of reference samples of CO ice, deposited at a temperature of 28.5 K and annealed to 33 K at different thicknesses. We developed a new algorithm to reconstruct the real and imaginary parts of the refractive index from the time-domain THz data. Results. The complex refractive index in the wavelength range 1 mm–150 μm (0.3–2.0 THz) was determined for the studied ice samples, and this index was compared with available data found in the literature. Conclusions. The developed algorithm of reconstructing the real and imaginary parts of the refractive index from the time-domain THz data enables us, for the first time, to determine the optical properties of astrophysical ice analogues without using the Kramers–Kronig relations. The obtained data provide a benchmark to interpret the observational data from current ground-based facilities as well as future space telescope missions, and we used these data to estimate the opacities of the dust grains in presence of CO ice mantles.

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