scholarly journals Numerical estimation of electrical resistivity in digital rocks using GPUs

2020 ◽  
pp. 306-318
Author(s):  
Т.С. Хачкова ◽  
В.В. Лисица ◽  
Г.В. Решетова ◽  
В.А. Чеверда
Keyword(s):  
Electrical Resistivity ◽  
Electric Field ◽  
Electric Current ◽  
Spectral Method ◽  
Numerical Estimation ◽  
Thomas Algorithm ◽  
Rock Samples ◽  
Partially Saturated ◽  
Heterogeneous Models ◽  
Homogeneous Media

Представлен алгоритм расчета потенциального электрического поля в образцах горных пород и предложены оценки их удельного электрического сопротивления (проводимости). Алгоритм ориентирован на расчет поля в существенно неоднородных моделях среды с частично насыщенными и полиминеральными образцами горных пород. В основе алгоритма – итерационные методы крыловского типа, в качестве предобусловливателя используется оператор, обратный к оператору Лапласа для однородной среды. Для вычисления предобусловливателя используется спектральный метод в направлениях, нормальных к основному направлению электрического тока, а серия одномерных задач решается методом прогонки. Решатель реализован с использованием графических процессоров (GPU) и позволяет обрабатывать образцы размером до 4003 вокселей на одном GPU. We present a numerical algorithm for computing the electric field in digital rock samples and estimating their electrical resistivity (conductivity). The main peculiarity of the algorithm is its applicability tostrongly heterogeneous models including partially saturated and multi-mineral rock samples. The algorithm is based on the iterative Krylov-type solver preconditioned by the inverse Laplace operator for homogeneous media. The preconditioner is computed using the spectral method in directions orthogonal to the direction of the main electric current, whereas the series of 1D problems are solved by the Thomas algorithm. We implement the algorithm using GPUs, which allows us to use a single GPU to solve the problems for samples whose size is up to 4003 voxels.

scholarly journals ANALISIS PENGARUH PENETRASI MEDAN LISTRIK LINTANG TINGGI KE LINTANG RENDAH TERHADAP IONOSFER SAAT BADAI GEOMAGNET (ANALYSIS OF THE ELECTRIC FIELD PENETRATION EFFECT FROM HIGH TO LOW LATITUDES ON THE IONOSPHERE DURING GEOMAGNETIC STORM)

2018 ◽  
Vol 14 (2) ◽  
pp. 97
Author(s):  
Anwar Santoso ◽  
Dadang Nurmali ◽  
Mira Juangsih ◽  
Iyus Edi Rusnadi ◽  
Sri Ekawati ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Current ◽  
High Latitude ◽  
Delay Time ◽  
Geomagnetic Storms ◽  
Equatorial Electrojet ◽  
Minimum Point ◽  
Low Latitude ◽  
Dst Index ◽  
Low Latitudes

The influence of geomagnetic storms on the ionosphere in the equatorial and low latitudes can be either rising or falling value of the value foF2 with the different response delay time. The difference in response is one of them allegedly influenced by the modification of Equatorial Electrojet (EEJ) generated by the penetration of high latitude electric field towards the low latitude electric field and the equator. Therefore, this paper analyzes the influence of the high latitude penetration of electric current to the low latitude electric current towards the ionosphere response to Indonesia's current geomagnetic storms using the data foF2 BPAA Sumedang (SMD; 6,910 S; 106,830E geographic coordinates or 16,550 S; 179,950 E magnetic coordinates) and data from the Biak geomagnetic field station (BIK; 1,080 S; 136,050 E geographic coordinates or  9,730 S; 207,390 E magnetic coordinates) in 2000-2001. The result showed that the injection of the electric field of the high latitudes to lower latitudes causing foF2 BPAA Sumedang to be disturbed. Onset of the foF2 disturbance in BPAA Sumedang started coincide with EEJ(HBIK-HDRW) and reached its minimum point with a time delay between 0 to 4 hours before and after Dst index reached the minimum point. For a delay time of 0 to 4 hours after the Dst index reached the minimum point, the results were in accordance with the research results from the prior research. However, for the time difference of between 0 to 4 hours before the Dst index reached the minimum point, the results differ from their results. AbstrakPengaruh badai geomagnet terhadap ionosfer di ekuator dan lintang rendah berupa naiknya nilai foF2 atau turunnya nilai foF2 dengan waktu tunda respon berbeda-beda. Perbedaan respon tersebut salah satunya diduga dipengaruhi oleh modifikasi Equatorial electrojet (EEJ) yang dihasilkan oleh penetrasi medan listrik lintang tinggi sampai daerah lintang rendah dan ekuator. Oleh karena itu, dalam makalah ini dilakukan analisis pengaruh penetrasi arus listrik lintang tinggi ke lintang rendah terhadap ionosfer saat badai geomagnet menggunakan data foF2 dari Balai Pengamatan Antariksa dan Atmosfer (BPAA) Sumedang (SMD; 6,910 LS; 106,830 BT koordinat geografis atau 16,550 LS; 179,950 BT koordinat magnet) dan data medan geomagnet dari stasiun Biak (BIK; 1,080 LS; 136,050 BT koordinat geografis atau 9,730 LS; 207,390 BT koordinat magnet) tahun 2000-2001. Hasilnya diperoleh bahwa penetrasi medan listrik dari lintang tinggi ke lintang lebih rendah Indonesia menyebabkan foF2 BPAA Sumedang terganggu. Onset gangguan foF2 BPAA Sumedang mulai terjadi bertepatan dengan EEJ(HBIK-HDRW) mencapai titik minimumnya dengan jeda waktu antara 0 sampai 4 jam sebelum dan sesudah indeks Dst mencapai minimum. Untuk beda waktu 0 sampai 4 jam sesudah indeks Dst mencapai minimum, hasilnya bersesuaian dengan hasil penelitian peneliti sebelumnya. Namun, untuk beda waktu 0 sampai 4 jam sebelum indeks Dst mencapai minimum, hasilnya merupakan temuan berbeda dari hasil mereka.

scholarly journals Time evolution of electric fields and currents and the generalized Ohm's law

2005 ◽  
Vol 23 (4) ◽  
pp. 1347-1354 ◽  
Author(s):  
V. M. Vasyliūnas
Keyword(s):  
Electric Field ◽  
Electric Current ◽  
Time Evolution ◽  
Time Scales ◽  
Current Density ◽  
Time Derivative ◽  
Electron Plasma ◽  
Displacement Current ◽  
Ohm’S Law ◽  
Ohm's Law

Abstract. Fundamentally, the time derivative of the electric field is given by the displacement-current term in Maxwell's generalization of Ampère's law, and the time derivative of the electric current density is given by the generalized Ohm's law. The latter is derived by summing the accelerations of all the plasma particles and can be written exactly, with no approximations, in a (relatively simple) primitive form containing no other time derivatives. When one is dealing with time scales long compared to the inverse of the electron plasma frequency and spatial scales large compared to the electron inertial length, however, the time derivative of the current density becomes negligible in comparison to the other terms in the generalized Ohm's law, which then becomes the equation that determines the electric field itself. Thus, on all scales larger than those of electron plasma oscillations, neither the time evolution of J nor that of E can be calculated directly. Instead, J is determined by B through Ampère's law and E by plasma dynamics through the generalized Ohm's law. The displacement current may still be non-negligible if the Alfvén speed is comparable to or larger than the speed of light, but it no longer determines the time evolution of E, acting instead to modify J. For theories of substorms, this implies that, on time scales appropriate to substorm expansion, there is no equation from which the time evolution of the current could be calculated, independently of ∇xB. Statements about change (disruption, diversion, wedge formation, etc.) of the electric current are merely descriptions of change in the magnetic field and are not explanations.

Novel Electro-FSI Model of Trabecular Network in the Brain Sub Arachnoid Space

2019 ◽  
Author(s):  
Khashayar Teimoori ◽  
Ali M. Sadegh ◽  
Bhaskar Paneri
Keyword(s):  
Cerebrospinal Fluid ◽  
Electrical Stimulation ◽  
Electric Field ◽  
Electric Current ◽  
Direct Current ◽  
Channel Model ◽  
Fibrous Tissue ◽  
Head Movements ◽  
Modeling Approach ◽  
The Brain

Abstract The brain is encased in the skull and suspended and supported by a series of three fibrous tissue layers: Dura mater, Arachnoid and Pia matter, known as the Meninges. Arachnoid trabeculae are strands of collagen tissues located in a space between the arachnoid and the pia matter known as the subarachnoid space (SAS). The SAS trabeculae play an important role in damping and reducing the relative movement of the brain with respect to the skull. The SAS is filled with cerebrospinal fluid (CSF), which is a colorless fluid that surrounds all over the brain inside the subarachnoid spaces. This fluid stabilizes the shape and position of the brain during head movements. To address normal and pathological SAS functions, under conditions where an electrical stimulation is applied, this study proposes a novel fully-coupled electro-Fluid-Structure Interaction (eFSI) modeling approach to investigate the response of the system of SAS-CSF under the applied electric current, which is provided by the transcranial Direct Current Stimulation (tDCS) technique according to the following steps. First, a two-dimensional channel model of the brain SAS with several trabecular morphologies is numerically simulated using the finite element (FE) method. The channel model is then subjected to a specific electric field intensity by applying a 1∼2mA direct current. COMSOL Multiphysics v. 5.3a software is used to perform the coupled eFSI numerical simulation in order to investigate the effects of the applied electric field on the flow of the CSF, thereby showing the deflection of the trabeculae inside the channel model. The results of this study demonstrate that the induced electric field causes less deflection of the trabeculae by exacerbating the velocity profile of the cerebrospinal fluid flow and decreasing the flow pressure applied on each trabecula inside the trabecular SAS channel. This electro-mechanostructural modeling approach is significant because of the applied current on the channel walls that can directly affect the CSF flow. In fact, the results of this study can open up a new horizon for future research on disorders like hydrocephalus, which involves an unusual production rate of the CSF inside the brain. This disorder may be controlled by applying an electric current in the brain, using one of the available brain stimulation techniques, i.e. tDCS. By using an electrical stimulation technique, one might control the dynamics of brain function and, therefore, regulate dysfunctionality through the first eFSI multiphysics modeling approach proposed in this study. Briefly, the brain SAS may be considered as a novel region for electrotherapeutic and electromechanical neuromodulation.

scholarly journals Electric Currents Connected With the Proton Flares of 7 July and 2 September, 1966

1971 ◽  
Vol 43 ◽  
pp. 417-421
Author(s):  
A. B. Severny
Keyword(s):  
Active Region ◽  
Field Strength ◽  
Magnetic Flux ◽  
Electric Field ◽  
Electric Field Strength ◽  
Electric Conductivity ◽  
Electric Current ◽  
Current Density ◽  
High Energy ◽  
Electric Currents

It is observed that the change of the net magnetic flux associated with flares can exceed 1017 Mx/s, which corresponds according to Maxwell's equation to the e.m.f. ∼ 109 V which is specific for the high energy protons generated in flares. It is shown that this value of e.m.f. can hardly be compensated by e.m.f. of inductance which should appear due to the actually measured motions in a flare generating active region. The values of electric field strength thus found, together with measured values of electric current density (from rotH), leads to an electric conductivity which is 103 times smaller than usually adopted.

scholarly journals A Mathematical Model for the Electrical Resistivity of Cement Paste at Early Ages Considering the Partially Saturated State

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3306 ◽  
Author(s):  
Ye Tian ◽  
Xin Xu ◽  
Haodong Ji ◽  
Zushi Tian ◽  
Xianyu Jin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Electrical Resistivity ◽  
Cement Paste ◽  
Isothermal Calorimetry ◽  
Setting Time ◽  
Degree Of Saturation ◽  
Early Age ◽  
Saturation State ◽  
Partially Saturated ◽  
Saturated State

For cementitious materials, electrical resistivity is often used in the study of the cement hydration process at early age, as one of the few indicators that can be continuously and non-destructively monitored. Variation characteristics of resistivity are widely reported to interact with the early-age performance of cement paste, such as hydration kinetics parameters and setting time. However, there is no reasonable mathematical model to predict the resistivity at early ages, especially within the first 24 h, due to significant changes in the porosity and degree of saturation. In this work, a mathematical model was developed by considering the partially saturated state and density change of C-S-H (calcium silicate hydrate). To verify the model, two experimental methods were chosen, including the non-contact electrical resistivity test and isothermal calorimetry test. The hydration heat and resistivity of cement paste with a water–cement ratio of 0.35 and 0.45 were continuously monitored for 3 days. In the resistivity test, embedded temperature sensors were used to monitor the internal temperature and temperature correction was treated carefully in order to obtain accurate data. The test results prove that the mathematical model can accurately predict electrical resistivity and describe the saturation state of early-age cement pastes under sealed curing.

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.

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