Magnetoencephalography inverse problem in the spheroid geometry

2019 ◽  
Vol 27 (2) ◽  
pp. 159-169 ◽  
Author(s):  
Petr I. Karpov ◽  
Tatyana Zakharova
Keyword(s):  
Inverse Problem ◽  
Exact Solution ◽  
Magnetic Fields ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Approximate Analytical Solutions ◽  
Wide Range ◽  
Ill Posed ◽  
The Brain

AbstractThe inverse problem of magnetoencephalography is ill-posed and difficult for both analytical and numerical solutions. Additional complications arise from the volume (passive) currents and the associated magnetic fields, which strongly depend on the brain geometry. In this paper, we find approximate analytical solutions for the forward and the inverse problems in the spheroid geometry. We compare the obtained results with the exact solution of the forward problem and deduce that for a wide range of parameters our approximation is valid. The analysis sheds new light on the role of the volume magnetic fields for solving the inverse problem of magnetoencephalography.

An Approximate Method for Transient Radial Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 225-256 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Infinite Series ◽  
Analytical Solutions ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Basic Theory ◽  
Variable Pressure ◽  
Flow Problems ◽  
Disturbed Zone ◽  
Approximate Analytical Solutions ◽  
Wide Range

Abstract The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including; gravity drainage of depletion-type reservoirs; multiple well systems; well interference. Introduction A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages - the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov, whopostulated a disturbed zone in the reservoir, the radius of which increases with time, andreplaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following:That the flow is irrotational.That the formation is of constant thickness.Darcy's Law is valid.The formation is saturated with a single homogeneous fluid. SPEJ P. 225^

scholarly journals Millimeter (MM) wave and microwave frequency radiation produce deeply penetrating effects: the biology and the physics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Martin L. Pall
Keyword(s):  
Magnetic Fields ◽  
Electric Fields ◽  
Cardiac Activity ◽  
Maximum Level ◽  
Voltage Sensor ◽  
The Body ◽  
Time Varying ◽  
The Brain ◽  
Mm Waves

Abstract Millimeter wave (MM-wave) electromagnetic fields (EMFs) are predicted to not produce penetrating effects in the body. The electric but not magnetic part of MM-EMFs are almost completely absorbed within the outer 1 mm of the body. Rodents are reported to have penetrating MM-wave impacts on the brain, the myocardium, liver, kidney and bone marrow. MM-waves produce electromagnetic sensitivity-like changes in rodent, frog and skate tissues. In humans, MM-waves have penetrating effects including impacts on the brain, producing EEG changes and other neurological/neuropsychiatric changes, increases in apparent electromagnetic hypersensitivity and produce changes on ulcers and cardiac activity. This review focuses on several issues required to understand penetrating effects of MM-waves and microwaves: 1. Electronically generated EMFs are coherent, producing much higher electrical and magnetic forces then do natural incoherent EMFs. 2. The fixed relationship between electrical and magnetic fields found in EMFs in a vacuum or highly permeable medium such as air, predicted by Maxwell’s equations, breaks down in other materials. Specifically, MM-wave electrical fields are almost completely absorbed in the outer 1 mm of the body due to the high dielectric constant of biological aqueous phases. However, the magnetic fields are very highly penetrating. 3. Time-varying magnetic fields have central roles in producing highly penetrating effects. The primary mechanism of EMF action is voltage-gated calcium channel (VGCC) activation with the EMFs acting via their forces on the voltage sensor, rather than by depolarization of the plasma membrane. Two distinct mechanisms, an indirect and a direct mechanism, are consistent with and predicted by the physics, to explain penetrating MM-wave VGCC activation via the voltage sensor. Time-varying coherent magnetic fields, as predicted by the Maxwell–Faraday version of Faraday’s law of induction, can put forces on ions dissolved in aqueous phases deep within the body, regenerating coherent electric fields which activate the VGCC voltage sensor. In addition, time-varying magnetic fields can directly put forces on the 20 charges in the VGCC voltage sensor. There are three very important findings here which are rarely recognized in the EMF scientific literature: coherence of electronically generated EMFs; the key role of time-varying magnetic fields in generating highly penetrating effects; the key role of both modulating and pure EMF pulses in greatly increasing very short term high level time-variation of magnetic and electric fields. It is probable that genuine safety guidelines must keep nanosecond timescale-variation of coherent electric and magnetic fields below some maximum level in order to produce genuine safety. These findings have important implications with regard to 5G radiation.

scholarly journals Perturbation Solutions For Magnetohydrodynamics (Mhd) Flow of in a Non-Newtonian Fluid Between Concentric Cylinders

2019 ◽  
Vol 24 (1) ◽  
pp. 199-211
Author(s):  
M. Yürüsoy ◽  
Ö.F. Güler
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Mhd Flow ◽  
Model Space ◽  
Viscosity Model ◽  
Concentric Cylinders ◽  
Approximate Analytical Solutions

Abstract The steady-state magnetohydrodynamics (MHD) flow of a third-grade fluid with a variable viscosity parameter between concentric cylinders (annular pipe) with heat transfer is examined. The temperature of annular pipes is assumed to be higher than the temperature of the fluid. Three types of viscosity models were used, i.e., the constant viscosity model, space dependent viscosity model and the Reynolds viscosity model which is dependent on temperature in an exponential manner. Approximate analytical solutions are presented by using the perturbation technique. The variation of velocity and temperature profile in the fluid is analytically calculated. In addition, equations of motion are solved numerically. The numerical solutions obtained are compared with analytical solutions. Thus, the validity intervals of the analytical solutions are determined.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Approximate Analytical Solutions to Nonlinear Inverse Boundary Value Problems

2016 ◽  
Author(s):  
P. Venkataraman
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Analytical Solutions ◽  
Traditional Approach ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Approximate Analytical Solutions ◽  
Inverse Boundary Value Problems

A nontraditional approach to the nonlinear inverse boundary value problem is illustrated using multiple examples of the Poisson equation. The solutions belong to a class of analytical solutions defined through Bézier functions. The solution represents a smooth function of high order over the domain. The same procedure can be applied to both the forward and the inverse problem. The solution is obtained as a local minimum of the residuals of the differential equations over many points in the domain. The Dirichlet and Neumann boundary conditions can be incorporated directly into the function definition. The primary disadvantage of the process is that it generates continuous solution even if continuity and smoothness are not expected for the solution. In this case they will generate an approximate analytical solution to either the forward or the inverse problem. On the other hand, the method does not need transformation or regularization, and is simple to apply. The solution is also good at damping the perturbations in measured data driving the inverse problem. In this paper we show that the method is quite robust for linear and nonlinear inverse boundary value problem. We compare the results with a solution to a nonlinear inverse boundary value problem obtained using a traditional approach. The application involves a mixture of symbolic and numeric computations and uses a standard unconstrained numerical optimizer.

The Correlation Between Ischemic Stroke and Thrombosis by Nanoscale Biomarker Analysis

2020 ◽  
Vol 16 (5) ◽  
pp. 676-684
Author(s):  
Guoqing Wang ◽  
Xiangpeng Shen ◽  
Qiangyuan Tian ◽  
Thangavel Lakshmipriya ◽  
Subash C.B. Gopinath
Keyword(s):  
Ischemic Stroke ◽  
Factor Ix ◽  
Clotting Factor ◽  
Clinical Biomarkers ◽  
Wide Range ◽  
Biomarker Analysis ◽  
Highly Correlated ◽  
Brain Artery ◽  
The Brain

Ischemic stroke, which is the fifth leading cause of death, is an attack in the brain due to blockage of a brain artery. It occurs when a sudden loss of blood flow to the brain leads to a reduction in the oxygen supply. A wide range of reasons have been found for ischemic stroke, including high blood pressure and associated thrombosis. Suitable biomarker analysis followed by proper treatment helps to prevent ischemic stroke. An aptamer is an artificial antibody generated against various clinical biomarkers from a smaller molecule of a whole cell. Recently, several researchers conducted biomarker analysis for ischemic stroke using aptamers. Furthermore, factor IX, which is a blood clotting factor, is highly correlated with thrombosis and plays a role in ischemic stroke. In this review, we summarized the potential role of aptamers in ischemic stroke by nanoscale analysis, and factor IX was the distinct focus of this review.

Suppression of Spin-Glass State in PrB6

2012 ◽  
Vol 190 ◽  
pp. 221-224 ◽  
Author(s):  
M.A. Anisimov ◽  
A.V. Bogach ◽  
V.V. Glushkov ◽  
S.V. Demishev ◽  
N.A. Samarin ◽  
...  
Keyword(s):  
Magnetic Fields ◽  
Spin Glass ◽  
Single Crystals ◽  
Phase Formation ◽  
Spontaneous Magnetization ◽  
Initial State ◽  
High Quality ◽  
Wide Range ◽  
Comprehensive Study

The comprehensive study of transverse magnetoresistance (MR) and magnetization has been carried out on the high quality single crystals of PrB6 in the wide range of temperatures 2-40K and magnetic fields up to 80kOe. In order to estimate the role of boron vacancies in the formation of the new spin-glass (SG) phase detected by Alekseev et al. below 20K the experiments were carried out on the ordinary (initial state) and annealed single crystals of PrB6. The data obtained demonstrate the appearance of spontaneous magnetization below TSG21.3K with M~1.6 emu/mol for initial state and the absence of spontaneous magnetization for the annealed PrB6 samples. On the contrary, quite similar behavior of MR was detected for various samples of PrB6. Our results suggest the existence of the aggregated boron vacancies which provoke the new SG phase formation in PrB6 at TSG.

A Mathematical Model Development for Simulating Nitrate Pollutant Transport along a River

2021 ◽  
Vol 57 ◽  
pp. 149-168
Author(s):  
Kayode O. Olowe ◽  
Muthukrishnavellaisamy Kumarasamy
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Surface Water ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Nitrate Concentration ◽  
Pollutant Transport ◽  
Spatial And Temporal Variation ◽  
Wide Range ◽  
Natural Rivers

Contamination of surface water bodies by a wide range of organic and inorganic pollutants has been a serious problem in the recent time, these have an effect on human and aquatic animals. The water quality deterioration calls for regular monitoring of the water quality in order to maintain the health and sustainability of the aquatic ecosystems. Accurate monitoring of discharged pollutants into the rivers may be time taking and labour intensive. Water quality models are significant tools for simulating water quality and controlling the surface water pollution. The purpose of this study is to develop a simplified mathematical model which is hybrid cells in series model (HCIS) to simulate the spatial and temporal variation of nitrate concentration in natural rivers. The HCIS model was formulated to serve as an alternative method to the Fickian based models. Analytical solutions for the first order reaction kinetics of nitrate with the advection and dispersion process were derived using Laplace transformation technique. The model considered the effect of nitrate concentration at several points along the river downstream by considering the transformation of nitrite to nitrate through nitrification process. In addition, the uptake of nitrate by algae for its growth and conversion of nitrate to nitrogen gas due to denitrification process were considered. The HCIS-NO3 model was applied to uMgeni River, South Africa to investigate the nitrate concentration along the river. Furthermore, the quantitative measures based on the coefficient of determination (R2) and standard errors (SE) were used to evaluate the performance of the model. The result shows that the simulated values agreed with the measured values of nitrate concentration in the river which resulted in a R2 value of 0.72 and a low standard error. Analytical solutions of HCIS - NO3 model were compared with the numerical solutions of the Fickian based ADE model for hypothetical problems. Comparison of the responses indicates that the HCIS - NO3 and ADE- NO3 models were in good agreement. The study shows that the hybrid model is a simple and effective tool for simulating pollutant transport in natural rivers.

scholarly journals Filamin A: key actor in platelet biology

Blood ◽  
2019 ◽  
Vol 134 (16) ◽  
pp. 1279-1288 ◽  
Author(s):  
Jean-Philippe Rosa ◽  
Hana Raslova ◽  
Marijke Bryckaert
Keyword(s):  
Gastrointestinal Tract ◽  
Cardiovascular System ◽  
Adhesion Molecules ◽  
Scaffold Proteins ◽  
Signaling Proteins ◽  
Filamin A ◽  
Critical Importance ◽  
Wide Range ◽  
The Brain

Abstract Filamins are scaffold proteins for signaling proteins and adhesion molecules, and mutations in filamin A (FLNa) cause a wide range of defects in the brain, cardiovascular system, gastrointestinal tract, and skeleton, as well as in megakaryocytes. Rosa and colleagues review the important role of FLNa in platelet development and its critical importance to proplatelet production by megakaryocytes.

Aspects of de Wit's Equations Governing the Apparent Spontaneous Yaw of a Ship

1989 ◽  
Vol 42 (1) ◽  
pp. 144-150
Author(s):  
J. O. Flower
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Linearized Equations ◽  
First Order ◽  
Approximate Analytical Solutions

de Wit has produced an analysis of the apparent spontaneous yaw of a ship when undergoing combined rolling and pitching. This analysis produces a set of four first-order simultaneous differential equations which govern the motion. In de Wit the numerical solutions of these equations for a couple of representative examples are given, as well as the corresponding analytical solutions to the linearized equations. In this communication it is shown how two of the four equations can be solved analytically; these solutions can be used to obtain approximate analytical solutions to the remaining two equations.

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