Surface integral equations for material layers modeled with tensor boundary conditions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94933/1/rds4585.pd

Numerical 3D modeling of heat transfer in human tissues for microwave radiometry monitoring of Brown fat metabolismo

Background: Brown adipose tissue (BAT) plays an important role in whole body metabolism and could potentially mediate weight gain and insulin sensitivity. Although some imaging techniques allow BAT detection, there are currently no viable methods for continuous acquisition of BAT energy expenditure. We present a non-invasive technique for long term monitoring of BAT metabolism using microwave radiometry. Methods: A multilayer 3D computational model was created in HFSS™ with 1.5 mm skin, 3-10 mm subcutaneous fat, 200 mm muscle and a BAT region (2-6 cm3) located between fat and muscle. Based on this model, a log-spiral antenna was designed and optimized to maximize reception of thermal emissions from the target (BAT). The power absorption patterns calculated in HFSS™ were combined with simulated thermal distributions computed in COMSOL® to predict radiometric signal measured from an ultra-low-noise microwave radiometer. The power received by the antenna was characterized as a function of different levels of BAT metabolism under cold and noradrenergic stimulation. Results: The optimized frequency band was 1.5-2.2 GHz, with averaged antenna efficiency of 19%. The simulated power received by the radiometric antenna increased 2-9 mdBm (noradrenergic stimulus) and 4-15 mdBm (cold stimulus) corresponding to increased 15-fold BAT metabolism. Conclusions: Results demonstrated the ability to detect thermal radiation from small volumes (2-6 cm3) of BAT located up to 12 mm deep and to monitor small changes (0.5°C) in BAT metabolism. As such, the developed miniature radiometric antenna sensor appears suitable for non-invasive long term monitoring of BAT metabolism

Elektromagnetik Dalgaların Dikdörtgen Kesitli Bir Silindirden Saçılması

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1996Bu çalışmada yüzeyleri empedans özelliği gösteren, dikdörtgen kesitli bir sonsuz uzun silindirden elektromagnetik dalgaların kırınımı incelenmiştir. Gelen dalganın "BİF çizgisel kaynak tarafından uyarıldığı var sayılarak problem, önce, birbirine bağlı üçüncü tipten iki Wiener-Hopf denkleminin oluşturduğu bir sisteme indirgenmiş; sonra da, bir takım dönüşümlerle ikinci tipten bir Predholm integral denklem sistemine indirgenerek iteratif bir yöntemle çözülmüştür. Bulunan çözüme dayanılarak, alanın, değişik bölgelerde gözlenen(gelen, yansıyan, kırman v.b.) bileşenlerinin açık ifadeleri çıkarılmıştır. Cismin boyutlarının ve yüzey empedansının değişik terimlere etki sini daha açık bir biçimde gözleyebilmek amacıyla, sonuçlar bazı sayısal örneklere uygulanmış ve ayrıntılı bir biçimde tartışılmıştır. It goes without saying that the scattering of electromagnetic waves by rectangular cylindrical bodies, which plays extremely important roles on the performance of actual communication systems constitutes a chal lenging problem in the diffraction theory. In this work this phenomenon is analyzed rigorously by assuming that the boundary of the cylinder can be modelled by impedance type conditions. The basic procedure consists of reducing the problem to a pair of simultaneus modified Wiener-Hopf equations(MWHE) of the third kind. By means of some elementary trans formations, these coupled equations are reduced into a system of Fredholm integral equations of the second kind involving also infinitely many un known constants and then solved by iterations. The unknown constants are determined numerically by solving certain linear algebraic equations. In order to show clearly the effects of various parameters on diffracted field, the results were applied to some illustrative examples. 2. Formulation of the Problem Let a rectangular cylinder S be illuminated by an electrical line source I parallel to the cylinder located through P(xo,yo,0) (see Fig.2.1). The source is assumed to be time harmonic with time factor exp(-iu:t) while the horizontal and vertical walls of the cylinder are characterized by differ- ent(homogeneous) surface impedances Z\ = 7}\Zq and Zi - 772-2/0, respec tively. Here Zq represents the free-space impedance, i.e.: Zq = y/^Ao- Then the total electric field outside the cylinder becomes parallel to the cylinder and independent of the z- coordinate, namely: E = u(x,y)ez. (1) The problem consists in finding an explicit expression of u(x, y). For the sake of analytical convenience, we will consider the following vi; regions Bn separately: #1 = {(*,y) #2 = {(x,y) #3 =?{(*, y) #4 = {(*,y) y > yo,x e (-co,oo)} y e (6, y0),x e (-co, c»)},, y6(-M),W>o} lZj y ±00 show that the function A(a)exp{iK(a)y} appearing in (4a) is regular in the strip Im(-k) aH*-b) + C{a)e-iK^a)^-h) = F-(a,y)e-iaa + Fx(a,y) + F+(a,y)eiaa, (6) viii where and iaaF-(a,y)= [ u-2(x,y)eiaxdx, (7a) J-oo /.OO iaaF+(a,y) = / u2{x,y)eiaxdx, (76) J a F1{a,y)= f u2(x,y)eiaxdx. (7c) J - a Owing to the well-known analytical properties of Fourier integrals, i*+(a) and F-(a) are regular functions in the upper(Jm(a) > Im(-k)) and the lower (Im(a) 0 as \a\ -? oo, Ima > Irn(-k) (8a) eiaaFi(a,y) -» 0 as \a\ -* oo,Ima > Im(-k) (86) and e~lQaF_(a,y) -> 0 as \a\ -> oo, Ima oo, Ima Qa - (- - ia)u3(-a, y)e~iaa (9) with /oo u3(x,y)eiaxdx := G-{a,y)t~iaa + G+(a,y)eiaa. (10) -oo The functions G-(a) and G+(a) appearing in (10) are regular functions in the upper(/m(«) > Im( - k)) and the lower(Jm(o/) a (12h) - [v.2(x,b) -u3(x,b)] - 0 |a:| > a (12i) oy - [u3(x,-b)-u4(x,-b)} = 0 \x\>a. (12 j) ay By taking into account (4a) and (6), C(a) can be solved directly from (12a) and (126) to give piatxo C(a) = klZoi- - eiK(°>)(yo-V. (13) 2A(«) v ' The determination, of the other coefficients yields a rather tough problem. In what follows we will recapitulate some basic steps in the method we follow for this purpose. From (126 - j) one gets rather easily (14a) + (1 - a^)g*me-iaa] + W1(a) + 2ikC(a)X(a) and fc Here M (a) and iV(ft) are known functions, namely: + (1 - aai)g°ie-ia*] + W2(a) - 2ikC(a)X(a). (146) M (a) = cosKb - K^-sinKb (15a) IK N(a) = sinKb + K~cosKb (156) ik while a*;0 and K^° are known constants defined by M(±aem) = 0, JV(± 0 (16) and Klf = K{±aX). (17) The remaining functions and constants appearing in (14a, 6), i.e.: P±(ft), Q±{cn), Wi,2(ar), /,'"." and g*>° are unknowns. The meanings of the subindices (- ), (+) are already known. Thus (14a, 6) constitute two modified Wiener-Hopf equations which permit us to solve the functions P±(ft), and Q±(ft) in terms of the unknown parameters f*i° and g^f. An approximate solution to these equations will be given in the next chapter. Here we confine ourselves to notice that after having determined the func tions P±(ft) and Q±(&), the coefficients A,B,D and G±{a) are written as follows: A(a) = 2.1\. e~iKya (18a) B(a) = R-{a)'-iaa +H+(a)eiaa - (1 - mK/k)C(a) 1 } {1 + mK/k) { } XI g.(g)e-'"« + S+(")c*" D{a) (i + mK/k) (18c) R±( Im(-k) and lower Im(a) ]^d +0-.S) + Ae2K") + Ae1(-<tfyia b and y < -b one should evaluate the following integrals: «aOr, y) = ~- / [B(a)eiKiy-k) + C{a)e-iKiy-b)]e-iaxda (29a) i y00 u4(x,y) = - D(a)e-*K{y+b)e-iaxda. (296) 2tt J_oo Here S(o), C(a) and D(a) are known functions given in (186), (13) and (18c), respectively. Evaluation of these integrals was made by using the well-known "saddle-point" technique. The results were applied to some numerical examples which permit us to grasp the effect of various param eters on the diffraction phenomena.DoktoraPh.D

Three Dimensional Moment Method Simulation of Penetrable Scatterers Consisting of Non-metallic and Circuit Analog Surfaces

http://deepblue.lib.umich.edu/bitstream/2027.42/21541/2/rl2520.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21541/1/rl2520.0001.001.tx

AMFIA v.1.0 User's Manual

http://deepblue.lib.umich.edu/bitstream/2027.42/21119/2/rl1003.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21119/1/rl1003.0001.001.tx

Scattering of electromagnetic waves by a rectangular impedance cylinder

A uniformly valid asymptotic solution is developed for the diffraction of a high-frequency wave by an infinitely long rectangular cylinder having different impedance walls. The incident wave is generated by a line source located parallel to the cylinder. The problem is reduced first to a system of modified Wiener-Hopf equations involving infinitely many unknown constants and then to a couple of infinite system of linear algebraic equations which are solved numerically. Explicit expressions of the dominant wave components existing in different regions are found. Some illustrative examples show the capability of the approach.Publisher's Versio

Simulation of 3D Non-metallic Scatterers with Circuit Analog Surfaces and Matrix Compression Based on the Adaptive Integral Method

http://deepblue.lib.umich.edu/bitstream/2027.42/21542/2/rl2521.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21542/1/rl2521.0001.001.tx

CADRISA User Manual

http://deepblue.lib.umich.edu/bitstream/2027.42/21543/2/rl2522.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21543/1/rl2522.0001.001.tx

Antenna Simulations on Ships for AMRFS Applications

http://deepblue.lib.umich.edu/bitstream/2027.42/21120/2/rl1004.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21120/1/rl1004.0001.001.tx