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| {{Expert-subject|date=March 2012}}
| | An underweight person can have low immunity, reduced stamina, plus a deficiency of nutrients in his body. So, fat control is important. There are many methods to determine the perfect fat of the person. Among them are, waist to height ratio, plus height to weight ratio.<br><br>There are certain aspects to really consider in a exercise regimen plus we want to seriously consider the following regarding overall body fat. The ideal body fat for a wellness guy adult is regarding 10 - 12%. The ideal body fat for a healthy woman adult 14 16%. BMI is generally an indicator of health plus is computed using charts that are based on age, height and current weight. Even when the body fat falls in your BMI or Body Mass Index it is actually nevertheless possible that you will not fall in the policies of body fat reported above. A really extreme athlete could not even apply to a [http://safedietplans.com/bmi-chart bmi chart] and it might moreover depend found on the sport. It really is distinctive to each individual. However if your close to a BMI then closer to desired body fat you're close to achieving the objective of flat difficult washboard abs.<br><br>The body mass index for females allows for the comparison of women of different heights in relation to bmi chart men their fat. Due to the truth that individual body compositions can fluctuate because some ladies might have more muscle mass than average (i.e. athletes) they will have a high BMI making it inaccurate at times.<br><br>Studies have shown which taking omega-3 fatty acids daily will assist prolong young searching skin. In truth, this could moreover bring back the elastic plus resilient structure of the dermis.<br><br>Lets begin with an average brick, like the multi-colored 1 at proper. We wish To make a little brick pile that has the same proportions because the initially brick, nevertheless is twice because big in every three dimensions. First we add a brick, inside purchase to double the length. Then alongside which, we add 2 more bricks to double the width.<br><br>The Track: Most marathon training programs might include track work because it helps bmi chart women develop the fast twitch muscles to build speed plus lung force throughout a race...getting older does not imply getting less competitive:) If I am training for a marathon, it actually makes a difference for me especially in the later miles of the race. Great article from Runner's World called "Running in Circles".<br><br>After my son was born I weighed out of the hospital at 192. That was after the baby was born. Since I was nursing, I lost the fat swiftly. In three months I was back to 135, however, then I stopped nursing. Because then I have gained back regarding 30 pounds, that puts me at 165. According to BMI (Body Mass Index) calculations, I am classified because "obese". Classifications are as follows: "Underweight", "Normal", "Overweight", and "Obese". BMI is calculated by the formula: fat (lb) / [height (in)]2 x 703. Divide the current weight by a height squared plus then multiply by 703. The amount we come up with should be interpreted according to the following: 18.5 or below = Underweight, 18.4 - 24.9 = Normal, 25.0 - 29.9 = Overweight, 30.0 or above = Obese.<br><br>If you don't fall inside the regular range, then get yourself checked with different appropriate techniques to figure out the amount of body fat. This can provide a greater perspective plus enable you to achieve or keep the perfect fat. |
| [[File:Radar cross section of metal sphere from Mie theory.svg|thumb|250px|Monostatic [[radar cross section]] [RCS] of a perfectly conducting metal sphere as a function of frequency (calculated by Mie theory). In the low frequency [[Rayleigh scattering]] limit where the circumference is less than the wavelength, the normalized RCS is σ/(πR<sup>2</sup>) ~ 9(kR)<sup>4</sup>. In the high frequency optical limit σ/(πR<sup>2</sup>) ~ 1]]
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| The '''Mie solution''' to [[Maxwell's equations]] (also known as the '''Lorenz–Mie solution''', the '''Lorenz–Mie–Debye solution''' or '''Mie scattering''') describes the [[scattering]] of [[electromagnetic radiation]] by a [[sphere]]. The solution takes the form of an analytical infinite series.{{elucidate|date=March 2012}} It is named after [[Gustav Mie]].
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| The term '''Mie theory''' is used on occasion; however, it is misleading because it does not refer to an independent physical theory or law. The phrase "the Mie solution (to Maxwell's equations)" is therefore preferable. Currently, the term "Mie solution" is also used in broader contexts, for example when discussing solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or generally when dealing with scattering problems solved using the exact Maxwell equations in cases where one can write [[separation of variables|separate equations]] for the radial and angular dependence of solutions.
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| ==Introduction==
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| A modern formulation of the Mie solution to the scattering problem on a sphere can be found in many books, e.g., in [[Julius Adams Stratton|J. A. Stratton]]'s ''Electromagnetic Theory''.<ref>{{Cite book|first=J. A. |last=Stratton|title=Electromagnetic Theory|location= New York|publisher= McGraw-Hill|year= 1941}}</ref> In this formulation, the incident plane wave as well as the scattering field is expanded into radiating spherical [[Vector (geometry)|vector]] wave functions. The internal field is expanded into regular spherical vector wave functions. By enforcing the [[boundary condition]] on the spherical surface, the expansion coefficients of the scattered field can be computed.
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| For particles much larger or much smaller than the wavelength of the scattered light there are simple and excellent approximations that suffice to describe the behaviour of the system. But for objects whose size is similar to the wavelength, e.g., water droplets in the atmosphere, latex particles in paint, droplets in emulsions including milk, and biological cells and cellular components, more exact approach is necessary.<ref name=r1>{{Cite book|first1=C. F.|last1= Bohren|first2=D. R. |last2=Huffmann|title=Absorption and scattering of light by small particles|location=New York|publisher= Wiley-Interscience|year=2010 |isbn= 3-527-40664-6}}</ref>
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| The Mie solution<ref>{{Cite journal|doi=10.1002/andp.19083300302|pages=377–445|title=Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen|year=1908|last1=Mie|first1=Gustav|journal=Annalen der Physik|volume=330|issue=3|bibcode = 1908AnP...330..377M }} [http://diogenes.iwt.uni-bremen.de/vt/laser/papers/RAE-LT1873-1976-Mie-1908-translation.pdf English translation], [http://diogenes.iwt.uni-bremen.de/vt/laser/papers/SAND78-6018-Mie-1908-translation.pdf American translation]</ref> is named after its developer, German physicist [[Gustav Mie]]. Danish physicist [[Ludvig Lorenz]] and others independently developed the theory of electromagnetic plane wave scattering by a [[dielectric]] sphere.
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| The formalism allows the calculation of the electric and magnetic fields inside and outside a spherical object and is generally used to calculate either how much light is scattered, the total [[optical cross section]], or where it goes, the form factor. The notable features of these results are the Mie resonances, sizes that scatter particularly strongly or weakly.<ref name=vdh>{{Cite book|first=H. C.|last= van de Hulst|url=http://books.google.com/books?id=6ivW_TgIdjIC&printsec=frontcover |title=Light scattering by small particles|location= New York|publisher= John Wiley and Sons|year= 1957|isbn=9780486139753}}</ref> This is in contrast to [[Rayleigh scattering]] for small particles and [[Rayleigh–Gans–Debye scattering]] (after [[Lord Rayleigh]], R. Gans and [[Peter Debye]]) for large particles. The existence of resonances and other features of Mie scattering, make it a particularly useful formalism when using scattered light to measure particle size.
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| ==Mie scattering codes==
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| Mie solutions are implemented in a number of codes written in different computer languages such as [[Fortran]], [[Matlab]], [[Mathematica]]. These solutions are in terms of infinite series and include calculation of scattering phase function, extinction, scattering, and absorption efficiencies, and other parameters such as asymmetry parameter or radiation torque. Current usage of "Mie solution" indicate series approximation to solution of Maxwell's equations. There are several known objects which allow such a solution: spheres, concentric spheres, infinite cylinders, cluster of spheres and cluster of cylinders, there are also known series solutions for scattering on ellipsoidal particles. For list of these specialized codes examine these articles
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| * [[Codes for electromagnetic scattering by spheres]] — solutions for single sphere, coated spheres, multilayer sphere, cluster of spheres
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| * [[Codes for electromagnetic scattering by cylinders]] — solutions for single cylinder, multilayer cylinders, cluster of cylinders.
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| A generalization that allows for a treatment of more general shaped particles is the [[T-matrix method]], which also relies on the series approximation to solutions of Maxwell's equations.
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| ==Approximations==
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| ===Rayleigh approximation (scattering)===
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| {{main|Rayleigh scattering}}
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| [[File:Knysnasunset.jpg|thumb|The change of sky colour at sunset (red nearest the sun, blue furthest away) is caused by Rayleigh scattering by atmospheric gas particles which are much smaller than the wavelengths of visible light. The grey/white colour of the clouds is caused by Mie scattering by water droplets which are of a comparable size to the wavelengths of visible light.]]
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| Rayleigh scattering describes the elastic scattering of light by spheres which are much smaller than the wavelength of light. The intensity, ''I'', of the scattered radiation is given by
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| :<math> I = I_0 \left( \frac{ 1+\cos^2 \theta }{2 R^2} \right) \left( \frac{ 2 \pi }{ \lambda } \right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 \left( \frac{d}{2} \right)^6,</math>
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| where ''I<sub>0</sub>'' is the light intensity before the interaction with the particle, ''R'' is the distance between the particle and the observer, ''θ'' is the scattering angle, ''n'' is the [[refractive index]] of the particle, and ''d'' is the diameter of the particle.
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| It can be seen from the above equation that Rayleigh scattering is strongly dependent upon the size of the particle and the wavelengths. The intensity of the Rayleigh scattered radiation increases rapidly as the ratio of particle size to wavelength increases. Furthermore, the intensity of Rayleigh scattered radiation is identical in the forward and reverse directions.
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| The Rayleigh scattering model breaks down when the particle size becomes larger than around 10% of the wavelength of the incident radiation. In the case of particles with dimensions greater than this, Mie's scattering model can be used to find the intensity of the scattered radiation. The intensity of Mie scattered radiation is given by the summation of an infinite series of terms rather than by a simple mathematical expression. It can be shown, however, that Mie scattering differs from Rayleigh scattering in several respects; it is roughly independent of wavelength and it is larger in the forward direction than in the reverse direction. The greater the particle size, the more of the light is scattered in the forward direction.
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| The blue colour of the sky results from Rayleigh scattering, as the size of the gas particles in the atmosphere is much smaller than the wavelength of visible light. Rayleigh scattering is much greater for blue light than for other colours due to its shorter wavelength. As sunlight passes through the atmosphere, its blue component is Rayleigh scattered strongly by atmospheric gases but the longer wavelength (e.g. red/yellow) components are not. The sunlight arriving directly from the sun therefore appears to be slightly yellow while the light scattered through rest of the sky appears blue. During sunrises and sunsets, the Rayleigh scattering effect is much more noticeable due to the larger volume of air through which sunlight passes. | |
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| In contrast, the water droplets which make up clouds are of a comparable size to the wavelengths in visible light, and the scattering is described by Mie's model rather than that of Rayleigh. Here, all wavelengths of visible light are scattered approximately identically and the clouds therefore appear to be white or grey.
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| ===Rayleigh Gans Approximation===
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| The [[Rayleigh Gans Approximation]] is an approximate solution to light scattering when the relative refractive index of the particle is close to unity, and its size is much smaller in comparison to the wavelength of light divided by |n−1|, where n is the [[refractive index]].
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| ===Anomalous diffraction approximation of van de Hulst===
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| The [[anomalous diffraction approximation]] is valid for large and optically soft spheres. The extinction efficiency in this approximation is given by
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| :<math> Q = 2 - \frac{4}{p} \sin{p} + \frac{4}{p^2} (1-\cos{p}),</math>
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| where ''Q'' is the efficiency factor of scattering, which is defined as the ratio of the scattering cross section and geometrical cross section π''a''<sup>2</sup>;
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| p = 4πa(n– 1)/λ
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| has as its physical meaning, the phase delay of the wave passing through the centre of the sphere;
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| where ''a'' is the sphere radius, ''n'' is the ratio of refractive indices inside and outside of the sphere, and ''λ'' the wavelength of the light.
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| This set of equations was first described by van de Hulst in (1957).<ref name=vdh/>
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| ==Applications==
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| Mie theory is very important in [[meteorology|meteorological]] [[optics]], where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and [[cloud]] scattering. A further application is in the characterization of [[aerosol|particles]] via optical scattering measurements. The Mie solution is also important for understanding the appearance of common materials like [[milk]], [[biological tissue]] and [[latex]] paint.
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| ===Atmospheric science===
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| Mie scattering occurs when the particles in the atmosphere are the same size as the wavelengths being scattered. [[Dust]], [[pollen]], [[smoke]] and microscopic water droplets are common causes of Mie scattering which tends to affect longer wavelengths. Mie scattering occurs mostly in the lower portions of the atmosphere where larger particles are more abundant, and dominates when cloud conditions are overcast.
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| ===Cancer detection and screening===
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| Mie theory has been used to determine if scattered light from tissue corresponds to healthy or cancerous cell nuclei using [[angle-resolved low-coherence interferometry]].
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| ===Metamaterial===
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| Mie theory has been used to design [[metamaterial]]s. This type of metamaterial is usually consisted of three-dimensional composites of metal or non-metallic inclusions periodically or randomly embedded in a low permittivity matrix. In such a scheme, the negative constitutive parameters are designed to appear around the Mie resonances of the inclusions: the negative effective [[permittivity]] is designed around the resonance of the Mie electric dipole scattering coefficient whereas negative effective [[permeability (electromagnetism)|permeability]] is designed around the resonance of the Mie magnetic dipole scattering coefficient, and double negative (DNG) is designed around the overlap of resonances of Mie electric and magnetic dipole scattering coefficients. The particle usually have the following combinations:
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| 1) one set of magnetodielectric particles with values of relative permittivity and permeability much greater than one and close to each other;
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| 2) two different dielectric particles with equal permittivity but different size;
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| 3) two different dieletric particles with equal size but different permittivity.
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| In theory, the particles analyzed by Mie theory are commonly spherical but, in practice, particles are usually fabricated as cubes or cylinders for ease of fabrication. To meet the criteria of homogenization, which may be stated in the form that the lattice constant is much smaller than the operating wavelength, the relative permittivity of the dielectric particles should be much greater than 1, e.g. <math>\scriptstyle \epsilon_\mathrm{r}>78(38)</math> to achieve negative effective permittivity (permeability).<ref name=Holloway2003>
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| {{cite journal
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| | doi = 10.1109/TAP.2003.817563
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| | title = A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix | |
| | year = 2003
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| | last1 = Holloway
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| | first1 = C. L.
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| | last2 = Kuester
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| | first2 = E. F.
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| | last3 = Baker-Jarvis
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| | first3 = J.
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| | last4 = Kabos
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| | first4 = P.
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| | journal = IEEE Transactions on Antennas and Propagations
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| | volume = 51
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| | issue = 10
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| | pages = 2596–2603 |bibcode = 2003ITAP...51.2596H }}
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| </ref>
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| <ref name=Zhao2009>
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| {{cite journal
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| | doi = 10.1016/S1369-7021(09)70318-9
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| | title = Mie resonance-based dielectric metamaterials
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| | year = 2009
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| | last1 = Zhao
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| | first1 = Q.
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| | last2 = Zhou
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| | first2 = J.
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| | last3 = Zhang
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| | first3 = F. L.
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| | last4 = Lippens
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| | first4 = D.
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| | journal = Materials Today
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| | volume = 12
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| | issue = 12
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| | pages = 60–69 }}
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| </ref>
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| <ref name=Li2012>
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| {{cite journal
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| | doi = 10.1109/tap.2012.2194637
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| | title = Traveling waves on three-dimensional periodic arrays of two different magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice
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| | year = 2012
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| | last1 = Li
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| | first1 = Y.
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| | last2 = Bowler
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| | first2 = N.
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| | journal = IEEE Transactions on Antennas and Propagations
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| | volume = 60
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| | issue = 6
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| | pages = 2727–2739 |bibcode = 2012ITAP...60.2727L }}
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| </ref>
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| ===Particle sizing===
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| Mie theory has been used in the detection of oil concentration in polluted water.<ref>{{cite journal|last1=He|first1=L|title=Rapid in situ determination of total oil concentration in water using ultraviolet fluorescence and light scattering coupled with artificial neural networks|journal=Analytica Chimica Acta|volume=478|pages=245|year=2003|doi=10.1016/S0003-2670(02)01471-X|last2=Kear-Padilla|first2=L.L|last3=Lieberman|first3=S.H|last4=Andrews|first4=J.M|issue=2}}</ref><ref>{{cite journal|last1=Lindner|first1=H|title=Measurements on Concentrated Oil in Water Emulsions Using Static Light Scattering|journal=Journal of Colloid and Interface Science|volume=242|pages=239|year=2001|doi=10.1006/jcis.2001.7754|last2=Fritz|first2=Gerhard|last3=Glatter|first3=Otto}}</ref>
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| Mie scattering is the primary method of sizing single sonoluminescing bubbles of air in water,<ref>
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| {{cite journal
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| |last=Gaitan
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| |first=D. Felipe
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| |coauthors=Lawrence A. Crum, Charles C. Church and Ronald A. Roy
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| |title=Sonoluminescence and bubble dynamics for a single, stable, cavitation bubble
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| |journal=The Journal of the Acoustical Society of America
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| |year=1992
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| |volume=91
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| |issue=6
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| |pages=3166
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| |doi=10.1121/1.402855
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| |url=http://scitation.aip.org/content/asa/journal/jasa/91/6/10.1121/1.402855
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| |accessdate=17 November 2013}}</ref><ref>
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| {{cite journal
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| |last=Lentz
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| |first=W. J.
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| |coauthors=Atchley, Anthony A.; Gaitan, D. Felipe
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| |title=Mie scattering from a sonoluminescing air bubble in water
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| |journal=Applied Optics
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| |date=May 1995
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| |volume=34
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| |issue=15
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| |pages=2648
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| |doi=10.1364/AO.34.002648
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| |accessdate=17 November 2013}}</ref><ref>
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| {{cite journal
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| |last=Gompf
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| |first=B.
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| |coauthors=Pecha, R.
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| |title=Mie scattering from a sonoluminescing bubble with high spatial and temporal resolution
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| |journal=Physical Review E
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| |date=May 2000
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| |volume=61
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| |issue=5
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| |pages=5253–5256
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| |doi=10.1103/PhysRevE.61.5253
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| |accessdate=17 November 2013}}</ref> and is valid for cavities in materials as well as particles in materials as long as the surrounding material is essentially non-absorbing.
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| ===Parasitology===
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| It has also been used to study the structure of ''[[Plasmodium falciparum]]'', a particularly pathogenic form of [[malaria]].<ref name="Serebrennikova2010">{{cite journal|doi=10.1364/AO.49.000180|pmid=20062504|title=Interpretation of the ultraviolet-visible spectra of malaria parasite Plasmodium falciparum|year=2010|last1=Serebrennikova|first1=Yulia M.|last2=Patel|first2=Janus|last3=Garcia-Rubio|first3=Luis H.|journal=Applied Optics|volume=49|issue=2|pages=180–8|bibcode = 2010ApOpt..49..180S }}</ref>
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| ==See also==
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| * [[Computational electromagnetics]]
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| * [[Light scattering by particles]]
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| * [[List of atmospheric radiative transfer codes]]
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| * [[Optical properties of water and ice]]
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| ==References==
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| {{Reflist|colwidth=30em}}
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| ==Further reading==
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| *{{Cite book |first=M. |last=Kerker |title=The scattering of light and other electromagnetic radiation |location=New York |publisher=Academic |year=1969 |isbn= }}
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| *{{Cite book |first=P. W. |last=Barber |first2=S. S. |last2=Hill |title=Light scattering by particles: Computational methods |location=Singapore |publisher=World Scientific |year=1990 |isbn=9971-5-0813-3 }}
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| *{{Cite book |first=M. |last=Mishchenko |first2=L. |last2=Travis |first3=A. |last3=Lacis |title=Scattering, Absorption, and Emission of Light by Small Particles |location=New York |publisher=Cambridge University Press |year=2002 |isbn=0-521-78252-X }}
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| *{{Cite journal |first=J. |last=Frisvad |first2=N. |last2=Christensen |first3=H. |last3=Jensen |title=Computing the Scattering Properties of Participating Media using Lorenz-Mie Theory |journal=ACM Transactions on Graphics |volume=26 |year=2007 |issue=3 |pages=60 |doi=10.1145/1276377.1276452 }}
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| *{{Cite journal |first=Thomas |last=Wriedt |title=Mie theory 1908, on the mobile phone 2008 |journal=Journal of Quantitative Spectroscopy & Radiative Transfer |volume=109 |year=2008 |issue=8 |pages=1543–1548 |doi=10.1016/j.jqsrt.2008.01.009 |bibcode = 2008JQSRT.109.1543W }}
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| *{{Cite journal |first=Ludvig |last=Lorenz|title=Lysbevaegelsen i og uden for en af plane Lysbolger belyst Kugle|journal=Det Kongelige Danske Videnskabernes Selskabs Skrifter|volume=6. Raekke, 6. Bind|year=1890|issue=1 |pages=1–62}}
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| ==External links==
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| *[http://www.thecomputationalphysicist.com JMIE] (2D [[C++]] code to calculate the analytical fields around an infinite cylinder, developed by Jeffrey M. McMahon)
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| *[http://code.google.com/p/scatterlib/ Collection of light scattering codes]
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| *[http://www.T-Matrix.de www.T-Matrix.de]. Implementations of Mie solutions in [[FORTRAN]], [[C++]], [[IDL (programming language)|IDL]], [[Pascal (programming language)|Pascal]], [[Mathematica]] and [[Mathcad]]
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| *[http://scatlab.org ScatLab]. Mie scattering software for Windows.
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| *[http://www.lightscattering.de/MieCalc/ Online Mie solution calculator] is available, with documentation in German and English.
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| *[http://omlc.ogi.edu/calc/mie_calc.html Online Mie scattering calculator] produces beautiful graphs over a range of parameters.
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| *[http://zakharov.zzl.org/lstar.php phpMie] Online Mie scattering calculator written on [[PHP]].
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| *[http://luxrerum.icmm.csic.es/?q=node/research/PG_material Mie resonance] mediated [[light diffusion]] and random lasing.
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| {{DEFAULTSORT:Mie Theory}}
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| [[Category:Radio frequency propagation]]
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| [[Category:Scattering, absorption and radiative transfer (optics)]]
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| [[Category:Visibility]]
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An underweight person can have low immunity, reduced stamina, plus a deficiency of nutrients in his body. So, fat control is important. There are many methods to determine the perfect fat of the person. Among them are, waist to height ratio, plus height to weight ratio.
There are certain aspects to really consider in a exercise regimen plus we want to seriously consider the following regarding overall body fat. The ideal body fat for a wellness guy adult is regarding 10 - 12%. The ideal body fat for a healthy woman adult 14 16%. BMI is generally an indicator of health plus is computed using charts that are based on age, height and current weight. Even when the body fat falls in your BMI or Body Mass Index it is actually nevertheless possible that you will not fall in the policies of body fat reported above. A really extreme athlete could not even apply to a bmi chart and it might moreover depend found on the sport. It really is distinctive to each individual. However if your close to a BMI then closer to desired body fat you're close to achieving the objective of flat difficult washboard abs.
The body mass index for females allows for the comparison of women of different heights in relation to bmi chart men their fat. Due to the truth that individual body compositions can fluctuate because some ladies might have more muscle mass than average (i.e. athletes) they will have a high BMI making it inaccurate at times.
Studies have shown which taking omega-3 fatty acids daily will assist prolong young searching skin. In truth, this could moreover bring back the elastic plus resilient structure of the dermis.
Lets begin with an average brick, like the multi-colored 1 at proper. We wish To make a little brick pile that has the same proportions because the initially brick, nevertheless is twice because big in every three dimensions. First we add a brick, inside purchase to double the length. Then alongside which, we add 2 more bricks to double the width.
The Track: Most marathon training programs might include track work because it helps bmi chart women develop the fast twitch muscles to build speed plus lung force throughout a race...getting older does not imply getting less competitive:) If I am training for a marathon, it actually makes a difference for me especially in the later miles of the race. Great article from Runner's World called "Running in Circles".
After my son was born I weighed out of the hospital at 192. That was after the baby was born. Since I was nursing, I lost the fat swiftly. In three months I was back to 135, however, then I stopped nursing. Because then I have gained back regarding 30 pounds, that puts me at 165. According to BMI (Body Mass Index) calculations, I am classified because "obese". Classifications are as follows: "Underweight", "Normal", "Overweight", and "Obese". BMI is calculated by the formula: fat (lb) / [height (in)]2 x 703. Divide the current weight by a height squared plus then multiply by 703. The amount we come up with should be interpreted according to the following: 18.5 or below = Underweight, 18.4 - 24.9 = Normal, 25.0 - 29.9 = Overweight, 30.0 or above = Obese.
If you don't fall inside the regular range, then get yourself checked with different appropriate techniques to figure out the amount of body fat. This can provide a greater perspective plus enable you to achieve or keep the perfect fat.