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| {{Expert-subject|date=March 2012}}
| | An underweight individual can have low immunity, reduced endurance, along with a deficiency of nutrients in his body. So, fat control is very important. There are many methods to decide the ideal fat of the person. Among them are, waist to height ratio, and height to weight ratio.<br><br>Doctors plus dietitians use body mass index (BMI) and measuring of the waist to assess a person's risk of developing certain illnesses, for instance, diabetes plus heart disease. If your BMI is better than 25, you're obese. BMI equal to or better than 30 indicates obesity.<br><br>So my friend's BMR is 1969 calories a day. With this info plus her doctor's recommendation, we've choose to go for 1400-1500 calories consumed a day and 50-60 minutes of quite small exercise a day. According to the objective calculator a reduction of 400-500 calories a day within the BMR can cause about 1 pound of fat lose per week, that is ideal.<br><br>First, we want to determine an BMI for a child. What is a BMI? BMI stands for body mass index which is a amount that takes into account the child's height-to-weight ratio. There is a somewhat complex formula for calculating BMI, but this could be completed immediately plus easily at a variety of sites that offer a [http://safedietplansforwomen.com/bmi-calculator bmi calculator women]. You simply connect your child's fat plus height and the program may calculate a child's BMI. Choosing a bmi calculator is because simple because doing a Google look for which phrase.<br><br>Economist Giorrio Brunello from the University of Padova, Italy said that BMI affects wages negatively in Europe. Moreover, the size of the effect is bigger for males because compared to women.<br><br>The easiest method to keep track of the calorie and fat consumption for the day is to keep a diary! Hide a tiny notepad and pen inside your purse particularly for this plus take it where we go. Write down what we eat for the day. A superb, free website to calculate how countless calories are in a food is actually a part of iGoogle!<br><br>There are 3 key places in California where you are able to get California Medical Weight Management system. San Ramon, Watsonville plus Santa Clara are three main locations. Get an appointment fixed with all the doctor from any of the clinic and fill the free consultation form online. Losing fat will be fun plus easy for sure from here. It is not surprisingly the last time to lose weight in the event you follow it properly. Moreover, it provides several more advantages which you are able to get once you join it. You will truly feel a existence changed. Hurry up plus join the weight loss program today. |
| [[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
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| | 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)]]
| |
| [[Category:Visibility]]
| |
An underweight individual can have low immunity, reduced endurance, along with a deficiency of nutrients in his body. So, fat control is very important. There are many methods to decide the ideal fat of the person. Among them are, waist to height ratio, and height to weight ratio.
Doctors plus dietitians use body mass index (BMI) and measuring of the waist to assess a person's risk of developing certain illnesses, for instance, diabetes plus heart disease. If your BMI is better than 25, you're obese. BMI equal to or better than 30 indicates obesity.
So my friend's BMR is 1969 calories a day. With this info plus her doctor's recommendation, we've choose to go for 1400-1500 calories consumed a day and 50-60 minutes of quite small exercise a day. According to the objective calculator a reduction of 400-500 calories a day within the BMR can cause about 1 pound of fat lose per week, that is ideal.
First, we want to determine an BMI for a child. What is a BMI? BMI stands for body mass index which is a amount that takes into account the child's height-to-weight ratio. There is a somewhat complex formula for calculating BMI, but this could be completed immediately plus easily at a variety of sites that offer a bmi calculator women. You simply connect your child's fat plus height and the program may calculate a child's BMI. Choosing a bmi calculator is because simple because doing a Google look for which phrase.
Economist Giorrio Brunello from the University of Padova, Italy said that BMI affects wages negatively in Europe. Moreover, the size of the effect is bigger for males because compared to women.
The easiest method to keep track of the calorie and fat consumption for the day is to keep a diary! Hide a tiny notepad and pen inside your purse particularly for this plus take it where we go. Write down what we eat for the day. A superb, free website to calculate how countless calories are in a food is actually a part of iGoogle!
There are 3 key places in California where you are able to get California Medical Weight Management system. San Ramon, Watsonville plus Santa Clara are three main locations. Get an appointment fixed with all the doctor from any of the clinic and fill the free consultation form online. Losing fat will be fun plus easy for sure from here. It is not surprisingly the last time to lose weight in the event you follow it properly. Moreover, it provides several more advantages which you are able to get once you join it. You will truly feel a existence changed. Hurry up plus join the weight loss program today.