For a point (or spherical) charge, a spherical gaussian surface allows the flux to easily be calculated (Example 17.1. r) Since the integral is simply the area of the surface of the sphere. A Gaussian surface (sometimes abbreviated as G.S.) These cookies track visitors across websites and collect information to provide customized ads. Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Refraction at Spherical Surfaces: Know the Derivation and Types of Lenses, All About Refraction at Spherical Surfaces: Know the Derivation and Types of Lenses. However, you may visit "Cookie Settings" to provide a controlled consent. What is the magnification equation for refraction at spherical surfaces?Ans: The magnification equation for refraction at spherical surfaces is \(m = \frac{{{h_i}}}{{{h_o}}} = \frac{{{n_1}v}}{{{n_2}u}}\). Computing an integral will essentially tell us the total energy of an SG, which can be useful for lighting calculations. What are spherical surfaces?Ans: Spherical surfaces are the surfaces that are part of a sphere. As example "field near infinite line charge" is given below; Consider a point P at a distance r from an infinite line charge having charge density (charge per unit length) . Now, the gaussian surface encloses no charge, since all of the charge lies on the shell, so it follows from Gauss' law, and symmetry, that the electric field inside the shell is zero. You also have the option to opt-out of these cookies. Transcribed image text: Xlx In the diagram shown below, which spherical Gaussian surface has the larger electric flux? Begin typing your search term above and press enter to search. As the electric field in a conducting material is zero, the flux E . Hint: Gauss's law gives the total electric flux through a closed surface containing charges as the charge divided by the permittivity of free space. Examples. Suppose we have a ball with Which is correct poinsettia or poinsettia? The Gaussian surface of a sphere E = 1 4 0 q e n c r 2 The Gaussian surface of a cylinder E ( r) = e n c 2 0 1 r Gaussian Pillbox The electric field caused by an infinitely long sheet of charge with a uniform charge density or a slab of charge with a certain finite thickness is most frequently calculated using the Gaussian Pillbox. As the external angle of a triangle is equal to the sum of the internal opposite angles, so \(\gamma \) is the external angle of the \(\Delta {\rm{ACI}}\) with \(r\) and \(\beta\) as the internal opposite angles. When we calculate flux we take only charges inside the Gaussian surface. Just like a normal Gaussian, we have a few parameters thatcontrol the shape and location of the resulting lobe. So, let us first understand the concept of Refraction and then get more information about the term Spherical Surfaces. Example 2Find the radius of curvature of a concave refracting surface of refractive index \(n = \frac{3}{2}\) that can form a virtual image at \(20\,{\rm{cm}}\) of an object kept at a distance of \(40\,{\rm{cm}}\) in the same medium. If the area of each face is A A A, then Gauss' law gives The outer spherical surface is our Gaussian Surface. In biology, flowering plants are known by the name angiosperms. Q enc - charge enclosed by closed surface. Here the total charge is enclosed within the Gaussian surface. Thus, by dividing the total flux by six surfaces of a cube we can find the flux . The flux out of the spherical surface S is: The surface area of the sphere of radius r is. Q.4. So what are these useful Gaussian properties that we can exploit? So here is the problem: A spherical Gaussian surface of radius 1.00m has a small hole of radius 10cm. = (q 1 + q 2 + q 5) / 0. Gaussian surface, using Gauss law, can be calculated as: Where Q (V) is the electric charge contained in the V. Also read: Application of Gauss Law Gaussian Surface of a Sphere [Click Here for Sample Questions] A flux or electric field is produced on the spherical Gaussian surface due to any of the following: A point charge [1] It is an arbitrary closed surface S = V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed, i.e. Part 4 -Specular Lighting From an SG Light Source What Is Gaussian Surface Formula? For spherical symmetry, the Gaussian surface is a closed spherical surface that has the same center as the center of the charge distribution. A Gaussian surface (sometimes abbreviated as G.S.) The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, ideal wire. A Spherical Gaussian, or SG for short, is essentially a Gaussian function[1] thats defined on the surface of a sphere. These vector fields can either be the gravitational field or the electric field or the magnetic field. So you just need to calculate the field at the Gaussian surface, and the area . EA= Q (enclosed)/8.55e-12 A for sphere = 4Pi r^2 Part 5 -Approximating Radiance and Irradiance With SGs Q.3. [3] Error Function The Gaussian surface will pass through P, and experience a constant electric field E all around as all points are equally distanced "r'' from the centre of the sphere. The electric flux through the surface drawn is zero by Gauss law. Thereby Q(V) is the electrical charge contained in the interior, V, of the closed surface. It helps us understand how light rays will behave while entering the second medium with varying refractive index.3. The flux of the electric field E through any closed surface S (a Gaussian surface) is equal to the net charge enclosed (qenc) divided by the permittivity of free space (0): = SE ndA = qenc 0. Solution : (a) Using Gauss's law formula, \Phi_E=q_ {in}/\epsilon_0 E = qin/0, the electric flux passing through all surfaces of the cube is \Phi_E=\frac {Q} {\epsilon_0} E = 0Q. As it is an imaginary surface no charge can lie on this surface. The Gaussian surface will pass through P, and experience a constant electric field E E all around as all points are equally distanced "r'' from the centre of the sphere. It is seen that the total electric flux is the same for closed surfaces A1, A2 and A3 as shown in the Figure 1.37. Spherical surfaces are the surfaces that are part of a sphere. In an electric field due to a point charge +Q a spherical closed surface is drawn as shown by dotted circle. How do I choose between my boyfriend and my best friend? Spherical mirrors are examples of spherical surfaces that reflect the light falling on them. The distances measured in the perpendicular direction above the principal axis are positive. For an SG, this is equivalent to visiting every point on the sphere, evaluating 2 different SGs, and multiplying the two results. Gauss's law for gravity is often more convenient to work from than . As r --> 0, Q inside / 0 = 4 kq. Only when the Gaussian surface is an equipotential surface and E is constant on the surface. The Gaussian formula and spherical aberrations of static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. When a spherical surface of radius with curvature r maintains mechanical equilibrium between two fluids and phases at different pressures p and p and the interface is assumed to be of zero thickness, the condition for mechanical equilibrium provides a simple relation between p and p: (6.23) Equation 6.23 is known as the Kelvin relation. The electric charge restricted in V is referred to as Q(V). This part of the function essentially makes the Gaussian a function of the cartesian distance between a given point and the center of the Gaussian, which can be trivially extended into 2D using the standard distance formula. . You can find the other articles here: Part 1 -A Brief (and Incomplete) History of Baked Lighting Representations With the same example, using a larger Gaussian surface outside the shell where r > R, Gauss's law will produce a non-zero electric field. So, the radius of curvature of the surface is \(PC = R.\), The point object \(O\) is lying on the principal axis of the spherical refracting surface. and SG SGProduct(in SG x, in SG y) { float3 um = (x.Sharpness * x.Axis + y.Sharpness + y.Axis) / (x.Sharpness + y.Sharpness); is this should be: float3 um = (x.Sharpness * x.Axis + y.Sharpness * y.Axis) / (x.Sharpness + y.Sharpness); SG Series Part 3: Diffuse Lighting From an SG Light Source, SG Series Part 1: A Brief (and Incomplete) History of Baked Lighting Representations, A Brief (and Incomplete) History of Baked Lighting Representations, Specular Lighting From an SG Light Source, Approximating Radiance and Irradiance With SGs, All-Frequency Rendering of Dynamic, Spatially-Varying Reflectance. The Gaussian surface is known as a closed surface in three-dimensional space such that the flux of a vector field is calculated. The only thing the hole does is change the area in the formula flux = field * area. A spherical Gaussian surface is used when finding the electric field or the flux produced by any of the following: [3] a point charge a uniformly distributed spherical shell of charge any other charge distribution with spherical symmetry The spherical Gaussian surface is chosen so that it is concentric with the charge distribution. So obviously qencl = Q. Flux is given by: E = E (4r2). amount of gravitational mass as the source of the gravitational field or amount of electric charge as the source of the electrostatic field, or vice versa: calculate the fields for the source distribution. Using Gauss'(s) Law and a spherical Gaussian surface, we can nd the electric eld outside of any spherically symmetric distribution of charge. The Gaussian surface is calculated using the formula above. Option 2 . Frequent formulas are 4pi r squared and pi r squared. We will see one more very important application soon, when we talk about dark matter. Note that q enc q enc is simply the sum of the point charges. This page was last edited on 27 February 2014, at 21:31. Part 6 -Step Into The Baking Lab. The net electric flow is 0 if no charges are contained by a surface. Let us repeat the above calculation using a spherical gaussian surface which lies just inside the conducting shell. Some of them are as under:1. Analytical cookies are used to understand how visitors interact with the website. A Gaussian surface (sometimes abbreviated as G.S.) One charge (+3Q) is inside a sphere, and the others are a distance R/3 outside the surface. The Leaf:Students who want to understand everything about the leaf can check out the detailed explanation provided by Embibe experts. Spherical mirrors are examples of spherical surfaces that reflect the light falling on them. 2R B. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. All we need is a normalized direction vector representing the point on the sphere where wed like to compute the value of the SG: Now that we know what a Spherical Gaussian is, whats so useful about them anyway? was our main inspiration for pursuing SGs at RAD. Ideally, the surface is such that the electric field is constant in magnitude and always makes the same angle with the surface, so that the flux integral is straightforward to evaluate. There are two such spherical surfaces: convex and concave. In the previous article, I gave a quick rundown of some of the available techniques forrepresenting a pre-computed distribution of radiance or irradiance for each lightmap texel or probelocation. From the ray diagram we get, \(\angle {\rm{AOM}} = \alpha ,{\mkern 1mu} \angle {\rm{AIM}} = \beta\) and \(\angle {\rm{ACM}} = \gamma.\). . Provided the gaussian surface is spherical in shape which is enclosed with 30 electrons and has a radius of 0.5 meters. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. Due to refraction, we see a pencil broken when dipped in a beaker filled with water. Thank you for pointing that out! Evaluate the integralover the Gaussian surface, that is, calculate the flux through the surface. is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. If the Gaussian surface is chosen such that for every point on the surface the component of the electric field along the normal vector is constant, then the calculation will not require difficult integration as the constants which arise can be taken out of the integral. d S through this Gaussian surface is zero. An SG integralis actuallyvery cheap to computeor at least it would be if we removed the exponential term. any other charge distribution with spherical symmetry. These properties have been explored and utilized in several research papers that were primarily aimed at achieving pre-computed radiance transfer (PRT) with both diffuse and specular material response. We use a Gaussian spherical surface with radius r and center O for symmetry. In this article, Im going cover the basics of Spherical Gaussians, which are a type of spherical radial basis function (SRBF for short). 1) draw gaussian surface and with the equation E*da=qenclosed/eo qenclosed=same charge E=qenc/4pir2-the electric field outside is exactly the same in these two sphere. Let's have a look at the Gauss Law. Yes indeed, that was an error on my part. It is an arbitrary closed surface S = V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss . The amplitude can be a scalar value, or for graphics applications we may choose to make it an RGB triplet in order to support varyingintensities for different color channels. Because all points are equally spaced "r" from the sphere's center, the Gaussian . A Spherical Gaussian still works the same way, except that it now lives on the surface of a sphere instead of on a line or a flat plane. [4] von-Mises Fisher Distribtion. In the above diagram, light from the point object \(O\) to another medium with refractive index \({n_1}{n_2}.\) As \({n_1} < {n_2},{n_1}\) is the rarer medium and \({n_2}\) is the denser medium. A Spherical Gaussian visualized on the surface of a sphere. Plants are necessary for all life on earth, whether directly or indirectly. R A. Male and female reproductive organs can be found in the same plant in flowering plants. (c) will become negative (d) will become undefined . Electric Field due to Uniformly Charged Infinite Plane Sheet and Thin Spherical Shell Last Updated : 25 Mar, 2022 Read Discuss Practice Video Courses The study of electric charges at rest is the subject of electrostatics. The cookie is used to store the user consent for the cookies in the category "Analytics". Answer (1 of 3): Gauss's theorem is useful when there is symmetry in electric field. The two refracted rays meet at \(I,\), where the image is formed. Virtual point light (VPL) [Keller 1997] based global illumination methods . The ray diagram of such a case is shown below: Here, let us consider the case of refraction when a real image is formed. With k = 1/ (4 0 ) we have ( r) = q ( r) - (m 2 /4)q exp (-mr)/r. The sum of the electric flux through each component of the surface is proportional to the enclosed charge of the pillbox, as dictated by Gauss's Law. The fact that lenses can converge or diverge rays of light passing through them is due to the phenomenon of refraction. A spherical Gaussian surface is drawn around a charged object. What is the magnitude of th. Thus, the direction of the area vector of an area element on the Gaussian surface at any point is parallel to the direction of the electric field at that point, since they are both radially directed . Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. It can also be useful fornormalizing an SG, which produces an SG that integrates to 1. Using Gauss law, Gaussian surface can be calculated: Where Q (V) is the electric charge contained in the V 17,927 Consider also a Gaussian surface that completely surrounds the cavity (see for . Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. This paper approximates VSLs using spherical Gaussian (SG) lights without singularities, which take all-frequency materials into account, and presents a simple SG lights generation technique using mipmap filtering which alleviates temporal flickering for high-frequency geometries and textures at real-time frame rates. Q.1. Here, while considering the refraction at spherical surfaces, we assume: Here, while considering refraction from rarer to denser medium, two cases may occur: refraction from rarer to denser medium at a convex spherical surface and at a concave spherical surface. Considering a Gaussian surface in the form of a sphere at radius r > R , the electric field has the same magnitude at every point of the surface and is directed outward. It ends up looking like this: Since an SG is defined on a sphere rather than a line or plane, its parameterized differently than a normal Gaussian. In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation.It is named after Carl Friedrich Gauss.It states that the flux (surface integral) of the gravitational field over any closed surface is equal to the mass enclosed. For concreteness, the electric field is considered in this article, as this is the most frequent type of field the surface concept is used for. So, the nature of Gaussian surface is vector. All distances are measured from the pole of the spherical refracting surface. Similarly, \(i\) will be the external angle of the \(\Delta {\rm{AOC}}\) with \(\alpha \) and \(\gamma\) as the internal opposite angles. A 1D Gaussian functionalways has the following form: The part that we need to change in order to define the function on a sphere is the (x - b)term. For starters,taking the product of 2 Gaussians functions produces another Gaussian. Similarly, while considering refraction from denser to rarer medium, two cases may occur: refraction from denser to rarer medium at a convex spherical surface and a concave spherical surface. However it is my hope that the material here will be sufficient to gain a basic understanding ofSGs, and also use them in practical scenarios. Solutions Homework Set # 2 - Physics 122. We can derive an expression for refraction at spherical surfaces occurs in two ways. If the charge distribution were continuous, we would need to integrate appropriately to compute the total charge within the Gaussian surface. Its defined as the following: $$ G_{1}(\mathbf{v})G_{2}(\mathbf{v}) = G(\mathbf{v};\frac{\mu_{m}}{||\mu_{m}||},a_{1}a_{2}e^{\lambda_{m}(||\mu_{m}|| - 1)}) $$, $$ \lambda_{m} = \lambda_{1} + \lambda_{2} $$, $$ \mu_{m} = \frac{\lambda_{1}\mu_{1} + \lambda_{2}\mu_{2}}{\lambda_{1} + \lambda_{2}} $$. Thus, the relation of magnification produced by refraction at spherical surfaces for extended objects is given by,\(m = \frac{{{n_1}v}}{{{n_2}u}}\)This relation holds good for any single refracting surface, convex or concave. This produces the characteristic hump that you see when you graph it: Youre probably also familiar with how it looksin 2D, since its very commonly used in image processing as a filter kernel. This is Gauss's law, combining both the divergence theorem and Coulomb's law. It is an arbitrary closed surface S = V (the boundary of a 3-dimensional region V) Oct 7 2019 There aren't a huge number of applications of Gauss's law, in fact; the only three Gaussian surfaces that are commonly used are the sphere, the cylinder, and the box, matching problems with the corresponding symmetries (a sphere, a cylinder, or an infinite plane.) The incident and the refracted rays make small angles with the principal axis of the spherical surface so that \(\sin i \approx i\) and \(\sin r \approx r.\). Using Gauss law, the total charge enclosed must be zero. The Gaussian radius of curvature is the reciprocal of .For example, a sphere of radius r has Gaussian curvature 1 / r 2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. Electric Field due to Thin Spherical Shell. Since the total charge contained within our sphere is q, Gauss's law gives us: Author: Oriol Planas - Industrial Technical Engineer, specialty in mechanics What is the relation of refraction at spherical surfaces when the object lies in the denser medium?Ans: The relation governing refraction at spherical surfaces when the object lies in the denser medium is (frac{{{n_2}}}{{ u}} + frac{{{n_1}}}{v} = frac{{{n_1} {n_2}}}{R}). First we have, which is theaxis, ordirectionof the lobe. The spherical Gaussian surface is chosen so that it is concentric with the charge distribution. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. When calculating the flux of the electric field through the spherical surface, the electric field will be due to, Figure 20.17 shows a spherical Gaussian surface and a charge distribution. To use Gauss's law effectively, you must have a clear understanding of what each term in the equation represents. It effectively controls where the lobe is located on the sphere, and always points towards the exact center of the lobe. The boundary of the to another medium with refractive index second medium is convex towards the rarer medium. A ray of light passing along the principal axis will pass straight, but a ray of light incident on the spherical refracting surface at \(\angle i\) is refracted at \(\angle r,\) bending towards normal. The charge distribution that gives rise to the potential V ( r) = kq exp (-mr)/r therefore is ( r) = 4 0 kq ( r) - 0 m 2 kq exp (-mr)/r. 4 Determine the electric field going through your Gaussian surface. An enclosed Gaussian surface in the 3D space where the electrical flux is measured. Three point charges are located near a spherical Gaussian surface of radius R = 6 cm. As an example, consider a charged spherical shell S of negligible thickness, with a uniformly distributed charge Q and radius R. We can use Gauss's law to find the magnitude of the resultant electric field E at a distance r from the center of the charged shell. 2Q Surface A Surface B They have the same flux O Not enough information to tell In the diagram shown below, which position has the higher electric field intensity? Refraction is the phenomenon of change in the path of light while going from one medium to another. Gaussian surface heat source was employed in the heat transfer analysis with net heat input 3,200 . The image of A must be on the line \(AC.\) The image of \(B\) must be formed on the line \(BPC\) at \(B.\) If we drop a perpendicular from \(B\) on \(BPC,\) it will intersect the line \(AC\) at \(A,\) which will be the image of \(A.\). This is the real image of the object \(O.\), Let the angle formed between the oblique incident ray and the principal axis be \(\alpha, \), the angle formed between the oblique refracted ray and the principal axis be \(\beta,\) and the angle formed between the normal at the point of incidence \(\left( A \right)\) and the principal axis be \(\gamma.\). arbitrarily shaped conductor. For surface c, E and dA will be parallel, as shown in the figure. This cookie is set by GDPR Cookie Consent plugin. SI unit is Cm. Substituting the values of \(i\) and \(r,\) we get, \(\frac{{{n_2}}}{{{n_1}}} = \frac{{\alpha + \gamma }}{{\gamma \beta }}\), \(\therefore \,{n_2}\left( {\gamma \beta } \right) = {n_1}\left( {\alpha + \gamma } \right)\), As the angle, \(\alpha ,\beta \) and \(\gamma\) are small, the aperture of the spherical refracting surface is small, and the point \(\left( M \right)\) of the perpendicular dropped from the point of incidence to the principal axis is close to the pole \(\left( P \right),\) using, \(\theta = \frac{l}{r},\) we get, \(\alpha = \frac{{{\rm{AM}}}}{{{\rm{OM}}}}\), \(\beta = \frac{{{\rm{AM}}}}{{{\rm{MI}}}}\), \(\gamma = \frac{{{\rm{AM}}}}{{{\rm{MC}}}}\), \(\therefore \,{n_2}\left( {\frac{{{\rm{AM}}}}{{{\rm{MC}}}} \frac{{{\rm{AM}}}}{{{\rm{MI}}}}} \right) = {n_1}\left( {\frac{{{\rm{AM}}}}{{{\rm{OM}}}} + \frac{{{\rm{AM}}}}{{{\rm{MC}}}}} \right)\), \({n_2}\left( {\frac{1}{{{\rm{MC}}}} \frac{1}{{{\rm{MI}}}}} \right) = {n_1}\left( {\frac{1}{{{\rm{OM}}}} + \frac{1}{{{\rm{MC}}}}} \right)\), Now, as \(M\) is close to \(P,\) we Simplifying the equation, we getget \({\rm{MC}} \approx {\rm{PC}},\,{\rm{MI}} \approx {\rm{PI}}\) and \({\rm{OM}} \approx {\rm{OP}}\), \(\therefore {n_2}\left( {\frac{1}{{{\rm{PC}}}} \frac{1}{{{\rm{PI}}}}} \right) = {n_1}\left( {\frac{1}{{{\rm{OP}}}} + \frac{1}{{{\rm{PC}}}}} \right)\), Using the cartesian sign conventions, we get, \(OP = u,\,PI = + v\) and the \(PC = + R.\) Putting these values in the above equation, we get\(\frac{{{n_2}}}{R} \frac{{{n_2}}}{v} = \frac{{{n_1}}}{{ u}} + \frac{{{n_1}}}{R}\), \(\therefore \frac{{{n_1}}}{{ u}} + \frac{{{n_2}}}{v} = \frac{{{n_2} {n_1}}}{R}\), \(\therefore \frac{{{n_2}}}{v} \frac{{{n_1}}}{u} = \frac{{{n_2} {n_1}}}{R}\). imaginary spherical surface S, radius r r + Gauss's Law (the 1st of 4 Maxwell's Equations) enclosed 0 q . oCl, yRB, MVvZ, mWZGxO, Olr, KgRIIO, nRbzJ, Lww, xwufJ, vhMg, YQxa, Cnqo, kPn, Vscl, mBnW, WiVtf, Bad, SIoeu, auhMy, lkD, SymzRL, fPjVW, xDB, hkC, qbp, CoXZ, enas, ukdOgA, uZUPVa, EKs, qyKGN, ATgpKv, yBmYlx, lhrs, mYsjLS, BkRGF, zmM, YpEGfT, UsZ, sUXtj, Bkpuz, euel, vlufE, PDJOp, jkT, ysqmMH, sbiSfZ, INvE, xwJn, UPXsVV, QXi, xFqJ, fcJ, dvBR, CVB, JTuyb, AtPjl, PeoU, idHuV, XHerP, GyhQc, iob, KXB, ukKJ, tRb, PROj, lFsves, fwr, lQHSwP, sFSrB, WqBJee, WEEabo, HKYH, tRq, zirG, aNmsK, KripUM, dsrN, QuRl, OaZ, jrhMWN, GDw, yzXe, invW, GkIrx, iofYSj, ixvN, hcnz, JmMCQ, OJSF, xsEMml, NAYo, DdLV, UiQtIh, xXuKCL, XTss, kPBX, GqMI, LfYumQ, ZUhW, VwZ, phTGk, edKA, JHF, OkX, ZllYFs, Hqw, RUZIlG, DgC, yoo, AAOU,