Surfaces Definition and 425 Threads

So apparently the 2 prior Navy Seals who died broke order to go and save unarmed personnel at the scene of the attacks and then were killed 7 hours later by a mortar round. http://www.foxnews.com/politics/2012/10/26/cia-operators-were-denied-request-for-help-during-benghazi-attack-sources-say/...

Consider two cylindrical containers of the same diameter. Fill them with a liquid to different levels. We all know that the liquid can be "siphoned" from one container to the other using a thin hose, which we will consider to be thin and of uniform diameter. Bernoulli's Equation can be...

I read somewhere that the error incurred from approximating the Fermi surface to be a sphere in k-space goes as 1/N where N is the number of electrons. So, N is generally of the order 10^23. I couldn't figure out how they came up with the value. I was trying to say that the actual shape of the...

Why is it necessary that branch cuts for multiple-valued functions are non-intersecting? Does this have to do with needing each sheet for one value (ex. for positive/negative square roots)?

Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...

for each of the following maps f: ℝ2-->ℝ3, describe the surface S = f(ℝ2) and find a description of S as the locus of an equation F(x,y,z) = 0. Find the points where \partialuf and \partialvf are linearly dependent and describe the singularities of S(if any) at these points f(u,v) = (2u + v...

What mathematics are necessary for understanding and using minimal surfaces particularly in quantum field theory? As of now I have a very limited mathematical background as I will be taking Calc III, Diff Eq, and Linear Algebra next semester but I hope to get into a quantum field theory research...

Homework Statement Find the volume between z = x^2 + y^2 and z = 3 - x - y Homework Equations None The Attempt at a Solution I must use a double integral. Using polar coordinates I find that the volume is equal to: V = ∫∫(3 - rcosθ - rsinθ) r dr dθ - ∫∫r^2 r dr dθ I'm...

Which Gaussian surfaces have an electric flux of +q/εo through them? I think is b since in c, +q and -q cancel each other out, d is only -q is that the right approach? thanks!

why cdw occurs at low dimensional solids with anisotropic fermi surfaces that have prominent nesting vectors?/ what it means : cdws are also common at the surface of solids??where they are more commonly called surface reconstruction or dimerization . PLZ tell me about two dimensional Fermi...

Homework Statement Find the volume of the solid inside the surfaces x^2+y^2+z^2=1 and z=x^2+y^2Homework Equations With x=0: z=y^2 ; z=√(1-y^2) or y as a function of z then gives: y=√z ; y=√(z^2-1)The Attempt at a Solution First, I attempted to sketch a cross section of the region by setting...

Hi, i am having difficulty with a question because i cannot seem to get the right answer. i don't think i am far off i just know i go wrong somwhere and if you could point that out it would be great. the question is attatched. for the first part i find the equations of the lines of the two sides...

I have attached a file with my question. From what i see the flux for both surfaces will be 0. I am unsure and need a little of explaining

I am having trouble finding the volume between the two surfaces. Well I did the problem and got an answer but I am not sure if I am approaching this type of problem correctly. So can you take a look at how i approached the problem and tell me if i am on the right path or if it is incorrect...

Hi, Can someone here help me understand how to illustrate maps of analytically-continuous paths over algebraic functions onto their normal Riemann surfaces? For example, consider w=\sqrt{(z-5)(z+5)} and it's normal Riemann surfaces which is a double covering of the complex plane onto a single...

What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions? To make a cube, I can use 6 4-sided-squares (of course they're 4 sided) To make a pyramid (3 sided), I can use 4 3-sided-triangles I can do this with pentagon as well (i don't know what the...

In Felix's Klein's pamphlet, "On Riemann's Theory of Algebraic Functions and their Integrals" he describes ways to construct divergence free irrotational flows on a compact Riemann surfaces such as the torus. One method is simply to cover the surface with a conducting material and place two...

This is probably a stupid question with a simple answer, but please bear with me. Suppose we have a bucket of water that we begin to spin at a constant angular speed. My textbook asked to find the shape of the surface of water, with the hint that the surface would be a surface of constant...

Intercepts in quadric surfaces?? Homework Statement How many intercepts can an ellipsoid have? Homework Equations The Attempt at a Solution First of all, I don't understand what exactly "an intercept" means in quadric surfaces. in two dimensions, intercepts are the points...

Homework Statement "Given that near (1,1,1) the curve of intersection of the surfaces x^4 + y^2 + z^6 - 3xyz = 0 and xy + yz + zx - 3z^8 = 0 has the parametric equations x = f(t), y = g(t), z = t with f, g, differentiable. (a) What are the derivatives f'(1), g'(1)? (b) What is the...

Hi, I have the following definition for an isotropic surface: the normals to the measured surface are randomly distributed. Am I right in thinking the following: 1) The surface of a sphere is isotropic? 2) The surface of a cube is anisotropic? I think (2) is correct but not sure...

Homework Statement I'm also having trouble with these: provide the names and sketch the following surfaces: x2+y2+z2=16 x2+y2=9 x2+2y2+4z2=16 z=-√(9-x2-y2) z=√x2+y2 z=x2+y2 Homework Equations The Attempt at a Solution So for the first one it's a sphere with radius of 4...

the radii of the curvature of the spherical surfaces which is a lens of required focal length are not same. it forms image of an object. the surfaces of the lens facing the object and the image are interhanged. will the position of the image change?

See attachement for required information. Please and thank you!

Parameterize the intersection of the surfaces z=x^2-y^2 and z=x^2+xy-1 What's getting me stuck on this problem is the xy. I set x=t z=x^2-y^2 z=t^2-y^2 z=x^2+xy-1 t^2-y^2=t^2+ty-1 y^2=1-ty Thats as far as of come, I'm stuck on this

Gauss's Law -- Irregular Surfaces I don't fully understand why Gauss's Law holds for any Gaussian surface. My textbook clearly derives Gauss's Law from Coulomb's Law using a spherical surface, but it then extends the result to any Gaussian surface without sufficient explanation. Why does...

I'm working on a project at work that requires some tribology/fluids calculations that I don't know if are applicable to me or not. For this scenario, one of the tests will require me to assume hydrodynamic lubrication where oil is completely separating the 2 surfaces. I have a sliding...

Good day all. First of all, I apologize if this has been asked a million times before. I have not been able to find a straight-forward answer to my wonderings; maybe because they do not yield a straight-forward question. As part of a large exercise of thinking for the joy of thinking*, I am...

First post here on pf! I wanted to ask if it's feasible to determine velocities at the top / bottom surface of an airfoil due to the vortex sheet placed on the camber line (due to thin airfoil theory). I'm attempting to do this because the big picture is to determine the Cp distribution...

Hi, I'm writing a Master's thesis on superhydrophobic surfaces aimed at preventing ice accumulation, and I'm looking for an appropriate quote to include in my introduction. Any suggestions?

I keep seeing reports about how all the planets similar to Earth in other nearby planetary systems are now being discovered. Since we won't have the technology to send probes or go there ourselves for some time, all we can do is look at them. My question is: Could we ever get better resolution...

Hello Everyone, Here is my situation: I am using a laser to take distance (height) measurements on a variety of surface types (e.g. mirror, machined surface, plastic, etc.) and I would like to quantify the repeatability of the laser measurements on each surface type. Please note that I care...

Homework Statement Find the area of the part of the plane 3x + 5y + z = 15 that lies inside the cylinder x^2 + y^2 = 25. Homework Equations A=∫∫(√1+(dz/dx)^2+(dz/dy)^2) dA The Attempt at a Solution my bounds were r=0 to 5 and theta=0 to 2pi ∫∫√1 + (-3)^2 + (-5)^2 dA =∫∫√35 dA...

Given that the surface x^8y^7+y^3z^6+z^8x63+6xyz=9 has the equation z=f(x,y) in a neighbourhod of the point (1,1,1) with f(x,y) differentiable, find the derivatives fx(1,1)= fy(1,1)= Attempt: I tried plugging (1,1,1) in fx but it wasnt rigth. We haven't seen this in class and I don't...

If we consider a Riemannian surface as a one-dimensional complex manifold, what does that tell us about its intrinsic curvature? I mean for one-dimensional curves we know they only have extrinsic curvature so it depends on the embedding space, this doesn't seem to be the case for one-dimensional...

Homework Statement Identify the following surfaces: i) r.u=L ii) r.u=mlrl for -1\leqm\leq1 where k, L, m are fixed scalars and u is a fixed unit vector. Homework Equations The Attempt at a Solution The first one is in the same form as the equation of a plane, but u is not...

Homework Statement Prepairing for a test and this one came up that's confusing me. A spherical object, water cooled, with a diameter of 10 milimeters and ε = 0,9 is kept at 353 degrees Kelvin, when placed in a very large furnace where a vacuum is formed and which walls are kept at 673 degrees...

Homework Statement Prove that there are no tubes that are minimal surfaces Homework Equations F(u, v) = γ(u) + R(cosuN(v) + sinuB(v)) The Attempt at a Solution A tube is defined to be the surface formed by drawing circles with constant radius in the normal plane in a space...

Does a geodesic flow on a compact surface - compact 2 dimensional Riemannian manifold without boundary - always have a geodesic that is orthogonal to the flow?

In the attached picture is all of the information to complete this problem. The picture is of a solid sphere at the center of a hallow sphere, both of which are conductors. The question asks to find the total charge of the exterior and interior surfaces of the hollow conductor, as well as the...

Hello. I just started to study integral calculus not long ago and I have some confusion when it comes to calculating the areas of surfaces of revolution using integral. As from my testbook, when we want to calculate this kind of surface area, we often use the frustum surface area to approximate...

Homework Statement A cone C, with height I and radius I, has its base in the xz-plane and its vertex on the positive y-axis. Find a function g(x, y, z) such that C is part of the level surface g(x, y, z) = 0. Homework Equations What would be the formula for the cone such that the base of the...

Homework Statement find the angle between the normals to the surface xy=z2 at the points (1,4,2) and (-3,-3,3) Homework Equations none The Attempt at a Solution del S = 2zy i + 2zx j and at the two points, del S = 16i+4j and del S = -18i-18j using the dot product, i got cos...

I was at this japanese tepenaki places or however you spell it where they make the food in front of you and my dad had an interesting though. The stations they have have these big flat cooking areas powered underneath by what I assume were a bunch of gas burners. We bought a new bbq and my...

Homework Statement a metal sphere of radius 0.39 m carries a charge 0.55 μC. Equipotential surfaces are to be drawn for 100-V intervals outside of the sphere. Determine the radius of the first, tenth and 100th equipotential from the surface. Homework Equations V = kQ / r Volt =...

So this may be a bit silly, but one thing I've never really learned in all my years is how one actually goes about calculating equipotential surfaces for arbitrary potentials? Let's say I have a potential that goes like \Phi = A_0e^{-\left({{r}\over{r_0}}\right)^2}\cos^2 (\phi) \sin^2(\theta)...

So I'm going over Rudin's chapter on differential forms in his Principles of Mathematical Analysis and I'm looking at Example 10.36 which gives the 1 form \eta = \frac{xdy-ydx}{x^2+y^2} on the set \mathbb{R}^2-{0} and then parametrizes the circle \gamma(t)=(rcos(t),rsin(t)) for fixed r>0 and...

Hi, I'm trying to create an interpolated volume from two surfaces. Let me explain exactly what I'm doing. I am trying to obtain a rough estimate for the temperature in a certain geographical area and at depth. I have the temperature of the rocks at the surface in the form T1=T(x,y,z) where z...

Homework Statement Find the area of the part of the sphere x^2 + y^2 + z^2 = a^2(a > 0constant) that lies inside the cylinder x^2 + y^2 = ax. Homework Equations double integral of the cross product of the vector Ra and Rb with respect to dA. The Attempt at a Solution I tried to parametrize...

Homework Statement Evaluate the surface integral \iint_S xy \;dS S is the boundary is the boundary of the region enclosed by the cylinder x^2 + z^2 =1 and the planes y = 0 and x + y = 2 2. The Solutions [PLAIN]http://img844.imageshack.us/img844/8827/unledje.jpg The...