What is Boundary: Definition and 999 Discussions

In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. The liquid or gas in the boundary layer tends to cling to the surface.
The boundary layer around a human is heated by the human, so it is warmer than the surrounding air. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boundary layer is the air layer (~ 1 km) near the ground. It is affected by the surface; day-night heat flows caused by the sun heating the ground, moisture, or momentum transfer to or from the surface.

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  1. S

    Intro to PDE: Related homogeneous boundary condtions

    (partial derivatives didn't carry over well, so I just used a d) Homework Statement Give an example (as simple as possible) of a reference temperature distribution r = r(x, t) satisfying the following boundary conditions DN: r(0, t) = A(t), (dr(L,t) / dx) = B(t); NN: (dr(0,t) / dx) =...
  2. D

    This could be the solution to your confusion.

    Hello hello, I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing...
  3. V

    Boundary Layer displacement thickness

    Hey guys, The streamlines just outside a boundary layer are pushed away from the wall by the displacement thickness \delta* and I understand that; \delta*=\int^{\infty}_{0}(1-\frac{u}{U})dy Now this is for flow over a plate with length x=4m. At x=0 is the leading edge and at x=4...
  4. M

    Are acoustic wave reflection and the boundary conditions truly interdependent?

    I am studying acoustic wave reflection. The boundary conditions of acoustics are continuity of pressure and normal particle velocity. Can anyone tell me if these boundary conditions are completely independent? (Since the pressure and particle velocity are in phase, I would believe they are not...
  5. F

    Differential equation with singular boundary conditions

    Hey guys, just need some hints with this doosey Homework Statement We have (x^2 y')' + ax^2y = 0 where a the eigenvalue (a sturm-lioville problem) (sp?) with y'(0)=y(1) = 0 and we get the hint to substitute f = y/x. The Attempt at a Solution Ok so i get the general solution being a sum of...
  6. N

    X in Boundary => x Isolated or Strict Limit (topological space)

    Although the intuition makes sense, I am having trouble determining why the following proposition is correct. The document leaves this as an exercise for the reader... great. Proposition: Suppose A is a set in a topological space, and dA is the boundary of A. If x is in dA, then x is either an...
  7. W

    Electrostatic boundary condition

    The question : Consider a thin spherical shell of radius R with a uniform charge density sigma. If a very small piece of this surface were removed, leaving a small hole, what would the electric field be at a point just above/below the hole? Relevent info : the field due to the patch of...
  8. P

    What are the Boundary Conditions for Dielectric Interfaces?

    Homework Statement Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that: D(1)-D(2)=free surface charge density=s where D(1) is the component of the first medium normal to the surface. But suppose that there's nothing else apart from two...
  9. A

    Momentum eigenfunctions with periodic boundary conditions

    Homework Statement A particle of mass m is confined to move in one dimension. its wavefunction is periodic with period L\gg 1 - i.e. periodic boundary conditions are imposed. a)Determine the eigenfunctions and eigenvalues of momentum. Normalise the eigenfunctions on the interval [0,L)...
  10. S

    Reflection coefficient at a copper boundary

    Homework Statement Calculate the reflection coefficient of copper for radio waves at frequency 50Ghz and yellow light (wavelength = 0.6 micrometers) Homework Equations Reflection coefficient: R = E(r)^2/E(I)^2 = (1-n/1+n)^2 Where E(r) is the electric intensity of the reflected wave...
  11. S

    How to calculate a integral on boundary

    Hi, I would like to calculate the following integration: \oint_{\Sigma}f(x,y)g(x,y)\mathbf{n}\cdot d\mathbf{s} where g(x,y)=0 on \Sigma, and \mathbf{n} is the outward pointing unit normal field of the boundary \Sigma. In this case does the integral equals to 0? Thanks!
  12. R

    Modes with boundary conditions

    If I have a finite boundary, say of length L. Is it possible to demonstrate that if I were to allow all possible CONTINUOUS values of a wave to exist (with unit amplitude) then deconstrutive interference destroys all waves except those with wavelength: k=\frac{n\pi}{L} Where n =0,1...
  13. M

    Periodic boundary conditions and Bloch's theorem

    One thing that's always bothered me about Bloch's theorem is the periodic boundary conditions which are imposed on the system. Clearly, when dealing with an actual solid, the more natural choice would be to impose zero at the boundaries. I know that periodic conditions make the math easier, but...
  14. Q

    Does any lattice or lattice shape has a periodic boundary condition?

    If not, then what are the conditions for us to construct a periodic boundary condition(PBC)? If so, then please help me construct a PBC for the lattice shape in the attachments. I want to ask that what lattice site m's left neighbor is and what lattice site i's down neighbor is.From the...
  15. N

    Non-Reflective Boundary Conditions for the Wave Equation

    I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me. I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which...
  16. N

    What is the boundary condition for a moving solid boundary in a viscous fluid?

    I am confused on the definition of the "no-slip" boundary condition because of two seemingly contradicting definitions. Definition 1: The no-slip condition for viscous fluid states that at a solid boundary, the fluid will have zero velocity relative to the boundary. Definition 2: The fluid...
  17. L

    Heat equation, initial and boundary numerical conditions

    Hello to all! Homework Statement for testing my program i need a heat equation with numerical initial and boundary conditions: Derivative[2, 0][f][x, t] == Derivative[0, 1][f][x, t] f[x, 0] == numerical f[0, t] == numerical, f[numerical, t] == numerical PS. to moders: please, if...
  18. G

    Solving Differential Equation with Boundary Conditions

    solve the next differential equation: y´´- a*y= \delta (x-d) with the boundary conditions: \left.\frac{\partial y}{\partial x} \right|_ {x=0} = 0 lim _{x\rightarrow\infty} y = 0 I get the homogeneous solution: y_H = C_1 exp (\sqrt{a}x) + C_2 exp (-\sqrt{a}x) and then to...
  19. S

    Boundary considerations in extremum problems

    Homework Statement We are given a word problem and asked find maxima/minima (ie a simple example would be to find the least amount surface area required to build a box of a given volume). Is it necessary to explicitly show that the relative interior max/min, calculated by setting the gradient...
  20. O

    Boundary layers seperating from a baseball based on the viscosity of the air

    finally in my search to understand why the boundary layer separates from the surface of a baseball I have come to understand that the reasons for the separation of the boundary layer from a baseball is incredibly similar to the separation of the boundary layer from a wing of an airplane after...
  21. O

    A question on boundary layers viscosity and air seperating frmo a ball

    a question on boundary layers viscosity and air seperating from a ball I have a few questions that have to do with a viscosity on the surface of an object, the boundary layer and the boundary layer separating from the surface of a baseball! 1) my first question is if we had a stationary...
  22. N

    Analytical solution of Laplace's equation with horrendous boundary conditions

    Hi, I'm trying to find an analytical solution of Laplace's equation: \phi_{xx} + \phi_{tt} = 0 with the tricky boundary conditions: 1. \phi(x=0,|t|>\tau)= 0 2. \phi(x\neq0, |t|>>\tau)=0 3. \phi_{x}(x=0, |t|<\tau)=-1 4. \phi_{t}(x, |t|>>\tau)=0 I have the following ansatz(I...
  23. H

    Wavepacket Envelope at Boundary

    Hi, I've had trouble finding an answer to this question and was wondering if anyone could help. What happens to the envelope of a wavepacket of light when it crosses the interface between two media? I know that the field of the wavepacket will be continuous across the boundary, but does...
  24. P

    Boundary of a torus or sphere?

    Homework Statement What is the boundary of a torus? What is the boundary of a sphere? The Attempt at a Solution Both 0?
  25. B

    Understanding Boundary Conditions: Why 33.22abe is False

    what do mean the author by the red underline line? http://img164.imageshack.us/img164/7404/contfv6.jpg Why would 33.22abe false? Thanks.
  26. J

    Proving R & Null are the Only Clopen Sets of R Without Boundary Points

    So, I know that R and null are clopen, but now to prove they are the only clopen subsets of R... without the idea of boundary points? I know how to do it with boundary points, but can it be done without?
  27. P

    Dimensionality and Boundaries: Exploring the Concept of Space

    If a space is of n dimension, then the boundary of this space is n-1 dimension or not?
  28. Y

    Boundary conditons and initial conditions of a vibrating rod

    Finding the vibrational motion of a rod. A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 \epsilon). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod. What are the...
  29. S

    Help~find the interior, boundary, closure and accumulation points of the following.

    a. 1/n + 1/m : m and n are both in N b. x in irrational #s : x ≤ root 2 ∪ N c. the straight line L through 2points a and b in R^n. for part c. i got: intA= empty ; bdA=clA=accA=L Is this correct? how about part a and part b...i am so confused...
  30. V

    FD approximation at internal boundary condition

    Hi, I have to solve diffusion-advection PDE using finite difference method. The problem has two regions with different diffusion coefficients and velocities. At the interface between the two regions types of boundary condition : 1. No contact resistance C1 = C2 - D1*dC1/dx + v1*C1 = -...
  31. L

    Interesting boundary value problem

    Homework Statement A solid sphere is placed in an otherwise uniform electric field. Its upper half is made up from a material with dielectric constant e_1; the other half has dielectric constant e_2. The plane at which the parts of the sphere intersect is parallel to the uniform field at...
  32. J

    Minimum boundary when dividing eqilateral triangle in 4 equal sized parts

    So I have an equilateral triangle an I want to divide it in 4 parts, all having the same area. This can be done in a multitude of ways of course. But assuming it's a garden and the division is about putting up a fence, which division uses the least fencing? Now I have two alternatives so...
  33. M

    How do I specify boundary conditions in Femlab for a circular system?

    Does anybody know how to put BC at the center of a circle.
  34. radou

    A boundary value problem discussion

    A boundary value problem "discussion" So, let's say we are given a function f : [0, 1] --> R and constants a, b, and we want to find u : [0, 1] --> R such that u''(x) + f = 0 on <0, 1> with u(1) = a and u'(0) = -b. One can easily obtain the exact solution to this problem merely by using...
  35. K

    Prove the boundary of rationals is real

    Homework Statement Let Q be the set of all rational numbers Prove bd(Q)=R Homework Equations The Attempt at a Solution Let x be a real number, then since the interval |x-r| contains both rationals and irrationals for arbitrary small r, so R is the boundary of Q. Is that right?
  36. Aquafire

    Does the Universe have a Boundary ?

    Subject: Does the Universe have a Boundary ? Since nothing can exist outside of the Universe, how then can the Universe have a boundary in any conventional sense? Surely, if time before time is considered potentially unfathomable; in similar vein to speak of a boundary to the...
  37. S

    Laplace's Equation Boundary Problem

    Homework Statement I have a two part question, the first part involves solving Laplace's equation u_{xx} + u_{yy} = 0 for the boundary conditions u_x(0,y) = u_x(2,y) = 0 u(x,0) = 0 u(x,1) = \sin(\pi x) for 0 < x < 2, 0 < y < 1. The second part now states a new boundary problem...
  38. S

    Stationary Solution to Reaction-Diffusion Eq w/ Boundary Conditions

    Homework Statement What is the stationary (steady state) solution to the following reaction diffusion equation: \frac{\partial C}{\partial t}= \nabla^2C - kC Subject to the boundary conditions C(x, y=0) = 1, C(x = 0, y) = C(x = L, y) (IE, periodic boundary conditions along the...
  39. L

    The Born Von Karman Boundary Conditions

    Hi to all community of Physic's help from Florence, looking at born-von karman BC I'm a bit confused. I put this condition when i assume periodicity of wave function where the period is the spatial dimension of my system. I found that BC first in solid state physic, then I've noticed that...
  40. M

    Solving Coupled ODEs with Boundary Conditions

    Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...
  41. P

    Boundary Conditions for Fermi Gas

    Hi I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?
  42. W

    What happens when a ray of light hits the boundary of the universe?

    I am not sure if the universe ever expanded at speed inferior to that of light, but if it did, I am curious to know what would have happened (if it didn't happen) if a light ray (or any electromagnetic wave that is) had hit the boundary of the universe?
  43. J

    Solving Diff.Eq. with Boundary Conditions: y(x) = x

    I need help figuring out the solution to this diff.eq. y(x) = x + (1/2)*∫(from u=-1 to 1)[ ( 1-| x – u | ) y(u) du] , x є [ -1, 1] I have to show that: y``(x) + y(x) = 0 , x є [ -1, 1] subject to: y(1) + y(-1) = 0 y`(1) + y`(-1) = 2 Thanks for any help you can give.
  44. M

    Turbulent Boundary layer thickness on a flat plate

    I am really confused. Would you please tell me what the turbulent boundary layer thickness is on a flat plate? There is a well-known Schlichting formula in the previous editions of his book “boundary layer theory”, which is: \delta = 0.37 X Re^{-0.2} But actually I could not find this...
  45. R

    Separation of Variables / Boundary Conditions

    Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...
  46. D

    Grain Boundary Properties & Magnetic Process of Alloys

    what are the properties of this alloy about grain boundary?and what is the process to have magnetic property to this alloy?
  47. C

    Canonical boundary conditions.

    how do you prove/show that there really is a vector space defined by certain boundary conditions? unfortunatly this part of pde's was glossed over in my professor's lecture notes and I don't recall him talking about it in class.
  48. quasar987

    What is the boundary of a surface?

    What is the boundary of a surface? A surface is a two dimensional manifold. I would like to know what constitute the boundary of a surface. (wiki is nor clear enough for me)
  49. J

    Deriving Solutions for Schrodinger's Equation with Boundary Conditions

    Schodinger's equation for one-dimensional motion of a particle whose potential energy is zero is \frac{d^2}{dx^2}\psi +(2mE/h^2)^\frac{1}{2}\psi = 0 where \psi is the wave function, m the mass of the particle, E its kinetic energy and h is Planck's constant. Show that \psi = Asin(kx) +...
  50. G

    Nonhomogeneous Boundary Value Problem

    I've got a nonhomogeneous BVP I'm trying to solve. Both my book and my professor tend to focus on the really hard cases and completely skipp over the easier ones like this, so I'm not really sure how to solve it. It's the heat equation in a disk (polar coordinates) with no angle dependence...
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