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

    Solving an eigenvalue equation with boundary conditions

    Suppose that we want to solve the eigenvalue equation with Dirichlet boundary conditions ## \bigg(-\frac{d^2}{dx^2}+V(x)\bigg) \phi_n = \lambda_n \phi_n,\ \ \ \ \ \ \ \ \ \ \ \ \ \phi_n(0)=0,\ \phi_n(1)=0, ## where ##0 < \lambda_1 < \lambda_2 < ...## are discrete, non-degenerate eigenvalues...
  2. K

    Definition of open boundary conditions

    I have a question I'm a little embarrassed to be asking: what is meant in condensed matter when someone describes a system with "open boundary conditions," say in one-dimension for simplicity? I am comfortable with the statement of fixed (Dirichlet) or free (von Neumann) boundary conditions, as...
  3. naima

    Understanding the Boundary of a Spinfoam and Spin Network in LQG Theory

    I read in wikipedia that the boundary of a spinfoam is a spin network. Is it true? How can we define what is the boundary of a finite connected spinfoam? I have the same question for a spin network. As in LQG boundaries are of paramount importance, I think that we have to define them. Thanks
  4. K

    Solving PDEPE without boundary conditions? heat transfer

    Hi all! I am trying to solve a system of partial differential equations in Matlab, with both derivatives in time and space domains. I am using the pdepe function for that. The system is, to be simple, a sort of solar thermal panel, made of three layers: an absorber plate, a fluid layer of...
  5. B

    ANSYS: What are vibrating feeder's boundary conditions?

    I have created such vibrating feeder model on SW but on ANSYS I'm only analyzing the frame. 1)How do I set up boundary conditions, I think I need elastic supports? 2)In modal analysis I have elastic, fixed supports, remote displacement - which should I use and in what directions? 3)Do I perform...
  6. M

    MHB Initial & Boundary Value Problem-Fourier

    Hey! :o We have the initial and boundary value problem $$u_{xx}(x,y)+u_{yy}(x,y)=0 , x^2+y^2<1 \\ u(x,y)=0 \\ u(1, \theta)=\sin{\theta}, 0< \theta< \pi$$ $$U_{\rho \rho}(\rho, \theta)+ \frac{1}{\rho^2} U_{\theta \theta}=0, 0< \rho<1, 0< \theta< \pi$$ We are looking for solutions of the form...
  7. PhysicsKid0123

    Boundary conditions of electric field?

    I'm reading griffiths electrodynamics and I am confused about a concept. Mainly because I might be interpreting it in different ways. Why does the equation contain an E with a negative in front? Namely, E_below. Isn't the Electric field pointing away from the surface with the surface charge...
  8. George Zucas

    Complex System Boundary Conditions

    Edit: Sorry about the vague title, it was intended to be complex beam system boundary conditions but somehow it turned out like this. Hello, I am trying to learn complex beam system designs and I sometimes struggle to assign boundary conditions. For example I am trying to design the lifting...
  9. Ahmad Kishki

    Disappearing terms in electrodynamics boundary conditions

    In the derivation of the boundary conditions we apply the integral form of maxwell's equations, but once we take a very small volume we find that some terms disappear like the displacement current as well as the time derivative of the magnetic field. Why do these terms disappear? For reference...
  10. N

    Griffith's E&M: Why is V_0(y) Missing from Equation 3.28?

    Does anyone here have a copy of Griffith's E&M? On page 128, condition III V=V_0 (y) when x = 0. Do you know why then value V_0(y) does not appear in in equation 3.28, V(x,y) = Ce^(-ky)sin(ky)? The author does not explain this.
  11. U

    Fermi Surface squashed by potentials

    Taken from my textbook: My understanding is that: One valence electron, 2 spin states -> Half-filled Brillouin zone Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries States nearer to zone boundaries get pushed down in energy further Since a fermi...
  12. A

    Electromagnetic boundary conditions for symmetric model

    I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential. From what I...
  13. O

    Robin boundary condition for cooling

    Hello all, I am solving a heat transfer problem for cooling of laminate plate in a cooling press and I intend to use a Robin boundary condition on one of the sides to evaporate heat away from the plate. The Robin boundary equation is specified thus: k∂T(t)/∂n + hT(t) = g(t) where k is the...
  14. A

    Dirichlet and Nuemann condition on the same boundary

    Hi, My final goal is to solve numerically Schrodinger's equation in 3D with some potential for the unbounded states, meaning that far away from the potential (at infinity) we may find a free wave and not something that goes to zero. The basic idea is that I have a particle in (0,0,0) that...
  15. S

    Standing Waves Under Boundary Conditions

    Homework Statement See the figure below. A thin pipe, open at both ends, with length 0.400 m and 1.0 cm diameter is placed vertically in a cylindrical bucket so that it nearly touches the flat bottom of the bucket, which has an area of 0.100 m2 . The air temperature is 22o C. Water is slowly...
  16. D

    Point belongs to the boundary - real analysis

    Hello, I have some trouble to solve this exercise Homework Statement E={ (-1)n (8n+7)/(4n-1) : n ∈ℕ} Show that 2∈[PLAIN]http://www.ilemaths.net/img/smb-bleu/derivepartielle.gifE Homework EquationsThe Attempt at a Solution We have to show that (2-r,2+r)∩ E ≠∅ and (2-r,2+r)∩ ℝ/E ≠∅ If I take...
  17. L

    Signature, boundary conditions and topology

    It is said that the metric tensor in GR is generally covariant and obey diffeomorphism invariance.. but the signature, boundary conditions and topology are not. What would be GR like if these 3 obey GC and DI too? Is it possible?
  18. I

    Mathematica Mathematica Ndsolve periodic boundary conditions

    Hello, Mathematica is very new to me. Please help. n=1,2,3...,10 and stepsize between n(2)-n(1)=0.1 It is periodic. I mean n(11)=n(1). i have a initial function which depends on n and i want to solve this equation by NDsolve like that u[n, t = 0] == 1/(2*n + 1) Do [ u[n, 0], {n, 0, 10...
  19. Coffee_

    Classical field theory, initial and boundary conditions

    Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...
  20. C

    MHB Applying Neumann Boundary Conditions in 1D

    Hi, I've been doing some work on the finite element method. I have been able to calculate the stiffness matrix and load vector and apply both homogeneous and inhomogeneous Dirichlet conditions but am stuck on calculating the Neumann conditions. I have the definition of it as...
  21. Feeble Wonk

    Boundary for an Infinite "Open" Space

    Please help! I read a statement by Lee Smolin (Time Reborn) that an "open" infinite universe necessarily has a "boundary", through which information would be received, which he used as an argument that cosmological models should prefer a "closed" universe approach. In fairness, he said that this...
  22. genxium

    What is the general boundary condition of wave-guides?

    By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides: ##E_{\parallel} = 0## -- (1)...
  23. C

    Need some help understanding boundary operator on simplicies

    I am currently reading up on some algebraic topology\differential geometry and have reached the section on de Rham theory. This is my first encounter with such notions and I am a little confused by what is meant when one applies a boundary operator to a simplex. Conceptually, I know that it...
  24. A

    Boundary conditions - unique solution

    I recently solved a differential equation with the solution: f(x) = Aexp(ikx) + Bexp(-ikx) with the periodic boundary condition f(x+L)=f(x). This condition leads to: Aexp(ikx)exp(ikL) + Bexp(-ikx)exp(-ikL) = Aexp(ikx) + Bexp(-ikx) (1) Now the way I figured out the constants A and B was that...
  25. rumborak

    Boundary absorption when simulating wave equation

    I wrote a wave equation simulation in C# a while ago, and while everything works fine, I am running into the expected problem that my simulation boundaries (ie the edges of the grid) reflect the waves coming to them. Obviously I want to keep the grid of reasonable size, so I looked into what...
  26. S

    Boundary Conditions for Hydrogen Schrodinger Equation

    If I am trying to derive the energy eigenvalues and quantum numbers for the hydrogen atom (basic hydrogen-1), I obviously need to solve the hydrogen Schrodinger equation and account for some boundary conditions. However, no website ever gives me the boundary conditions. What would be the...
  27. K

    Boundary of a chain, Stokes' theorem.

    Hi, I'm studying multivariable analysis using Spivak's book "calculus on manifolds" When I see this book, one strange problem arouse. Thank you for seeing this. Here is the problem. c0 , c1 : [0,1] → ℝ2 - {0} c : [0,1]2 → ℝ2 - {0} given by c0(s) = (cos2πs,sin2πs) : a circle of radius 1 c1(s) =...
  28. M

    MHB Find equation system for boundary value problem

    For $\Omega = (0,1)^2 \subseteq \mathbb R^2, f \in C(\Omega)$ consider the boundary value problem: $-\Delta u(x,y) + u(x,y) = f(x,y)~ \forall (x,y) \in \Omega \\u(0,y) = u(1,y)~ \forall y \in (0,1) \\ u(x,0) = u(x,1)~ \forall x \in (0,1)$ For discretization let be: $n \in \mathbb N,~ h=...
  29. Y

    Fluid mechanics question--slip boundary condition for gas?

    In solving the Navier Stokes equation, the typical boundary condition imposed on the tangential velocity at a solid surface is that of no-slip. However, it is known that for gaseous flow there always exists a non-zero velocity near the wall, especially at relatively big Knudsen number. Is there...
  30. J

    Wave equation boundary problem

    Homework Statement The question is Ytt- c^2Yxx =0 on the doman 0<x< +infinity where initia conditions are y(x,0) = e^-x^2 = f(x) , Yt(x,0) =x*e^-x^2 = g(n) and boundary condition is y(0,t) = 0 and c = 2 Homework Equations D'Almbert solution 1/2(f(x+ct)+f(x-ct))+1/2c∫ g(n) dn over the...
  31. W

    More on Universal Cover of a Surface with Boundary

    I am trying to understand in more detail the answer to: http://math.stackexchange.com/questions/673187/universal-cover-of-a-surface-with-boundary It is mentioned that the universal cover of a hyperbolic surface ##S## with geodesic boundary is a closed disk ##D^2## with a Cantor set removed from...
  32. 5

    Dealing with boundary conditions in system of ODEs

    Homework Statement I'm trying to plot the steady state concentration of yA vs. x, yB vs x and yu vs x using centered finite difference method. Homework Equations The Attempt at a Solution τ represents the dimensionless time variable, so steady state would mean that the left hand side of...
  33. R

    Periodic Boundary Conditions and which Hamiltonian to use

    Homework Statement Example Question: an electron with mass m is confined in a thin wire, with periodic boundary conditions applied in the x direction and harmonic potentials in the y and z direction. Write an expression for the wave functions in the ground state. Write down all the energy eigen...
  34. ssamsymn

    Find a Fractal Object with Known Boundary Term

    For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related. Also found some 1-d examples, but I need d>3 dimensional objects since my calculations...
  35. DivergentSpectrum

    What are the Boundary Conditions for Solving Poisson's Equation?

    As i understand, the purpose of laplaces/poissons equation is to recast the question from a geometrical one to a differential equation. im trying to figure out what are the appropriate boundary conditions for poissons equation: http://www.sciweavers.org/upload/Tex2Img_1418842096/render.png...
  36. V

    Heat Equation Boundary Conditions

    Homework Statement Let a slab 0 \le x \le c be subject to surface heat transfer, according to Newtons's law of cooling, at its faces x = 0 and x = c , the furface conductance H being the same on each face. Show that if the medium x\le0 has temperature zero and medium x=c has the...
  37. moriheru

    Boundary conditions of non relativistic strings

    I am currently reading Zwiebach and intend on reading Becker and Polchonski afterwoods. In chapter 4 he slves a partial differential equation with the Dirichlet and Neumann BC. My question is what the difference is between the two BC.(BC=Boundary conditions). Thanks for any help.
  38. G

    Normalizing boundary conditions

    Hi All, This is my first post on these forums. I am not looking for a solution to this problem but more interested in seeing if someone can point me to a resource that can explain the following. Thanks in advance for any help. I'm trying to solve a pde which gives a temperature profile. We...
  39. W

    Hyperbolic Manifold With Geodesic Boundary?

    Hi All, I am trying to figure out the details on giving a surface S a hyperbolic metric with geodesic boundary, i.e., a metric of constant sectional curvature -1 so that the (manifold) boundary components, i.e., a collection of disjoint simple-closed curves are geodesics under this metric. So...
  40. A

    Poisson equation with three boundary conditions

    I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions...
  41. V

    Solving Differential Eqs with Critical Point: Initial Conditions & Solutions

    Hello, I have two different discrepancies to this system: a) How and when is possible to have more solution of differential eq. or their system for same initial problem? For example this is happening in following system. It is written about this system: "Different value of constant \dot{M}=4\pi...
  42. aditya ver.2.0

    Is there a boundary present for our universe?

    My question is the same as the title 'Is there a boundary present for our universe?'
  43. M

    Boundary Layer Theory: Displacement & Momentum Thickness Explained

    Hi, could you tell the physical meaning of the displacement and momentum thickness of a boundary layer.And why the stream line diverges away from the body in the boundary layer to conserve mass?
  44. tom.stoer

    Definition of boundary, Stokes' theorem

    this is a rather stupid question regarding preliminaries for the definition of boundaries the question is whether every closed n-1 dim. closed submanifold C of an arbitrary n-dim. manifold defines a volume V; i.e. whether \partial V = C can be turned around such that V is defined as the...
  45. G

    Rectangular Potential Barrier Boundary Conditions with E=V

    Homework Statement I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0). Homework Equations...
  46. Vigardo

    Boundary conditions for a grid tube under combined loading

    Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...
  47. baby_1

    Unit vector in Magnetic boundary condition

    Hello I'm getting confused when I want to use magnetic boundary equation could you tell me how we define the unit vector(an) in this equation? for example you assume that we have two different region (A in red and B in yellow) which vector (1,2,3,4) is right for equation and which is right...
  48. E

    Electric surface current on a PEC

    Hello! When considering the boundary conditions for the electromagnetic field \mathbf{E}, \mathbf{H} on the surface of a Perfect Eletric Conductor we have: \mathbf{E} \times \mathbf{\hat{n}} = 0 \mathbf{J}_S = \mathbf{\hat{n}} \times \mathbf{H} the tangential electric field should vahish...
  49. E

    Electromagnetism equivalence theorem

    Hello! In http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf, pages 19-20, the Love's Theorem in Electromagnetism is declared. In presence of some electric sources \mathbf{J} and magnetic sources \mathbf{M} enclosed by an arbitrary geometrical surface S, which produce outside S a...
  50. CFDFEAGURU

    ANSYS Mechanical APDL - Rotating Boundary Conditions

    All, I recently completed a project where transient thermal boundary conditions are rotated around a cylinder for a general number of revolutions. In reality, the cylinder rotated but it was much easier to rotate the thermal conditions around the model in the ANSYS environment. I used 360...
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