Isotropic Definition and 123 Threads

Isotropy is uniformity in all orientations; it is derived from the Greek isos (ἴσος, "equal") and tropos (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

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  1. T

    What Does an Isotropic Cartesian Tensor Look Like in Higher Dimensions?

    Does anyone have a proof of what a isotropic cartesian tensor should look like in three or four dimensions?
  2. L

    Orienational order parameter in isotropic systems

    Hi everyone, I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter S is often used: S=\left\langle\frac{1}{2}\left(3\cos^{2}\theta-1\right)\right\rangle with \theta the angle of the molecule with a "director" (the magnetic field in...
  3. A

    Isotropic absorption and emission

    Something I've yet to understand: If a molecule has a dipole moment about a given access than absorption of a photon can readily occur. However, if it is possible to preferentially orient molecules by applying an electric field, would the rate of absorption be greatly increased or decreased? It...
  4. Z

    What Is the Intensity of Isotropic Sound Waves from a Loudspeaker?

    Homework Statement A loudspeaker emits sound isotropically with a power of 100db. Find the intensity in w/m at a distance of 20 from the source Homework Equations Intensity=power/area, For sound wave... power=ro*a*2pi^2*f^2*v*A^2, and I=2pi^2*ro*f^2*v*A^2. db=10log_10_(I/I_0_)...
  5. Vigardo

    Inflation of a clamped isotropic and thin circular plastic membrane

    Appreciated experts, I want to model the inflation of a thin and isotropic circular plastic membrane clamped by a ring. I need to determine the maximum deflection at the pole, stresses, strain, etc..., as a function of the applied pressure difference. The large deflection range complicates it...
  6. H

    Isotropic crystal and energy band

    Since all the directions are equivalent in an isotropic crystal, can we deduce that the energy band is exactly spherical?
  7. R

    Why wasn't the Big Bang an isotropic explosion?

    I'm sure I'm making a plethora of naive assumptions in this question, but I was just thinking that the Big Bang, or the birth of our universe should logically be isotropic if space and time is assumed to be homogenous and infinite in every direction.
  8. A

    Anisotropic instead of isotropic metric deriving acceleration

    In this documentation from Nasa a procedure to get to what I guess is the gravitational acceleration according to the post-Newtonian expansion at the 1PN-level for the spherically symmetric case is found: http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf The procedure is...
  9. M

    He most general form of the metric for a homogeneous, isotropic and st

    What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) signature) ds^2=dt^2+a^2(t)g_{ij}(\vec x)dx^idx^j Now the static condition. If I'm not mistaken...
  10. C

    Is there a connection between spinors and isotropic vectors in QM and QFT?

    I've been trying to wrap my head around spinors, and I think I'm beginning to understand the mathematical formalism, but one thing in particular continues to confuse me. Whenever I read anything mathematically rigorous on spinors, the authors refer to spinors being associated with isotropic...
  11. J

    How to Solve for L^2 and Lz in an Isotropic Harmonic Oscillator?

    Homework Statement Homework Equations The Attempt at a Solution
  12. R

    Model Steel for Large Deformation: Multilinear Isotropic Hardening

    I am trying to do a problem on Material Non-linearity , to model steel for large deformation , beyond yield point , I have tensile testing data for the steel ( in form of Engineering stress vs Engineering strain). for defining the model , I chose Multilinear Isotropic hardening now there...
  13. S

    Isotropic and homogeneous of space

    we say the universe around us is isotropic and homogeneous. it means that all direction and points are the same for some special class of reference. if this is true why we say in large scale universe is isotropic and homogeneous? it seems that the space, itself, to be isotropy and...
  14. B

    Linear isotropic dielectric mixture two materials

    Homework Statement Consider an x1:x2 mix of two linear isotropic dielectrics (by volume). x1+x2=1. On large length scales the mixture is homogenous and can be characterized with a dielectric constant ε_mix but on short length scales the material is granular so the dielectric constant is...
  15. M

    Elasticity, free energy of isotropic body mismatch

    I'm looking at the free energy of a body (theory of elasticity) but I can't really square the general expression with the one usually used for isotropic bodies. According to wikipedia (http://en.wikipedia.org/wiki/Elastic_energy), Landau & Lifgarbagez etc the general expression for the free...
  16. K

    Proving Homogeneous & Isotropic FRW Universe Energy-Momentum Tensor

    Hi everyone, It's not a real homework problem, but something I am trying to do that I haven't found in the literature. I am still stating the problem as if it was a homework Homework Statement Consider a FRW Universe. That is, ℝ x M, where M is a maximally symmetric 3-manifold, with a RW...
  17. S

    Isotropic antenna Transmit and Receive power

    Homework Statement Plot and compare the path loss (dB) for the free-space and plane-Earth models at 800MHz vs distance on a logarithmic scale for distances from 1m to 40Km. Assume that the antennas are isotropic and have a height of 10m Homework Equations Free space: P_R=\frac{P_T G_T...
  18. E

    Isotropic Observer: Are They Always At Rest?

    It is said that in the case of a homogeneous and isotropic spacetime, the surfaces of homogeneity must be orthogonal to the tangents to the world lines of the isotropic observer. Does this mean that the isotropic observers are always at rest in a surface of homogeneity?
  19. R

    How Does an Infinite Static Arrangement Collapse Under Gravity?

    Can anyone explain this to me? If we have an infinite amount of balls arranged in a kind of cubic matrix, in an infinite and static space...how the heck would that collapse on itself due to gravity? Thanks folks
  20. H

    Isotropic harmonic potential degeneracy of two identical particles

    Hello Everyone, I've come across the following question and can't seem to get the right answer out:Homework Statement Two identical particles are in an isotropic harmonic potential. Show that, if the particles do not interact and there are no spin-orbit forces the degeneracies of the three...
  21. J

    Transposing Terms for an Isotropic Oscillator

    Homework Statement The problem asks us to find the equation for an isotropic oscillator in the form of an equation for an ellipse. I'm in PHYS 212, Analytic Mechanics. Homework Equations x=Acost(ωt) y=5Acos(ωt-.6435) The equations I found for x and y. The Attempt at a...
  22. D

    Are spheres isotropic and cubes anisotropic?

    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...
  23. Spinnor

    Shoot a bullet at a half-infinite isotropic elastic solid.

    Say we shoot a bullet that travels in the theta = 0 direction (we are in spherical coordinates). Say the bullet strikes and sticks to a half-infinite isotropic elastic solid that begins at the theta = 90 degrees plane. Is it true that longitudinal waves generated by the bullets impact will be of...
  24. W

    Isotropic crystals & anisotropic crystals

    Alright my question is: why do single crystals properties vary with direction (anisotropic) when it is a perfect crystalline structure. I mean doesn't that mean that the atoms are ordered correctly so shouldn't that mean that at every direction its the same magnitude? I really need help because...
  25. B

    Prove that transversly isotropic materials have 5 independant elastic constants

    Homework Statement So I need to prove that transversly isotropic materials have 5 independent elastic constants. I can prove that an orthotropic material has 9 independent elastic constants. I need to use the transformation matrix to show that some of the 9 mentioned components are equal for...
  26. E

    Verifying that a tensor is isotropic

    I'm supposed to verify that this fourth-rank tensor is isotropic assuming cartesian coordinates: [A]_{}[/ijkl]=[δ]_{}[/kl][δ_{}[/kl] from what I gathered being isotropic means that it stays the same no matter what the rotation is I have no clue how to even start this problem or what I am...
  27. N

    Is Local the Same as Isotropic in Physics?

    Hi Say I have two expressions of the form F(r, t) = \int{dr'\,dt'\,\,x(r,r',t,t')g(r',t')} and F'(r, t) = \int{dt'\,\,x'(r,t,t')g'(r, t')} It is clear that F' is local in space, whereas F is non-local in space. Is it correct of me to say that F' describes an isotropic...
  28. K

    Prove Levi-Civita Symbol is Only 3D Isotropic Tensor

    My fluid mechanics textbook says so but gives no proof, I see why it's isotropic but I can't think of why it's the only isotropic tensor in 3D space.
  29. P

    Isotropic average of a cosine function

    Hi, please look at the following equation. \frac{3}{16}\frac{\nu_{Q}^{2}}{(1+K_{iso})\nu_{0}} \left(\frac{7}{2} \cos^{4}\theta - 3\cos^{2}\theta + \frac{5}{6}\right) In the paper I am reading, this is simplified considering the isotropic average of a cosine function to...
  30. S

    What Is the Difference Between Isotropic and Anisotropic Thermal Conductivity?

    Hi to all Can some one help me for below question: What is different between "isotropic thermal conductivity" with " anisotropic thermal conductivity" ? where and when we must use isotropic or anisotropic ? which one is more accurate? I solve an example in a FEM software and it is...
  31. E

    Is the Net Flux from an Isotropic Source Zero?

    Hi everybody. Apologies for asking what may be a very simple question, but in every textbook I've read, they say that the net flux through an area dA from an isotropic emitter is zero. But it also says that the sun is an isotropic emitter. Now hold on, the net flux from the sun is clearly...
  32. F

    Elastic and isotropic constitutive relationship

    Hi everybody, I have just a question about elastic and isotropic constitutive relationship Why does the stress tensor need an indeterminate hydrostatic term for an incompressible material? for both solids and fluids.
  33. P

    Legendre Polynomials - expansion of an isotropic function on a sphere

    Hello. I don't know what to do with one integral. I am sure it is something very simple, but I just don't see it... For some reason I am not able to post the equations, so I am attaching them as a separatre file. Many thanks for help.
  34. J

    How can the Universe be flat and isotropic?

    If I understand these terms at all, I don't understand how the Universe can be Euclidean, isotropic and finite in spatial extent, all at the same time. It seems to me that if there's a finite amount of matter in it, then it needs to be closed to be isotropic and it can't be isotropic if it's...
  35. C

    Clock in isotropic gravitational field

    1. How would clock in isotropic gravitational field, for example at centre of earth, tick compared to the clock at surface of earth? 2. How would clock in the center of Earth tick compared to the clock at center of sun?
  36. H

    3D isotropic harmonic oscillator vs. diatomic molecule

    The Hamiltonian of the diatomic molecule is given by H = p1^2 / 2m + p2^2 / 2m + 1/2 k R^2, where R equals the distance between atoms. Using this result, given in standard texbooks, I keep geting C = 9/2 kT instead of 7/2 kT for heat capacity. I've traced down my problem to the potential energy...
  37. R

    What is exact difference btwn ISOTROPIC and HOMOGENEOUS materials

    what is exact difference btwn ISOTROPIC and HOMOGENEOUS materials (kindly don't tell definition of those things)
  38. R

    Isotropic inhomogeneous metric

    Hi everyone, I have been looking for a spherical symetric, static, isotropic and inhomogeneous metric, so far I had found the LTB metric which could be one possible candidate, but i was thinking more like a inhomogeneous FRW metric. I appreciate your suggestions and thank you for your time.
  39. N

    2D isotropic mass-spring system, need to find maximum distance from origin

    Homework Statement I have a 2D isotropic mass-spring system. The mass is pulled a distance A=1m, and then given an upwards kick with a velocity v_0. The k=1, m=1kg. I need to find the furthest distance from the origin the mass will travel in its orbit. Homework Equations x(t)=A_x\cos(\omega...
  40. D

    Understanding Isotropic Decay: Solving Jackson's Problem

    I am trying to solve a problem from Jackson's and it says that the decay in particle's rest frame is more or less isotropic. I was wondering if somebody could help me figure the meaning of an 'isotropic decay' here. Thank you in advance.
  41. H

    General Relativity, Flat isotropic universe

    Homework Statement We are looking at an isotropic flat universe, with the metric ds^2 = dt^2 - b(t)^2(dx^2 + dy^2 + dz^2) I need to write down the energy conservation equation \frac{dV}{V} = -\frac{d\epsilon}{\epsilon + p} We have been given the solution to be 3\ln(b) = -\int...
  42. S

    Isotropic and kinematic ahrdening(metals)

    I've been trying to figure out difference between isotropic and kinematic hardening (modeling plasticity in metals). As I see,kinematic hardening can model reversible nbehaviour of metals (Bauschinger effect). In isotropic hardening, the yield surface increase in size, but remain the...
  43. T

    Intensity and Power of isotropic sound

    Homework Statement An electronic point source emits sound isotropically at a frequency of 3000 Hz and a power of 34 watts. A small microphone has an area of 0.74 cm2 and is located 158 meters from the point source. a) What is the sound intensity at the microphone ? b) What is the power...
  44. Spinnor

    Trying to understand isotropic vectors.

    From: http://www.sjsu.edu/faculty/watkins/spinor.htm "Let X=(x1, x2, x3) be an element of the vector space C^3. The dot product of X with itself, X·X, is (x1x1+x2x2+x3x3). Note that if x1=a+ib then x1·x1=x1^2=a2+b2 + i(2ab), rather that a2+b2, which is x1 times the conjugate of x1. A...
  45. C

    What is the Diffusion Tensor for Isotropic Media?

    Does anyone know how to write the diffusion tensor (coefficient) for a isotropic media? It should be a matrix but I can't find it in the literature. Maybe you guys know it or can help. Jackson doesn't have it. Cheers
  46. G

    Isotropic and Homogeneous material

    What's the difference between Isotropic and Homogeneous material? Thanks for your help
  47. D

    Kinematic and Isotropic Hardening

    Hello, Could anyone help explain what Kinematic and Isotropic hardening are. Any brief explanation or reference to a good book that explains these topics would be very useful. Thank you
  48. L

    Isotropic rank 3 pseudotensor help

    Can anybody show me how any isotropic rank 3 pseudotensor can be written as a_{ijk}=\lambda \epsilon_{ijk} for the isotropic rank 2 tensor case [i.e. a_{ij}=\lamda \delta_{ij} ], my notes prove it by considering an example i.e. a rotation by \frac{\pi}{2} radians about the z axis.
  49. L

    Show Isotropic Tensor: \epsilon _{{{\it ijm}}}\epsilon _{{{\it mkl}}}

    I've been asked to show that \epsilon _{{{\it ijm}}}\epsilon _{{{\it mkl}}} is an isotropic tensor using \epsilon _{{{\it ijk}}}\det \left( M \right) =\epsilon _{{\alpha \beta \gamma }}m_{{i\alpha }}m_{{j\beta }}m_{{k\gamma }} . Then to take the most general form for a fourth rank tensor...
  50. B

    Is the Universe Homogeneous or Isotropic?

    I recently read an article about whether the http://dailyphysics.com/" and/or isotropic. (the story is at the top - sorry I couldn't get the link to the permanent article to work here) “gargantuan ripples in the density of matter across the universe, known as baryon acoustic oscillations” is...
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