Anisotropic Definition and 49 Threads

In this popular science article [1], they say that if our universe resulted to be non-uniform (that is highly anisotropic and inhomogeneous) then the fundamental laws of physics could change from place to place in the entire universe. And according to this paper [2] anisotropy in spacetime could...

The Taylor microscale in isotropic turbulence is given by: $$\lambda = \sqrt{ 15 \frac{\nu \ v'^2}{\epsilon} }$$ where v' is the root mean square of the velocity fluctuations. In general, for velocity fluctuations in three dimensions: $$v' =...

The cosmological principle holds that at large enough scales, the universe is homogeneous and isotropic (i.e. symmetrical). But, there is meaningful evidence from astronomy observations of anisotropy at the largest observable scales in the universe, which a new preprint (discussed below) sets...

I am learning about designing semiconductors but I had some issues understanding some things about the structure of Si. About lattice structure: 1) Why does an FCC has 8 atoms per cell? Doesnt has 14? About wafers 1) I know you can have wafers along different surfaces. What information can I...

Calculate the wavelength for an ##E_x## polarized wave traveling through an anisotropic material with ##\overline{\overline{\epsilon}}=\epsilon_0diag({0.5, 2, 1})\text{ and }\overline{\overline{\mu}}=2\mu_0## in: a. the y direction b. the z direction Leave answers in terms of the free space...

In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector. i) Calculate the angle between the...

The Friedman Equations is based on the cosmological principle, which states that the universe at sufficiently large scale is homogeneous and isotropic. But what if, as an hypothesis, the universe was anisotropic and the clustering of masses are aligned to an arbitrary axis (axial pole), how...

Homework Statement Hello, I'm studying anisotropic elasticity. One of the books I'm using is Lekhnitskii's. The book presents the general equations of the theory of elasticity for an orthotropic body as follows: Homework Equations The Attempt at a Solution However, when I combine the...

Hello everyone, I'm taking Mechanics of Materials II this semester which includes Anisotropic Hooke's Law, Plane Stress & Strains, Mohr Circle and so on. I need a video source of these topics. The videos on youtube mostly have bad camera position. I want something like coursera stuff but there...

Does a sphere made of an elastically anisotropic material (eg. a material of cubic symmetry) subject to an hydrostatic pressure retains its spherical shape ?

Here I am only considering 4 adjacent electrons in electron beam, especially the 2 electrons that are moving in tandem with velocity v. Moving charge will generate circular magnetic current. you can imagine magnetic flux as current, just like electric current. So, the question is same to find...

In an image processing paper, it was explained that a 2D Gabor filter is constructed in the Fourier domain using the following formula: $$ H(u,v)=H_R(u,v) + i \cdot H_I(u,v)$$ where HR(u,v) and HI(u,v) are the real and imaginary components, respectively. It also mentions that the real and...

Hi, I understand stress, strain but when it moves on to 3 dimension anisotropic materials using tensors and stiffness matrices I get confused with einstein's notation. can someone please help me out in this regard to undrstand how stiffness and compliance matrices get reduced for monoclinic...

Hi This question may have already been answered elsewhere. If so please accept my apologies in advance. I am confused! The textbok(s) I am reading describe a whole bunch of different causes for there being temperature fluctuations in the CBM, so I am confused about which one(s) of these...

Regarding the anisotropic etching of the (110) silicon wafer, why will the (110) oriented wafers form perpendicular trenches with the (111)?

Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...

Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...

Hi all, I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...

I can understand the derivation of bulk modulus (K) for isotropic material. However I have difficulty to do the same for anisotropic material. to start with we have the definition: mean_stress = K * (strain_xx+strain_yy+strain_zz) My question is for anisotropic material: Is mean_stress =...

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...

Hi, I am in the middle of revising for and a classical electromagnetism exam, and I've hit a wall when it comes to tensor equations. I know that for anisotropic materials: J=σE and E=ρJ And that in component form the first equation can be written as J_i = σ_{ij} E_j What I'm wondering...

Hi, I am in the middle of revising for and a classical electromagnetism exam, and I've hit a wall when it comes to tensor equations. I know that for anisotropic materials: J=σE and E=ρJ And that in component form the first equation can be written as J_i = σ_{ij} E_j My question is, does...

Hey guys! (I am not sure if I should post this thread in Physics or Mathematics) I have had some issues with developing expressions for the polarizations (material displacement) of waves propagating in anisotropic media. To bring you guys up to speed I have to start a few steps before the...

I working on a problem involving periodic vs. non-periodic 2-d anisotropic linear oscillators. I am trying to understand why it is that for a ratio of angular velocities that is rational, the motion of the oscillator is periodic. Versus the case where the ratio of angular velocities in...

Hello! (I am sorry for probable mistakes. English is not my native language. I have never written anything about mathematics and physics in English.) I have an electrostatic problem. I need to find an electric potential \psi (\vec{E}=-\nabla\psi) in anisotropic, inhomogeneous medium...

Hi all, I'm working on a heat transfer problem with a gas stream in a tiny tube. At my dimensions and flow rates, the flow still has a parabolic velocity profile. The mean radial velocity of the gas is zero, and I've treated the radial aspect of the heat transfer as strictly diffusion...

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...

Hi all: I have a question about the anisotropy properties of SINGLE CRYSTAL. The definition of the isotropy in WiKi is that the properties of the materials are the identical in ALL directions. If so, none of the single crystal is isotropic even though you can find such XYZ planes that the...

Hey, I was going over my electromagnetics course material and I realized we didn't learn much about anisotropic mediums (and still we had some homework questions about them). I'm trying to find some information about transition between anisotropic mediums, or even to be more specific -...

Hello All If there is spherically symmetric gaussian charge density (http://en.wikipedia.org/wiki/Poisson%27s_equation) \rho(\mathbf{r})=\frac{q_{i}}{(2 \pi)^{3/2} \sigma^3} e^{- \frac{\lvert r \rvert^2}{2 \sigma^2}} then it will have have potential \phi(r) by solving Poisson equation...

Hello, I'm brushing up on my heat transfer / vector calculus, when I realized that my notes were all for isotropic heat transfer. i.e. q(vector) = k(scaler) del(u) However, there are cases, such as pyrolytic graphite where the thermal conductivity, k, cannot be described as a scaler...

I need to calculate the density of states for a dispersion relation which is like the free electron dispersion, but with one effective mass in the kx, ky directions, and a different effective mass in kz. So I need to integrate the inverse gradient of E(k) over a surface of constant energy, ie...

Homework Statement The particle with the mass m is in 2D potential: V(r)=\frac{m}{2}(\omega_x^2x^2+\omega_y^2y^2),\quad \omega_x=2\omega_y, and is described with wave package for which the following is valid: \langle x\rangle (0)=x_0,\ \langle y\rangle (0)=0,\ \langle p_x\rangle (0)=0\...

Homework Statement have band dispersion \epsilon = \epsilon_c + \frac{h^2 k_x^2}{2 m_x} + \frac{h^2 k_y^2}{2 m_y} + \frac{h^2 k_z^2}{2 m_z} Show density of states is g(\epsilon) = \frac{m^{3/2}}{\pi^2 h^2} \sqrt{2|\epsilon - \epsilon_c|} Homework Equations 2 \frac{d\vec{k}}{(2\pi)^3} =...

Homework Statement Consider a particle of mass m moving in a 3D-anisotropic oscillator potential: V(\vec{r}) = \frac{1}{2}m(\omega^{2}_{x}x^{2}+\omega^{2}_{y}y^{2}+\omega^{2}_{z}z^{2}). (a) Frind the stationary states for this potential and their respective energies. Homework Equations...

What Does "Anisotropic Effective Mass" Mean? I'm reading "The Defintion of Mach's Principle" by Julian Barbour: http://arxiv.org/abs/1007.3368 from July of this year, and it contains a paragraph (Section 9 bottom of page 23) I do not understand, the beginning of which says: I have...

If I am given that mica has a modulus of 52GPa parallel to the c-axis and 179 GPa perpendicular to the c-axis, how do I figure out the elastic modulus of a polycrystalline mica where grains are oriented randomly?

The Anisotropic World What is the design of our Universe? Why it is not things that are important but the symmetry principles? What is the origin of the inconceivable effectiveness of mathematics in natural science? Is there any scientific proof of the Pythagoras idea that everything is number...

I've stumbled upon a problem whilst doing my master thesis The problem is to construct the anisotropic conductivity tensor for a material that exhibits Anisotropic magnetoresistance. The problem has left me quite baffled, and coming to think of it, I've never seen a proper treatment of...

Hi guys Please take a look at this familiar picture: http://www.astr.ua.edu/keel/galaxies/wmap_map.jpg Does this imply that the universe was not perfectly homogeneous or that it was anisotropic at the time of photon-decoupling? Since the CMB-fluctuations are because of the different...

i find in the literature 1. space is homogeneous and isotropic and time homogeneous, at least if judged by observers at rest in S(0). 2. in the isotropic system S(0) the velocity of light is "c" in all directions, so that clocks can be synchronized in S(0) and one way velocities relative to...

It turns out that this work has a timely significance. In reacting to Martin Bojowald's bounce article in July 2007 Nature Physics one or more blog personalities spoke as if they understood LQC to deal only with the homogeneous and isotropic case. It doesn't. Current LQC does not only deal with...

Hi, I'm constructing an interferometry experiment, in which I'm using a Michelson-Morley-type interferometer. However, the only beam splitter I have which preserves polarization is physically small (a few mm), and so in my setup the beam in each arm is not split. The reflection off the mirror...

CONGRATULATIONS TO Martin Bojowald! http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1137v1.pdf Lattice refining loop quantum cosmology, anisotropic models and stability Martin Bojowald∗ 09 April 2007 Standard Theory SU(3)xSU(2)xU(1).…. String …. Have not done it. He is the first to...

Anisotropic speed of light?? I hope this paper is appropriate to discuss here, as it demonstrates some interesting, if highly controversial, results. http://xxx.lanl.gov/abs/astro-ph/0608223" If you are interested in learning about relativity, avoid this thread, if you are an expert I'd love...

we have a non magnetic but anisotropic dielectric medium which has the following relationships between D and E Dx = k1*Ex, Dy = k2*Ey, Dz = k3*Ez we have to show that waves propogate in the z-dir'n at one speed only. I can't get the wave eq'n to fall out. Usually you just use...

Do you aggree that there is an inertial reference frame in which light in free space propagates isotropically whereas in all other inertial reference frames its propagation is anisotropic?

http://arxiv.org/abs/astro-ph/0602377.

The cosmological models of Lemaitre-Tolman-Bondi describe spherically symmetric universes with isotropic but inhomogeneous space, i.e. there are concentric shells with different mean mass densities. The LTB line element is: ds^2 = -dt^2 + \frac{(R'(t, r))^2}{1+2E(r) r^2}dr^2 + R^2(t...