, 5) Show that k-ko-Ghki is equivalent to Bragg's law, i.e. 2dhkl sin θ where Ghk-...
Given a time-varying angle θ and a constant angle φ: Show that sin(θ(t) + (p) can be expressed as kisin(0(t)) + kcos(0 (t)) where kı and k are constants. (5 points) 5. where Kı
Problem:5 Show that [Ae(kx + Be-k] and [C cos kxD sin kx] are equivalent way of writing the same function of x, find the constants C and D in terms of A and B, and vice versa.
A sin(nkoa), where A and na Let us suppose that the interplanar force constant K is of the form, K = ko are constants and p runs over all integers. Such a form is usually expected in metals. Use this in the Force equation du(na) Fn = M t2 du(na) -K (2u(na) – u((n + 1)a) – u((n − 1)a)) = Mºu dt2 (1) Find oin terms of k and ko (ii) Find out (iii) Plot o’ vs k (iv)...
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4, determine the stagnation points of the flow, if any. Hint: For stagnation point (W.,Vo,V)-(0,0,0) @s 2
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
This is problem 1 chapter 5 from Ashcroft.Kindly provide neat
and step by step solution.
1. (a) Prove that the reciprocal lattice primitive vectors defined in (5.3) satisfy (2)3 b. (b2 x bz) = = (5.15) a,.az a3) (Hint: Write b, (but not b, or by) in terms of the a, and use the orthogonality relations (5.4).) (b) Suppose primitive vectors are constructed from the b, in the same manner (Eq. (5.3)) as the b, are constructed from the a....
Help please. I would really appreciate clear, full
explanation of the method used. like and comment are rewarded for
good answer.
(a) Let v(r) be a scalar function of r, where r V +y? +22 (i) Show that (i) If F Vu) evaluate Jc Fdr where C is straight line going from the point defined by vector r1 to the point defined by r2 (b) Consider a body with a surface defined by 2(x2 + y2) + 4z2 1 (i)...
Consider the n × n matrix M = In-Z(Z,Z)-1Z', where Z is n × K. i. Show that M is idempotent and find its rank. ii. In case Z is just the n x 1 unit vector, i.e. Z- (1,....1)', what form does the vector Mz take? Note that x is any n- dimensional column vector
Consider the n × n matrix M = In-Z(Z,Z)-1Z', where Z is n × K. i. Show that M is idempotent and find its...
Please show all work
Consider a plane wave -ik.r E(r) = Ege = Eye-i(k+x+kyy+kzz) (1.1) where Eo = amplitude vector constant in space (complex phasor with direction) = E.(w) = Ey(w)|eibe (1.2) k= Ýk +ý k+2 kg r = x + ŷ y + 2 z k(w) = k} + k + k Wype = (1.3) (1.4) 27 (1.5) (a) Using the fact that V E(r) = 0 in the absence of sources, and the vector identity V.(VA) = V(VA)...
show work
5) If Y-A × N × (75 + K/N), where K = 1000, N = 20, and A-10, what happens if K doubles and N doubles? A) Y is unchanged. B) Y increases by 50%. C) Y doubles. D) Y quadruples.
5) do = E•dA, where E = (28 V/m²) xy î - (8.3 V/m) sin(2z/n) k, and the area element dA = 0.45 dxdz j - 0.89 dxdy k. Find the expression for do by taking the dot product.