Components Definition and 949 Threads

I know that taking the scalar product of the harmonic (Laplacian) friction term with ##\underline u## is $$\underline u \cdot [\nabla \cdot(A\nabla \underline u)] = \nabla \cdot (\underline u A \nabla \underline u) - A (\nabla \underline u )^2 $$ where ##\underline u = (u,v)## and ##A## is a...

Hello, I am looking to build an LED Panel for a film/video application. I have a few specific requirements in mind. 1) Color Accuracy beyond general CRI ratings. 2) Flicker Free to Camera (What specifications in LED drivers should I be looking for to ensure this flicker free application?) 3)...

For example, we have this two potencial wells approaching, the electron is confined in one. the final appearance will be like this: THEN, if we know a wave packet is formed by many frequencies, but in a potencial well there are just few frequencies allowed, energy levels, so let's say, one...

I have read many GR books and many posts regarding the title of this post, but despite that, I still feel the need to clarify some things. Based on my understanding, the contravariant component of a vector transforms as, ##A'^\mu = [L]^\mu~ _\nu A^\nu## the covariant component of a vector...

Hello, everyone. :) All I could gather is that, if I'm correct, lattices are spans of the column vectors of the matrix within the "LAT()" notation and the X and Y occurrences are unit placeholders (such as the pixel unit (since this is in the context of image processing)). And, as an attempt...

Hi, I have a simple question but I want to be 100% sure that my reasoning is correct. Take a look at this picture showing forces acting on an airfoil: Green forces (X and Y components) are known from CFD software but I need the values of blue components (lift and drag). Of course for zero...

Hello, Anybody have any good sources of mixed up old electrical components? For example: an old drawer full of mixed up resistors and capacitors; wax caps and jumbled up stuff? I have a HUGE jar that I am trying to fill up with this type of thing for my lab and was just wondering if anybody...

hello, I am new here, nice to meet you here. I want to learn knowledge related to electronic components, can you recommend me some books or online website for me to study? thanks in advance

Dear all, I'm having a small issue with the notion of Lie-derivatives after rereading Carroll's notes https://arxiv.org/abs/gr-qc/9712019 page 135 onward. The Lie derivative of a tensor T w.r.t. a vector field V is defined in eqn.(5.18) via a diffeomorphism ##\phi##. In this definition, both...

Hi, I understand and I'm sorry that there are going to be many loopholes in what I'm trying to put together and that too without any mathematical formulation but I don't even know where and what to start with. Suppose we have a finite length insulated hollow cylinder filled with with air at 1...

Hello everyone, I was wondering which field of study teaches how to make electronic components. For example, I would like to learn how to make resistors, caps, led, transistors... I have more or less of the theory, such as what the Dirac gaps are, if we talk about semiconductor... But what I...

Anyone know how to derive ##u^0=\frac {dt} {d\tau}=\frac {1} {\sqrt {1-\mathbf {v}^2}}## and ##u^j=\frac {dx^j} {d\tau}=\frac {v^j} {\sqrt {1-\mathbf{v}^2}}##?

This was my attempt at a solution and was wondering where did I go wrong: -\frac{\partial}{\partial p_\mu}\frac{1}{\not{p}}=-\frac{\partial}{\partial p_\mu}[\gamma^\nu p_\nu]^{-1}=\gamma^\nu\frac{\partial p_\nu}{\partial p_\mu}[\gamma^\sigma...

Our problem involves a graph G that is simple and connected, where every biconnected component is a cycle that has at least four vertices in it. The maximum number of components we can get from removing a cut vertex is 4, and we are asked to find tight bounds on the chromatic number of G. My...

The problem is for us to consider a biconnected decomposition, and that proof for a graph, the degrees of all the vertices in a graph is even iff the degrees of all the vertices in all of its maximal biconnected components is even For solving that if the degrees of all the vertices in the...

The first part I'm fairly sure is just the regular gradient in polar coordinates typically encountered: $$\nabla u= \hat {\mathbf e_r} \frac {\partial u} {\partial r} + \hat {\mathbf e_\theta} \frac 1 r \frac {\partial u} {\partial \theta}$$ or in terms of scale factors: $$=\sum \hat...

F1x = 120. Cos 300 = 103.92 ; F1y = 120.sin 300 = 60N F2x = 150.cos 110 = - 51.30, F2y = 150.sin 110 = 140.95 why taking angle 110 instead of 70 for finding the magnitude of F2 in X and Y components?

Hi all, A solution contains ions, positive and negative ones (i.e k+ cl-). Is there a simple but passive way (without adding any kind of energy) to separate by exemple the potassium ions from the solution? (IMHO, I do not think so)

I attempted to use the relation that B = gradient crossed with A; however, I'm strguggling with how to setup the question. I think that alternatively the problem can be solved using the Poisson equation that A(r) = (mu/4pi)integral{(J(r)/r}dtau; however, here to I am struggling with the setup.

I am really stuck on part a. For part b: strain x = (1/19*10^9)(137000+.36*95000) strain y =(1/19*10^9)(-95000-.36*137000) Is this right? For part c: sigma xx'=(sigma x+sigma y)/2+(sigma x -sigma y)cos(2*28)/2+sigma xy sin(s*28) sigma yy'=(sigma x+sigma y)/2-(sigma x -sigma y)cos(2*28)/2-sigma...

I feel this is an easy arithmetic, but I can’t figure out how to get it to work out. Let’s say I have an overall metric of sales data that can be broken down by 5 sales reps. In 2016, each rep makes a certain number of phone calls and their success rate is # of sales divided by # of calls...

Homework Statement I have been working on defining the transpose in a tensorial view using the kroneck delta tensor.Homework Equations I will use tensor notation The Attempt at a Solution Let Tjk be a 2nd level tensor: (Tjk)TP = Tkj My first attempt is: δjkTjk δkj = Tkj However if tensor...

Hi, The origin of this question was contemplating how to express the impedance of an inductor as a function of frequency, for non sinusoidal voltage wave-forms such as triangle waves, but in particular rectangular pulse trains. So going back to basics, I watched this video: He derives the...

Hello, In 2D kinematics, the acceleration vector ##a(t)## can be expressed either in Cartesian coordinates ##a_x## and ##a_y## or in polar coordinates ##r## an ##\theta##. It depends on the problem. But it is also possible to express the acceleration ##a(t)## in the so called "intrinsic...

Homework Statement Theorem: If ##X## is a topological space, each path component of ##X## lies in a component of ##X##. If ##X## is locally path connected, then the components and the path components of ##X## are the same. I need help locating errors in my proof. Please help. Homework...

In this context the author is deriving the net outflow through 2 surfaces.to do so he is calculating the difference between x components ofthe vector V which is; so now my question is here the 2 surface are parallel to each other and have same area so their respective x components should be...

I am reading Miroslav Lovric's book: Vector Calculus ... and am currently focused n Section 1.3: The Dot Product ... I need help with an apparently simple matter involving Theorem 1.6 and the section on the orthogonal vector projection and the scalar projection ...My question is as follows: It...

Hi! I was trying to understand circular motion and came across two problems. I would really appreciate if you could help me with those. Question 1: In the picture below let's assume that the angle θ is 1 radian, i.e. 57.3°, radius is 1 m. It would mean that the length of arc AB is also 1 m...

Homework Statement (Translating from a Polish high school textbook, so if anything is unclear please let me know). An object moves on a trajectory described by the parabola ##y=\frac{1}{2\lambda}x^2## such that the ##x## component of its velocity is constant and equal to ##v_0##. The...

Homework Statement Prove that $$\bf{ a \times ( b \times c ) = \phi [ b(a \bullet c) - c(a \bullet b) ]} $$ for some constant phi Homework EquationsThe Attempt at a Solution So I have used the unit vectors i, j, and k and found out that phi = 1. With the main part of the proof, we are not...

Homework Statement A box of mass X kg hangs motionless from two ropes, as shown in the diagram. The angle of rope 1 is specified amount of degrees. Choose the box as the system. The x-axis runs to the right, the y-axis runs up, and the z-axis is out of the page. What is the magnitude of |F2|...

Let's assume this is hypothetical...and may need to be in a different forum... but I am just looking for advice, maybe I am being too critical or perhaps not critical enough to get the proper inspections and repairs. Assume my 2016 Chevrolet 1500 (2419kg) was struck by a vehicle of mass...

Why are the resultant's X and Y components of two forces equal the sum of the X and Y components of the two forces?

Hi, So recently my charging port on my phone broke so I tried to charge it up internally (Connecting to the inner side of micro USB port from the circuit board) which I regret doing... As I was holding the charging wires in place I the wire slipped and touched the data wires in the micro USB...

Homework Statement Before diving into the quantum-mechanical superposition principle, let’s get some practice with superposition in classical physics. Consider an electromagnetic wave propagating in the z-direction, which is a superposition of two linearly polarized waves. The electric field...

Hello! (Wave) Let linear map $f: \mathbb{R}^3 \to \mathbb{R}^2$, $B$ basis (unknown) of $\mathbb{R}^3$ and $c=[(1,2),(3,4)]$ basis of $\mathbb{R}^2$. We are given the information that $cf_s=\begin{pmatrix} 1 & 0 & 1\\ 2 & 1 & 0 \end{pmatrix}$. Let $v \in \mathbb{R}^3$, of which the coordinates...

I've noticed that a very easy way to generate the Lorentz transformation is to draw Cartesian coordinate axes in a plane, label then ix and ct, rotate them clockwise some angle \theta producing axes ix' and ct', use the simple rotation transformation to produce ix' and ct', then just divide...

Homework Statement Two points in a plane have polar coordinates P1(2.500m, pie/6) and P2(3.800m, 2pie/3) . Determine their Cartesian coordinates and the distance between them in the Cartesian coordinate system. Round the distance to a nearest centimeter.Homework Equations Ax=Acosθ Ay=Asinθ...

Homework Statement Hello everyone, I am currently experiencing a problem plotting harmonics in Excel. I'm only able to plot the fundamental wave properly, I can't figure out how to plot the 3rd and 5th harmonic as they have a different frequency. Can you point me in the right direction...

I'm interested in making a Thompson's Coil after seeing my University's physics II (EM) professor demonstrate Faraday's Law to us using it. It seems like a fun device to demonstrate various principles of Electromagnetism to lay people (Induced Voltage by Faraday's Law, Resistive Heating...

Hello, Riemann tensor ##R^i_{jkl}## 4 indexes, and it should be matrix 16x16 in spacetime if we have time coirdinate - 0 and space coordinates -1,2,3. But how should I write the components to matrix? For example ##\begin{pmatrix}R^0_{000} & R^1_{000} & R^2_{000} ... \\ R^0_{100} & R^1_{100} &...

Homework Statement I don't understand how to form an equation using the knowledge that, 'When ##t=4##, ##P## is moving parallel to the vector ##\mathbf {j}##'. I've seen the solution, and not a single part of it makes sense. I haven't attempted any question like this before, so I have no idea...

Homework Statement in the picture. Homework Equations F=ILcrossB Along with the original question, the other picture contains the solution with different numbers. I was just wondering why when finding the force on the wire instead of making dl= R*dtheta and going through the integration and...

I ran across the explanation below of a car on a banked turn (no friction) on a High School teacher's website. I'm assuming this is incorrect, because how can the normal force in this situation equal mg/cos when an object on an inclined plane has a normal force equal to mg * cos? The high...

This has been bugging me for a while, and I feel like I’m missing or misunderstanding some crucial piece of information, so please advise me: the scalar product of two vectors (say ##\mathbf v## and ##\mathbf w##) is given using the metric: ##g_{\alpha \beta} \mathrm v^{\alpha} \mathrm...

Homework Statement Homework Equations I'm guessing trigonometric identities such as sin(a)cos(b) = 1/2(sin(a+b)+sin(a-b)) might be relevant. The Attempt at a Solution I've been thinking of some way to get an approximation of each harmonic by working with the Fourier series representation...

I am working (as an undergraduate) assisting in the repair of a JEOL Scanning Electron Microscope. Without going into too much detail, some components of the SEM control system may be damaged and need complete replacement. I am working with an instrument engineer who has mentioned that he has...

Hi PF! Let's say I have a 3X3 matrix ##K## and a much larger square matrix, call it ##M##. I am trying to add ##K## into ##M## along the diagonals. It's difficult for me to explain (and hence code) so I've attached a picture. Does anyone know a good way of doing this? Notice overlap is only in...

Homework Statement Two balls with mass m and 4m collide at the location x=y=0 and stick. Their initial velocities just before the collision can be represented as v1=(i+j) v and v2=(j-i)v' respectively. Their final velocity vf makes an angle θ with the +x axis. Find v and v' in terms of vf and...

Hi I am studying force components on a inclined plane. I understand the concept of breaking vectors into X , Y Components relative to the horizontal plane however what I can't seem to make sense of is how the ratios of a triangle and the main input force being the hypotenuse of the triangle...