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  1. H

    Transfer of Quantum State

    An experimenter, A, has prepared four photons with known polarization states. In another lab, experimenter B has prepared four photons with random orientation. Is it possible, for the photons prepared by B, to take the polarization states of the photons prepared by A, without B knowing the...
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    Coefficient of (1+x+x^2)^n

    I need to find a formula that describe the sequence shown above. (The sequence is highlighted.) I am aware that the sequence is the coefficient of the polynomial (1+x+x^2)^n, and have tried using Taylor's expansion. Still, I can't get a nice formula that describe the sequence. Any help/hint...
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    Modelling of Car Impact

    I am trying to model the following situation: Let say i have an obstacle with known mass, and I know the coefficient of static and dynamic friction between the obstacle material and the floor. A car travelling at a fixed velocity is to impact the obstacle. For simplicity i will first consider...
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    Hyperplane math homework

    Homework Statement [PLAIN] [Broken] The Attempt at a Solution I understand that the determinant represents the set of points, x in R_k which lies in the hyper plane passing through the points p1, p2.....p_k. I also know, that if the...
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    Wavefront Simulation using Geometry Optics and Physical Optics

    I am required to simulate the propagation of a the wavefront produced by a laser light (about 633 nm) passing through a system of lens and undergoes a few reflection. What I did at the moment is to do ray tracing, record the optical path length of each ray, then connect every point of the same...
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    Solving Laplacian Equation Analytically

    I wish to solve a 2D steady state heat equation analytically. The boundary is a square. The top side is maintained at 100 C, while the other sides are maintained at 0 C. The differential equation governing the temperature distribution will be the laplacian equation. To solve the equation...
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    Calculate the change in entropy of the universe

    Homework Statement Calculate the change in entropy of the universe as a result of the following process: A copper block of mass 0.4 kg and heat capacity 150 JK-1 at 1000C is placed in a lake at 100C. 2. The attempt at a solution change in entropy (copper) = mc ln (T2 / T1)...
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    Reversibility of Otto Cycle

    Theoretically, we can have reversible isochoric expansion and isochoric compression. Is Otto Cycle reversible then? I read that the efficiency of all reversible engine between two heat reservoir would have the same efficiency. However, since the efficiency of an Otto Cycle is lower than...
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    Infinitesimal Strain Tensor

    I read that [Broken] I am not so sure about the last term. Shouldn't it be [Broken] instead?
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    Del Operator for Cylindrical Coordinate [Broken] Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?
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    Divergence Theorem [Broken] I am stuck at the last step. Can anyone give some hints? Thanks in advanced.
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    Magnetic moment

    Quote from "Spin Stabilized Magnetic Levitation of Horizontal Rotors", L. A. Romero, from SIAM Journal of Applied Mathematics. "Suppose we have a rotor that has two equal dipoles on the axis of symmetry, each pointing in the direction of the axis of symmetry. We suppose that the magnets are...
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    The commercial toy, Levitron, can achieve stable magnetic levitation

    The commercial toy, Levitron, can achieve stable magnetic levitation due to gyroscopic stabilization and axis precesion. The Levitron toy sold in market has a vertical spinning axis, and so far I have not found a variation with horizontal axis. Is it allowed in Earnshaw's theorem, for a...
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    Visualization of Magnetic Field

    Suppose I have an electric motor, and I wish to visualize how the magnetic field change by time. Is it possible for me to visualize the magnetic field line without using iron powder or ferrofluid? Is it possible to have multiple hall sensors to detect magnetic field strength in various location...
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    N-doped region tend to flow to the p-doped region

    When a diode is first manufactured, the electrons in the n-doped region tend to flow to the p-doped region due to diffusion effect. In the process, a depletion region is formed until the electric field in the depletion region cancel out the diffusion effect. Hence an equilibrium is reached. (or...
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    Earnshaw's Theorem and a photon

    Imagine there is a hollow sphere charged with positive charge, distributed evenly. Then a proton is placed in the cavity. Would the proton levitate stably in the middle of the cavity? By Earnshaw Theorem, any configuration of system with fixed field strength which obey inverse square law will...
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    Demagnetization of a permanent magnet

    When we magnetize a ferromagnetic material, we provide an input of energy. Is it possible to demagnetize a magnet, and convert a fraction of the energy to usable work? (Of course, this is not a useful way to generate work, and some fraction of the input energy is lost)
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    Hollow Spherical Magnet

    Is it possible, thematically or practically, to construct a hollow spherical magnet with inner surface and external surface of opposite polarity? How would the magnetic field looks like? Assuming it is possible, what would happened if I place a smaller hollow spherical magnet, but of the...
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    Motor which operate solely on magnet and gravity?

    I received an assignment from my professor which sounds like follow: "Suggest a motor which operates only on magnets and gravitational force." While I did make a search online and found some model which seems to work, I am sill a little skeptical (There are videos online, but none of them...
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    Newtonian Motion Simulation

    Homework Statement [Broken] [Broken] Homework Equations Euler's Method, Runge Kutta 4th Order Method The Attempt at a Solution I have solved the motion equation for the above question using...
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    Bluetooth Remote Control

    Is it possible to remote control electric appliances directly using a bluetooth enabled cell phone (without PC and laptops as intermediate)?
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    Angular acceleration of a pendulum on an accelerating train

    If I hang a pendulum on the ceiling of an accelerating train (with an initial angular displacement), how would the angular acceleration be affected? My intuition told me that the angular acceleration of the pendulum should be affected by the acceleration of the train. But...whether the...
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    Bessel function

    Homework Statement [Broken] [Broken] Homework Equations The Attempt at a Solution [Broken] May I know which part of my solution...
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    Static, Moment

    Homework Statement The wall crane in Fig. 3 supports a load of 800 N. Determine the horizontal and vertical components of reaction at the pins A and D. Also, what is the force in the cable at the winch W?
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    Range of x[0] for Newotn Raphson method to be valid

    Homework Statement Using Newton-Raphson's method, find the solution to the equation x = tan x in the interval \pi/2 to 3\pi/2. Find an interval, in which any starting value generates a sequence that converges to the solution . Homework Equations Newton Raphson's Method The Attempt...
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    Limit of sequence

    Homework Statement an+1=an/2 + 1/an Prove that the above sequence converge and find the limit. Homework Equations The Attempt at a Solution I have used Maple 12 to compute up to 10 term, using different initial value of a0. I found that the sequence is approaching square root of...
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    Equilibrium of Rigid Body

    Homework Statement Determine the reactions at the base of the light pole shown in fig.1 Homework Equations Summation of force and moment of a system in equilibrium is 0. The Attempt at a Solution The resultant force of due to the weight of the light pole and lamp is 185g N...
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    IR Spectroscopy

    Quote from Organic Chemistry, L.G. Wade, Jr.: "Not all molecular vibrations absorb IR radiation." "One of the component of an electromagnetic wave is E field. This field alternately stretches and compresses a polar bond." "If this alternate stretching compressing of the bond occurs at the...
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    Integral test

    Homework Statement The nth term for a sequence is the square root of [n/ (n^4 + 1)] Investigate whether it is convergence or divergence. Homework Equations Ratio test and integral test The Attempt at a Solution Ratio test will fail for this question, since no conclusion can be...
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    Rotational Motion of Celestial Body

    I understand that the Sun's gravity force provides the centripetal force for the Earth to orbit around it. However, what provides the torque for the rotational motion of Earth?