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5

A beam splitter works like a mirror that transmits part of the light. So there is always part of light that goes directly through without changing the direction. The rest gets reflected from the diagonal, which represents the reflecting surface. Therefore, beam coming from the left will be reflected downwards (as is shown in your case 1) but the beam ...

2

So, buckling is the bifurcation of static equilibrium. And thus: More technically, consider the continuous dynamical system described by the ODE $\dot x=f(x,\lambda)\quad > f:\mathbb{R}^n\times\mathbb{R}\rightarrow\mathbb{R}^n.$ A local bifurcation occurs at $(x0,λ0)$ if the Jacobian matrix $\textrm{d}f_{x_0,\lambda_0}$ has an ...

2

Do you understand how neutrino beams are made for such experiments? The beam from some more mundane particle accelerator is used to direct high energy particles (often protons) into a target which generates a spray of assorted products containing many pions and kaons. This secondary beam is filtered and selected for momentum by passing it through ...

2

Yes, and the formula you already have still works. Take z to be the optical path length: refractive index n times physical distance. A Gaussian beam in glass diverges in exactly the same way as in free space, only 'squeezed' in the z direction by a factor of n.

1

The bucking formula comes from a stability analysis of the restoring moment inside the beam. Actually as compressive forces are applied to a beam, its natural frequency drops, and when you reach the Euler's limit the natural frequency of the beam becomes zero. By definition this is the point the beam will not behave at all in a static fashion and will move ...

1

Since you seem to be using finite differences, you should look at the paper of Hadley, titled 'Transparent Boundary Condition for the Beam Propagation Method' - without any treatment of the boundary values you're automatically assuming a Dirichlet boundary condition. You can incorporate the boundary conditions into your square-root differential operator ...

1

Buckling is not limited to thin columns, it is also important, e.g., for thin shells under compression; for example, if pressure in a poorly designed tank is below atmospheric pressure, the tank can buckle under atmospheric pressure (it happens to large oil tanks, railway car tanks - you name it; you can easily find a lot of impressive images on the net).

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