How to Repair, Restore, or Reinstall Grub 2 with a Ubuntu Live CD

Mount the partition your Ubuntu Installation is on (with the root partition "/").


sudo mount /dev/sdc2 /mnt

sudo mount --bind /dev /mnt/dev &&
sudo mount --bind /dev/pts /mnt/dev/pts &&
sudo mount --bind /proc /mnt/proc &&
sudo mount --bind /sys /mnt/sys


sudo chroot /mnt

grub-install /dev/sdc # grub-install --recheck /dev/sdc
update-grub

exit &&
sudo umount /mnt/sys &&
sudo umount /mnt/proc &&
sudo umount /mnt/dev/pts &&
sudo umount /mnt/dev &&
sudo umount /mnt



Reboot your computer, and Grub2 screen will be on.
 

Why V_dc >> V_ac for electrostatic actuators ?

Consider a parallel plate capacitor with one fixed and one free electrode. If a voltage V is applied to the capacitor, the free electrode will experience an attractive electrostatic force of magnitude 

F = 1/2*e*A*V^2/g^2, where e is the dielectric constant of the material between the plates, A is the capacitor area,V is the voltage across the capacitor, and g is the electrode spacing. Because the force depends on the square of the voltage, the second harmonic of the applied voltage will be generated. For operation at the first harmonic, a dc bias Vbias is applied to the capacitor along with the RF signal such that V(t) = Vbias + Vac cos (wt +phi) . By making the bias voltage much larger than the time varying voltage, the dominant time varying force becomes F=e*A*Vbias*Vac/g^2 cos (wt + phi ).

Acoustic model for far distance propagation coupling with CFD

Is the acoustic model for far distance propagation coupling with CFD can handle sound propagation over different media like air, water?

Direct prediction of far‐field noise in a CFD code is made somewhat impractical because of the meshing and timestep requirements.

• First, you must solve the time accurate compressible Navier‐Stokes equations. Accurately resolving the propagation of acoustic waves imposes timestep restrictions such that the Courant number is in the range of 1‐2 at most. This restriction can be highly costly. 
• Second, the CFD mesh must span all the way to the reception points with enough spatial resolution to directly resolve acoustic waves over the propagation distance with minimal to no numerical damping. 

These requirements do not make practical sense for many industrial applications. Practical predictions of farfield sound pressure levels are made by first starting with a time accurate CFD calculation of the near field region. Boundary and interior noise sources are taken from the transient CFD calculation, and used as input to an acoustic code using the Lighthill analogy. This method is however a one‐way approach that ignores coupling between acoustics and the flow field, and assumes the fluid behaves as an ideal gas.