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Feb
20
comment Force from point charge on perfect dipole
The general formula for the force is, as you correctly stated $F=q\Delta E$, which is conveniently written in a geometrical form as the dot product $$\vec F=\vec\nabla\vec E \cdot q\Delta\vec r =\vec \nabla\vec E \cdot\vec P$$ Note that $\vec\nabla\vec E$ is a matrix. However, when you work in any other coordinate system, the gradient $\vec \nabla$ is no longer the simple expressions that you are used to. You can derive the formula for it by differentiating the expression $$\vec E=E_r\hat r+E_\phi \hat \phi+E_\theta\hat\theta$$ and remembering that the unit vectors are also space-dependent.
Feb
18
comment Showing constraint is nonholonomic
You can explicitly build an example that shows that these constraints are not path-independent.
Feb
16
comment Connection between momentum and energy
Answer: the question is ill-posed.
Feb
14
comment How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?
Each time you're making it worse! You want to do fracture? God forbid. References about fracture of amorphous solids: here and here and here and here.
Feb
14
comment How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?
Note that whenever irreversible deformation occurs, $\epsilon_{ij}$ is not even defined any more, as the reference configuration changes. So this whole approach of developing $$\sigma_{ij}=C_{ijkl}\epsilon_{ij}+\partial_t(\dots\epsilon_{ij})+\dots$$ is basically invalid. It seems, though, that what you're looking for is standard isotropic visco-elasticity. So grab the textbook I recommended and read the first few chapters. It's fairly easy.
Feb
13
answered Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?
Feb
12
awarded  Organizer
Feb
12
revised How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?
edited tags
Feb
12
answered How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?
Feb
10
comment Abstract, generic derivations of energy
You put the "Hamiltonian-mechanics" tag, so you know the answer. If your equations of motion are derived from an Hamiltonian, then the Hamiltonian can be considered as an "energy",
Feb
5
comment Symmetries of separable potential
I don't think the notation you use is standard. What are these symmetries? What does "separable" mean?
Feb
2
revised Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?
typos
Feb
2
answered Does the Banach-Tarski paradox contradict our understanding of nature?
Feb
1
answered Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?
Jan
29
answered One dimensional Schrödinger equation equation with initial condition, finding the probability of the particle's future position
Jan
22
comment What are conditions for the existence of a critical value (for a phase transition)?
The Hamiltonian has dimensions of energy. It must contain some interaction constant with dimensions of energy (in the Ising model - the interaction $J$. In liquid-gas transition - the Lenard-Jones energy scale, etc..)
Jan
22
comment How do electrical devices suck electricity?
Tiny correction: the question refers, most probably, to an AC case, where a factor of $\sqrt{2}$ has to be added.
Jan
22
comment What are conditions for the existence of a critical value (for a phase transition)?
I cannot imagine such a case. If the phase transition occurs as a function of $T$, this means that you're working with a Hamiltonian, and average expressions of the form $e^{-\beta H}$. And if you have a Hamiltonian, you have an energy scale.
Jan
22
comment What are conditions for the existence of a critical value (for a phase transition)?
If you set $k_b=1$, and there's no reason not to do so, then temperature is measured energy units. So clearly, if you multiply ALL energy scales in your system by 2, then $T_c$ will also be multiplied by 2. This is what I meant. I can't quite understand your question beyond that.
Jan
22
answered What are conditions for the existence of a critical value (for a phase transition)?