# Tagged Questions

The tag has no usage guidance.

272 views

### How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why? Please try to give a different explanation ...
65 views

### Eulerian mass conservation on a stream line to Lagrangian mass conservation

if the density of a fluid particle is conserved on a streamline, $$\frac{d\rho}{dt}=0.$$ Why does this mean $$\frac{\partial \rho}{\partial t}+(\mathbf{v}\cdot\nabla)\rho=0$$ is true everywhere? Why ...
76 views

### Partial derivatives vs total derivatives in thermodynamics

The specific heat of a system is defined as $$C_z = T \left( \frac{\partial S}{\partial T} \right)_{z=\text{const}}$$ Sometimes however, I find the same definition, but with total derivatives ...
41 views

53 views

### Dependence of scattering amplitudes on Mandelstam variables

It is well-known that scattering amplitudes in QFT are tensors, hence e.g. scalar amplitudes /written in momentum space/ depend only on the Mandelstam variables of the external momenta, involved in ...
44 views

### Specific heat at constant volume

Me and my friend came across this derivation is some lecture notes of our thermal physics module. We have been trying to calculate the partial differential of the internal energy but cannot get the ...
104 views

### Discrete Laplacian with geodesic distances

Normally, I have a a scalar function f(x,y), sampled on a two dimensional, regularly spaced grid in Cartesian coordinates. Evaluating the Laplacian of this function just requires the standard ...
161 views

Although I find it mathematically dubious, we said that $$\Delta \frac{1}{r} ~=~ -4\pi \delta^3({\bf r}).$$ Now, I was wondering is there a similar relation to the delta function if we look at $$\... 0answers 212 views ### Scale-invariant differential operator For example, the differential operator Laplacian is$$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$My questions are: Is it scale-invariant? what is scale-... 0answers 154 views ### Implicit Differentiation, A doubt v=v_c(\tau, t) is a smooth function and suppose we have a relation y_c(\tau,v_c;t)=0 when x_c is written in the form x_c=c+ty_c(\tau,v_c;t), c is real constant, t is real number denotes ... 0answers 14 views ### Why does the material derivative and transport theorem look different? Reynolds transport theorem says that  \frac{d\int\phi}{dt}=\int\left(\frac{\partial\phi}{\partial t} + \nabla\cdot(\phi\otimes v) \right)  Why is the material derivative not defined as what's ... 0answers 25 views ### Relation between differentiation of one-form basis and Christoffel Symbols If I want to covariantly differentiate a one form then I can write: \nabla_\beta \tilde p = \dfrac{\partial p_\alpha}{\partial x^\beta} \tilde \omega^\alpha + p_\alpha \dfrac{\partial \tilde \omega^... 0answers 41 views ### differentials in physics Often I find the following expressions in physics books: Say we have a current density \vec{j}=\rho\vec{v} through a surface \vec{F} of particles N in the volume V with the density \rho=dN/dV... 0answers 43 views ### Different subscripts for \nabla operators while deriving force on system of many particles Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy U(x,y,z)of the particle+field system: Total (external) force on ... 0answers 47 views ### Confused about something in Landau classical mechanics On page 7 in Landau and Lifshitz Mechanics He writes: We have L'=L(v'^2)=L(v^2+2ve+e^2) now the confusing part comes (for me): He writes: Expanding this expression in powers of e and neglecting ... 0answers 32 views ### What is the derivative of the length vector in the direction of the original unit vector? What is the derivative of the length vector? I am asking this question becuase I have seen, in Prof. M. S. Sivakumar's youtube video, the result that \dot{|r|} \hat{r} = \dot{r} Where,  \mathbf{r}... 0answers 35 views ### Advection Operator shift in scalar product Can someone help me with advection operator shifts? I can't figure out the rule for the shift inside of a scalar product. The terms (u,(v\cdot \nabla)\delta v)_\Omega and (u,(\delta v\cdot \nabla)... 0answers 49 views ### Mode expansions of fields This is a very simple question but would appreciate it if someone could clarify - I've heard different things from different people so I'm a little bit confused yet the question is simple: Given the ... 0answers 48 views ### Force of Leaky Bucket over time Indie Lab Procedure: I attached a cylindrical can to a force sensor. On the bottom of the can I drilled holes of various diameters. I then added a volume of water while collecting data from the force ... 0answers 48 views ### A Lie derivative \mathcal{L}_{\alpha^A} with respect to a spinor \alpha^A? Suppose we work with Minkowski flat space M (just to make things easy). If \textbf X is a Killing vector field it is possible to define the Lie derivative of an spinor \alpha^A with respect to \... 0answers 27 views ### Evaluating derivatives with respect to certain vector axis So, I am trying to work in Spherical coordinates. I have a predefined fixed axis, \hat{v}_0, so that \alpha=\vec{r}.\hat{v}_0 Now, I am interested in the following: f(r,\alpha)=\... 0answers 74 views ### Can I Wick-contract terms with derivatives with terms without derivatives? Consider for example the QCD three point vertex, can I contract a gluon field with the gluon field with a derivative in the vertex? 0answers 178 views ### What is the meaning of symbols \delta f and \delta^2f? Professor was using these symbols to derive the continuity equation. He defined the infinitesimal mass as \delta^2m=\rho \delta V and the mass that leaves some closed boundary \partial V as \... 0answers 111 views ### Are Laplace Operator and mean curvature exactly the same thing for 2D function? Let's assume we study 2D function/surface f(x,y). Then Laplace Operator is defined as:$$\nabla^2 f=\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}$$And the mean curvature: let \... 0answers 173 views ### Index Notation Double Curl My question is about Einstein notation. It does not matter the specifics of this example (the del operator could be another random vector), I just want to know if my assumption about notation is ... 0answers 153 views ### How to do this index notation differentiation? I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ?$$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} \left(2\...
They state that the chemical potential in a canonical ensemble is given by: $$\mu = -kT \frac{\partial{\ln Z(N,V,T)}}{\partial{N}} \tag{1}$$ But if I use the definition of chemical partial (which I ...