What is Cross: Definition and 1000 Discussions

A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally.
A cross of oblique lines, in the shape of the Latin letter X, is also termed a saltire in heraldic terminology.
Throughout centuries the cross in its various shapes and forms was a symbol of various beliefs. In pre-Christian times it was a pagan religious symbol throughout Europe and western Asia. In ancient times, the effigy of a man hanging on a cross was set up in the fields to protect the crops. The cross was even considered a male symbol of the phallic Tree of Life; thus it often appeared in conjunction with the female-genital circle or oval, to signify the sacred marriage, as in Egyptian amulet Nefer with male cross and female orb, considered as an amulet of blessedness, a charm of sexual harmony.

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  1. B

    I Understanding Nuclear Fusion Cross Section Diagrams

    I'm working on programming a particle simulation that visually shows the nuclear fusion reaction rate of deuterium at different densities and temperatures, but I'm having trouble understanding exactly how nuclear fusion cross section diagrams are supposed to be interpreted. (The simulation...
  2. agnimusayoti

    Indefinite integral of cross product of 2 function

    I've tried with this work in attachment. i&m not sure of my answer is correct.
  3. G

    Calculating the time to cross a river

    Could I please ask for help on the last part of this question: So, part b, I get the right time but not the right distance. Book answers are: distance = 1/6 and time = a/V. Here's my (faulty?) reasoning (LaTeX isn't working for me): The boat is steered due east and so would have a velocity...
  4. JD_PM

    I Why does the trace show up while computing unpolarized cross sections?

    I've been studying different scattering processes (from Mandl & Shaw QFT's book, chapter 8) and there's always a common step I do not understand: the showing-up of the trace. Let me give two specific examples. Lepton Pair Production ##( e^+ (\vec p_1, r_1) + e^- (\vec p_2, r_2) \rightarrow l^+...
  5. JD_PM

    I Understanding the (polarized) cross section for Compton Scattering by electrons

    I have specific questions, but let's first give context. Initially we have an electron with momentum ##p=(E, \vec p)## and spin state ##u_r (\vec p)## and a photon with momentum ##k=(\omega, \vec k)## and polarization state ##\epsilon_s (\vec k)##. Finally we have ##p'=(E', \vec p')##, ##u_r'...
  6. qnach

    A Software for cross section calculations using .cif files

    Is there any software available to calculate cross section using .cif file?
  7. H

    Matrix and cross section of the Xf -> Xf process

    The attempt at a solution follows as an attachment. If you are only interested in the solution without the derivation, look at page 1 and page 9.
  8. imselva

    Conduction heat transfer with varying cross section

    How to modify this Formula? and arrive at the solution. Q = -K(Th-Tc)A/thickness
  9. K

    I Simple explanation for cross section ratio

    Hello! Is there any simple (i.e. using some physics arguments, without actually doing the math) explanation for why $$\sigma(pp \to \pi^+d)/\sigma(np\to\pi^0d)=2$$ where d is the deuteron? Thank you!
  10. P

    Easy tool to see a cross section?

    I need to visualize what the cross section is of an oval tube is at angles of 10 degrees, 20, 30 up to 60. Is there an easy way to do this online somewhere or is there a mechanical drawing trick that can be done to see this result?
  11. A

    Solving Cross Section Confusion: Adding Positive and Negative Ions

    ik that i have to add the positive and negative ions but the cross section (surface) confuses me how do i resolve this?
  12. W

    I Cross Section Formula in Peskin and Schroeder

    On page 105 of Peskin and Schroeder's book it says that the integral over ##d^2b## in the expression: $$d\sigma = \left(\Pi_f \frac{d^3 p_f}{(2\pi)^3}\frac{1}{2E_f}\right) \int d^2b\left(\Pi_{i=A,B} \int \frac{d^3 k_i}{(2\pi)^3}\frac{\phi_i(k_i)}{\sqrt{2E_i}} \int \frac{d^3...
  13. Diracobama2181

    How Do I Solve These Scattering Cross Section Problems?

    a) I have $$d\sigma=-\beta sin(\theta)d(\theta)+2\gamma sin(\theta)cos(\theta) d\theta$$ and $$d \Omega=2\pi sin(\theta) d \theta$$ so $$\frac{d\sigma}{d \Omega}=-\frac{\beta}{2\pi}+2\gamma cos(\theta)=|f(\theta)|^2$$ b) $$\sigma(\theta)=\alpha+\beta cos(\theta)+\gamma...
  14. weningth

    A Cross section from subgraph in electron-proton DIS

    I am currently following R.K. Ellis et al.: QCD and Collider Physics, pp. 99 to understand how to arrive at the parton density functions starting from the matrix elements in electron-proton deep inelastic scattering (see figure below). But there seems to be a very fundamental concept that I...
  15. E

    A How do I calculate the cross section for W+W->gamma>l+ l- at the tree level?

    Can anyone help me about cross section calculation of W+W->gamma>l+ l- (leptons), at the tree level? I am stuck to writing amplitude,after written Feynman rules, because of massive vector boson polarization states. How should I do?
  16. M

    Biology What are the vascular structures of this cucumber cross section?

    We were asked to label the vasculature structures of a cucumber cross section (complex tissue). I just wanted to know if my labels were accurate. Image attached 1. Xylem 2.— 3. Sieve elements 4. Phloem
  17. D

    Engineering Determine a suitable cross sectional area for strength

    Lenght=300mm, Force at the end of the handlebar is 200N What i would like to know is: does that 20x20mm end piece affect the calculation process in any way? and whether there are more than 3 types of stresses in this case. First stress being moment created by the 200N and second stress is shear...
  18. Arman777

    I Cross Section of DM: What Are the Particle Candidates?

    What are the cross sections of the DM particle candidates ?
  19. J

    Vector Cross Product With Its Curl

    Starting with LHS: êi εijk Aj (∇xA)k êi εijk εlmk Aj (d/dxl) Am (δil δjm - δim δjl) Aj (d/dxl) Am êi δil δjm Aj (d/dxl) Am êi - δim δjl Aj (d/dxl) Am êi Aj (d/dxi) Aj êi - Aj (d/dxj) Ai êi At this point, the LHS should equal the RHS in the problem statement, but I have no clue where...
  20. dRic2

    I Wave function of a scattered particle and cross section

    In Landau-Lifsits's book about non relativistic QM it is said that if I have a particle described by a plane wave ##\phi = e^{ikz}## (I think he choses the ##z## direction for simplicity) the wave function after the scattering event is (far from the scattering event) $$\psi \approx e^{ikz} +...
  21. dRic2

    Hamiltonian Mechanics: why paths in state space never cross each other

    I'm reading a book about analytical mechanics and in particular, in a chapter on hamiltonian Mechanics it says: "In the state space (...) the complete solutionbof the canonical equations is pictured as an infinite manifold of curves which fill (2n+1)-dimensional space. These curves never cross...
  22. U

    Radar Cross Section simulation with CST

    I'm trying to understand how CST measures the RCS of an object. If not specified by me, it gives me (with a very brief simulation even for complex objects) graphs, both 3D and 2D, entitled 'Bistatic RCS'. With this wording I think that there is an antenna in a different direction than the one...
  23. S

    Use of an Impact Test in the cross section design of a component

    If I have impact test data showing energy absorbed by notched specimen, how do I utilize this data while designing. In my case, i am trying to design the valve which closes by striking on valve seat, how do i use the impact test results for this design?
  24. S

    Automotive Design of a Valve stem cross section in a Steam turbine emergency valve

    I want to design cross section area required for valve stem when valve is closed under spring force. Valve stem should be designed for buckling load but I am unable to calculate buckling load coming due to impact force coming when valve bangs on valve seat. Valve is having concentric spring. Is...
  25. F

    A Forecast with Fisher formalism : loss or gain of information

    In the context of a forecast, I am currently working on Fisher's formalism which is part of a more general theory, that of information. My problem applies to estimating cosmological parameters from input data with the Fisher formalism and recipes to build a Fisher matrix. The context is...
  26. Clara Chung

    Question about differential cross section

    I have attached the two pages in my notes and I have the following question. 1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?) 2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...
  27. Avatrin

    I Understanding the cross product and rotations

    Hi I have used cross products thousands of time without really knowing what it actually does; I know how to compute it, but I don't feel like I understand it. Also, when it shows up in physics/kinematics contexts, it's only because the magnitudes of the vectors involved have to be multiplied...
  28. S

    I Can the cross product concept be completely replaced by the exterior product?

    Do we really need concept of cross product at all? I always believed cross product to be sort of simplification of exterior product concept tailored for the 3D case. However, recently I encountered the following sentence «...but, unlike the cross product, the exterior product is associative»...
  29. A

    B Differential cross sections in Pythia

    Dear Users, I would like to ask you how can I plot d_sigma/d_omega and d_sigma/d_theta for any collision (for instance, proton and proton) using pythia event generator. I would be greatful if you could tell me how make it. Any ideas would be appreciated. Kind regards.
  30. C

    Effect of cross section shape of an iron core in a solenoid?

    I know the basic equations of a solenoid carrying a current, the consequences of having an iron core inside one, and how that derives from Ampere's law. But these suggest that the only figure of merit is the cross section area of an iron core and the solenoid, not their shape. Thinking in more...
  31. D

    B Can event horizons cross for passing black holes at high speed

    Scenario: You have two black holes approaching, one from the left (A), one from the right (B), each at speed S. They are offset vertically. S is sufficiently high that they will deflect passed each other without merging. Question: Suppose the speed S is high enough so that the event...
  32. rpthomps

    I Interpretation of a cross section vs energy graph

    Hello. I am reading DeAngelis - Introduction to particle and astroparticle physics and I have come across a plot showing proton proton cross section vs energy. I am trying to reconcile the statement in the book that says cross section total = cross section elastic whenever there is no available...
  33. D

    I Relation Between Cross Product and Infinitesimal Rotations

    Looking into the infinitesimal view of rotations from Lie, I noticed that the vector cross product can be written in terms of the generators of the rotation group SO(3). For example: $$\vec{\mathbf{A}} \times \vec{\mathbf{B}} = (A^T \cdot J_x \cdot B) \>\> \hat{i} + (A^T \cdot J_y \cdot B)...
  34. K

    I What is the cross section of a graviton?

    In particle physics there is usually a cross section for a particular particle . I came up with a cross section of 1.07 x 10^-42 m^2 for a graviton.
  35. S

    Calculate Torque on a Particle with Given Force and Position | Homework Solution

    Homework Statement Force F⃗ =−11j^N is exerted on a particle at r⃗ = (8i^+5j^)m. What is the torque on the particle about the origin? Express your answer using two significant figures. Enter coordinates numerically separated by commas.Homework EquationsThe Attempt at a Solution F: 0i, -11j...
  36. SchroedingersLion

    I Ridge Regression Cross Validation

    Hello guys, I have some difficulties understanding the procedure of cross validation to estimate the hyperparameter ## \lambda ## in Ridge Regression. The Ridge Regression yields the weight vector w from $$ min_w ( ||Y-Xw||^2 + \lambda ||w||)$$ X is the data matrix that stores N data vectors...
  37. Specter

    Why does the cross product of two direction vectors....

    Homework Statement [/B] Hopefully this is in the correct section I looked around for others but this seemed like the right one. Find the scalar, vector, and parametric equations of the plane that passes through the points P(1,0,4), Q(3,1,-6), and R(-2,3,5). Homework EquationsThe Attempt at a...
  38. K

    A Why does the cross section for Dark Matter decrease with increasing mass?

    Hello! In most papers that present exclusion plots as cross section versus mass, the plot has a specific shape in which mostly the cross section decreases with mass. I am a bit confused why. If you assume that the density and speed of DM is constant, shouldn't a higher mass (and hence a higher...
  39. Ajdin Palavric

    Using PDFs to Compute the Total Cross Section

    Homework Statement I would like to compute the total cross section of a lepton pair production using parton distribution functions. The main problem I am having is the numerical computation and the order of magnitude I am getting as a final answer, which so far definitely indicates that...
  40. Ibix

    I Detecting Crossing Event Horizon w/ "Closed Box" Experiment

    @Grinkle recently asked a question about detecting crossing the event horizon, which got me thinking. I think that, at least in principle, I can deduce when I cross an event horizon with a "closed box" experiment, basically by measuring tidal forces. I'm planning to see if the maths works, but...
  41. F

    How to add area moments of inertia for varying cross sections

    Hello I am doing a shaft design layout for a spindle to minimize deflection and I have to calculate the area moment of inertia for a shaft overhang.The shaft overhang is the distance from a bearing to the end of the shaft. Here is a picture detailing the location of the overhang. The black...
  42. parazit

    I The Maxwellian Averaged Cross Section

    Hi, Please forgive my ignorance but, can somebody please explain the Maxwellian Averaged Cross Section briefly and basically? Thank you in advance.
  43. B

    How to calculate the speed of a cross flow water turbine?

    How to calculate the speed of cross flow water turbine? Help, I'm struggling on our machine design.
  44. Alianos

    Emission cross section and laser performance

    How does the emission cross section of an emitting atom (such as Yb atoms in glass) affect the laser performance, namely the slope efficiency (signal power vs absorbed pump power) and laser threshold? Thanks a lot
  45. J

    Radar Cross section Vs Reflection Coefficient

    I am working on HFSS and designing Antennas for LOW RCS , in all previous works they calculate the S11 parameter for the unit cell then make an array form this unit cell and calculate the RCS , my question is what is the relation between S11 and RCS and why we calculate S11 for the unit...
  46. CDL

    Determining a Scattering Cross Section (Quantum Mechanics)

    Homework Statement Consider scattering of a particle of mass ##m## on the potential $$U(r) = \begin{cases} 0, & r \geq b\\ W, & r < b \\ \end{cases}$$ Where ##W## is some arbitrary chosen constant, and the radius ##b## is considered a small parameter. Find the cross section ##\sigma## in the...
  47. beefbrisket

    I Meaning of cross terms in line element

    In a problem from Hartle's Gravity, we are asked to express the line element in non-Cartesian coordinates u, v which are defined with respect to x, y. I have no problem getting the new expression for the line element, but then we are asked if the new coordinate curves intersect at right angles...
  48. R

    Self-inductance of a toroid with a rectangular cross section

    I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?
  49. ChrisVer

    A Question about a cross section from PDG

    Hi everyone, I was wondering, is the cross section at Eq 50.25 in http://pdg.lbl.gov/2017/reviews/rpp2017-rev-cross-section-formulae.pdf correct? Because I see a term in the denominator with \frac{1}{s\Gamma} whereas in several other references, the propagator term in the matrix element comes...
  50. Nathan Warford

    B How Can Point Particles Have Cross Sections?

    This is a topic that I have tried researching and I have not been able to find any meaningful information about it. The standard model of particle physics describes particles as point-like objects with no spatial extent. What I can't wrap my head around is how true point particles can...
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