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. O

    What is a differential cross section?

    In particle physics, what is a differential cross section? I think I understand what a cross section is, but I can't find any information on what a differential cross section is. I don't see how a cross section could be differentiated.
  2. A

    Finding Moment of Interia of a 'Loop' when given Density & Cross sectional area

    Homework Statement I eventually have to solve for maximum angular acceleration of the loop in a magnetic field, and I have gotten everything with the exception of the moment of inertia, so I won't include the emf and B known variables. Known: a copper wire with a density of \rho = 8960...
  3. G

    Derivation of the differential cross section

    hi i am currently looking for a derivation of the differential cross section, that is not an abuse of mathematics, cause all derivation i found use differentials that are treated like fractions and so on? greetings Gavroy
  4. R

    Calculate Cross Section Area of Steel Rod for 3 Tonne Tension

    Homework Statement A medium carbon annealed steel rod has a rectangular cross section and must cope with a tension of 3 tonnes. The thickness of the rod is 15mm. Calculate the size of the cross section. Homework Equations ? The only formula I know with CSA and force is: stress = Force...
  5. Z

    Approximating Integrals with Deriv & Discont: Help Needed!

    I'm trying to do an integral, in which the integrand is composed of arbitrary functions and contains a derivative of the variable of integration. Further still, the integral is over a discontinuity. Because these are arbitrary functions I assume there is no exact solution, but I'm looking for...
  6. N

    Cross product on undivided to components vector

    he question asks to find the ratio between E0 and B0 and the ratio between w and k ? E and B are on the x-y plane they are given as verctors without any components dividing no x direction part,y direction part,z direction part so when when i use the maxwell equations \nabla\times...
  7. S

    Casimir's Trick/Evaluating Cross Sections

    Hi all. I'm working on a project at the moment, and I've run into some questions regarding the 4-d Levi Civita tensor contracted with the metric tensor. I'm working on finding the cross-section for neutrino-proton scattering. While ccontracting the hadronic and leptonic tensors, I end up...
  8. Orion1

    Stellar nuclear fusion: Mean cross section and velocity theorem

    I am inquiring as to what the theorem function is for the mean product of cross section and velocity for stellar fusion reactions? \langle \sigma v \rangle Mean product of nuclear fusion cross section and velocity. \langle \sigma v \rangle Maxwell–Boltzmann probability density function: f(v)...
  9. F

    Explanation of the cross product

    Can someone please explain to me the motivation for these definitions of the cross product? Let A = (a1, a2, a3), B = (b1, b2, b3). Let A and B be the magnitudes of A and B, respectively, and let \theta be the angle between the vectors. A X B = AB sin(\theta) A X B = (a2b3 - a3b2, a3b1...
  10. atyy

    What is a Cross Over? Definition & Effects

    What is a cross over? It seems to be something like a "qualitative change" without a phase boundary, in the vicinity of the end of a phase boundary. But what is the proper definition? How is it different from other sorts of continuous changes? Is it something that an experimentalist can detect?
  11. fluidistic

    Cross product expressed in the cylindrical basis

    Homework Statement It's not a homework question but a doubt I have. Say I want to write \vec A \times \vec B in the basis of the cylindrical coordinates. I already know that the cross product is a determinant involving \hat i, \hat j and \hat k. And that it's worth in my case...
  12. C

    Cross Correlation Functions: Advanced Applications & Conclusions

    Hi. Can somebody recommend a good book (advanced level) dealing with applications of cross correlation functions? I mean what kind of conclusions can be drawn etc?
  13. Y

    Using cross product to find angle between two vectors

    Homework Statement Find the angle between \begin{align*} \vec{A} = 10\hat{y} + 2\hat{z} \\ and \\ \vec{B} = -4\hat{y}+0.5\hat{z} \end{align*} using the cross product. The answer is given to be 161.5 degrees. Homework Equations \left| \vec{A} \times \vec{B} \right| = \left|...
  14. I

    Finding Linear Transformation that will remove cross product term.

    Homework Statement Find a linear transofmration from X={x1,x2,x3} to U={u1,u2,u3} which will remove the cross product term in the quadratic form of equation 2X12+4X22+5X32-4X1X3 and thus write the resulting quadratic form in u1,u2,u3. Homework Equations The Attempt at a Solution No...
  15. J

    Neutron Capture Cross Section Dependence on Target Material Temperature

    So I have been reading about the cross section of neutron capture and have been reading about how the cross section for neutrons in a given material depends on neutron energy, the most important factor obviously. But I have not seen as much information on how, for a neutron of a given thermal...
  16. J

    How Much Force Can a Human Femur Withstand Before Breaking?

    Homework Statement The Femur bone in the human leg has a minimum effective cross section of about 3.0 cm2 How much compressible force can it withstand before breaking Homework Equations Compressive Strength (bone)(N/m2) = 170 x 106 P = F/A The Attempt at a Solution Not sure what a...
  17. E

    Question about interpreting absorption cross sections

    Hi everyone, I was wondering if I can get a little help interpreting absorption cross sections. I would like to figure out how long I would have to shine a particular light on a monolayer of molecules to expect an appreciable fraction of isomerization. Here is how far I've gotten so far...
  18. S

    Semi-circle cross section volume

    Homework Statement base of a solid is bounded by y=\sqrt{x}, the x-axis, and x=9. each cross-section perpendicular to the x-axis is a semi-circle. find the volume of the solid Homework Equations The Attempt at a Solution I found the answer to be 81\pi/16 by the following steps...
  19. D

    What is the angle between B and C if A.B = 0 and A x C = 0?

    Homework Statement Given A . B=0 and A x C=0...whats the angle b/w B and C? Homework Equations The Attempt at a Solution..
  20. J

    Quick question about neutron scattering and absorption cross sections

    Does the absorption cross section to scattering cross section ratio of an isotope vary with neutron energy or stay constant? I have heard that cross sections in general are inversely proportional to velocity (eg the fission cross section of U235 is about 1000 times higher for thermal neutrons...
  21. F

    How can anything cross the event horizon of a BH?

    Ok, although I had hoped to avoid having to ask a stupid question, it seems as though I'm just too dense to figure this one out on my own. Generally I can, with the help of Google, and the combined wisdom of the internet, deduce an answer. But either Google, the internet, or my brain has failed...
  22. D

    Calculating a cross section

    Hi. I am looking for some help calculating a cross section to derive the frequency of reaction in the early universe. The reaction taking place is: \nu_e + n \longleftrightarrow p + e^- After some calculation I came here: n_\nu \langle \sigma v \rangle = \frac {(2\pi)} {8 m^2}...
  23. F

    How do you remember the order for the cross product in this surface integral?

    Homework Statement \iint \mathbf{F} \cdot \mathbf{dS} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{dA} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{\hat{n}}dA = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \frac{\mathbf{r_u}...
  24. S

    Volume of Polar Solids with Cross Sections

    Homework Statement I'm trying to find the volume of a Polar shape with semi-circular cross sections. Since it is a polar graph, does that mean the cross sections are to be swept across the graph from 0 to 2π in triangular sections? I'm aiming to create one side of a three...
  25. O

    Volume of Solids with know CROSS SECTIONS

    Homework Statement In Problems 1-5, let R be the region bounded by y = x^2 + 3, y = 2x, x = 0, and x = 4. Each problem will describe the cross sections of a solid that are perpendicular to the x-axis. Write an integral expression that can be used to find the volume of the solid (do not...
  26. M

    Proving three 3D points are collinear with Cross Product

    Hi. I've been studying for a test and have been scouring my text for methods of proving points in 3-dimensional space are collinear. The best I can see is that the cross-product of the vectors must equal zero. Can someone explain how to do this a little more clearly?
  27. L

    Question about cross and dot product

    Homework Statement Note: \nu is del could not find it... I need to prove the \nu*E=0 and \nu x E=-dB/dtHomework Equations E(s\phizt)=(Acos(Kz=wt)/s)s^ The Attempt at a Solution so for the first one \nu*E=0 I thought it would be d/ds(E) but what they did was 1/s d/ds(s E) no idea why they...
  28. J

    Cu-65(N,G)Cu-66 Cross Sections

    Hi I am trying to calculate the relative abundance of Cu-66 and Cu-64 in a sample of copper after it has been exposed to a PuBe neutron source for a few days. I have cross section data for the Cu-65(N,G)Cu-66 and Cu-63(N,G)Cu-64 nuclear reactions. I also have the energy spectrum for the PuBe...
  29. E

    Projectile Motion in 3rd, finding out where 2 paths cross

    Homework Statement 2 projectiles, one at the origin the other at (0,100,0)m, have initial speeds of 35 m/s and 55 m/s respectively, and have direction cosine angles (45,60,60) and (60,135,60) respectively. Both are under the influence of gravity and experience a force of air resistance that...
  30. A

    Solving Problem Involving Cross Product

    Hey, I have a problem that can be written in the following form: u=v x w where u, v, w are 3by1 vectors and x is the cross product. now I want to write v in term of u and w, but I have no idea of how to get vector v out of the previous equation. Someone who can help me with this...
  31. Astronuc

    Tornados cross the Gulf State in US

    Tornados and storms have caused 200 fatalities during the last two days. Several towns in 5 states were hit. Tuscaloosa Mayor Walt Maddox stated that "hundreds of businesses and homes were destroyed." In April, more than 800 tornados have been recorded. Apparently this shatters the old...
  32. A

    Cross Section Equation of Antonov 140, B-707, Cessna-210 & Citation

    hi guys, I was wondering what is the equation of cross section between fuselage and wing of the below airplanes:antonov 140 , B-707 , cessna-210 , cessna citation. Can anyone help?a book or a refrence or whatever you have
  33. A

    Airplane Fuselage-Wing Cross Section Equations and References

    hi guys, I was wondering what is the equation of cross section between fuselage and wing of the below airplanes:antonov 140 , B-707 , cessna-210 , cessna citation. Can anyone help?a book or a refrence or whatever you have
  34. E

    Cross Post from Classical Physics: Calculus in Impulse Momentum Theorem

    Hi, This is my first post. Sorry for the mistakes it certainly contains. I have two questions. First, is there a tutorial for using embedded LaTex? I found some general tutorials on LaTex, but I couldn't get some of the commands listed in that tutorial to work in the embedded LaTex code...
  35. K

    How Thick Should a C12 Target Be for 1% Proton Interaction at 10 GeV?

    Homework Statement What target thickness d is necessary to ensure that 1 % of all protons with a laboratory momentum of 10 GeV interact in a C12 – target? Homework Equations I have found af formula that states cross section = N_Reac/(N_beam * N_A * ro*d/M) Where N_Reac is the...
  36. J

    Dot and cross product properties?

    Knowing: u * (v x w) = 5 where u, v and w are vectors. What is [Proj u (v x w)] * u Ive been staring at the dot and cross product properties in my book for a while and I don't see how to do it.
  37. A

    Vector's Cross Product, HELP , Please

    So, the other day, I was learning about Scalars and Vectors and about Dot product and Cross Product. Now, in Cross Product, I was just thinking, when my thought slipped on the following stone: What is the physical implication of => aXb(cos\vartheta) ? I mean, how would you represent it on a paper?
  38. M

    How do Kinematic Cuts Affect Cross-Section Calculation?

    Hi everybody, I have a experimental question. In cross-section calculation of production of particles (say D), one counts the number of produced D. To selection the D one has to apply some kinematic cuts. If cuts are tight, number of D will be less and if cuts are loose, number of D will be...
  39. H

    Intuitive description of Cross Sections

    Does anybody know of any good references that explain the concepts/mathematics behind cross sections particularly well? Websites, textbooks, whatever...
  40. J

    Solid angles and Cross sections

    Homework Statement A thin (1mg/cm^2) target of 48-Ca is bombarded with a 10-nA bean of alpha particles. A detector, subtending a solid angle of 2E-3 steradians, records 15 protons per second. If the angular distribution is isotropic, determine the total cross section, in mb, for the reaction...
  41. M

    Cross Product Proof: u X v X w = u X (v X w)

    Homework Statement (u X v) X w = u X (v X w) Iff (u X w) X v = 0 Homework Equations (u X v) = -(v X u) The Attempt at a Solution I know that I am supposed to prove this by proving P --> Q and Q --> P I know that if (u X w) X V = 0 then (u X w) is a scalar multiple of v. How...
  42. R

    Reduced homology of sphere cross reals?

    tex doesn't seem to be working right...sry for the notation. Working through of a proof of the generalized jordan curve theorem. Keep getting stuck on calculating the reduced homology of S^n by R, (ie n-sphere cross the real line). My book (hatcher) seems to imply its 0 except the n^th...
  43. K

    Cross section energy dependence

    Hey, The hard cross-section of a 2 to 2 inelastic scattering goes as 1/E^2, where E is the center of mass energy. However, the cross-section in proton proton collisions increases with energy. My question is; does anybody have a good explanation for this and/or a good reference where I can...
  44. B

    Volume of Solid using cross sections

    Homework Statement Find the volume of a solid whose base bounded by y=x+1 and y=x^2-1, with cross section of a square perpendicular to x-axis The Attempt at a Solution So i set up the problem like this delta volume= y^2*delta x, that being the area of the square where i get loss is...
  45. P

    Cross Product Proof: Proving Distance Formula for a Point Not on a Plane

    Homework Statement Let P be a point not on the plane that passes through the points Q, R and S. show that the distance d from P to the plane is d = (|a.(bxc)|)/(|axb|) where a = QR and b = QS and c = QP (those are lines between given two points) Homework Equations |axb| =...
  46. Y

    Question in the curl of a cross product.

    This might be math problem, but I only see it in EM books. \nabla X (\vec A X \vec B) \;=\; (\vec B \cdot \nabla)\vec A - \vec B(\nabla \cdot \vec A) -(\vec A \cdot \nabla)\vec B + \vec A ( \nabla \cdot \vec B) . What is \vec A \cdot \nabla ?
  47. R

    Differential cross section signature

    Homework Statement Hi, I'm currently carrying out a computing project on Resonant Scattering and when I have identified a resonant state, I need to examine whether it has a "particular signature". However, I'm not really sure what this means... Homework Equations The differential...
  48. K

    Cross Product of Magnetic Field(B) and Velocity of Charged Particle(v).

    Homework Statement Hi there. I am currently taking physics 30(algebra physics course) and we are in the electrostatics unit. I am curious as to why, when trying to find the force acting on a charged particle moving perpendicular to a magnetic field, the force results in a direction that is...
  49. W

    Gymnast doing an Iron Cross

    Gymnast pictured below performing an Iron Cross has a mass of 65.00 kg. Assume that the forces in the cables are symmetric and that he is in static equilibrium. A. Draw a complete free body diagram of the gymnast (just him – he is the system). B. Calculate the vertical and horizontal...
  50. L

    Many particle system - problem with cross product

    in a many particle system we have a center of mass R and position vector of the ith particle with respect to centre of mass is r_i. hence the position vector measured from the origin is R_i=R+r_i. why does R\times\sum (m_i \dot{r}_i) =0, where \dot{r}_i denotes the rate of change wrt time...
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