Cross Definition and 1000 Threads

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. a lone fishy

    Least time for boat to cross (theory)

    Homework Statement [/B] To cross a river with a current (flowing downstream) in the least amount of time, a boat should point a) directly at the opposite shore b) somewhat upstream c) somewhat downstream d) in a direction that will take the boat directly across e) downstreamHomework...
  2. T

    MHB Problem with cross multiplication

    Hello, I have been poring over this problem for days, and I would really appreciate some help. I'm not sure if it's an algebra problem exactly. It's from my physiology class. The professor said it's simple cross multiplication, and I asked him to explain it again, but I didn't understand his...
  3. E

    Cross Phase Modulation in Optical Fibers (Fiber Optics)

    Hello everyone. I have been practicing for my exam in fiber optics, and stumbled upon the following question: We have a transmission system with 3 channels, composed of a single mode fiber and a dispersion compensation fiber. Specifications are given for each. We need to calculate the channel's...
  4. ognik

    MHB Is the Cross Product of Orbital Angular Momentum Always Zero?

    Hi - from orbital angular momentum components, $[L_x, L_y] = iL_z$ My book claims 'Hence, $ \vec{L} \times \vec{L} = i\vec{L} $' I'm keen to know how they get that, an also why that cross products isn't = 0, like $A \times A$ would be ?
  5. ognik

    MHB Why Is There a Difference in Orbital Angular Momentum Calculation Methods?

    I got to here in a simple exercise (orb. ang. momentum cords), realized I was applying something I didn't understand ... $L = -i \begin{vmatrix}\hat{x}&\hat{y}&\hat{z}\\x&y&z\\\pd{}{x}&\pd{}{y}&\pd{}{z}\end{vmatrix}$ I 'know' it equates to $L_x =-i \left( y\pd{}{z} - z\pd{}{y} \right) $ - but...
  6. saybrook1

    Finding cross sections for top quark production

    Homework Statement The problem asks me to find \frac{d\sigma}{dz} for u\bar{u} \rightarrow t\bar{t} via the strong interaction and then to find the total cross section via QCD. I'm wondering what the difference is? I was just going to write the feynman rules for QCD to get the amplitude and...
  7. W

    Can someone tell me how they did cross product?

    Homework Statement Angular momentum is the cross product of r and mv. But why is there mvR outside of the paranthesis? And where did the v go in the second paranthesis - shouldn't the second paranthesis be (-v*sin(ωt), v* cos(ωt)). Does anyone have any idea how they did the cross product...
  8. parazit

    FLUKA Code : Total Cross Section Calculation

    Hi folks, I'm working on Fluka nowadays which you can found from here if you are not familiar. It's a very useful and widely used Monte Carlo simulation package. My main goal is to be able to perform total cross section calculation with it. So far, please consider I'm a rookie, I've done some...
  9. J

    Integrating over a cross product?

    Lets look at the force on a wire segment in a uniform magnetic field F = I∫(dl×B) I am curious if, from this, we can say: F = I [ (∫dl) × B] since B is constant in magnitude and direction
  10. ognik

    MHB How does using cross product to find shortest distance work?

    A method for finding the shortest distance between 2 skew, non intersecting lines is to 1st find the common normal, using $ \vec{n} = \frac{\vec{v_1} \times \vec{v_2}}{|\vec{v_1} \times \vec{v_2}|} $ I'm looking for a proof or intuition as to why this is true please? Then apparently we get the...
  11. J

    Does an AC current have to cross zero?

    So my question is simple. If the current doesn't change sign, is it considered AC or DC? I seem to recall we called it DC when I briefly saw it. However after a quick google search I'm confused. Some said that for example an AC signal offset with a DC signal to show this behaviour should be...
  12. S

    Pressure standing wave pattern, change cross sectional area

    Homework Statement See pictures. There are 2 parts to the problem but I can probably figure out the second part once I get the first part. [/B] Homework Equations Antinodes (minimum pressure) at Nodes (maximum pressure) at [/B] Equation for a standing wave: The Attempt at a Solution...
  13. thegirl

    Cross product imaginary numbers

    Hi, I was just wondering if you have a cross product can you multiply out the constants and put them to one side. So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E. Is that correct?
  14. M

    Question about torque as a cross product

    So yeah, I understand that you can calculate torque as F*d, and you get a "number". But when you calculate a cross product of torque, r x F, what does that actually give you? It is a vector, perpendicular to F and r, but what "is" that? I mean, is it like an axis around which the object is...
  15. Schwarzschild90

    Particle momenta and cross section

    Will someone explain this step to me?
  16. A

    Divergence of Cross Product Relation

    Homework Statement The problem is given in the following photo: Actually I did the first proof but I couldn't get the second relation. (Divergence of E cross H). Homework Equations They are all given in the photo. (a) (b) and (c). The Attempt at a Solution What I tried is to interchange...
  17. F

    Cross correlation for two m-sequences

    Calculate the discrete period cross correlation function for the pair of m-sequences given by - G1(D) = 1 + D2 + D5 and G2(D) = 1 + D2 + D3 - D4+ D5 I started by drawing the shift register diagrams and calculating each state, but that is a long process and I don't know how would i show the...
  18. A

    Why is the E cross B drift velocity constant in charged particle motion?

    Homework Statement good afternoon, I am a problem with the E cross B drift velocity calculus from a charged particle. At first, an eletron is submitted a uniform magnetic field and have a circular trajetory. After, appear a uniform eletric field that create a drift velocity. The equations...
  19. Telemachus

    Applications of multiple ionization cross sections

    Hi there. I'm working with this stuff of multiple ionization (in particular, double ionization). There are some references I've found on the applications in applied physics for this theoretical work, for example, plasma physics, accelerator physics, radiotherapy, which are listed in some papers...
  20. G

    Solve Double Cross Product Problem in $\mathbb{R}^3$

    Homework Statement If ##u,v,w\in\mathbb{R}^3##, show that ## u\times(v\times w) = (u.w) v - (u.v) w ##. Homework Equations The Attempt at a Solution Since ## u\times(v\times w)##, ##v## and ##w## are orthogonal to ##v\times w##, these vectors are coplanar. Therefore, there must be reals ##...
  21. P

    MHB Did my book do this wrong? (Vector Cross Product)

    Reading a book about 3d math, and I am confused as to what happened on this Vector Cross Product problem. I'm thinking there was just an error that wasn't caught. For the first row, instead of (3)(8)-(-4)(-5) shouldn't it have been (3)(8)-(4)(-5) and had the same displayed result of 44? And for...
  22. P

    Proving volume of box using cross and dot product

    Homework Statement The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...
  23. P

    Finding dot product, cross, and angle between 2 vectors

    Homework Statement [/B] Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units. a) find A dot B b) find A x B c)...
  24. Brandon Hawi

    Cross Product of Parallel Vectors is the zero vector (why?)

    Hello, PF! I had a quick question that I hoped maybe some of you could help me answer. The question is simple: Why is the cross product of two parallel vectors equal to the zero vector? I can see this easily mathematically through completing the cross product formula with two parallel...
  25. B

    How to calculate Young's modulus of layered cross section

    Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of...
  26. rogerk8

    Cross product evaluation (for the Lorentz Force).

    Let's say we have: \vec{E}=E_x\vec{i}_x+E_y\vec{i}_y+E_z\vec{i}_z and \vec{B}=B_x\vec{i}_x+B_y\vec{i}_y+B_z\vec{i}_z and the Lorentz Force 0=q(\vec{E}+\vec{v}X\vec{B}) which due to \vec{E}X\vec{B}=\vec{B}X(\vec{v}X\vec{B})=vB^2-B(\vec{v}\cdot \vec{B}) and transverse components only...
  27. D

    Do supersolids or BECs have higher fusion cross sections?

    The Lawson criterion suggests that a chain fusion reaction will only occur in a confined plasma. Since it's a product of temperature and pressure (or density) a chain reaction would be virtually impossible in a cold target at pressures attainable in a lab. Likewise, the Coulomb barrier makes it...
  28. M

    Problem involving dot and cross product

    Homework Statement https://www.dropbox.com/s/8l90hahznjlv9d0/vector%20problem.png?dl=0 Homework Equations Dot and Cross product The Attempt at a Solution although I know the dot and cross product, I'm not sure what I'm being asked or how to proceed? any help?[/B]
  29. C

    Calculating absorption cross sections

    How can I calculate the absorption cross section of a harmonic oscillator in an EM field?
  30. S

    How does the cross product work?

    Hello, I hope this is the right forum section. I'm having trouble understanding how calculating the cross product arrives at the final result. When I do something simpler like multiplying a vector by a scalar, I can easily visualize in my head how each component "shrinks" or "grows". With the...
  31. C

    Deriving Cross Section from Imaginary Part of Action: Exploring the Link

    Can someone point towards how to derive that the cross section is proportional to the imaginary part of the Action? Also, I thought the Action was a real number? Thanks!
  32. U

    Production of Z boson - Cross Section

    Homework Statement Calculate the ratio ##R = \frac{\sigma_{had}}{\sigma_{\mu+\mu-}}## for energy around ##10~GeV##. At sufficiently high energies, the ##e^+e^- \rightarrow \mu^+ \mu^-## reaction can proceed via the ##Z^0## boson. Assuming vertex factors for EM and weak interaction are the same...
  33. O

    Cross product of 2 vectors of same magnitude

    Homework Statement Vectors A and B both have magnitude M. Joined at the tails, they create a 30' angle. What is A x B in terms of M? Homework EquationsThe Attempt at a Solution 0? OR M^2? Sqrt(3)M/3?
  34. M

    Linear Algebra; Transformation of cross product

    Pre-knowledge A matrix is a linear transformation if, T(u+v)= T(u) +T(v) and T(cu)=cT(u). Theorem 8.4.2 If V is a finnite dimensional vector space, and T: V-> V is a linear operator then the following are equivalent. a) T is one to one, b) ker(T)=0, c)...
  35. J

    Cross product in arbitrary field

    Let \mathbb{F} be an arbitrary field, and let a,b\in\mathbb{F}^3 be vectors of the three dimensional vector space. How do you prove that if a\times b=0, then a and b are linearly dependent? Consider the following attempt at a counter example: In \mathbb{R}^3 \left(\begin{array}{c} 1 \\ 4 \\ 2...
  36. U

    How Do You Calculate Cross Sections in Electron-Neutrino Scattering?

    Homework Statement [/B] (a) Find the ratio of cross sections. (b) Find the cross section for electron-neutrino scattering by first writing down relevant factors. Homework EquationsThe Attempt at a Solution Part (a)[/B] These represent the neutral current scattering for the muon-neutrino and...
  37. X

    The Optical Theorem (Total cross section?)

    I am going over the optical theorem (specifically from Sakurai) and I just have a simple couple of questions. The optical theorem says \sigma_{total}=\frac{4\pi}{k}\text{Im}(f(0)) Where ##f(0)## is the scattering amplitude in the forward direction. (Which I am assuming means the direction...
  38. Z

    Question about Resonance Cross Sections

    Hi All, I have a question about resonance cross sections. I have been doing the design work on the reactor I want to propose for testing at Oak Ridge National Labs, and have run into a problem. It is an accelerator driven reactor transmuting thorium into uranium, then burning the uranium by...
  39. tg85

    K-Long and K-Short pion decay cross sections

    In the text-book example of CP violation in the kaon system, the usual statement is that the KS decays much faster than the KL because the phase space is larger for a decay into two pions, compared to three pions. (See, for example, Griffiths or "Modern Particle Physics" by Thomson.) I was...
  40. U

    Cross Section for e+e- in EM interaction - Is it the same?

    I was studying my notes and specifically for the ##e^+e^- \rightarrow \mu^+ \mu^-## process, cross section is given by \sigma = \frac{4\pi}{3} \left( \frac{\alpha \hbar c}{W} \right)^2 where ##\alpha = \frac{g_{EM}^2}{4\pi}## and ##W## is the centre of mass energy. Is this the same for...
  41. C

    Neutron cross section in fission

    I was reading about control rods in a nuclear reactor. The carbon rods slow down the neutrons so they can interact better and induce fission. Is the reason that they don't interact when raveling fast is this because the have a smaller de broglie wavelength?
  42. U

    Special H boson with very high cross section?

    Homework Statement (a) Explain the results. (b) Why is the cross section much higher? Suggest the dominant decay product pair.[/B] Homework EquationsThe Attempt at a Solution [/B] Part(a) For a centre of mass energy of ##170GeV##, you produce pairs of oppositely charged ##W^{\pm},W^{\mp}##...
  43. Pronoy Roy

    Why cross product has a direction but dot product doesn't?

    Can anyone tell me why?
  44. 5

    Dimensional Analysis of Flux Equation for cross filtration

    Homework Statement The following equation is presented in my textbook, with very little context and J is simply described as the "trans-membrane fluid flux, which can be modeled by using Darcy’s law." Typically in this bioseparations class, when we discuss permeate flux, it is a unit volume...
  45. C

    Vector Cross Product Homework: Find a×(a-2b+c)

    Homework Statement Given a×b=-i-j+3k and c×a=2i-3j+k, find a×(a-2b+c) Homework Equations Cross product (DONE WITHOUT MATRICES). The Attempt at a Solution a[/B]×b=c=-(b×a)is all I'm getting to at this point
  46. ShayanJ

    Pair production differential cross section

    In one of my classes, I should give a talk about pair production cross section in front of the class and so I'm now searching for resources. But I can't find a place where the differential cross section for pair production process is given. Anyone knows somewhere I can find it and , preferably...
  47. D

    Information about absorption cross section

    Hydrogen - Halpha cross section i need the absorption cross section for the absorption of an H-alpha photon by a hydrogen atom, in the correct state of course, which I'm pretty sure is neutral hydrogen, n=2. I am needing this for a project, so i also need a reliable source where this comes...
  48. S

    Find Fusion Cross Sections for All Isotope Pairs - Data/Book/Program/Formula

    Is there a book or database that lists all (or many) pairs of isotopes along with the energy at which they have the higest probability of fusion and what that probability is? Or is there a program that uses models to make a guess given a pair? Or a formula I could use to make the guess myself...
  49. V

    Calculation of total ionization cross section

    Hai all, I need some help in understanding the calculation of total ionization cross section. As per the literatures, for a gas capable of multiple ionization, the total cross section is a charge-weighted sum of partial ionization cross sections. To be more elaborate, consider the case of...
  50. K

    Cross products vanish Classical Mechanics

    As seen in the picture, this question is about an object moving in the x-y plane. But I don't get why in equation 8.9 the cross terms vanish? If anyone can help me, that would be really nice.
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