![]() Even though the problem is a static problem, I am loath to simply throw the imaginary components away because it is possible that there are some phase effects that the integrals are showing me. Now, as I fool around with the numerical integration making the sizes and distances of the spheres different, these imaginary components to the solutions begin to show up.not always but under certain circumstances. Using spheres I also do not have additional relative orientation geometries to make thing even more intractable. If I further modify the geometry from disks to spheres using cylindrical symmetry, the integrand is only a little more complex and the same limits on finding an analytical solution exist. I switched to numerical integration so long ago I forget how I got there!!! ![]() If I extend the ring into a disk, the resulting integral is similar to an elliptical integral but cannot be solved analytically because now the denominator of the integrand contains additional spatial variables, at least if am correctly recalling my efforts at having Mathematica solve that integral. If I replace the test charge with another coaxial ring, my result is an elliptical integral. If the test charge is off-axis, the mutual force requires the solution to an elliptical integral. If the test charge is on the ring axis, the solution is trivial. If I put a test charge in the vicinity of the first ring, I find a mutual force between the ring and the test charge. ![]() Take a charged ring.so much charge per unit area of the ring. They may mean something that I simply cannot throw away or at least I do so at some risk to the validity of my results. But the numerical integration works very nicely, except that over a certain limited range and size of variable these pesky imaginary components spring up. My integrals are similar to Elliptical integrals, but there are additional terms in the denominator of the integrand function that make an analytical solution impossible. On the other hand, I remember some old physics scattering problems in which the imaginary parts represented phase shifts that caused the output wave functions to oscillate with interference patterns.and these were measured and seemed to be real effects. My take away is that I CAN ignore the imaginary component, even if it is very large. I relied on the smart PhDs working for me to get it right!!! LOL. Once I went into management my brain atrophied. ![]() Again in the distant past my Fortran integrals using the simple numerical models and were all in the real domain. My experience in the complex domain was limited to various engineering discussions and formal methods such as Laplace transforms. Finance, Statistics & Business Analysis.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. For example, if the user finishes using it just before 10am and then once again wants to use it around 10:10am, the user will need to login again.Wolfram Data Framework Semantic framework for real-world data. Depending on this, the user will need to login once again through the Mathematica Portal to use mathematica if the time between the two invocations of mathematica falls after the hour mark. The restriction file gets updated on an hourly basis ( i.e for example: 9am, 10am, etc). IMPORTANT : Users need to log in first through the Mathematica portal from the machine on which they want to invoke mathematica. You will receive an email after your account is validated.Īfter you receive the email kindly take note of the following instructions. New users, please register in the above portal and submit the PDF application with sign & seal from your guide/supervisor and submit in SERC room 103. Users already registered for using Mathematica, kindly login using the above link from the machine in which you would like to invoke Mathematica and then start to use it.
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