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    How does the phase noise of the LO effect IF accuracy?

    Hi, I have a roughly 1.1 GHz signal to be downconverted to 100 MHz by mixing it with a 1 GHz local oscillator. I am not sure how to choose the performance of the LO. In particular: let's assume the LO has a jitter of 100 fs rms. At 1 GHz this corresponds to a frequency error of 100 kHz. Does...
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    A Combinatorial optimization problem

    Hi, I have the following optimization problem. I have a list of tasks that I should be able to perform with my tools. Each tool costs a certain amount of money, and may be used to carry out a finite number of tasks. The goal is to choose an optimal set of tools in such a way that the toolset can...
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    Frequency measurement -- how to choose sampling ?

    Hi, let's say I want to measure the frequency f of a periodic signal. I may take N data points with an arbitrary timestep of T. The question is how shall I choose T for a fixed N to have the best accuracy? In principle the frequency resolution is 1/(N*T) when taking the Fourier transform...
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    MRI technology

    Hi all, I am wondering about the actual technological parameters of a modern MRI. In particular I mean sensitivity, i.e. the order of magnitude of the signals to be detected and the noise levels in practice. Can somebody recommend a good reference about the subject from an engineering...
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    Good thermal conductor but insulator

    Hi, Does anybody know a material which is a good thermal conductor and an insulator at the same time (at temperatures around 4 K) and is "easy" to fabricate? For e.g. sapphire fulfils the first two requirements, but is extrmely hard.
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    Designing a microwave cavity

    Hi all, I need a proper software for designing microwave cavities. I intend to use simple base geometries (e.g. closed box) with some modifications, like holes for optical access or for feeding the MW. These modifications however may seriously affect the Q factor, the frequency or might...
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    Calculate the following limit ( not sure if possible!)

    Homework Statement Calculate the following limit for real t -s. \sum_{n=0}^{∞} exp[i\cdot \sqrt{n + 1}\cdot t] / n! Homework Equations None The Attempt at a Solution Without the root it's trivial... I am not sure if it is even possible to give a closed form, I am out of ideas...
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    Spinons vs. psinons

    Hi, I've recently read an introductory review of Bethe ansatz for antiferromagnetic spin-1/2 Heisenberg chains : cond-mat: 9809163. I understand that the elementary excitations above the ground state in absence of magnetic field are spinons. The article claims that when a finite magnetic...
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    Elliptic function - different definitions

    Elliptic function -- different definitions Hi, I have recently discovered, that the definition of the complete elliptic integral of the first kind in Wolfram Mathematica (EllipticK[m]) is different from the usual (K(m)), given in Abramowitz-Stegun. Their domains are not the same. In...
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    System of equations in GSL

    Hi, I need to solve the following system of equations: qa = fa (qa, qb, qc, qd) qb = fb (qa, qb, qc, qd) qc = fc (qa, qb, qc, qd) qd = fd (qa, qb, qc, qd) where all the variables and functions are complex. However, there are some additional constraints for the variables, lets call...
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    Capacitance of loops

    Hi, Does anybody know a nice formula for the capacitance of two metallic wire loops with equal radius R? (The center of the loops are above each other, their distance is d. The whole system is in vacuum) Thank you!
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    Latex - superscript & subscript together

    latex -- superscript & subscript together Hi, I need to use expressions that have arguments, multiple superscript and subscript indices at the same time, e.g V(ij)_{\sigma_1\sigma_2}^{\tau_1\tau_2} Is it possible to force latex to make this formula more compact, ie. to put the...
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    Abs. value of momentum in QM

    Hi, I am looking for the operator representing the absolute value of a particle's momentum. In other words: the square root of the laplacian (preferably in 3 dimensions, but 2 would also be fine). I am aware, that integral formulas exist for this operator, but is it possible to express it...
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    Graphene - Green's function technique

    Graphene -- Green's function technique Hi, I am looking for a comprehensive review about using Matsubara Green's function technique for graphene (or at least some hints in the following problem). I have already learned some finite temperature Green's function technique, but only the basics...
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    Integral help

    Hi, I need some help to calculate this integral: \int _0^{2\pi}\frac{x^n}{\sqrt{1-m\cos x}}dx, where 0<m<1. What I've already tried: took the binomial series of (1-m cos(x))^(-1/2), this results in integrals like \int_0^{2\pi} x^n(\cos x)^k dx After this I've replaced cos(x)^k as a...
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    Feynman-Kac formula

    Hi, can anyone explain to me, how the Feynman-Kac formula is used to obtain the following expression for the N-particle canonical partition function of a Bose gas (with interaction potential V)? Z=1/N!Ʃ_{π\in S_N}Ʃ_{x1,...,xn}E[ exp(-∫_0^β Ʃ_{i<j}V(X_i(s), X_j(s) ds*indicator(X_i(β)=xπ(i)...
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    Sata 5400rpm vs usb2 7200rpm

    Hi, I need to expand my storage capacity on my notebook. I'm considering 2 options: 1 TB internal 5400 rpm with sata (or sata2 if my notebook is capable of) or 2 TB external 7200 rpm with usb 2 (the hdd can do usb 3, but I don't have usb 3 port in my computer) Can you give me...
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    Cross correlation

    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?
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    Book about vibrations

    Hi, Can anybody recommend an advanced book concerning mechanical vibrations? I'm especially interested in vibrations of a spehere, hemispehere and bell. Thank you!
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    Möbius transformations and SO(3)

    Hi, I was given the following problem, and i couldn't solve it yet: Give a bijection between the elements of SO(3) and the fractional linear transformations of the form \varphi_{z,w}\,(u)=\frac{zu+w}{-\bar wu+\bar z}, where u\in \mathbb C\cup \{\infty\};\, z,w\in \mathbb C. Any ideas...
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    Interesting problem

    Hi everybody, On a probability theory lecture I met an interesting problem: Let f : [0;1] -> R a bounded, 3 times continously differentiable function. Calculate the following limit n * \int_0^1 \int_0^1 ... \int_0^1 f(\frac{x_1+...+x_n}n)-f(0.5) dx_1...dx_n while n -> infinity Any ideas?