What is Analytical: Definition and 278 Discussions

Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separation isolates analytes. Qualitative analysis identifies analytes, while quantitative analysis determines the numerical amount or concentration.
Analytical chemistry consists of classical, wet chemical methods and modern, instrumental methods. Classical qualitative methods use separations such as precipitation, extraction, and distillation. Identification may be based on differences in color, odor, melting point, boiling point, solubility, radioactivity or reactivity. Classical quantitative analysis uses mass or volume changes to quantify amount. Instrumental methods may be used to separate samples using chromatography, electrophoresis or field flow fractionation. Then qualitative and quantitative analysis can be performed, often with the same instrument and may use light interaction, heat interaction, electric fields or magnetic fields. Often the same instrument can separate, identify and quantify an analyte.
Analytical chemistry is also focused on improvements in experimental design, chemometrics, and the creation of new measurement tools. Analytical chemistry has broad applications to medicine, science and engineering.

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  1. FEAnalyst

    Analytical verification of FEA involving preloaded bolt

    Hi, I'm working on a simple FEA involving a preloaded bolt: The bolt is modeled as a single part (shank + head + nut), glued (perfect bonding) to both rings. Pretension force ##F_{preload}=200 \ N## is applied in the first step of the analysis while in the second, pretension force stops...
  2. kartini99

    I 1D Heat Transfer Analytical Wall

    Hello everyone, I'm trying to solve the transient heat transfer problem within the ID wall. The material is steel, and it is isotropic. The properties are given below : L = 5 mm qin = 0 Tinf = 100 deg C Tini = 20 deg C rho = 7850 kg/m3 cp = 460 W/Kg.K k = 45.8 W/m.K h = 20 W/m^2.K alpha = k /...
  3. G

    I Are EM signals also analytical backwards in time?

    Hi. If I turn on an antenna, it starts sending out radiation. If I turn it off again, the radiation doesn't instantly disappear but dies out smoothly (exponentially?). But this also means the radiation is never completely gone. This looks time-asymmetric, which is weird for electrodynamics. It...
  4. S

    I Analytical proof of LASER production

    Is there analytical proof that a photon Pe will be emitted by an excited atom Ae when another photon Pp of the same frequency is passing by Ae in LASER production? I tried using Feynman diagram to show a high probability of this event. I failed (most likely because I am not an expert in QFT)...
  5. tworitdash

    A Analytical form of a summation

    I have a equation with a double sum. However, one of the variables in one of the sums comes from a stochastic distribution (Gaussian to be specific). How can I get a closed form equivalent of this expression? The U and Tare constants in the equation. $$ \sum_{k = 0}^{N_k-1} \bigg [ \big[...
  6. Pipsqueakalchemist

    Mechanics of machine force analysis with analytical method

    So I was looking at this example problem in my textbook and I don’t understand how they got -168.1 degrees. The part I’m confused with is the first part of the 2nd picture, there’s a coma in the inverse tan, I don’t know what that means.
  7. FEAnalyst

    Hyperelastic problems - analytical solutions?

    Hi, I have recently become interested in analytical solutions of various advanced solid mechanics problems, mostly nonlinear ones. I consider simple geometries and loads (like bending of beams, torsion of shafts, or internal pressure in pipes), but for nonlinear materials. I have learned that...
  8. derya

    A Analytical solution for an integral in polar coordinates?

    Hi, I am trying to find open-form solutions to the integrals attached below. Lambda and Eta are positive, known constants, smaller than 10 (if it helps). I would appreciate any help! Thank you!
  9. M

    Approach analytical calculation for a beam frame

    Hi all, Currently I am working on a home-project, making a trike. Now just for fun and because I like to calculate things, I calculated the deflection of a frame with a load. The frame is shown in the picture below, I added the force for clarity. With my analytical calculation I found a...
  10. S

    I Analytical formula for the number of patterns by using combinations?

    A 4×3 matrix which has all elements empty, now I select any two consecutive elements until all elements are selected. I assign an index number (1 to 12) to the matrix element, in one row there are only 1,2,3 elements and 3 & 4 are not consecutive. for example, if I select index 1 & 2 of the...
  11. tworitdash

    MATLAB MATLAB IFFT doesn't match the analytical one

    I have a Gaussian shape frequency domain spectrum of which I am calculating the Inverse Fourier transform. I use both IFFT of MATLAB and also an analytical expression of Mathematica. They are not the same. I don't know where it is wrong. I have pasted both the figures. The numerical one has...
  12. F

    A Analytical expression of Cosmic Variance - Poisson distribution?

    I have an expression of Matter Angular power spectrum which can be computed numerically by a simple rectangular integration method (see below). I make appear in this expression the spectroscopic bias ##b_{s p}^{2}## and the Cosmic variance ##N^{C}##. ## \begin{aligned}...

    Analytical question: circular rotation

    Can a point P on the smaller wheel trace a straight line path inside the circular road (like the walls of a well)
  14. FEAnalyst

    Blade containment - simplified analytical approach

    Hi, one of the most interesting experimental tests performed for rotating machinery (such as gas turbines) is blade containment test - if the blade detaches from the hub, it can't break through the cover of the turbine because it could result in catastrophic damage (especially in case of...
  15. W

    Analytical solution for freefall....

    The freefall wiki entry wiki Freefall has an analytic solution for freefall distance in a gravitational field, but ... it doesn't seem to work ... at least i can't get it to work ... here is my MATLAB program to test it ... clear G=6.7e-11; % gravitational constant m^3/(kg*s^2) mEarth =...
  16. greg_rack

    Solving System of Equations: Understanding the Analytical Reasons

    Hi guys, I managed to solve this problem just by "rewriting" the first equation of the system as ##t=f(x)## and then substituting that in the second ##y=f(t)## equation, ending(of course) up with the sought ##f(x,y)## function. The problem here is I didn't really understand what I have done and...
  17. B

    The definition of generalised momentum

    Why, in lagrangian mechanics, do we calculate: ##\frac{d}{dt}\frac{\partial T}{\partial \dot{q}}## to get the (generalised) momentum change in time instead of ##\frac{d T}{dq}##? (T - kinetic energy; q - generalised coordinate; p - generalised momentum; for simplicity I assumed that no external...
  18. FEAnalyst

    Complex frames - analytical calculations

    Hi, I came across some interesting frames recently. Here they are: I wonder if all these frames can be solved analytically. If yes then how to do it ? Examples a) and d) are planar frames with diagonal members while b) and c) are spatial frames: b is subjected to uniformly distributed load...
  19. B

    Poisson Ratio -- Finding a corresponding analytical solution for the strain

    Hi, I ran into problems using the poisson ratio. For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge. Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir. The material parameters are E = 100, and v...
  20. H

    Solving an Electrical Engineering Challenge with a Tank of Electrolyte Liquid

    So I am working on a project where I have a tank, which has a volume of electrolyte liquid inside it. This is coupled to a battery which charges it, and gives it energy. I will have a copperband arround it, so i can measure a potential voltage from the electrical field. So what I need to...
  21. A

    Analytical Mechanics: Regularity Conditions on Constraint Surface

    Hi, In my course in analytical mechanics, it is said that for a system of n particles subjected to r constraint equations, it is necessary to impose regularity conditions on the constraint surface defined by G = 0 where G is a function of the position of the position of the particles and time...
  22. FEAnalyst

    Plastic bending - analytical calculations

    Hi, I have a question regarding plastic bending of beams (assuming bilinear elastoplastic material - with or without hardening) . In literature one can find calculations of load capacity for those beams. But what else can be calculated in such case ? Stresses ? Deflection ? Where can I find...
  23. M

    Fully analytical solution for the "Leaky Integrate and Fire" Neuron model

    Does anyone know if it is possible to develop a fully analytical solution for a leaky integrate and fire neuron driven by arbitrary time-varying current? Here's what I have so far (setting as many possible constants to 0 and 1): The equations: ## \dot{V} = - V + I(t) ## and if ##V(t) = 1##...
  24. I

    A Combining model uncertainties with analytical uncertainties

    This is my problem : it all starts with some very basic linear least-square to find a single parameter 'b' : Y = b X + e where X,Y are observations and 'e' is a mean-zero error term. I use it, i find 'b', done. But I need also to calculate uncertainties on 'b'. The so-called "model uncertainty"...
  25. jk22

    I Mixed topic : from FEM to analytical solution via limits?

    Is this anyhow possible ? The system would be a wave equation modelized by a finite elements basis in space and time. Is there any method to do the limit discretization->continuum with paper and pencil ?
  26. Luke Tan

    I Peak of Analytical Fourier Transform

    In a numerical Fourier transform, we find the frequency that maximizes the value of the Fourier transform. However, let us consider an analytical Fourier transform, of ##\sin\Omega t##. It's Fourier transform is given by $$-i\pi\delta(\Omega-\omega)+i\pi\delta(\omega+\Omega)$$ Normally, to find...
  27. dRic2

    Can analytical mechanics be deduced from Newtonian mechanics?

    As you can see from the very last line of my post, this whole post may come from the fact that I don't get sarcasm o0)Hi, reading the above mentioned book I ran into the following footnote: Postulate A was earlier stated as: An alternative, but equal, version of Postulate A is given the page...
  28. DrClaude

    What is the Difference Between FFT Scaling and Analytical Fourier Transform?

    When considering the forward FFT of a mathematical function sampled at times ##t = 0, \Delta, \ldots, (N-1) \Delta##, following the usual convention, we have something like $$ H(f) = \int_{-\infty}^{+\infty} h(t) e^{-2 \pi i f t} dt \quad \Rightarrow \quad H_k = \sum_{n=0}^{N-1} h_n e^{-2 \pi i...
  29. O

    Analytical mathematical modeling of the torque caused by the laundry

    Hello my dear physicists, I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...
  30. M

    B Is there an analytical solution to this equation?

    So I've derived the rocket equation in empty space and with constant gravity. Now I am interested in adding air resistance. I'm aware that there are 2 different models as if 0<Re<1 then F_drag=k*v and if 1000<Re<30000 then F_drag=1/2*A*rho*CD*v^2. And for my purpose the second model is most...
  31. X

    Analytical proof that L and C are linear devices?

    I mean I know they are linear since they obey the ohms law. But I don't quite understand the reasoning that since, say, V=Ldi/dt and taking a derivative is a linear operation therefore it is a linear device?? I can verify that sin'(x) = cos(x) or sin(x+90) so the signal is time shifted but...
  32. dRic2

    Analytical solution to mono-group kinetics with a ramp of reactivity

    Consider the mono-group model and a ramp in reactivity like ##\rho = -\gamma \beta t## The system is $$\frac {dP}{dt} = \frac {\rho - \beta}{\Lambda} P + \lambda C$$ $$ \frac {dC}{dt} = \frac {\beta}{\Lambda} P - \lambda C$$ 1st method: assume that the concentration of precursor doesn't...
  33. B

    I Analytical Open Channel Rectangular Fluid Flow

    Hi All, I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.I've already found information involving a rectangular flow...
  34. S

    Analytical solution of the Photon Diffusion Equation

    Homework Statement Hello, I am currently working on photon diffusion equation and trying to do it without using Monte Carlo technique. Homework Equations Starting equation integrated over t: int(c*exp(-r^2/(4*D*c*t)-a*c*t)/(4*Pi*D*c*t)^(3/2), t = 0 .. infinity) (1) Result...
  35. T

    A Determine PDE Boundary Condition via Analytical solution

    I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...
  36. N

    Integration of an analytical expression

    I have an equation regarding integration equation. Given: where is found analytically to be: My question is what is the analytical equation for equation 3? I hope that anyone may help me regarding this matter. This is the paper I referred: https://arxiv.org/pdf/1503.05793.pdf Thank you.
  37. hilbert2

    A Analytical function from numerable point set

    Sometimes there are functions that are initially defined for only integer values of the argument, but can be extended to functions of real variable by some obvious way. An example of this is the factorial ##n!## which is extended to a gamma function by a convenient integral definition. So, if I...
  38. danielFiuza

    A Solution?: Quintic Equation from Physical System

    First time in this forum, so greetings to everyone! I am currently working with some physical models in the field of natural ventilation and I came across the following 5th order polynomial equation (quintic function): $X^{5}+ C X - C =0$ This is the steady state solution of a physical system...
  39. Ziezi

    Discrepancies between numerical and analytical solutions

    The analytical solutions are: \begin{equation} \psi(x) = \begin{cases} Ce^{\alpha x}, \text{if } x < -\frac{L}{2}\\ Asin(kx) + Bcos(kx), \text{if } -\frac{L}{2} \leq x \leq \frac{L}{2}\\ Fe^{-\alpha x} , \text{if } x > \frac{L}{2} \end{cases} \end{equation}...
  40. Pushoam

    Obtaining the equation of motion using analytical mechanics

    Let's consider a particle moving along x – axis, its position at t = 1s is 1m and speed is 1 m/s. How can one calculate acceleration on the basis of this information?
  41. Rx7man

    Analytical Thinkers: How to be Spontaneous & Romantic

    I know I can't speak for everyone here, but I would presume that most people in the sciences have either naturally or through schooling become analytical thinkers. Especially for the ones that are naturally analytical, have you found difficulty in being spontaneous, romantic, artistic, or any...
  42. Jianphys17

    Is understanding analytical mechanics essential for studying QM?

    Hi at all. I'm wondered is necessary learn well analytical mechanic ( eg learning The Goldstein's book), for understand and study QM ?
  43. vanhees71

    The Homopolar Generator: An Analytical Example - Comments

    Greg Bernhardt submitted a new PF Insights post The Homopolar Generator: An Analytical Example Continue reading the Original PF Insights Post.
  44. A

    Modeling analytical solution of 1D heat equation

    I am trying to write code for analytical solution of 1D heat conduction equation in semi-infinite rod. The analytical solution is given by Carslaw and Jaeger 1959 (p305) as $$ h(x,t) = \Delta H .erfc( \frac{x}{2 \sqrt[]{vt} } ) $$ where x is distance, v is diffusivity (material property) and t...
  45. P

    A The analytical linear tetrahedron method?

    The pioneering work by G. Lehmann, M. Taut, please see the attached files or download from wiley On the Numerical Calculation of the Density of States and Related Properties, http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220540211/abstract The question is how the middle line of Eq. (3.9)...
  46. Jianphys17

    Better textbook for analytical mechanics

    Hi at all. According to you which of the two texts, between Landau-Lifshitz (mechanics) and the Goldberg (classical mech) is better for study Analytical Mech ? Or there are other better ones ?
  47. S

    A Analytical evaluation of r^l integral

    Hello, I need to find the matrix elements of in the particular case where l = 1. This should have an analytical solution but I have no idea where to start with this demonstration. Any suggestions on where to start digging?Ty!
  48. J

    A Analytical Integration of a Difficult Function

    Is it possible to integrate the following function analytically? ##\int_{0}^{\infty} \frac{\exp{-(\frac{A}{\tau}+B\tau+\frac{A}{\beta-\tau})}}{\sqrt{\tau(\beta-\tau)}}d\tau,## where ##A##, ##B## and ##\beta## are real numbers. What sort of coordinate transformation makes the integral bounded...
  49. T

    Analytical Chemistry Concentration Calc Question

    A lab mate and I are discussing how to properly interpret LCMS results and coming to different conclusions. We are taking a solid food sample and extracting it with 50:50 acetonitrile/water to determine the concentration of melamine in the food sample. Standard solutions were made that range...
  50. saybrook1

    Analytical bending of a deformed beam

    Hi guys; I have an analytical solution for the deformation of a beam due to a couple with moments C_1 and C_2 with boundary conditions y=0 and x=±(L/2) where L≡length of the beam. The derivation from the Bernoulli-Euler equation is below: \begin{align*}...