Advection Diffusion Equation Abstract

\chapter{The Leggett-Garg Inequalities} Consider a system characterized by a dichotomous observable, which assumes values $\pm1$. Leggett-Garg inequalities (from now on LGI) set constrains on the value accessible to the two-times correlations functions $C_{ij}= \langle Q_{i}Q_{j} \rangle$, obtain measuring it at $t_{i}$ and $t_{j}$. The simplest of them is: \begin{equation}\label{LGI} -3 \leq K \leq 1 \end{equation} \begin{equation}\label{K} K=C_{12}+C_{23}-C_{31} \end{equation} This inequality is the focus of this chapter. Sections 2.1 is dedicated to the two assumptions required to obtain the inequality, a proof of (\ref{LGI}) is given. In section 2.2 I examine under which conditions a violation of (\ref{LGI}) can be observed, particular

In the next steps the density of water between 30-40 °C, 40-50 °C and 50-60 °C was measured. Then our results ρ vs T and also density vs temperature values given in the Steam Tables were plotted on the same graph in order to compare. In the second part the density of water was measured by density bottle. The densities obtained from the experiment are 995, 992.5, 991, 990 kg/m3 for the first part and

Lab Report 1 Logarithmic Plotting Devin Edwards ENGR 3070L CRN: 27194 January 17, 2018 Dr. Margraves Objective The purpose of this experiment is to graph and look at the logarithmic plots and write corresponding exponential equations that match the “Best Fit” line of the data points. Theory The data in Table 1 can be represented by the exponential equation given in equation 1 below. Equation 1 is also used for Cartesian plots: Q=KH^n (1) On this type of plot a straight line is drawn representing the slope intercept form in equation 2: y=mx+b (2) The variables are switched out allowing it to represent the same relationship in logarithmic form, where y is log(Q), x is log(H), n is m, and b is log(K): log⁡(Q)=log⁡(K)+n[log⁡(H)] (3)

• Using the calculated values plot a graph between log (Re) and log (f). • Further, using Prandtl and Karman’s formula for rough pipes substitute the value for Reynolds’ number and friction factor and hence, find the value of pipe roughness ks. RESULTS After tabulating the obtained results, we can observe the value of friction factors for each flow rate are as follows: And we obtain the following log (Re) vs. log (f) graphs for Laminar flow: And for Turbulent

In the given problem, the instructions were given to find the partial pressure of the reactant and the product using different equations. The equations used the formulas of (PNO2)^2/PN2O4=0.60 and PN2O4+PNO2=.050. To find the unknown values, it is necessary to rearrange to solve. After rearranging, continue by putting the values into the quadratic formula to calculate the partial pressure. The quadratic formula was found to be (-0.60±√(〖0.60〗^2-4(1)(-0.30)))/(2(1)), using PNO2 as “x”.

Then, the averages for each test were calculated and recorded in Table 2. The results were then transferred to Graph 1, which displays the effect of change in volume on pressure and illustrates the inverse relationship between the variables. Graph 2 demonstrates 1/volume versus pressure, and should have a linear best fit line that goes through the origin. However, due to the line of best fit not going through the origin, it is indicted that there are random and systematic errors. Graph 3 demonstrates pressure times volume versus pressure and should be a horizontal line.

Colorimetric determination of total protein in serum is based on the biuret reaction. The serum protein reacts with copper sulphate in the presence of sodium hydroxide. The Rochelle salt (K-Na-tartarate) contained in the biuret reagent is utilized to keep the formed cupric hydroxide in solution which gives the blue colour. The absorbencies of the sample (A sample) and of the standard (A standard) were read against the reagent blank in the spectrophotometer at a wavelength of 545nm. The total serum protein concentration (C) was calculated as follows: C (mg/dl) = A sample × concentration of the standard A standard.

From the line equation, rate was derived, rate is equal to the slope of the line. This procedure was repeated for two other solutions, generating three sets of results and three separate rates. The order of the each reactant, hydrogen peroxide and KI, was determined by creating a table that contained the volume of each reactant in each solution and the rate from the line equation. From this the

In this analytical study to determine the nonlinear effects of covariate three non-parametric methods Penalize spline, restricted cubic spline and natural spline in Cox model were used. The ability of nonparametric methods was evaluated to recover the true functional form of linear, quadratic and nonlinear functions, using different simulated sample sizes. Data analysis was carried out using R 2.11.0 software and significant levels were considered 0.05. Spline: The most common method of estimating function of f in equation (1) is the use of splines. Spline linear estimator is as

Write this down when you start the titration. Next, you must determine the volume of the solution delivered to reach the equivalence point. Next, you will find the moles of base used in the titration: *Note that the volume of base is in L, not in mL   Determine number of moles of HCl in flask: If you write the balanced reaction for the neutralization of sodium hydroxide and hydrochloric acid, you will see that the reaction proceeds in a 1:1 fashion. That is, for every hydroxide (OH‐) ion added, it can neutralize exactly one hydronium (H+) ion. This is not always the case for neutralization reactions, and is thus not always the case for acid‐base titrations.