experiment 1 measurement

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Experiment 1 - Measurements

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EXPERIMENT 1 - MEASUREMENT OF LENGTH, MASS AND TIME

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1.3: Experiment 1 - Measurements

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Measurements and the Irrational Number Pi

Learning Objectives

By the end of this lab, students should be able to:

• Accurately measure materials using a home made ruler.
• Select appropriate measuring device for each application.
• Select appropriate number of significant figures for each measurement.
• Convert between units or measurement using dimensional analysis.
• Differentiate between accurate and precise measurements in an aggregate set of data.
• Graph a set of data and determine the slope with Google sheets.

Prior Knowledge:

• 1B.1: Units of Measurement
• 1B.2: Making Measurements: Experimental Error, Accuracy, Precision, Standard Deviation and Significant Figures
• 1B.3: Mathematics in Chemistry
• 1B.5: Graphs and Graphing

Introduction

In this lab, students will work in groups of 3-5 people using Zoom breakout groups while collaborating on a Google Doc, and will create two scales based on the width of their own pointer finger (PF) as a base unit to determine the value of Pi. Students will use their PF unit to create a scale of the Fist, where 1 Fist (F) unit is equal to the width of 5 PF units. Once this scale is completed, students will then create a more precise scale, called the deciFist scale, where each deciFist (dF) unit is equal to 1/10th the length of the Fist unit (10 dF is equal to 1 F). After creating these two scales, students will then find 5 circular objects of varying sizes around their house, measure the circumference and diameter of each object with their homemade scales, and then use Google Sheets to plot these measurements and determine the value of Pi. 

• Week 1 :  Students work in their group to design a protocol for building a ruler based on the width of their pointer finger. Each student individually performs the experiment and plots their data in Google Sheets.
• Week 2 : Students pool all of the data from their group, plot with Google Sheets, and work up their data and turn in individual worksheets.

In this lab you may need to obtain supplies, so if you go to the store be sure to follow proper COVID-19 hygienic protocols, wear a mask, wash your hands thoroughly and maintain safe distance from fellow shoppers.  Please review these protocols from the CDC .

• two strings or shoe laces that can be marked on
• two different colored markers that will show up on your string (such as red and blue)
• firm paper (thin cardboard from food packaging can be used)
• one object needs to have a diameter larger than the width of two of your fists
• one object needs to have a diameter smaller than the width of three of your fingers
• the other three object need to be various sizes
• ruler with metric units (cm)
• cell phone with camera
• laptop or computer with camera, speakers and microphone hooked up to internet

Pre-Lab Primer

This assignment is an individual assignment to be completed on your own with the help of the "Prior Knowledge" links at the top of this page. The assignment will be due 10 minutes before your lab begins. Late work will not be accepted.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

Interactive Element

In-Lab Assignments

Week 1: february 1st - february 4th, measurements experiment design proposal.

Using Zoom breakout groups, collaboratively work with your group on the assignment in your Google Classroom called " Measurements Experiment Design Proposal ". You can see a preview of this document below. Your group needs to develop a protocol for how to build the two rulers mentioned above (one with Fist Scale and one with deciFist Scale) by using the width of your pointer finger (PF) as a base unit. Since you will be measuring circular objects, the rulers need to be made of a flexible material.  Use the information on this LibreTexts page to help you complete the assignment. NOTE : You are not making the actual rulers yet. Your group is only brainstorming how those rulers could possibly be made.

Building and Using Your Rulers

Each group will share their experiment design proposal with the class. After each group has shared, the lab instructor will generate a  Standardized Experimental Protocol , which everyone will follow to create their own rulers. This document will be posted in your Google Classroom. You will then use your two rulers to make circumference and diameter measurements of the five circular objects that you found around your house. 

You will be in contact with your group via Zoom. You can help each other with the ruler building process and you can discuss your Google Sheets data and graphs, but each individual person will be making their own ruler and measurements.

These two scales measure the same unit of length (the width of 5 pointer fingers, which we call the Fist unit), but they both have different precision. When making measurements, students must report the correct number of significant digits based on the scale they are using (all certain values and the first "guestimate", section 1B.2.1.2  of your LibreTexts).

Graphing your Data to Determine the Value of Pi

You will use a Google Sheet in your Google Classroom called " Group Graphing Assignment " to record the measurement data of each of the 5 objects from both of your rulers. It is called a group assignment, but each individual student will have their own tab to input their data on. Make sure you are reporting your measurements with the correct number of significant digits based on the ruler you used to make those measurements. NOTE: The Google Sheet may not allow you to put the correct number of significant digits. If this happens, there are two buttons at the top of the Google Sheet that you can use to add or remove decimal places. If you need help finding these buttons, ask your group members or your lab instructor.

As you enter your data, the Google Sheet will make a graph of the data for you. The slope for each of your graphs should be very close to the value of Pi (3.14159...) once you have entered all of your measurements. If this is not the case, you may have made your rulers incorrectly or you may not have read the correct measurement value from the ruler. Double check your work. If there is error this week that doesn't get corrected, there will still be error next week since you will be using the same measurements again.

The sheet below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

Week 2: February 8th - February 11th

Individual graphing assignment.

Last week, when you input your measurement data into Google Sheets, a graph was automatically created for you. This week you will be responsible for making your own graphs. Before you begin, take 5 minutes to watch the  "Graphing with Google Sheets"  video below. In your graphs, you will be required to include all of the graphical elements that are mentioned in the video.

Video \(\PageIndex{1}\): Tutorial on using Google sheets for linear graphs created by Bob Belford ( https://youtu.be/muF0eJkN9CQ )

After watching the video, you can open the assignment in your Google Classroom called  Individual Graphing Assignment . For this assignment, you will be combining the Week 1 measurement data from yourself and each of your group members, and then creating four graphs.

• Graph 1: Use all group members' data from the Fist Scale and include the origin point (0,0)
• Graph 2: Use all group members' data from the Fist Scale and do not include the origin point (0,0)
• Graph 3: Use all group members' data from the deciFist Scale and include the origin point (0,0)
• Graph 4:  Use all group members' data from the deciFist Scale and do not include the origin point (0,0)

The sheet below is a preview only. You will be able to find your assignment to work on in Google Classroom.

Individual Lab Report

After you finish your individual graphs, you will be asked to complete the Individual Lab Report . This assignment is an individual assignment to be completed on your own during lab. It will be due at the end of your lab period. You can discuss questions with your group members, but all work must be your own, including the images of your supplies and rulers.

For some problems, you will be asked to show your work. You should keep track of your work on a piece of paper and label with the question number it belongs to. There will be a box at the end of the document for you to insert an image of your work. Do not insert the image under each individual question.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

Post-Lab Problem Set

After you have had a chance to work on data analysis with your group during lab, you will be given the Measurements Post-Lab Problem Set.  This is an individual assignment that must be completed on your own, and it is based on your Pre-Lab Primer and your In-Lab Assignments. This assignment will be due the day after your lab meets by 5 p.m. For example, if your lab is on Monday, the Post-Lab Problem Set will be due on Tuesday at 5 p.m. No late work is accepted.  

Contributors and Attributions

Robert E. Belford  (University of Arkansas Little Rock; Department of Chemistry) led the creation of this page for a 5 week summer course. 

Elena Lisitsyna contributed to the creation and implementation of this page.

• Mark Baillie coordinated the modifications of this activity for implementation in a 15 week fall course, with the help of Elena Lisitsyna and Karie Sanford.

Physical Review Research

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Effects of measurement power on state discrimination and dynamics in a circuit-QED experiment

L. tosi, i. lobato, m. f. goffman, c. metzger, c. urbina, and h. pothier, phys. rev. research 6 , 023299 – published 20 june 2024.

• No Citing Articles
• INTRODUCTION
• CQED SETUP WITH ATOMIC CONTACTS
• EFFECT OF THE PHOTON NUMBER ON THE…
• EFFECT OF PHOTON NUMBER ON DRESSED QUBIT…
• INTRINSIC DYNAMICS: IMPLICATIONS FOR…
• DISCUSSION AND CONCLUSIONS
• ACKNOWLEDGMENTS

We explore the effects of driving a cavity at a large photon number in a circuit-QED experiment where the “matterlike” part corresponds to a unique Andreev level in a superconducting weak link. The three many-body states of the weak link, corresponding to the occupation of the Andreev level by 0, 1, or 2 quasiparticles, lead to different cavity frequency shifts. We show how the nonlinearity inherited by the cavity from its coupling to the weak link affects the state discrimination and the photon number calibration. Both effects require treating the evolution of the driven system beyond the dispersive limit. In addition, we observe how transition rates between the circuit states (quantum and parity jumps) are affected by the microwave power, and compare the measurements with a theory accounting for the “dressing” of the Andreev states by the cavity.

• Received 10 October 2023
• Revised 24 October 2023
• Accepted 29 April 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.023299

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

• Research Areas

Authors & Affiliations

• 1 Quantronics group, Service de Physique de l'État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
• 2 Devices and Sensors Group and Balseiro Institute, Centro Atómico Bariloche, CNEA, CONICET, Argentina
• * [email protected]

Article Text

Vol. 6, Iss. 2 — June - August 2024

Subject Areas

• Quantum Physics
• Superconductivity

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Continuous monitoring of the quantum state of an atomic-size contact: (a) microwave setup: a continuous microwave tone at the frequency of the bare resonator f r is sent to the microwave cavity. The reflected signal is amplified at low temperature by a Josephson parametric converter (JPC), then mixed with a local oscillator tone to obtain the homodyne components I and Q of the response. One point every 10 ns is recorded with a fast acquisition card, resulting in time traces like the ones shown in (b), which display jumps between states. (c) The cavity is a coplanar quarter-wavelength microwave resonator patterned in a 150-nm-thick Nb film on a Kapton substrate. (d) An aluminum loop is fabricated near the resonator shorted end. (e) The loop contains a narrow suspended bridge that can be broken, under cryogenic vacuum, by bending the substrate. Atomic-size weak links hosting Andreev bound states are obtained by bringing the two resulting electrodes back into contact. Different atomic configurations are obtained by fine-tuning the substrate curvature.

Pointer states positions vs probe tone amplitude. Predicted position of the center of the pointer states corresponding to | g 〉 and | e 〉 , on both sides of the horizontal axis, and | o 〉 ( χ 0 / κ = 0 ), as a function of the normalized probe tone amplitude n 0 (color scale), and for n crit = 1000 , 100 , 30 , 10 . The color curves correspond to χ ( 0 ) / κ = 0 , 0.25 , 0.5 , 1 , and 2. Circles correspond to S 11 ( f ) for n 0 = 5 , 10 , 15 , 20 , and using Q t = 950 , Q i = 4500 . The panel at n crit = 1000 is the closest to the linear regime: the position of the clouds evolves almost linearly with n 0 .

Histograms of the values of ( I , Q ) recorded during continuous measurements at various probe amplitudes. (a) Contact with f A = 6.33 GHz , at increasing probe amplitudes n 0 . In each panel, the color is associated to the value of n 0 , and the brightness in the color scale encodes the number of counts per pixel, with a linear variation from 0 to 12000. (b) Panels correspond to nine different contacts, with f A given in GHz in the text box. Colors correspond to increasing probe amplitudes as in (a): n 0 ≈ 1 (black), 4 (blue), 8 (cyan), 12 (magenta), and 16 (red) (precise values in Table  1 ). Color brightness scale limits are set between max/6 and max to reduce histogram overlaps. Dashed circles correspond to predictions for n 0 S 11 ( f ) , globally scaled for each contact in order to account for the measurement gain, shifted and rotated to align with the clouds. Crosses indicate the positions of the center of the three clouds inferred from the analysis of the traces, at all values of n 0 . Solid lines are predicted positions n 0 S 11 ( ± χ ( n ¯ ( n 0 ) ) + δ ω ) , and n 0 S 11 ( δ ω ) , scaled, rotated, and shifted as the circles. A constant frequency shift δ ω was adjusted in each series, see Table  1 .

Schematic explanation of a DDROP (double drive reset of population) measurement. The protocol consists in performing the qubit 2-tone spectroscopy in presence of a tone at frequency f 0 = ω 0 / 2 π close to that of the cavity. Left: steady state population of the ground state of the qubit calculated in the dispersive approximation, as a function of ω 0 , and of drive frequency ω 1 . According to Eq. ( 3 ), the average number of photons in the cavity n ¯ g is described by a lorentzian with a maximum at ω 0 − ω r = − χ 0 ( > 0 ) , when the qubit is in its ground state, and a mirrored lorentzian centered at ω 0 − ω r = χ 0 ( < 0 ) for n ¯ e corresponding to the excited state. The blue (red) dashed line corresponds to ω 1 − ω q ( 0 ) = 2 n ¯ g χ 0 ( = 2 n ¯ e χ 0 ) and describes the Stark shift of the qubit transition. A and B correspond to the qubit driven at ω 1 = ω q ( 0 ) + 2 n ¯ g χ 0 and ω 1 = ω q ( 0 ) + 2 n ¯ e χ 0 respectively. In both cases, a cavity drive at ω 0 = ω r − χ 0 creates a coherent state in which only some upper levels of the | g 〉 ladder are significantly populated (populations represented with disks). In A, the qubit is driven at its shifted frequency, ω 1 − ω q ( 0 ) = 2 n ¯ g χ 0 giving rise to Rabi oscillations between the two ladders around the n ¯ g th level (populations of involved levels shown with grey disks). As in the qubit excited state | e 〉 the cavity drive is not resonant, cavity decay transfers the population to the lowest states of the ladder (black disks). This leads to a steady state with an accumulation of population in the excited state (heating). In B, the qubit drive is resonant with ω 1 − ω q ( 0 ) = 2 n ¯ e χ 0 , giving rise to Rabi oscillations between the two ladders around the n ¯ e th level (populations of involved levels shown with grey disks). Here, the cavity drive, which is resonant when the qubit is in | g 〉 , transfers the population to higher energy levels of the | g 〉 ladder. As a result, the population of | g 〉 becomes larger than at thermal equilibrium (cooling). Simulation parameters: f q = 7.15  GHz, g / 2 π = 0.078  GHz, n ¯ = 50 ,   f r = 8.77 GHz , and κ / 2 π = 9.2 MHz .

DDROP measurements for qubits at 7.15 and 8.2 GHz using a cavity drive amplitude corresponding to n ¯ = 25 and n ¯ = 22 photons respectively (see discussion on calibration in the text). The qubit and cavity drive pulses are applied simultaneously during 10 µ s followed by a 1 µ s measurement pulse at f r = 8.77 GHz . The grey scale corresponds to the population p g of the ground state. The smaller contrast at f A = 8.2 GHz is attributed to a shorter lifetime than at 7.15 GHz. The dashed lines correspond to Eq. ( 11 ). While for 7.15 GHz the experiment resembles Fig.  4 , a simplified dispersive theory would predict an erroneous qubit shift. The effect is more pronounced when the qubit frequency approaches the cavity frequency, as one observes non-Lorentzian resonances arising from the nonlinearity.

DDROP measurement of a contact with f A ≈ 7.15 GHz with increasing cavity drive power. Dashed lines are fits, yielding the dependence of cavity mean occupation n ¯ g (blue) and n ¯ e (red) according to Eq. ( 8 ), hence the photon number at resonance n 0 shown in the rightmost panel (during data acquisition, f A slightly drifted: 7.15 GHz for the first two panels, then 7.12 GHz, and 7.2 GHz for the last one).

Dependence on Andreev frequency f A of the coupling g , the cavity pull χ 0 and the critical photon number n crit . The black vertical lines correspond to the Andreev frequencies of the measured atomic contacts. The blue line corresponds to the resonator bare frequency f r .

Contributions to the dressed dynamics. Each panel shows the qubit levels | g 〉 and | e 〉 (blue and red), the cavity, and cavity levels (magenta). Black and cyan rectangles represent the baths that couple to the qubit through σ x , y and σ z , respectively. Magenta rectangle correspond to a bath coupled to the cavity. Bath energy levels are shown in green as a collection of harmonic oscillators. The two shifted ladders below schematize the energies of the combined states | g , n 〉 ≡ | g 〉 ⊗ | n 〉 and | e , n 〉 ≡ | e 〉 ⊗ | n 〉 (grey) and dressed states | g , n 〉 ¯ and | e , n 〉 ¯ (black). (a) Dressed, (b) Purcell, (c) dephasing-induced, (d) excitation-induced and (e) cavity-excitation-induced relaxation. The direction of the photon wavy arrows assume f r < f q < 2 f r . (a') to (e') are the corresponding excitation processes, with all the arrows pointing in the opposite direction. (a”) to (e”) Dependence of the rates as a function of the cavity occupation n , for different values of the detuning Δ (0.5, 1, 2, 4 GHz), and using the experimental parameters g / 2 π = 85 MHz and f r = 8.77  GHz.

Definition of the transition rates between states. (a) Rates between all states, with the distinction between odd states with different spin | o ↓ 〉 and | o ↑ 〉 . (b) Equivalent diagram with a spin-degenerate odd state.

Relaxation and excitation transition rates as a function of photon number for different contacts ( f A indicated on each panel from f A = 4.94 to 14.4 GHz, with symbolic representation of the relative position of f A (red cross) relatively to f r (black tick) on a segment representing the interval 4–15 GHz). Arrows on the x axis indicate the value of n crit . Rates are obtained from the analysis of time traces with a boxcar average of 10 points. Continuous lines correspond to calculated dependencies using the theoretical expressions in Eq. ( 15 ) with prefactors shown in Fig.  19 .

Parity jump transition rates as a function of photon number for different contacts ( f A indicated on each panel from f A = 4.94  GHz top-left to 14.4 GHz right-bottom). Rates are obtained from the analysis of time traces with a boxcar average of 10 points. Orange and red disks signal results that depend significantly on filtering, and hence are less significant (see Appendix  pp3 ).

Intrinsic relaxation and excitation rates as a function of Andreev frequency f A . (a) Comparison of the Purcell rate Γ κ = κ 0 [ f A ] ( g Δ ) 2 extracted from the fits (symbols) with theoretical photon emission rate Γ EM , ↓ (solid line), using T EM = 300  mK. (b) Intrinsic relaxation rate Γ ↓ 0 (symbols) compared with phonon emission rate Γ ph , ↓ (solid lines), using C ph = 40 s − 1 GHz − 4 and T ph = 200  mK. (c) Total intrinsic relaxation rate Γ κ + Γ ↓ 0 (red squares) and emission rate Γ κ * + Γ ↑ 0 (blue squares), from the analysis of the full dependence of the rates with photon number. Rates from the extrapolation of the data at n ¯ = 0 (black diamonds). Solid lines are comparison with theory describing photon and phonon emission and absorption.

Intrinsic parity jumps transition rates as a function of f A obtained from extrapolation of data of Fig.  11 towards n ¯ = 0 .

Histograms of all the values of ( I , Q ) recorded during continuous measurements at various probe amplitudes for the same nine contacts as in Fig.  3 , with f A given in GHz in the text box.

Effect of smoothing of the time traces, for strong measurement power. The results of the HMM analysis are shown for decreasing smoothing factors (from top to bottom), for the contact at f A = 7.5 GHz , at n ¯ g = 163 and n ¯ o = 226 : red lines indicate the most probable state at each time. Left panels shown the same excerpt of a trace ( I and Q quadratures) with the various smoothing; right panels show the corresponding histograms in the ( I , Q ) plane (grey scale), with the position of the clouds as found from the HMM analysis. Error bars indicate the size of the clouds. Bottom panels show on the left the evolution of the rates with smoothing; on the right the evolution of the position of the clouds.

Effect of the smoothing of the time traces, for weak measurement power: same parameters as Fig.  15 , except that n ¯ g = 10 and n ¯ o = 23 . The very high rates found at low smoothing correspond in the reconstructed trace (red) to very short dwell times, which are averaged out by the smoothing.

Relaxation and excitation transition rates as a function of photon number for different contacts ( f A indicated on each panel from f A = 4.94  GHz to 14.4 GHz, with symbolic representation of the relative position of f A (red cross) relatively to f r (black tick) on a segment representing the interval 4–15 GHz). Arrows on the x axis indicate the value of n crit . Rates obtained from the analysis of time traces with less filtering are represented with bigger symbols (see text). Orange and red disks signal results that depend significantly on filtering, and hence are less significant. Continuous lines correspond to calculated dependencies using the theoretical expressions in Eq. ( 15 ) with prefactors shown in Fig.  19 .

Parity jump transition rates as a function of photon number for different contacts ( f A indicated on each panel from f A = 4.94  GHz top-left to 14.4 GHz right-bottom). Rates obtained from the analysis of time traces with less filtering are represented with bigger symbols (see text). Orange and red disks signal results that depend significantly on filtering, and hence are less significant.

Prefactors of the different contributions to the dressed dynamics (see Fig.  8 ) obtained from comparison with the data in Fig.  10 as a function of the relevant frequencies. Top (bottom) panel: dressed, Purcell (inverse Purcell), dephasing-induced, excitation- (relaxation-) induced and cavity-excitation-induced relaxation (cavity-relaxation-induced excitation). (The disposition of the panels corresponds to that in Fig.  8 ).

Cavity mean occupation vs cavity-drive detuning δ = f r − f 0 for g / 2 π = 85  MHz, f q = 8 GHz at increasing drive power, in blue. In black lines, the result in the dispersive limit, with a constant resonance shift χ 0 = − 0.009  GHz. Red line shows χ ( n ) .

Relaxation experiment: the qubit is initially in the excited state and evolves towards the thermal population in a time scale given by T 1 . Red (blue) points correspond to the simulation for g / 2 π = 85  MHz ( g = 0 ), while lines are exponential fits (same parameters as in Fig.  20 ).

Comparison between the rates renormalization obtained from numerical simulations of the time evolution (symbols), and the theoretical prediction (lines). [(a) and (a')] Renormalization of Purcell relaxation and cavity-relaxation-induced excitation rates [see Figs.  8  and 8 ] for different values of | Δ | / g , all other contributions being set to zero. The Purcell term is always present when one simulates the effect of the other terms. In the other panels, Δ / g = 5 , and the corresponding curves Γ ↓ a and Γ ↑ a † are recalled with black dashed lines. Simulated rates are represented with blue and red squares. In each panel, we also show for the largest value of the parameter ( Γ ↓ 0 ,   Γ ↑ 0 , or Γ ϕ = 5 Γ κ ) the result of the simulation with the Purcell contribution subtracted (operation symbolized with a black arrow). [(b) and (b')] Renormalization of relaxation and excitation rates for Γ ↓ 0 / Γ κ = 5 , 1, and 0 (b) corresponds to dressed relaxation [see Figs.  8 ] and 8 to relaxation-induced excitation [see Figs.  8 ]. [(c) and (c')] Renormalization of relaxation and excitation rates for different values of Γ ↑ 0 / Γ κ . (c) corresponds to excitation-induced relaxation [see Fig.  8 ] and 8 to dressed excitation [see Fig.  8 ]. [ 8  and 8 ] Renormalization of relaxation and excitation rates for different values of Γ φ / Γ κ . (d) corresponds to dephasing-induced relaxation [see Fig.  8 ] and 8 to dephasing-induced excitation [see Fig.  8 ]. Parameters: κ / 2 π = f r / 950 ,   g / 2 π = 50  MHz, and f r = 8.77  GHz. We note that in this treatment of the time evolution for the open system the frequency dependence of the noise spectra are not taken into account.

Comparison of experimental data presented in Fig.  5 with DDROP simulations, for f A = 7.15  GHz and f A = 8.2  GHz. The parameters chosen for the simulation are g / 2 π = 85 MHz ,   κ = 58 µ s − 1 ,   A 1 / 2 π = 1.05  MHz, and Γ ↓ = 0.116 µ s − 1 ( 0.12 µ s − 1 ), Γ ↑ = 0.156 µ s − 1 ( 0.05 µ s − 1 ), Γ ϕ = 0.00937 µ s − 1 ( 0.016 µ s − 1 ), for f A = 8.2  GHz ( f A = 7.15  GHz) respectively, leading to p t h = 0.1 (0.15), T 1 = 0.640 µ s ( 3 µ s ), and T 2 = 1.250 µ s ( 5.45 µ s ).

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Mathematics > Optimization and Control

Title: measure this, not that: optimizing the cost and model-based information content of measurements.

Abstract: Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) problem to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, \texttt{SciPy}, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO$_2$ capture. Both case studies show how examining the Pareto-optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

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Development and implementation of a novel split-wise model to predict the cutting forces in milling of Al2024 for minimum error

• Original Research
• Published: 20 June 2024

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• Thomas Heitz 1 , 2 ,
• Ning He   ORCID: orcid.org/0000-0003-2231-7482 1 ,
• Muhammad Jamil 1 &
• Daniel Bachrathy 2  

Accurate prediction of cutting force is essential not only for estimating power and torque but also for precise chatter prediction, where even the derivative of the cutting force function is crucial. The traditional cutting force model does not consider the runout, and the enhanced models that consider it are often difficult to be established due to the need of physical runout measurements. This study proposes a newly developed split-wise model to predict the cutting forces in Al2024. This model includes the calculation of the cutting force considering individual teeth which leads to the determination of 6 force coefficients of different values per tooth. The experiments were conducted on milling Al2024 for two set of experiments ( \(V_{fz}\) = 375–675 m/min, \(a_e\) = 4–12 mm, \(a_p\) = 0.5–1 mm, D =16 mm) and ( \(V_{fz}\) = 220–440 m/min, \(a_e\) = 0.5–1 mm, \(a_p\) = 0.5–1 mm, D =2 mm). For the first set, the comparative error determined from the split-wise and classic models is 5.6% and 7.8%, respectively. For the second set, the error is 11% and 15.7%, respectively. Therefore, the split-wise cutting force model is capable of adapting the runout and consequently improving the prediction of the cutting force with both large and small tools operations. Additionally, the split-wise may find applications in advanced manufacturing technologies allowing industries to enhanced productivity and quality.

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Acknowledgements

The authors would like to express gratitude to the China Scholarship Council (CSC) for providing financial support during the course of this study.

This work was funded by the National Natural Science Foundation of China (NSFC) [Grant No. 52250410358 and 51975289] and by the Hungarian National Research, Development and Innovation Office [Grant No. NKFI FK-138500].

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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Thomas Heitz, Daniel Bachrathy, Muhammad Jamil, and Ning He. The first draft of the manuscript was written by Thomas Heitz, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Heitz, T., He, N., Jamil, M. et al. Development and implementation of a novel split-wise model to predict the cutting forces in milling of Al2024 for minimum error. Int J Adv Manuf Technol (2024). https://doi.org/10.1007/s00170-024-13913-0

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Received : 09 November 2023

Accepted : 27 May 2024

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DOI : https://doi.org/10.1007/s00170-024-13913-0

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Applicability of digital image photogrammetry to rapid displacement measurements of structures in restricted-access and controlled areas: case study in korea.

1. Introduction

2. materials and methods, 2.1. field investigation, 2.2. monitoring of the mse wall, 2.3. displacement measurement field experiment on mse wall, 3. results and discussion, 3.1. evaluating the cause of cracks on the mse wall facing at the case site, 3.2. monitoring results, 3.3. discussion of applicability of digital image photogrammetry, 4. conclusions.

• The cause of the facing crack of the MSE wall in this research’s case study site was evaluated based on the results of the electrical resistivity survey. The evaluation results confirmed that an abnormal area occurred in the corner of the structurally vulnerable MSE wall due to the groundwater infiltration of the original ground and reinforced earth mass. In other words, it was observed that it caused the facing crack and deformation of the MSE wall.
• In order to evaluate the applicability of digital image photogrammetry in restricted-access and controlled areas, the displacement of the MSE wall was monitored using the traditional monitoring method and digital image photogrammetry. The monitoring results showed that the displacement values showed similar elapsed time trends for both methods, but digital image photogrammetry results exhibited larger displacements than the traditional monitoring results. Nevertheless, the error of the digital camera applied for digital image photogrammetry was lower than that of the cellphone camera.
• In order to evaluate the accuracy of digital image photogrammetry, the error rate was analyzed. The results showed that the error at a specific location was similar between the digital camera and the cellphone camera. However, it was found that digital image photogrammetry using a digital camera with a consistent error occurrence tendency is highly applicable to rapid structural deformation monitoring in restricted-access and controlled areas.
• It was found that research on the effect of the camera’s pixels on the error was necessary in order to improve the accuracy and error resolution of digital image photogrammetry using a digital camera. In addition, the effect of the aligned image on the accuracy of the measurement coordinates in the 3D transformation of the 2D image acquired from the digital camera must be studied. It was also evaluated that the position of the digital camera may have contributed to the error rate of the measurement results. Therefore, research should continue to evaluate the limitations of the image acquisition distance and angle of the digital camera.

Author Contributions

Institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Choi, C.-H.; Han, J.-G.; Hong, G. Applicability of Digital Image Photogrammetry to Rapid Displacement Measurements of Structures in Restricted-Access and Controlled Areas: Case Study in Korea. Appl. Sci. 2024 , 14 , 5295. https://doi.org/10.3390/app14125295

Choi C-H, Han J-G, Hong G. Applicability of Digital Image Photogrammetry to Rapid Displacement Measurements of Structures in Restricted-Access and Controlled Areas: Case Study in Korea. Applied Sciences . 2024; 14(12):5295. https://doi.org/10.3390/app14125295

Choi, Chang-Hwan, Jung-Geun Han, and Gigwon Hong. 2024. "Applicability of Digital Image Photogrammetry to Rapid Displacement Measurements of Structures in Restricted-Access and Controlled Areas: Case Study in Korea" Applied Sciences 14, no. 12: 5295. https://doi.org/10.3390/app14125295

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