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I N T E R D I S C I P L I N A R Y L I V E L Y A P P L I C A T I O N S P R O J E C T
PHYSICAL CONCEPTS EXAMINED: 1. Concept of a mobile source for vehicle emissions2. Optimal driving speeds to minimize emissions3. Total vehicle emissions for a given speed profile
COMPUTING REQUIREMENT: 1. Spreadsheet and ability to use it2. Calculator and ability to use it
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Contents1. Introduction2. Remote Emission-Sensing Technique3. Emission Data Collection4. Data Conversion5. Regression Analysis6. Emission-Based Speed Optimization7. Real-World ApplicationsReferencesSample SolutionNotes for the InstructorAbout the Authors
1. IntroductionCars, trucks, motorcycles, and buses emit significant quantities of carbon
monoxide (CO), hydrocarbons (HC), nitrogen oxides (NOx), and fine particles(PM). These chemical compounds play dominant roles in air pollution prob-lems. In the densely populated Northeast, where the air pollution problem isespecially severe, the Environmental Protection Agency (EPA) has projectedthat highway vehicles will account for approximately 38% of the total NOx in-ventory and 22% of the total HC inventory in 2005, in spite of the tighter motorvehicle standards in the 1990 Clean Air Act Amendment (CAAA) (Figure 1).
Figure 1. Traffic.
Vehicle emissions, especially CO, NOx, and HC, are harmful to the healthof humans. CO is a tasteless, odorless, and colorless gas produced throughthe incomplete combustion of carbon-based fuels. CO enters the bloodstreamthrough the lungs and reduces the delivery of oxygen to the body’s organsand tissues. The health threat from exposure to CO is most serious for those
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who suffer from cardiovascular disease, particularly those with angina or pe-ripheral vascular disease. Exposure to elevated CO levels is associated withimpairment of visual perception, work capacity, manual dexterity, learningability and performance of complex tasks. NOx emissions also produce a widevariety of health and welfare effects. Nitrogen dioxide can irritate the lungs andlower resistance to respiratory infection (such as influenza). NOx emissions areimportant in acid rain, affecting both terrestrial and aquatic ecosystems. At-mospheric deposition of nitrogen leads to excess nutrient enrichment problems(“eutrophication”). Finally, HC, in combination with NOx in the presence ofheat and sunlight, will form ozone. Ozone forms readily in the atmosphere,usually during hot summer weather. Ground-level ozone is the prime ingre-dient of smog, the pollution that blankets many areas during the summer.Short-term exposures (1–3 hours) to high ambient ozone concentrations havebeen linked to increased hospital admissions and emergency room visits forrespiratory problems.
With the rapid increase of the number of motor vehicles along with world-wide economic development, the vehicle emission problem has worsened.Many governments have started to implement certain vehicle emission-controlstrategies. Steady progress in reducing certain air pollution problems is occur-ring in the US, Europe and Japan. Globally, the use of advanced pollution-control technology, especially catalysts has been spreading, as has the use ofunleaded gasoline. However, the continued economic growth in the world re-quires the use of strategies that do not impose negative effect on the economicdevelopment, in other words, do not restrict vehicle ownership. Examplesof such strategies that have already been implemented in many cities in theworld include advanced traffic-control techniques, integrated transportationplanning process, and Intelligent Transportation Systems (ITS) technologies.
Past research has shown that driving patterns greatly influence the amountof vehicle emissions. Frequent acceleration and deceleration tend to generatemore emissions than smoother driving. An effective traffic signal timing plancan smooth traffic flow in a manner that reduces the emissions. In addition, wellplanned transportation projects or activities can change the driving patterns ofvehicles in the city at a more macroscopic level.
2. Remote Emission-Sensing TechniqueThe key to success in developing an emission-control strategy is obtaining
accurate quantification of vehicle emissions under various traffic and envi-ronmental scenarios. The remote emission-sensing device that is used in thisproject is called SMOG DOG. It performs environmental monitoring to measureautomotive emissions. The SMOG DOG can simultaneously measure emissionconcentrations of CO, HC, NOx, and CO2 in the dispersing exhaust cloud ofvehicles. A special feature of the SMOG DOG is its capability in detecting avehicle’s instantaneous speed and acceleration rate.
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Figure 2. SMOG DOG in action.
3. Emission Data CollectionSMOG DOG was used to collect vehicle emission data from a freeway on-
ramp in Houston, TX (Figure 2). The operation of SMOG DOG requires thatthe vehicle be in motion. Hence, the emission data for the idling mode arenot collected. Instead, vehicle idling emissions will be calculated based on theregression models that are developed. Table 1 illustrates the emission data onCO and HC concentrations that were collected.
Problem: Develop models relating vehicle speed and vehicle exhaust emissionsof CO and HC. Formulate speed recommendations based on your model andthe given data. Use of spreadsheet technology is strongly recommended. Inputthe data in Table 1 into a spreadsheet (4 columns). You will add four morecolumns in Requirement 2 and two more in Requirement 4.
Requirement 1Use the data in Table 1 to
• plot the CO concentration (%) vs. speed data, and
• plot the HC concentration (%) vs. speed data.
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Table 1.
CO and HC concentration data collected by SMOG DOG in Houston.
Data # Speed (mph) CO% HC% Data # Speed (mph) CO% HC%
4. Data ConversionTo develop models relating vehicle speed to emission quantities, we intro-
duce two emission quantities: emission factor (g/mi) and emission rate (g/s).
The emission factor is the number of grams emitted when the vehicletravels one mile.
The emission rate is the total emission in grams that a vehicle emitsper second.
We define the following variables:
• CO%: CO emission concentration (%);
• HC%: HC emission concentration (%);
• COs: CO emission rate in grams per second (g/s);
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• HCs: HC emission rate in grams per second (g/s);
• COm: CO emission factor in grams per mile (g/mi);
• HCm: HC emission factor in grams per mile (g/mi);
• u: a vehicle’s instantaneous speed in miles per hour (mph);
• uoptimal: optimal speed (mph) that minimizes emissions;
• b0, b1, c0, c1: constant values (regression model coefficients).
Conversion of emission concentrations to emission rates is problematic.Many scientists and engineers use the following linear correlation relationships,developed for the emission concentrations and emissions factors by the SouthCoast Air Quality Management District (SCAQMD).
Conversion from emission concentrations to emission factors:
COm (g/mi) = 11.1 × CO% + 21.3, (1)
HCm (g/mi) = 63.3 × HC% + 1.7. (2)
Conversion from emission concentrations to emission rates:
COs (g/s) =COm (g/mi) × u mph
3600, (3)
HCs (g/s) =HCm (g/mi) × u mph
3600. (4)
Requirement 2Use (1)–(4) to convert the CO/HC concentrations in Table 1 to CO/HC
emission factors and CO/HC emission rates. Expand your spreadsheet tableto include the 8 columns: Data #, Speed, CO%, HC%, COm, HCm, COs, andHCs.
Requirement 3Draw four graphs to show the relationships between speed and CO/HC
emission factors as well as CO/HC emission rates using the data prepared inRequirement 2. Based on your visual analysis of these graphs, which rela-tionships display a better regularity of shapes and trends; emission factors oremission rates?
Vehicle Emissions 457
5. Regression AnalysisIn many engineering and scientific applications, relationships between vari-
ables are established by first collecting data from experimental studies in eitherthe laboratory or the field. This data is then plotted and relationship discerned.In this project, the two variables in the relationship represent the speed andthe CO/HC emission rates. Because of potential errors in measurement, thedata shown in the graphs drawn in Requirement 3 may not fall precisely on asmooth curve. For this reason, the task of the analysis becomes threefold:
• to hypothesize the mathematical form of the relationship between the twovariables (model postulation);
• to estimate the parameters of the model based on the collected field data(model calibration); and
• to determine how well the calibrated relationship explains the observed data(goodness of fit).
This analysis process is called regression.Scientific research on vehicle emissions has shown that the best mathemat-
ical function to model the relationship between the speed and the CO or HCemission rate is the natural logarithm, expressed in the following forms:
ln(COs) = b0 + b1u, (5)
ln(HCs) = c0 + c1u. (6)
The speed u is the independent or explanatory variable. The emission rates, COsor HCs, are called the dependent or explained variables. The constant coefficientsc0 and c1 are the model parameters. Data from Requirement 2 can be used toplot ln(COs) vs. speed and ln(HCs) vs. speed. Calibrating the model meansdetermining the unknown values of the parameters in (5) or (6) to obtain thebest fit to these plots. The goodness of fit is measured by the coefficient ofcorrelation, r. Its value can range from −1 to +1. If r is near +1, there exists ahigh positive correlation; if it is near−1, there exists a high negative correlation;and if it is around zero, there exists no correlation between the independentand the dependent variables.
Requirement 4Use the regression technique and the data prepared in Requirement 2 to
calibrate (5) and (6). The data for COs and HCs prepared in Requirement 2need to be transformed by the natural logarithm (ln) before a simple linearregression can be carried out. Hint: Add columns for ln(C0s) and ln(HCs) toyour spreadsheet table constructed in Requirement 2. Then plot the ln(C0s)vs. speed and form the linear regression. Repeat for ln(HCs) vs. speed.
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Requirement 5Calculate the coefficient correlations for the regressions in Requirement 4.
Are the models acceptable? Why? Draw the line plot for each of the regressionequations generated.
6. Emission-Based Speed OptimizationEmission rates (g/s) can be transformed into emission factors (g/mi) by
solving (3) for COm and (4) for HCm. The new equations are:
COm (g/mi) =COs (g/s) × 3600 (s/h)
u (mi/h), (7)
HCm (g/mi) =HCs (g/s) × 3600 (s/h)
u (mi/h). (8)
Equations (3) and (4) for the emission rates are in the form y = mx, where theslopes are COm/3600 and HCm/3600. Because these slopes are positive, theemission rates are monotonically increasing functions of speed; hence, thereare no minimum values for a moving vehicle. The situation is less clear for theemission factors described by (7) and (8). These equations can be transformedinto explicit functions of speed by solving for COs and HCs in the results ofRequirement 4 and then substituting these results into (7) and (8). Doing thisyields
COs (g/s) =3600eb0+b1u
u, (9)
HCm (g/s) =3600ec0+c1u
u. (10)
A graphical analysis can now be made to determine what speeds will min-imize the emission factors. Knowledge of these speeds is critical informationfor developing an advanced traffic management scheme to reduce emissionamounts.
Requirement 6Draw a graph with two curves, one for the relationship between the speed
and the CO emission rate, and the other for the relationship between the speedand the CO emission factor. Draw a second graph with two curves, one for therelationship between the speed and the HC emission rate, and the other for therelationship between the speed and the HC emission factor. Let the speed bemeasured starting from 0 to 70 mph in increments of 5 mph. Then calculatethe emission rates by solving for COs and HCs in the equations generated inRequirement 4, and the emission factors using (9) and (10). Based on the visualanalysis of the graphs, is there a speed that can minimize the emission factor?
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Requirement 7Approximate the speeds corresponding to the minimum points on the emis-
sion factor plots. What speed do you recommend for minimizing both the COand HC emission factors? Hint: On a graphing calculator, use the trace featureto trace a point along the curve to the minimum position or use the table featureto determine the coordinates of the minimum point. For a spreadsheet, iteratethe function values to determine the minimum.
7. Real-World ApplicationsIf all drivers traveled at the optimal speed, the total CO or HC emissions
would be the minimum. On the other hand, if vehicles are driven at varyingspeeds, the resulting emissions will be higher. To analyze such a pattern, we as-sume two different speed profiles experienced by two different vehicles. Bothvehicles are driven for 30 s, but the first vehicle travels at a constant speed of35 mph while the speed of the second vehicle varies between 29 and 42 mph (seeTable 2). After 30 s, both vehicles have driven the same distance, 1540 ft. Al-though both vehicles have been driven the same distance during the same timeperiod, it is expected that the resulting vehicle emissions would be different.Table 2 illustrates the details of these two different speed profiles.
Requirement 8Based on Table 2, plot two graphs, one for the constant speed profile, and
one for the varying speed profile. For each speed profile, there should betwo curves, one for the relationship between time and speed, and one for therelationship between time and the distance. Use different y-axes for speed anddistance.
Requirement 9Use the regression equations derived from Requirement 4 to calculate the
CO and HC emissions at each second for the two different speed profiles inTable 2. Make your calculation in a table. Then, calculate the total CO and HCemissions for the entire travel of the two speed profiles. What can you concludefrom your calculations?
Requirement 10Assume that an accident happened on a location of a freeway segment. A
police officer came to the scene to process the necessary paperwork for thisaccident and towing vehicles came to remove all vehicles involved. It took a
total of 40 min from the start of the accident to the time when the accident sceneis completely cleared. During this period, a total of 200 vehicles have to stop.Assume the average wait is 30 min per vehicle. Calculate the total additionalCO and HC emissions that were generated by these 200 vehicles due to thetraffic accident. What can you conclude from your calculation? Hint: Derivethe idling emissions rates by setting the speed equal to zero in the results ofRequirement 4.
ReferencesEuropean Conference of Ministers of Transport (ECMT). 291. Vehicle Emission
Reductions. Paris, France: OECD Publications Services (2, rue Andre Pascal,75775 Paris Cedex 16, France).
Sorbe, N. 1995. Hughes Employee Vehicle Exhaust Remote Sensing and Emis-sions Evaluation Project. Report prepared for the Mobile Source Air Pollu-tion Reduction Review Committee (MSRC) under the AB2766 Program. ElSegundo, CA: Hughes Environmental Systems, Inc.
Vehicle Emissions 461
Yu, L. 1998a. Collection and Evaluation of Modal Traffic Data for Determinationof Vehicle Emission Rates under Certain Driving Conditions. ResearchReports 1485-1, 1485-2, and 1485-3F for TxDOT Project No. 0-1485, Centerfor Transportation Training and Research. Houston, TX: Texas SouthernUniversity.
. 1998b. Remote vehicle exhaust emission-sensing for traffic simu-lation and optimization models. Journal of Transportation Research Part D:Transport and Environment 3: 337–347.
CO% Versus Speed
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60 70 80 90
Speed (mph)
CO
Co
nce
ntr
atio
n (
%)
462 24.4 (2003)
Title: Vehicle Emissions
Sample SolutionRequirement 1: The graphs between the speed and CO and HC concentrationsare shown in Figures S1 and S2.
Figure S1. CO concentration vs. speed.
Based on visual analysis of these graphs, clearly the speed is not correlatedwith the CO or HC concentrations. The data are scattered and do not show anyregularity of shapes or trends.
Requirement 2: The generated table is shown in Table S1.
Requirement 3: See Figures S3–S6. A visual analysis of the graphs suggeststhat the CO/HC emission rates have greater regularity of shape and trend withthe speed than do the CO/HC emission factors.
Requirement 4: The resulting regression equations are:
ln(COs) = −2.46215 + 0.028383u, or COs = e−2.46215+0.028383u,
ln(HCs) = −4.91624 + 0.030929u, or COs = e−4.91624+0.030929u.
HC% Versus Speed
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 10 20 30 40 50 60 70 80 90
Speed (mph)
HC
Co
nce
ntr
atio
n (
%)
CO (g/mi) Versus Speed
0.0000
5.0000
10.0000
15.0000
20.0000
25.0000
30.0000
35.0000
40.0000
45.0000
0 10 20 30 40 50 60 70 80 90
Speed (mph)
CO
Em
issi
on
s (g
/mi)
Vehicle Emissions 463
Figure S2. HC concentration vs. speed.
Figure S3. CO emission factor vs. speed.
Data # Speed CO% HC% COm(g/mi) HCm(g/mi) COs(g/sec) HCs(g/sec)
Requirement 5: r(COs) = 0.9089, r(HCs) = 0.8644.Both correlation coefficients are close to one, so both regression equations
have acceptable goodness of fit. Since r(COs) is slightly higher than r(HCs),the regression equation for COs is better than the one for HCs.
Figure S7. Line plot for the speed and the CO emission factor.
Requirement 6: From Figures S9–S10, there clearly exists a speed value thatminimizes either the CO emission factor or the HC emission factor. On theother hand, the emission rates are monotonically increasing functions of thespeed.
Requirement 7: uoptimal for CO = 35 mph; uoptimal for HC = 32 mph.
Speed Line Plot
-10
-5
00 50 100
Speed
ln(H
C)
LN(HC)
Predicted LN(HC)
CO Emissions Versus Speed
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Speed (mph)
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/mi)
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)
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CO (g/sec)
HC Emissions Versus Speed
0
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0 20 40 60 80
Speed (mph)
HC
(g
/mi)
0.00
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0.05
0.06
0.07
HC
(g
/sec
)
HC (g/mi)
HC (g/sec)
Vehicle Emissions 467
Figure S8. Line plot for the speed and the HC emission factor.
Figure S9. Relationships between the CO emission rates/factors and the speed.
Figure S10. Relationships between the HC emission rates/factors and the speed.
Speed Profile 1 - Constant Speed
0
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1400
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0 5 10 15 20 25 30
Time (sec)
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ft)
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Speed Profile 2 - Varying Speed
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0 5 10 15 20 25 30
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eed
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i/hr)
Distance (ft)Speed (mph)
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Requirement 8: See Figures S11–S12.
Figure S11. Illustration of constant speed profile.
Figure S12. Illustration of varying speed profile.
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Requirement 9: See Table S2.
Table S2.
Second-by-second calculations.
Constant Speed Profile Varying Speed ProfileTime Speed 1 CO 1 HC 1 Speed 2 CO 2 HC 2
For the CO emissions, the varying speed profile generates a total of 7.04 gcomparing with the 6.91 g for the constant speed profile (2% higher). Similarlyfor the HC emissions, the varying speed profile generates a total of 0.663 g com-paring with the 0.649 g of emissions for the constant speed profile (2% higher).Since the optimal speed is 35 mph for CO and 32 mph for HC, the constantspeed profile in this requirement should result in the minimum CO emissionsand close to minimum HC emissions. Although the 2% higher emissions doesnot seem like a significant amount, this is just for 30 s for a single vehicle. Youcan imagine how much additional emissions would be generated if all vehiclesin the city drive at varying speeds of a significant level. On the other hand, thetraffic managers should try to implement traffic management strategies thatwould encourage or force drivers to drive at desired and constant speeds.
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Requirement 10: Set speed to 0 in the regression equations in Requirement 4to derive the idling emission rate in units of grams per second:
COs when idling = e−2.46215+0.028383u= 0.08525 g/s,
HCs when idling = e−4.91624+0.030929u= 0.00733 g/s.
Therefore, during the 30 min delay, a vehicle will emit the following total COand HC emissions:
CO idling emissions for one vehicle for 30 min = 0.08525 × 30 × 60=153.45 g,
HC idling emissions for one vehicle for 30 min = 0.00733 × 30 × 60= 13.194 g.
Therefore, the total CO emissions for 200 vehicles = 153.45 × 200 = 30,690 g andthe total HC emissions for 200 vehicles = 13.194 × 200 = 2,639 g.
From the above calculation, we can see that one traffic accident can resultin considerable additional CO and HC emissions. Considerably more emis-sions will be produced if many traffic accidents happen in the city. Therefore,reducing the number of traffic accidents can reduce the vehicle emissions.
Vehicle Emissions 471
Title: Vehicle Emissions
Notes for the InstructorThis project is designed for students to practice algebraic calculations, data
analysis, and optimization using real-world vehicle emission data. The vehicleemission issue is becoming more and more important because of the stricterregulations imposed by the U.S. Environmental Protection Agency (EPA). Ve-hicle emissions are a big source of air pollution and are related to many of ourhealth problems.
The key to the successful completion of this project is a clear understandingof the sequence of the data, the definitions of the variables, the relationshipsbetween variables, as well as the algebraic, data analysis, and optimizationconcepts. Any additional information related to vehicle emission-control canbe introduced in the class. The instructor can introduce various emission datacollection techniques. The instructor can also introduce more complicated mod-eling and data analysis techniques.
The simplest regression equation is used in this project, which althoughnonlinear, includes only one variable. The instructor can encourage studentsto test various regression formulas and different combinations of variables. Forinstance, other regression models to consider include
COs = b0 + b1u + b2u2,
HCs = c0 + c1u + c2u2.
Requirements 4–9 can be repeated with these other regression formulas.The instructor can also encourage students to search literature on other
existing vehicle emission models. Students can compare the calculation resultsbetween the models developed in this project and other models.
472 24.4 (2003)
About the Authors
Lei Yu is Professor and Chairperson of the Trans-portation Studies Department at Texas Southern Uni-versity. He is also a Changjiang Scholar of Beijing Jiao-tong University. He received a bachelor’s degree inTransportation Engineering from Northern Jiaotong Uni-versity, Beijing, China and a master’s degree in Pro-duction and Systems Engineering from Nagoya Insti-tute of Technology, Nagoya, Japan. His Ph.D. degreein Civil Engineering was awarded by Queen’s Univer-sity in Kingston, Ontario, Canada. His research inter-ests involve highway traffic operations and modeling,
urban transportation planning, the ITS-related technologies and applications,and vehicle exhaust emission modeling. Since 1994, Yu has been the Princi-pal Investigator (PI) of more than 25 research projects that were sponsored byTexas Department of Transportation (TxDOT), Federal Highway Administra-tion (FHWA), Federal Transit Administration (FTA), Southwest Region Univer-sity Transportation Center (SWUTC) program, National Institute of Standardsand Technology (NIST), and Houston Advanced Research Center (HARC); thetotal funding amount is over $2 million. Dr. Yu has published more than 50research papers in the Journal of Transportation Research, Transportation ResearchRecords, and the Journal of Transportation Engineering, as well as in various peer-reviewed conference proceedings. Dr. Yu is an active member of the Institute ofTransportation Engineers (ITE), the American Society of Civil Engineers (ASCE)and the Transportation Research Board (TRB). He is a registered engineer inthe State of Texas. He also belongs to numerous committees, councils, and taskforces in regional, state, national, and international organizations.
Don Small graduated from Middlebury College andreceived his Ph.D. degree in mathematics from the Uni-versity of Connecticut. He taught mathematics at ColbyCollege for 23 years before joining the Mathematics Depart-ment at the U.S. Military Academy in 1991. He is activein the calculus and college algebra reform movements—developing curricula, authoring texts, and leading facultydevelopment workshops. Active in the Mathematical As-
sociation of America (MAA), Don served a term as Chairman and two termsas Governor of the Northeast Section and has been a long-term member ofthe MAA’s CRAFTY committee. His interests are in developing curriculumthat focuses on student growth while meeting the needs of partner disciplines,society, and the workplace. He is also a member of AMATYC and AMS.