?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F179%2F&rft.title=Resistance+Monitoring&rft.creator=Westbrook%2C+Rex&rft.creator=Bohun%2C+Sean+C.&rft.subject=Materials&rft.subject=None%2FOther&rft.description=The+problem+considered+was+that+of+estimating+the+temperature+field+in+a+contaminated+region+of+soil%2C+using+measurements+of+electrical+potential+and+current+and+also+of+temperature%2C+at+accessible+points+such+as+the+wells+and+electrodes+and+the+soil+surface.+%0A%0AOn+the+timescale+considered%2C+essentially+days%2C+the+equation+for+the+electrical+potential+is+static.+At+any+given+time+the+potential+%24V%24+satisfies+the+equation+%24%5Cnabla+%5Ccdot+(%5Csigma+%5Cnabla+V+)+%3D+0%24.+Time+enters+the+equation+only+as+a++parameter+since+%24%5Csigma%24+is+temperature+and+hence+time+dependent.%0A%0AThe+problem+of+finding+%24%5Csigma%24+when+both+the+potential+%24V%24+and+the+current+density+%24%5Csigma+%5Cpartial%7BV%7D+%2F+%5Cpartial%7Bn%7D%24+are+known+on+the+boundary+of+the+domain+is+a+standard+inverse+problem+of+long+standing.+It+is+known+that+the+problem+is+ill+posed+and+hence+that+an+accurate+numerical+solution+will+be+difficult+especially+when+the+input+data+is+subject+to+measurement+errors.%0A%0AIn+this+report+we+examine+a+possible+method+for+solving+the+electrical+inverse+problem+which+could+possibly+be+used+in+a+time+stepping+algorithm+when+the+conductivity+changes+little+in+each+step.%0A%0ASince+we+are+also+able+to+make+temperature+measurements+there+is+also+the+possibility+of+examining+an+inverse+problem+for+the+temperature+equation.+There+seems+to+be+much+less+literature+on+this+problem%2C+which+in+our+case+is+essentially%2C+a+first+order+equation+with+a+heat+source.(We+neglect+thermal++conductivity%2C+which+is+small+compared+with+the+convection).+Combining+the+results+of+both+inverse+problems+might+give+a+more+robust+method+of+estimating+the+temperature+in+the+soil.&rft.date=2002&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F179%2F1%2Fmacmillan.pdf&rft.identifier=++Westbrook%2C+Rex+and+Bohun%2C+Sean+C.++(2002)+Resistance+Monitoring.++%5BStudy+Group+Report%5D+++++