Cold Regions Science and Technology
|
|
- Hector Beasley
- 5 years ago
- Views:
Transcription
1 Cold Regions Science nd Technology 97 () 97 Contents lists ville t ScienceDirect Cold Regions Science nd Technology journl homepge: Mesurements of snow sl displcement in Extended Column Tests nd comprison with Propgtion Sw Tests A. vn Herwijnen,,K.W.Birkelnd WSL Institute for Snow nd Avlnche Reserch SLF, Dvos, Switzerlnd USDA Forest Service Ntionl Avlnche Center, Bozemn, MT, USA rticle info strct Article history: Received 7 Decemer Received in revised form July Accepted July Keywords: Snow frcture Snow stility tests Avlnche forecsting Prticle trcking The Extended Column Test (ECT) hs ecome incresingly populr for ssessing snowpck stility. Wht hppens to the snow sl nd the underlying wek lyer during the test remins lrgely unknown. Such work hs een done for the Propgtion Sw Test (PST), ut not for the ECT. We therefore nlyzed high-speed videos of ECTs nd djcent PSTs using prticle trcking to etter understnd the mechnics of the ECT. Our results show tht in n ECT, tpping on one end of the column hd no oservle effect on the opposite end, nd tht frcture initites in n re of the wek lyer directly under the shovel t the free edge of the column. We oserved no signs of progressive dmge ccumultion in the wek lyer during tpping, ut rther single rpid collpse when frcture initited. In contrst, in PSTs, we oserved sl ending prior to wek lyer frcture. During frcture, wek lyers in ECTs compct on the order of severl mm, similr to mesurements otined from PSTs. Mesured propgtion speeds, on the order of to m s, were lso similr to those from PSTs. The similrities etween ECT results nd those with PSTs give us confidence tht the frcture mechnics re similr regrdless of the triggering mechnism. From prcticl perspective, our results suggest tht the ECT is indeed mesuring the propensity of crck to propgte t the smll scle of the ECT lock, thus providing informtion on criticlly importnt property of snow stility in our tests. Elsevier B.V. All rights reserved.. Introduction Dry snow sl vlnches re preceded y frcture of wek snowpck lyer elow cohesive sl of snow. An initil wek lyer crck must first rech criticl size efore it expnds rpidly, relesing sl vlnche (e.g. Schweizer et l., ). Wek lyer crcks cn form nturlly (e.g., due to snow loding) or rtificilly (e.g., due to skier loding or explosive triggers). Avlnche workers nd reserchers utilize snow stility tests to chrcterize snow strtigrphy nd estimte whether prticulr slope is stle or unstle. Idelly, results from these tests should provide unmiguous informtion on the ese of crck initition nd the propensity for crck propgtion, oth of which re required for snow sl vlnche relese (e.g. vn Herwijnen nd Jmieson, 7). However, given the inherent limittions of the vrious tests in replicting the vlnche relese process nd the sptilly vrile nture of the mountin snowpck, snow stility test results re not unmiguous nd require expert interprettion (Schweizer nd Jmieson, ). Nevertheless, numer of different studies demonstrte the usefulness of snow stility tests for ssessing vlnche risk (e.g. Föhn, 97; Simenhois nd Birkelnd, 9; vn Herwijnen nd Jmieson, 7). Snow stility tests consist of isolting lock of snow of pre-defined dimensions nd incrementlly loding the lock up to mximum lod. Corresponding uthor. Tel.: + 7. E-mil ddress: vnherwijnen@slf.ch (A. vn Herwijnen). While one gol of these tests is to identify potentil wek lyers, the primry gol is to evlute the lod required to frcture them, i.e. to crete n initil crck tht will propgte. Trditionlly, the most commonly used tests were the Rutschlock test (Föhn, 97), consisting of. y m lock of snow loded y skier, nd the compression test, consisting of y cm lock of snow loded y tpping on snow shovel (Jmieson, 999). While the loding step t wek lyer frcture minly reltes to crck initition, dditionl informtion on crck propgtion is otined through qulittive frcture oservtions (e.g. Schweizer nd Jmieson, ). In recent yers, reserchers developed two new field tests to investigte frcture initition nd frcture propgtion long the wek lyer, nmely the Extended Column Test (ECT) nd the Propgtion Sw Test (PST) (Guthier nd Jmieson,, ; Sigrist nd Schweizer, 7; Simenhois nd Birkelnd, 9; vn Herwijnen nd Jmieson, ). The ECT involves isolting lock 9 cm cross-slope y cm upslope nd then progressively loding one side of the lock y tpping on snow shovel, similr to compression test (Simenhois nd Birkelnd,, 9). Avlnche workers hve rpidly dopted the ECT since its introduction in. It hs ecome the most populr stility test in the pst two yers y SnowPilot users (Chot et l., ), eing conducted in lmost % of the pits (Birkelnd nd Chot, ). The usefulness of the test s forecsting tool for predicting vlnche conditions hs een studied in severl different snow climtes nd countries (e.g. Ross nd Jmieson, ; Simenhois nd Birkelnd, -X/$ see front mtter Elsevier B.V. All rights reserved.
2 9 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () 97 Tle Overview of the snow properties t ech field site. Site N ECT N PST θ (degrees) F H (m) ρ sl (kg m ) A. DH 9 9 B. SH 7 9 C. FC D. SH E. SH 7 F. SH 9 G. SH The numer of ECTs (N ECT ), the numer of nd PSTs (N PST ), slope ngle (θ), wek lyer grin form (F), sl depth (H) nd men sl density (ρ sl ) re shown for ech site. The oserved wek lyer grin forms were: depth hor (DH), surfce hor (SH) nd fceted grins (FC). 9; Winkler nd Schweizer, 9). However, the processes leding to wek lyer frcture in the ECT hve thus fr not een investigted. The PST involves isolting lock tht is cm cross-slope y cm upslope (or the wek lyer depth, whichever is greter) nd then cutting the wek lyer with snow sw until wek lyer frcture (Guthier nd Jmieson, ). The populrity of the PST hs risen stedily since its introduction. It ws the third most common field test mongst SnowPilot users for the winter of / (Birkelnd nd Chot, ). In contrst to the ECT, the PST hs een the suject of severl detiled studies focusing on the mechnics of the test to etter understnd some of the fundmentl processes involved in snow frcture (e.g. Bir et l., ; vn Herwijnen nd Heierli, 9; vn Herwijnen et l., ). Much of this work utilizes prticle trcking, where video recording of the test is mde with high speed cmer nd mrkers re inserted into the snowpck to nlyze snow displcement using prticle trcking softwre. In this study we pply the sme prticle trcking technique used in PST studies to the ECT. The gol is to etter understnd the mechnics of the ECT, such s whether or not the whole lock is ffected y the tpping, where the frcture initites, nd whether frcture speeds in the ECT re similr to those mesured with the PST. An improved mechnicl understnding of the test will help to etter interpret test results nd evlute potentil limittions.. Methods.. Dt collection We collected dt t seven sites during the / winter in southwest Montn, USA (Tle ). At ech field site, we did mnul snow profile to otin informtion on snow strtigrphy nd performed one or severl ECTs nd PSTs ccording to the procedure outlined in Greene et l. (). In some cses, our ECTs hd wider columns, llowing us to etter evlute wek lyer frcture t distnces frther from the tpping re (Fig. ). Our PSTs lso hd longer columns, nd we modified the columns to hve slope norml, rther thn verticl, column ends, s suggested y other reserch (Bir et l., ; Heierli, ; vn Herwijnen nd Heierli, ). After excvting test columns from the surrounding snow cover, we inserted lck plstic mrkers into the snow wll ove the wek lyer. Using cmer on tripod pointing directly t the pit wll, we mde video recordings of the tests t frmes per second. We stood off to the side during the ECTs while tpping so s not to ostruct the cmer view of the mrkers (Fig. ). A chllenge encountered during ECTs ws tht snow often fell in front of the mrkers directly elow the snow shovel during tpping, nd mrkers fell out of the pit wll s the lock ws compressed (Fig. ). This mde it difficult, or in some cses impossile, to ccurtely trck the displcement of mrkers immeditely elow the shovel. This prolem did not ffect mrkers further wy from the shovel... Dt nlysis We utilized prticle trcking velocimetry (PTV) lgorithm to nlyze the displcement of the mrkers in the imges of the video recording (Crocker nd Grier, 99). Coordintes re ssigned to the centroid of ech mrker y using sptil nd pss filter to serch for locl rightness minim. In this wy, the position of the mrkers in ech video frme cn e determined with men ccurcy of. mm. The ccurcy of the prticle trcking softwre depends on the size nd the qulity of the imges, i.e. signl-to-noise rtio. We used coordinte system ligned with the slope: the x-xis pointing in down-slope direction prllel to the snow surfce, the z-xis pointing towrds the ground norml to the snow surfce. We defined the displcement of mrker in the slope prllel direction u x nd in the slope norml direction u z s the displcement reltive to the initil position, tht is, the verge position of the mrker p prior to movement. In the following, solute displcements U ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u x þ u z re lso reported. For propgting crcks, there is dely etween u z of susequent mrkers. The time dely etween the onset of movement etween mrkers is proportionl to the distnce etween the mrkers nd ws used to clculte the propgtion speed c of frcture, s outlined in vn Herwijnen nd Jmieson (). We estimted uncertinties in c using Monte Crlo method to ccount for the PTV mesurement uncertinty nd uncertinties ssocited with the scling distnce mesurement (±%). By mking rndom drws from the proility distriutions for the input quntities (ssumed norml), we evluted the resulting distriution. The vlues of c reported here re the men of the respective distriutions nd the reported uncertinty is twice the stndrd devition of the respective distriutions, which gives level of confidence of pproximtely 9%. Fig.. () The experimentl setup consisted of recording ECTs with lck mkers inserted into the pit wll on high speed videos. () During tpping, flling snow prtilly oscured mrkers directly under the shovel, mking trcking those mrkers difficult or impossile.
3 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () Results We nlyzed the displcement of the sl in 9 ECTs nd PSTs t seven different sites with slope ngles (θ) rnging from to (Tle ). The mjority of wek lyers consisted of uried surfce hor (SH), while one wek lyer consisted of depth hor (DH) nd one of fceted grins (FC). We tested vriety of sls (Fig. ), including soft new snow (site D), soft fceted snow (sites A, F nd G), rounded snow (sites B nd E), nd wind deposited snow (site C). Sl thickness, mesured verticlly, rnged from. to.7 m nd men sl density rnged from to kg m... Snow displcement in ECTs Tpping on the lock during ECTs minly compcted the snow directly elow the snow shovel nd hd little influence deeper in the snow cover or further wy from the shovel. For exmple, the snow column in test ECT_E ws sustntilly compressed directly elow the shovel prior to wek lyer frcture (Fig. nd ). In this experiment, the wek lyer consisted of uried surfce hor which frctured fter 7 tps. Frcture rrested efore crossing the entire column nd crck through the sl occurred pproximtely hlfwy through the column (Fig. ). The solute displcement of mrkers in the upper hlf of the sl directly elow the shovel exhiited the lrgest displcements (drk nd light lue curves in Fig. c). On the other hnd, prior to wek lyer frcture, we did not mesure ny displcement of mrkers closer to the wek lyer nd further wy from the shovel (green, ornge nd red curves in Fig. c). Note tht for these ltter mrkers the displcements oserved fter ech tp, indicted with the dshed lines in Fig. c, were rtifcts resulting from snow flling in front of the mrkers. Prior to wek lyer frcture, we did not mesure ny displcement of the mrkers closest to the wek lyer in ECTNs, i.e. ECTs in which the frcture rrested efore crossing the entire column. In ECT_F, the initil wek lyer frcture ws not oserved in the field. Susequent tps then resulted in dditionl wek lyer compction (Fig. ). In ll ECTPs, i.e. ECTs in which the frcture crossed the entire column, we lso did not oserve ny displcement for mrkers closest to the wek lyer prior to wek lyer frcture. This is clerly seen for row of mrkers directly ove the wek lyer in test ECT_B in Fig.. These results lso show tht sl displcement due to wek lyer frcture strts t the free Fig.. Results from experiment ECT_E (ECTN 7). () Imge tken t the strt of the test. The colored dots show the mrkers for which the displcements re shown. () Imge tken t the end of the test showing considerle crushing of the column, prtil wek lyer frcture nd sl frcture. (c) Totl displcement with time. The colors of the displcement curves correspond to the mrkers indicted with the colored dots in (). The dshed lines correspond to tps. end of the column efore propgting to the other side. This ehvior ws oserved in ll ECTPs. In ll our ECTs, u z rnged from. to 9. mm in the re where the wek lyer frctured (Tle ). In ECTPs, u z fter wek lyer frcture either decresed (ECT_D, ECT_D, ECT_D nd ECT_F) or incresed (ECT_B nd ECT_B) throughout the column (Fig. ). In ECTNs, on the other hnd, u z decresed to zero typiclly within. to. m from the free edge of the column (Fig. ). Note tht in some experiments we could not determine the totl slope norml displcement due to sliding of the lock fter wek lyer frcture... Snow displcement in PSTs Progressively swing the wek lyer during PSTs resulted in ending of the sl prior to wek lyer frcture, s previously reported (Bir et l., 7 Site A 7 Site B 7 Site C 7 Site D 7 Site E 7 Site F 7 Site G FF F P FF F P FF F P FF F P FF F P FF F P FF F P Fig.. Overview of the snow strtigrphy t ech site. The hnd hrdness is shown for the lyers ove the wek lyer (lue) s well s for the wek lyer (red). The depth is shown reltive to the top of the wek lyer.
4 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () 97 ; vn Herwijnen nd Heierli, ). While the slope norml displcement ssocited with sl ending ws generlly smll, on the order of. mm, it ws clerly oserved in the u z curves of mrkers closest to the free end of the column, independent of susequent frcture distnces (rrows in Fig. ). Like in ECTs, sl displcement cused y weklyerfrcturestrtedtthefreeendofthecolumneforepropgting to the other end of the column (Fig. ). Note tht in experiment PST_F the initil wek lyer frcture ws not oserved in the field. Susequent swing then resulted in dditionl nd rupt wek lyer collpse (Fig. ). After wek lyer frcture, u z rnged from. to. mm in the PSTs (Tle ). In PSTs where the wek lyer frctured through the entire column, u z fter wek lyer frcture generlly decresed (PST_B, PST_C, PST_C nd PST_G) long the column, except for experiment PST_B (Fig. 7). In PSTs where the wek lyer did not frcture through the entire column, u z decresed to zero within. to. m from the free edge of the column (Fig. 7)... Propgtion speed Propgtion speeds in ECTPs rnged from to m s (Tle ), while in PSTs c rnged from 9 to m s (Tle ). Despite our reltively short columns, smll vritions in c with distnce were oserved (not shown), lthough no consistent trend ws present. Propgtion speeds in ECTs either incresed (ECT_A, ECT_A, ECT_B, ECT_B nd ECT_D), were reltively constnt (ECT_C nd ECT_D), or decresed (ECT_A, ECT_D nd ECT_F). Likewise, propgtion speeds in PSTs either incresed (PST_B), were reltively constnt (PST_A, PST_C, PST_C nd, PST_E), or decresed (PST_B nd PST_G). We mesured the propgtion speed for oth ECTs nd PSTs t three sites (sites A, B nd C). Vlues from oth tests were in resonle greement, except for site C, where c mesured in the ECT ws lrger thn in oth djcent PSTs (compre Tles nd ). Despite the lrge rnge of c vlues, they re consistent with previous mesurements (Johnson Tle Overview of ECT results nd PTV mesurements. Test Test result W (m) (mm) c (m s ) ECT_A ECTP.. ± ECT_A ECTN.. ECT_A ECTN.... ECT_A ECTP.. ± 9 ECT_A ECTP.9. 7 ± ECT_B ECTP....7 ± ECT_B ECTP ± ECT_C ECTP 7.. ± 9 ECT_D ECTN ECT_D ECTN....7 ECT_D ECTP ± ECT_D ECTP.... ± 7 ECT_D ECTP ± ECT_E ECTN ECT_F ECTP.... ± ECT_F ECTN.... ECT_F ECTN.... ECT_G ECTN....7 ECT_G ECTN ECT results re shown ccording to Greene et l. (): ECTP## frcture initites nd propgtes cross the entire column on tp ##; ECTN## frcture initites without full propgtion on tp ##. Width of the column (W), PTV mesurement ccurcy (), the rnge of slope norml displcement in the re where the wek lyer frctured (u z )nd frcture speed with mesurement uncertinty (c) re lso shown. The column slid down-slope fter frcture. Frcture propgtion eyond the re elow the shovel ut not cross the entire column. et l., ; vn Herwijnen nd Jmieson, ; vn Herwijnen et l., ) (Fig. ). Comining our dt with dt from previous studies results in sttisticlly significnt reltionship etween propgtion speed nd men sl density (Person r =., p =. ; Fig. ). Furthermore, c lso correlted significntly with u z (Person r =., Fig.. Slope norml displcement with time for the row of mrker closest to the wek lyer in tests () ECT_F (ECTN ) nd () ECT_B (ECTP ). The colors of the lines correspond to the distnce of the mrkers to the free edge of the column in m, s indicted in the legend. The dshed lines correspond to tps.
5 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () ECT_B ECT_B ECT_D ECT_D ECT_D ECT_F ECT_A ECT_D ECT_D ECT_E ECT_F ECT_F ECT_G ECT_G.. Horizontl distnce (m). Horizontl distnce (m) Fig.. Men totl slope norml displcement fter wek lyer frcture with horizontl distnce long the column for () ECTPs nd () ECTNs. The colors of the lines correspond to the experiments indicted in the legend. p =. ; Fig. ), confirming results previously reported y vn Herwijnen nd Jmieson ().. Discussion While the PST hs een the suject of severl detiled studies focusing on frcture initition, frcture propgtion nd crck fce friction (Bir et l., ; vn Herwijnen nd Heierli, 9, ; vn Herwijnen nd Jmieson, ), thus fr the processes leding to wek lyer frcture nd frcture propgtion in the ECT re mostly unknown. The results presented here therefore provide vlule insight into the mechnics of the ECT nd llow for detiled comprison with the PST. Note tht in some cses we used non-stndrd test columns in our experiments. Some cution is therefore wrrnted when pplying our results to stndrd tests, s very little is known out the influence of test geometry on results. Overll, the mesurements suggest tht there is no grdul dmge ccumultion in the wek lyer during tpping in n ECT. Indeed, no noticele displcement ws oserved in mrkers directly ove the wek lyer prior to frcture (Figs. nd ). Furthermore, the mesurements lso show tht tpping on the column minly compresses the snow directly elow the shovel nd does not ffect the fr end of the column (Fig. ). We therefore hypothesize tht wek lyer frcture in n ECT cn only occur fter the sl hs een compressed enough to trnsmit sufficient stress to the wek lyer for frcture. At the criticl loding step, the wek lyer ruptly frctures over n re roughly equl to the width of the shovel, since in most ECTNs u z decresed to zero within. to. m from the free edge of the column (Fig. ). Thus, in our mostly soft sls, criticl crck lengths were roughly. to. m. Hrder sls my differ in this respect. In contrst, in PST n unstle crck is creted y grdully cutting the wek lyer with snow sw until crck propgtion egins. Even though criticl crck lengths in PSTs re typiclly round. to. m, longer criticl crck lengths hve lso een documented (e.g. Ross nd Jmieson, ). Progressively cutting the wek lyer with snow sw results in ending of the overlying snow sl (Fig. ), providing the energy necessry for crck propgtion (Bir et l., ; Heierli et l., ; Sigrist nd Schweizer, 7; vn Herwijnen nd Heierli, ). Thus, when performing PST, sl properties re not ltered s they re during n ECT c Fig.. Slope norml displcement with time for the row of mrkers closest to the wek lyer in tests () PST_D, () PST_F nd (c) PST_B. The colors of the lines correspond to the distnce of the mrkers to the free edge of the column in m, s indicted in the legend. The rrows indicte the mrker displcement ssocited with sl ending prior to wek lyer frcture.
6 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () 97 PST_B PST_B PST_C PST_C PST_G... Horizontl distnce (m) 9 7 PST_D PST_F.. Horizontl distnce (m) Fig. 7. Men totl slope norml displcement fter wek lyer frcture with horizontl distnce long the column for () PSTs with complete wek lyer frcture nd () PSTs with prtil wek lyer frcture. The colors of the lines correspond to the experiments indicted in the legend. Though the processes involved in reching the criticl crck length prior to propgtion differ for ECTs nd PSTs, our oservtions on wek lyer frcture re consistent for oth tests. First, the totl slope norml displcement fter wek lyer frcture ws similr (compre Figs. nd 7). This result lso confirms tht tpping on the snow column in ECTs does not result in incresed wek lyer collpse, s lredy oserved for compression tests y vn Herwijnen nd Jmieson (). Second, similr fluctutions were oserved in the totl slope norml displcement fter wek lyer collpse in oth tests. These likely relte to smll scle chnges in microstructurl properties of the wek lyer (e.g. crystl size or lyer thickness) nd hve lso een oserved in much longer PSTs (vn Herwijnen et l., ). Third, in oth tests, sl displcement due to wek lyer frcture strts t the free end of the column nd propgtes to the other end (compre Figs. ndc). Fourth, if crck propgtion rrests efore crossing the entire column, susequent tpping or swing results in further compction of the wek lyer (compre Figs. nd).fifth,oservedcrckpropgtion speeds were similr for oth tests (Fig. ), nd no consistent trends in c were oserved. This is in line with results presented y vn Herwijnen et l. (), who found no consistent trend in propgtion speeds in much longer PSTs. All in ll, our oservtions on crck propgtion in ECTs re consistent with results otined from PSTs. Tle Overview of PST results nd PTV mesurements. Test r c (m) L (m) (mm) c (m s ) PST_A.7,.. PST_A... 7 ± PST_B ± PST_B..... ± PST_C ± PST_C..... ± PST_D..... PST_E.,.. PST_E.7.. ± PST_F..... PST_G ± Criticl cut length (r c ), column length (L), PTV mesurement ccurcy (), the rnge of slope norml displcement in the re where the wek lyer frctured (u z )ndfrcture speed with mesurement uncertinty (c) re shown. The column slid down-slope fter frcture. Wek lyer frcture rrested efore reching the end of the column. From prcticl point of view, our mesurements show tht ECT nd PST results relte to frcture initition nd propgtion, oth of which re necessry for vlnche relese. Both these snow stility tests therefore provide vlule informtion with regrd to snow slope stility evlution, s lredy shown in vrious studies (e.g. Ross nd Jmieson, ; Simenhois nd Birkelnd, 9; Winkler nd Schweizer, 9). However, mny questions remin s to how results from smll scle stility tests relte to lrge scle processes involved in vlnche relese, such s the influence of the free edges on test results, the significnce of prtil crck propgtion nd the role of snow sl compction in ECTs.. Conclusions Using high-speed video recordings in comintion with prticle trcking velocimetry, we nlyzed the displcement of the snow sl in 9 ECTs nd PSTs t seven different sites. Despite the fct tht the ECT is widely used snowpck stility test, little ws known out wht hppens to the sl nd wek lyer during the test. Our results prtilly fill this gp, providing etter understnding of the mechnics of the ECT. Our results led to some importnt conclusions:. Tpping only ffects the snow immeditely elow the shovel since we did not oserve ny mrker displcement t the fr end of the column prior to wek lyer frcture. This suggests tht the ECT is indexing not only crck initition, ut lso crck propgtion.. Tpping minly compresses the sl. We did not oserve ny progressive dmge in the wek lyer prior to frcture, when the wek lyer collpses.. Propgtion speeds mesured in ECTs were consistent with mesurements in djcent PSTs nd previously pulished results. During frcture, wek lyers in ECTs compct on the order of severl mm, similr to mesurements otined from PSTs. Mesured propgtion speeds (on the order of to ms ) re lso similr to those from PSTs. The similrities etween our results nd those with PSTs give us confidence tht the frcture mechnics re similr regrdless of the triggering mechnism. However, importnt differences do exist etween the PST nd ECT. In PST, n unstle crck is creted y cutting the wek lyer with snow sw until crck propgtion occurs. The crck length is thus grdully incresed resulting in ending of the overlying sl. On the other hnd, with the ECT the frcture is initited y tpping on the top of
7 A. vn Herwijnen, K.W. Birkelnd / Cold Regions Science nd Technology 97 () 97 ECT PST vn Herwijnen et l. () vn Herwijnen nd Jmieson () Johnson et l. () c (m s ) c (m s ) density (kg m ) u y (cm) Fig.. () Propgtion speed with men sl density. () Propgtion speed with men totl slope norml displcement fter wek lyer frcture. Note the logrithmic scle. The rs indicte the mesurement uncertinty. the lock. No sign of progressive dmge in the wek lyer ws oserved, nd it ppers tht t the criticl loding step, i.e. the finl tp, the wek lyer frctures over n re directly under the shovel. Depending on snow conditions, this crck will either e lrge enough to propgte or frcture will rrest. Building on oservtionl studies which show tht ECT results correlte with stility (e.g. Simenhois nd Birkelnd, 9), this study shows tht ECT results relte to frcture initition nd propgtion, oth of which re required for vlnche relese. Though this increses our confidence in ECT results for ssessing vlnche dnger, we continue to cution people tht stility tests re only one prt of vlnche dnger ssessments. In the end, holistic pproch utilizing wether, snowpck, nd vlnche oservtions, in ddition to stility test results, is necessry for good decision-mking in vlnche terrin. Acknowledgments We thnk Ron Simenhois for reviewing this pper for us. Thnks lso go to the Glltin Ntionl Forest Avlnche Center for providing informtion nd logisticl support for this work, nd to Brd Crpenter, Wes Frnsworth, Eric Knoff, Alex Mrienthl, nd Royn Wooldridge for helping out in the field. References Bir, E., Simenhois, R., Birkelnd, K., Dozier, J.,. A field study on filure of storm snow sl vlnches. Cold Regions Science nd Technology 79,. Birkelnd, K.W., Chot, D.,. Chnges in stility test usge y SnowPilot users. Proc. Int. Snow Sci. W., Anchorge, AK, USA, pp.. Chot, D., Khrl, M., Birkelnd, K., Anker, C.,. SnowPilot: new school tool for collecting, grphing, nd dtsing snowpit nd vlnche occurrence dt with PDA. Proc. Int. Snow Sci. W., Jckson Hole, WY, USA, p. 7. Crocker, J., Grier, D., 99. Methods of digitl video microscopy for colloidl studies. Journl of Colloid nd Interfce Science 79, 9. Föhn, P., 97. The Rutschlock s prcticl tool for slope stility evlution. IAHS-AISH Pul., pp.. Guthier, D., Jmieson, B.,. Evluting prototype field test for wek lyer frcture nd filure propgtion. Proc. Int. Snow Sci. W., Telluride, CO, USA, pp. 7. Guthier, D., Jmieson, B.,. Evlution of prototype field test for frcture nd filure propgtion propensity in wek snowpcklyers. ColdRegions Sciencend Technology, Greene, E., Atkins, D., Birkelnd, K., Elder, K., Lndry, C., Lzr, B., McCmmon, I., Moore, M., Shrf, D., Sterenz, C., Tremper, B., Willims, K.,. Snow, Wether nd Avlnches: Oservtion Guidelines for Avlnche Progrms in the United Sttes. Americn Avlnche Assocition, Pgos Springs, CO, USA. Heierli, J.,. Anticrck Model for Sl Avlnche Relese. Ph.D. thesis Universität Krlsruhe (TH). Heierli, J., Gumsch, P., Ziser, M.,. Anticrck nucletion s triggering mechnism for sl vlnches. Science,. Jmieson, J., 999. The compression test fter yers. The Avlnche Review,. Johnson, B.C., Jmieson, J.B., Stewrt, R.R.,. Seismic mesurements of frcture speed in wek snowpck lyer. Cold Regions Science nd Technology,. Ross, C., Jmieson, B.,. Compring frcture propgtion tests nd relting test results to snowpck chrcteristics. Proc. Int. Snow Sci. W., Whistler, BC, Cnd, pp. 7. Ross, C., Jmieson, B.,. The Propgtion Sw Test: slope scle vlidtion nd lterntive test methods. Journl of Glciology, 7. Schweizer, J., Jmieson, B.,. Snowpck tests for ssessing snow-slope stility. Annls of Glciology, 7 9. Schweizer, J., Jmieson, J., Schneeeli, M.,. Snow vlnche formtion. Reviews of Geophysics,. Sigrist, C., Schweizer, J., 7. Criticl energy relese rtes of wek snowpck lyers determined in field experiments. Geophysicl Reserch Letters, L. Simenhois, R., Birkelnd, K.,. A field test for frcture initition nd propgtion. Proc. Int. Snow Sci. W. Workshop, Telluride, CO, USA, pp. 79. Simenhois, R., Birkelnd, K.W., 9. The Extended Column Test: test effectiveness, sptil vriility, nd comprison with the Propgtion Sw Test. Cold Regions Science nd Technology 9,. vn Herwijnen, A., Heierli, J., 9. Mesurement of crck-fce friction in collpsed wek snow lyers. Geophysicl Reserch Letters, L. vn Herwijnen, A., Heierli, J.,. A field method for mesuring sl stiffness nd wek lyer frcture energy. Proc. Int. Snow Sci. W., Lke Thoe, CA, USA, pp. 7. vn Herwijnen, A., Jmieson, B.,. High-speed photogrphy of frctures in wek snowpck lyers. Cold Regions Science nd Technology, 7. vn Herwijnen, A., Jmieson, B., 7. Frcture chrcter in compression tests. Cold Regions Science nd Technology 7,. vn Herwijnen, A., Jmieson, B., 7. Snowpck properties ssocited with frcture initition nd propgtion resulting in skier-triggered dry snow sl vlnches. Cold Regions Science nd Technology,. vn Herwijnen, A., Schweizer, J., Heierli, J.,. Mesurement of the deformtion field ssocited with frcture propgtion in wek snowpck lyers. Journl of Geophysicl Reserch Erth, F. Winkler, K., Schweizer, J., 9. Comprison of snow stility tests: extended column test, Rutschlock test nd compression test. Cold Regions Science nd Technology 9, 7.
1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationShear and torsion interaction of hollow core slabs
Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationEffects of peripheral drilling moment on delamination using special drill bits
journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment
More informationLAMEPS Limited area ensemble forecasting in Norway, using targeted EPS
Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute
More informationIndustrial Electrical Engineering and Automation
CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull
More informationA027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationAvalanches induced by earthquake in North Tochigi prefecture on 25 February 2013
Interntionl Snow Science Workshop Grenole Chmonix Mont-Blnc - 3 Avlnches induced y erthquke in North Tochigi prefecture on 5 Ferury 3 Hiroki Mtsushit, *, Shinji Iked, Ysuhiko Ito, Msru Mtsuzw nd Hiroshi
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationSet up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass
Applied Physics Reserch; Vol. 5, No. 1; 013 ISSN 1916-9639 E-ISSN 1916-9647 Published by Cndin Center of Science nd Eduction Set up Invrible Axiom of orce Equilibrium nd Solve Problems bout Trnsformtion
More informationExamples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field
Suslt illumintion studies through longitudinl nd trnsversl wve propgtion Riz Ali *, Jn Thorecke nd Eric Verschuur, Delft University of Technology, The Netherlnds Copyright 2007, SBGf - Sociedde Brsileir
More informationGenetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
More informationContinuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom
Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive
More informationDiscrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17
EECS 70 Discrete Mthemtics nd Proility Theory Spring 2013 Annt Shi Lecture 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion,
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationDerivations for maximum likelihood estimation of particle size distribution using in situ video imaging
2 TWMCC Texs-Wisconsin Modeling nd Control Consortium 1 Technicl report numer 27-1 Derivtions for mximum likelihood estimtion of prticle size distriution using in situ video imging Pul A. Lrsen nd Jmes
More informationPhysics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018
Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.
More information13.4 Work done by Constant Forces
13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push
More informationA REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007
A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus
More informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationReview of Calculus, cont d
Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some
More informationSimulated climate vegetation interaction in semi-arid regions affected by plant diversity
SULMNTARY INFORMATION DOI: 0.038/NGO96 Simulted climte vegettion interction in semi-rid regions ffected y plnt diversity M. Clussen,,*, S. Bthiny, V. Brovkin nd T. Kleinen []{Mx lnck Institute for Meteorology,
More informationSynoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?
Synoptic Meteorology I: Finite Differences 16-18 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution
More information5: The Definite Integral
5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
More informationFully Kinetic Simulations of Ion Beam Neutralization
Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion
More informationDiscrete Mathematics and Probability Theory Summer 2014 James Cook Note 17
CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking
More informationQUADRATURE is an old-fashioned word that refers to
World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More information1 Bending of a beam with a rectangular section
1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationTemperature influence compensation in microbolometer detector for image quality enhancement
.26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*
More informationHomework Assignment 6 Solution Set
Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know
More information4 VECTORS. 4.0 Introduction. Objectives. Activity 1
4 VECTRS Chpter 4 Vectors jectives fter studying this chpter you should understnd the difference etween vectors nd sclrs; e le to find the mgnitude nd direction of vector; e le to dd vectors, nd multiply
More information1.2 What is a vector? (Section 2.2) Two properties (attributes) of a vector are and.
Homework 1. Chpters 2. Bsis independent vectors nd their properties Show work except for fill-in-lnks-prolems (print.pdf from www.motiongenesis.com Textooks Resources). 1.1 Solving prolems wht engineers
More information7.1 Integral as Net Change Calculus. What is the total distance traveled? What is the total displacement?
7.1 Integrl s Net Chnge Clculus 7.1 INTEGRAL AS NET CHANGE Distnce versus Displcement We hve lredy seen how the position of n oject cn e found y finding the integrl of the velocity function. The chnge
More information1 Online Learning and Regret Minimization
2.997 Decision-Mking in Lrge-Scle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationDiverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms
In the formt provided y the uthors nd unedited. ULEMENTAY INFOMATION VOLUME: 1 ATICLE NUMBE: 0189 iverse modes of eco-evolutionry dynmics in communities of ntiiotic-producing microorgnisms Klin Vetsigin
More informationVorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen
Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:
More informationThis chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
More informationA Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE
Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationThe practical version
Roerto s Notes on Integrl Clculus Chpter 4: Definite integrls nd the FTC Section 7 The Fundmentl Theorem of Clculus: The prcticl version Wht you need to know lredy: The theoreticl version of the FTC. Wht
More informationBend Forms of Circular Saws and Evaluation of their Mechanical Properties
ISSN 139 13 MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No. 1. 5 Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology,
More informationMATH 144: Business Calculus Final Review
MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationMatching patterns of line segments by eigenvector decomposition
Title Mtching ptterns of line segments y eigenvector decomposition Author(s) Chn, BHB; Hung, YS Cittion The 5th IEEE Southwest Symposium on Imge Anlysis nd Interprettion Proceedings, Snte Fe, NM., 7-9
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More informationReview of basic calculus
Review of bsic clculus This brief review reclls some of the most importnt concepts, definitions, nd theorems from bsic clculus. It is not intended to tech bsic clculus from scrtch. If ny of the items below
More informationPrep Session Topic: Particle Motion
Student Notes Prep Session Topic: Prticle Motion Number Line for AB Prticle motion nd similr problems re on the AP Clculus exms lmost every yer. The prticle my be prticle, person, cr, etc. The position,
More informationAPPROXIMATE INTEGRATION
APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be
More information3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.
SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd
More information5.1 How do we Measure Distance Traveled given Velocity? Student Notes
. How do we Mesure Distnce Trveled given Velocity? Student Notes EX ) The tle contins velocities of moving cr in ft/sec for time t in seconds: time (sec) 3 velocity (ft/sec) 3 A) Lel the x-xis & y-xis
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationMA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp.
MA123, Chpter 1: Formuls for integrls: integrls, ntiderivtives, nd the Fundmentl Theorem of Clculus (pp. 27-233, Gootmn) Chpter Gols: Assignments: Understnd the sttement of the Fundmentl Theorem of Clculus.
More informationAnalytically, vectors will be represented by lowercase bold-face Latin letters, e.g. a, r, q.
1.1 Vector Alger 1.1.1 Sclrs A physicl quntity which is completely descried y single rel numer is clled sclr. Physiclly, it is something which hs mgnitude, nd is completely descried y this mgnitude. Exmples
More informationChapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
More informationStudent Session Topic: Particle Motion
Student Session Topic: Prticle Motion Prticle motion nd similr problems re on the AP Clculus exms lmost every yer. The prticle my be prticle, person, cr, etc. The position, velocity or ccelertion my be
More informationFORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81
FORM FIVE ADDITIONAL MATHEMATIC NOTE CHAPTER : PROGRESSION Arithmetic Progression T n = + (n ) d S n = n [ + (n )d] = n [ + Tn ] S = T = T = S S Emple : The th term of n A.P. is 86 nd the sum of the first
More informationForces from Strings Under Tension A string under tension medites force: the mgnitude of the force from section of string is the tension T nd the direc
Physics 170 Summry of Results from Lecture Kinemticl Vribles The position vector ~r(t) cn be resolved into its Crtesin components: ~r(t) =x(t)^i + y(t)^j + z(t)^k. Rtes of Chnge Velocity ~v(t) = d~r(t)=
More informationSpecial Relativity solved examples using an Electrical Analog Circuit
1-1-15 Specil Reltivity solved exmples using n Electricl Anlog Circuit Mourici Shchter mourici@gmil.com mourici@wll.co.il ISRAE, HOON 54-54855 Introduction In this pper, I develop simple nlog electricl
More informationTrigonometric Functions
Exercise. Degrees nd Rdins Chpter Trigonometric Functions EXERCISE. Degrees nd Rdins 4. Since 45 corresponds to rdin mesure of π/4 rd, we hve: 90 = 45 corresponds to π/4 or π/ rd. 5 = 7 45 corresponds
More informationCS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata
CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationHow do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?
XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=
More informationHomework Solution - Set 5 Due: Friday 10/03/08
CE 96 Introduction to the Theory of Computtion ll 2008 Homework olution - et 5 Due: ridy 10/0/08 1. Textook, Pge 86, Exercise 1.21. () 1 2 Add new strt stte nd finl stte. Mke originl finl stte non-finl.
More informationAB Calculus Review Sheet
AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More informationINVESTIGATION OF BURSA, ESKIKARAAGAC USING VERTICAL ELECTRICAL SOUNDING METHOD
INVESTIGATION OF BURSA, ESKIKARAAGAC USING VERTICAL ELECTRICAL SOUNDING METHOD Gökçen ERYILMAZ TÜRKKAN, Serdr KORKMAZ Uludg University, Civil Engineering Deprtment, Burs, Turkey geryilmz@uludg.edu.tr,
More informationHamiltonian Cycle in Complete Multipartite Graphs
Annls of Pure nd Applied Mthemtics Vol 13, No 2, 2017, 223-228 ISSN: 2279-087X (P), 2279-0888(online) Pulished on 18 April 2017 wwwreserchmthsciorg DOI: http://dxdoiorg/1022457/pmv13n28 Annls of Hmiltonin
More informationPurpose of the experiment
Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen
More informationQuantum Nonlocality Pt. 2: No-Signaling and Local Hidden Variables May 1, / 16
Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 1 / 16 Non-Signling Boxes The primry lesson from lst lecture
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More information4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationCompiler Design. Fall Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz
University of Southern Cliforni Computer Science Deprtment Compiler Design Fll Lexicl Anlysis Smple Exercises nd Solutions Prof. Pedro C. Diniz USC / Informtion Sciences Institute 4676 Admirlty Wy, Suite
More informationMethod of Localisation and Controlled Ejection of Swarms of Likely Charged Particles
Method of Loclistion nd Controlled Ejection of Swrms of Likely Chrged Prticles I. N. Tukev July 3, 17 Astrct This work considers Coulom forces cting on chrged point prticle locted etween the two coxil,
More informationA Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System
SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 16-0, Orlndo FL. (Minor errors in published version corrected.) A Signl-Level Fusion Model for Imge-Bsed
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 2
PHYS 1111 - Summer 2007 - Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement
More informationWeek 10: Line Integrals
Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.
More informationSection 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40
Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since
More informationINTRODUCTION. The three general approaches to the solution of kinetics problems are:
INTRODUCTION According to Newton s lw, prticle will ccelerte when it is subjected to unblnced forces. Kinetics is the study of the reltions between unblnced forces nd the resulting chnges in motion. The
More informationA study of Pythagoras Theorem
CHAPTER 19 A study of Pythgors Theorem Reson is immortl, ll else mortl. Pythgors, Diogenes Lertius (Lives of Eminent Philosophers) Pythgors Theorem is proly the est-known mthemticl theorem. Even most nonmthemticins
More informationThe Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
More information4.1. Probability Density Functions
STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of
More informationThings to Memorize: A Partial List. January 27, 2017
Things to Memorize: A Prtil List Jnury 27, 2017 Chpter 2 Vectors - Bsic Fcts A vector hs mgnitude (lso clled size/length/norm) nd direction. It does not hve fixed position, so the sme vector cn e moved
More information8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
More informationLINEAR ALGEBRA APPLIED
5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order
More informationDesigning Information Devices and Systems I Discussion 8B
Lst Updted: 2018-10-17 19:40 1 EECS 16A Fll 2018 Designing Informtion Devices nd Systems I Discussion 8B 1. Why Bother With Thévenin Anywy? () Find Thévenin eqiuvlent for the circuit shown elow. 2kΩ 5V
More informationSection 4: Integration ECO4112F 2011
Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationThermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings
Journl of Physics: Conference Series PAPER OPEN ACCESS Therml Stility of Ti-C-Ni-Cr nd Ti-C-Ni-Cr-Al-Si Nnocomposite Cotings To cite this rticle: A V Andreev et l 2015 J. Phys.: Conf. Ser. 652 012057 View
More informationSolution Manual. for. Fracture Mechanics. C.T. Sun and Z.-H. Jin
Solution Mnul for Frcture Mechnics by C.T. Sun nd Z.-H. Jin Chpter rob.: ) 4 No lod is crried by rt nd rt 4. There is no strin energy stored in them. Constnt Force Boundry Condition The totl strin energy
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More informationReview of Probability Distributions. CS1538: Introduction to Simulations
Review of Proility Distriutions CS1538: Introduction to Simultions Some Well-Known Proility Distriutions Bernoulli Binomil Geometric Negtive Binomil Poisson Uniform Exponentil Gmm Erlng Gussin/Norml Relevnce
More information