Computers&Concrete, An International Journal, Vo. 4, No. 4, August 2007 MECHANISMS OF SULFATE IONIC DIFFUSION IN POROUS CEMENT BASED COMPOSITES
|
|
- Moses George Barber
- 6 years ago
- Views:
Transcription
1 Computers&Concrete, An Internatonal Journal, Vo. 4, No. 4, August 27 MECHANISMS OF SULFATE IONIC DIFFUSION IN POROUS CEMENT BASED COMPOSITES P. Gospodnov, M. Mronova 2, R. Kaandjev * Insttute of Mechancs, BAS png@mbm.bas.bg, robert@nfo.mbm.bas.bg 2 Central Laboratory of Physco-Chemcal Mechancs, mronova@clphchm.bas.bg Abstract The paper consders a theoretcal model for the study of the process of transfer of sulfate ons n saturated porous meda mneral compostes. In ts turn, the model treats dffuson of sulfate ons nto cement based compostes, accountng for smultaneous effects such as fllng of mcrocapllares wth ons and chemcal products and lqud push out of them. The proposed numercal algorthm enables one to account for those smultaneous effects, as well as to model the dffusve behavor of separate sectons of the consdered volume, such as nert fllers. The cases studed llustrate the capabltes of the proposed model and those of the algorthm developed to study dffuson, consderng the specmen complex confguraton. Computatons show that the theoretcal assumptons enable one to qualtatvely estmate the expermental evdence and the capabltes of the studed composte. The results found can be used to both assess the sulfate corroson n saturated systems and predct and estmate damage of structures bult of cement-based mneral compostes. Keywords Dffuson, Sulfate Attack, Cement Paste, Corroson, Mathematcal Model, Numercal Analyss. Introducton Mneral cement-based compostes such as concrete are wdely appled n structure buldng. They are often exposed to the nfluence of aggressve lqud meda. The sulfate corroson of real concrete structures s a popular phenomenon. To analye ts destructve effects, on needs to study the behavor of the most mportant concrete component the cement paste (cement stone), mmersed n a lqud aggressve sulfate medum. The mpact of the aggressve medum s realed by a penetraton of sulfate ons nto the lqud that flls the pores of the cement paste. Snce ons are charged partcles, an electrc potental occurs when they enter the pore-fllng lqud. Possbltes of modelng the transfer of ons n unsaturated systems are dscussed n Marchand et al.22, and n saturated systems n Marchand et al. 2. The on transfer, accountng for the acton of electrostatc forces, s followed by employng the Nernst-Plank model, (Stansh et al. 24, Samson et al. 999c), whle n cases of strong onc soluton and especally under the strong nteracton of several on speces, an extended model that regards chemcal actvty s used n Samson and Marchand 999. Consderng saturated system, the mathematcal model needs to be completed wth Posson s equaton n order to fnd the electrc potental, whle relatons for the calculaton of the coeffcents of ons chemcal actvty n electrolytc solutons are part of the extended model (Samson et al. 999a). Samson et al. 999b proposes a homogenaton technque whch allows for averagng the results for the concentraton of the porefllng soluton over the entre materal volume. Our studes consder the acton of an aggressve sulfate medum n a saturated system, assumng that the effect of other on speces can be dsregarded. The pore space of the nvestgated cement paste prsmatc specmen has been prevously flled wth water, and the specmen has been mmersed and kept n water for 28 days after castng. It s also assumed that on moton can only occur n the lqud phase. * Correspondng author
2 2. Mathematcal model Ion transfer n the lqud phase that flls the pores of a saturated system s generally due to two mechansms dffuson transfer and mgraton owng to electrostatc forces. On the other hand, lqud moton wthn the pores s due to fllng them wth products of the developed heterogeneous chemcal reacton. That reacton takes place on the pore wall as a result of the nteracton of ons wth the cement stone. The pores are formally treated as capllares (mcro-capllares), shaped as straght crcular cylnders and wth symmetry axes parallel to the coordnate axes. The present study accounts for the effect of the sulfate ons, only, whle ther nteracton wth other on speces s dsregarded. Consder cement stone capllares n partcular and the materal balance of an elementary volume of the area under control. Then, the followng equaton of on transport can be wrtten, accountng for the heterogeneous chemcal reactons that develop on the capllary walls: c = dv ( J T ) kc () t or n the one-dmensonal case c = ( J T ) kc (2) t x where J J T = J dff + J U (3) As stated, snce ons are electrcally charged partcles, an electrc potental occurs when they enter the soluton that flls the capllares. Thus, the flux of on transfer J T has two components the frst one J dff s due to the dffuson force whle the second one J U to the drvng force of the electrc potental U (Stansh et al. 24 ).. Quantty c ( x, t) n Eqs. ()-(2) s the current concentraton value, q ( x, t) s the quantty of chemcally reacted ons at a pont wth coordnates x and at a moment t, and k s the coeffcent of chemcal reacton rate. The frst term n the rght-hand sde (RHS) of Eq. (3) can be expressed by Fck s frst law: c J dff = k dff (4) x whle the second one has the followng form accordng to the smplfed model of Nernst-Plank, (Samson et al. 999c): VF kdff U J U = c (5) RT x Multpler k dff n Eq. (4) s the coeffcent of dffuson of sulfate ons wthn the whole volume, consstng of a cement matrx and capllares flled wth lqud. It reflects the materal porosty, structure and capllary shape. V s the valence of sulfate on, F s Faraday s constant, U s the dffuson potental, R s the unversal gas constant, T s the temperature. The mathematcal model should be completed wth an equaton for determnng the dffuson potental U. It has the form (Samson et al. 999c):. 2 ρ U + = (6) ε where ρ s densty of the electrc charge and ε s the medum delectrc constant. The consderaton of the on flux due to the drvng force of the dffuson potental s sgnfcant n two cases, manly when an external electrc potental s appled or a smultaneous transfer of two and more on speces s n operaton. When consderng the transfer of sulfate ons, only, under sothermal condtons, the account for the effect of Nernst-Plank yelds model complcatons. On the other hand, the model proposed by Eqs. ()-(6) does not account for some characterstc features of the process,.e. change of the capllary volume as a result of the precptaton of chemcal reacton products on the capllary walls, as well as the resultng push out of the capllary-fllng lqud. Note also that lqud moton exports part of the ons out of the capllares and n a drecton opposte to that of flux J.
3 In prevous papers (Gospodnov et al. 999), (Mronova et al.22) we propose a model of dffuson transfer consderng heterogeneous chemcal reacton and lqud push out of the capllares resultng from the capllary fllng. The model can be presented n the followng form:: c 2 = dv( Deff gradc) dv( V c) k( k q) c (7) t where the spatal operators dv ( ) and grad ( ) are of the type K K dv() () grad() j () (8) = x = x For one dmensonal case - K=. The last term n the RHS of Eq. (7) s a source term whch models the heterogeneous chemcal reacton between the sulfate ons n the soluton and the capllary walls. The term also reflects the change of the capllary reactng surface. Projectons V, =, K, of velocty V n Eq. (7) denote the lqud mean velocty wthn the cross secton of the capllary along axes x, =, K. The effectve dffuson coeffcent wthn the whole volume has the form (Gospodnov et al 999) : ( k ) 2 Deff = D q, (9) where D = k exp β c x,..., xr, t. c. () [ ( ( ) )] dff 5 Constant β s a parameter and c s a characterstc value of the concentraton the concentraton of the soluton whch the specmen s mmersed n, k denotes the coeffcent of capllary fllng and the quantty of chemcally reacted ons q s found from q t ( x x, t) = k c( x,..., x, τ) d,,..., R R τ () o For fxed values of the rest of the coordnates x m, m, the velocty component V s calculated by means of the followng ntegral along the capllary length, wthn boundares [, x ], (Mronova et al. 22). V η G = = η= U 2kk ( k q) c dη, U = L / 2 x, G = L / 2, =, R Snce the orgn of the coordnate system s the center of the specmen symmetry, the velocty s ero for x = and t s maxmal for x = / 2. The velocty drecton concdes wth the postve drecton L of axs Ox. V s found calculatng the ntegral Eq. (6). The lower ntegraton lmt s L / 2 x, whle the upper one - L / 2. Thus, velocty V ( x,..., xr, t) can be found at each pont of the area consdered. Velocty components Vm ( x,..., xr, t), m, m [,..., R] are smlarly found. The model s completed by specfyng a ero ntal dstrbuton of the concentraton, condtons at the specmen-soluton nterface and symmetry condtons, Mronova et al. 22. Note however that the model outlned above descrbes the dstrbuton of sulfate ons wthn the lqud phase that flls the capllary space of the cement paste. 3. Numercal soluton The equatons of transfer Eqs.(7) - (8), together wth the ntal and boundary condtons pose a nonsteady boundary value problem. It s completed by the ntegral relatons Eq. (2), gvng the quantty of chemcally reacted ons, as well as by the ntegral relatons Eq. (3), necessary for the calculaton of the velocty feld of the lqud pushed out of the cement stone capllares. (2)
4 (a) L 2 /2 y (b) +N*M +N L 3 /2 O y - + x L /2 x -N -N*M Fg. Coordnate system and dscretaton scheme The problem s solved usng an mplct dfference scheme and t s reduced to solvng a sparse system of lnear algebrac equatons wth a non-symmetrc band matrx. The algorthm used s descrbed n detal n Gospodnov 25. The dscretaton scheme s shown n Fg..a. Numbers of N, M and L cross sectons wth planes perpendcular to the coordnate axes x, y and, respectvely, are ntroduced along each axs, startng from the coordnate system orgn. Let x, y and are numbers of the dscretaton sectons (Fg. ) perpendcular to axes х, y and. Obvously, N, M, L. The number of a grd knot for fxed values of x, y and s determned by the followng relaton: ( ) * N + ( ) * N M x = + (3). x y * Thus, the unknown values of the quanttes sought at each knot of the dskreted area can be numbered usng one ndex, only. Besdes, the soluton of the ntal boundary value problem outlned above s reduced to the soluton of a dfference value problem for a lneared system of (N*M*L) algebrac equatons wth a dagonal and weakly flled matrx. The algorthm thus developed s completed by a numercal procedure for calculatng the ntegrals of type Eq. (3) along the three coordnate axes. The specfc features of cases of sub-areas wth conductvty, dstnctly dfferent from that of the matrx (e.g. nert fller), are dscussed n Gospodnov 25. The model thus desgned can be effectvely appled to dsclose the character of a number of complex phenomena observed durng the sulfate aggresson of cement paste. 4 Results and dscusson Havng set forth the mathematcal model of dffuson transfer of sulfate ons n cement stone, we proceed wth the dscusson of some expermental evdence and calculaton results. We have consdered n our prevous study (Mronova et al. 22), sulfate ons dffuson n prsmatc specmens, thus modelng the development of the sulfate attack on real structural elements, whch s a problem of essental practcal mportance. The specmens tested are long prsms wth cross secton.8 x -2 x.5 x -2 m. As found, they are dvded nto two parts a thn external corrupted layer and an ntact cement core, Fg. 2. y Fg.2. Prsmatc cement paste specmen, layered after a sulfate attack from 5 % sulfate soluton; tme of mmerson 9 months. The specmens tested are long prsms wth cross secton.8 x -2 x.5 x -2 m.
5 However, the study of the mechansm of formaton of the external corrupted layer as a result of the sulfate attack s a dffcult task. To model that process, we have studed the development of sulfate ons dffuson n thn cement paste specmens, mmersed n aqueous solutons of Na 2 SO 4. The specmens have been fabrcated form SRP cement, type 35, n complance wth the Bulgaran standard. The materal chemcal composton s specfed n Mronova et al. 22. Specmens have been soldfyng for 28 days n pure water after preparaton and pror to mmerson. Then, they have been mmersed and kept n water solutons of Na 2 SO 4 of dfferent concentraton and for dfferent perods of tme. Fg. 3 shows the sequence of cement stone degradaton n tme, dependng on the soluton sulfate concentraton. It summares the expermental fnds of our prevous studes (Mronova et al. 22, Kaandjev et al. 25). Immerson duraton 864 hours (2 months); lateral specmen vew a) concentraton of Na 2 SO 4 n the soluton % Immerson duraton 864 hours (2 months); lateral specmen vew b) concentraton of Na 2 SO 4 n the soluton 5% Immerson duraton 864 hours (2 months); lateral specmen vew c) concentraton of Na 2 SO 4 n the soluton % Fg. 3. Cement paste degradaton n tme, regardng dfferent soluton sulfate concentratons As seen n Fg. 3 and specfcally for the hgher concentratons of the sulfate soluton, partal destructon of the specmen takes place after a perod of 2 months of mmerson, and dffuson and ts accompanyng effects (fllng of the cement stone pores wth ons and chemcal products, mcrocrack formaton etc.) change the materal structure. Hence, a perod shorter than 2 months of mmerson can be taken as a reasonable tme lmt for the cement stone saturaton wth sulfate ons from the hgher sulfate solutons, where the materal dffusve behavor can be taken as smlar to that of the external corrupted layer of the bulk specmen shown n Fg. 2. Thus, the analyss of ons dffuson n thn specmens, based on the model proposed proves useful for analyng the on transfer n bulk specmens and n real structural elements. In what follows, we gve some calculaton results found usng the dffuson model desgned.
6 We consder sulfate ons dffuson nto thn cement paste specmens wth dmensons.5x -2.5x -2.2 =2 m, beng mmersed n 5% aqueous soluton of Na 2 SO 4. The calculaton are performed usng the followng values of the parameters, partcpatng n the model ()-() and found analyng the expermental evdence of Gospodnov et al. 999.: - coeffcent of on dffuson n the water soluton k dff =.34 x -3 m 2 /s - fttng parameter partcpatng n Eq. (): β =.297 m 3 /kg; - constant of the chemcal reacton rate: k =.35 x -7 s - - coeffcent of pore fllng: k =.5 m 3 /kg - content of the sulfate ons n the 5% sulfate soluton kg/m 3 Fgures 4, 5 and 6 present the numercal results of the study of D dffuson of sulfate ons wthn the specmen. Due to symmetry, ons penetraton from x= to the symmetry lne x=. x -2 m s followed. Concentraton profle, c Concentraton profle, c c [kg/m 3 ] c [kg/m 3 ] x* [m] x* -2 [m] Fg.4 Dstrbuton of the ons concentraton D case q [kg/m 3 ] Chemcally reacted quantty, q 3 2 q [kg/m 3 ] Chemcally reacted quantty, q x* -2 [m] x* -2 [m] Fg.5 Dstrbuton of the chemcally reacted quantty of ons- D case D eff [m 2 /s] x -2 Effectve dffuson coeffcent D eff [m 2 /s] 7 x Effectve dffuson coeffcent x* -2 [m] x* -2 [m]
7 Fg.6. Dstrbuton of the effectve dffuson coeffcent D case Notatons of the curves n Fg.4, 5 and 6 correspond to the followng perods of mmerson: - 2 hours, 2 36 hours, 3 6 hours, 4 26 hours (3 month), hours (6 months), hours (9 months). The calculaton results show that ons penetraton s comparatvely ntensve at the start of process, whle the current concentraton attans a maxmal value on the symmetry lne for a 3-months of mmerson and then t starts decreasng but wth weaker ntensty Fg. 4. Ths s due to the proceedng chemcal reacton, where part of the penetratng ons precptate on the capllary walls as partcpatng n chemcal compounds, and to the nverse convectve transfer owng to the occurrng lqud push as a result of the capllary partal fllng. Besdes, the process of on connecton due to the chemcal reactons s more ntensve than the transfer of ons ncomng from the surroundng soluton. Ths s confrmed by the ncrease n tme of the quantty of chemcally reacted ons Fg. 5. The character of the process s addtonally elucdated by the results found for the change of the effectve dffuson coeffcent Fg. 6. At the process start and near the nterface, the coeffcent values are the hghest ones, and the coeffcent vares wth the largest gradent. Then, due to the pore fllng and decrease of the concentraton mpetus, the dstrbuton curve tends to a straght lne and the mean value of the effectve coeffcent of dffuson tends to decrease along the coordnate axs x. The model proposed, together wth the numercal algorthm desgned, allows consderng more complex 3D cases of ons dffuson, as s that shown n Fg. 7. The specmen under consderaton s a prsm wth dmensons L =.5 m, L2 =.8 m, L3 =.9 m. It s assumed that two cylndrcal bodes of nert fller are located n /8 th of the specmen volume. Snce the specmen s symmetrc wth respect to the coordnate axes x= y= и =, the spatal dstrbuton of the ons concentraton, the quantty of chemcally reacted ons and the dstrbuton of the effectve dffuson coeffcent are plotted for /8-th of the specmen volume n the fgures below. Ths confguraton of the specmen s chosen to llustrate the capabltes of the numercal soluton. Fg.7. Schematc representaton of the nert fller sub-area n /8 th volume:: R =. m; R2 =.85 m; xc =.25 m; =.25 m; c of the specmen y =.5 m ; c The features of the concentraton front dstrbuton, outlned n the analyss of the case of D dffuson, are also characterstc for the 3D case. Besdes, for values of the concentraton closer to the concentraton of the surroundng lqud ths specfcty s more dstnct as compared to the case of hgher concentratons. Fg. 8 a, b, c shows comparson of the change n tme of two sosurfaces c const = [kg/m 3 ] and c const = 25 [kg/m 3 ]
8 Fg.8 Isosurfaces of the ons concentraton. Tme of mmerson a) month b) 4 months c) months The sosurface of the lower concentraton value ( kg/m 3 ) penetrates wthn the specmen, and the change of ts locaton between the 4-th and the -th month of mmerson s relatvely weak. The sosurface of the hgher concentraton value (25 kg/m 3 ) penetrates wthn the specmen for about 4 months of mmerson, and then draws back. Besdes, t s observed that the sosurface locaton s closer to the specmen external surface for months of mmerson as compared to ts locaton for month of mmerson. These results confrm the concluson drawn for the D case and further clarfy the role of the effects, accompanyng the sulfate ons dffuson,.e. capllary fllng and lqud push out of them. As a further llustraton, Fg. 9 shows the subsequent change n tme of the quantty of chemcally reacted ons.
9 Fg.9 Isosurfaces of the chemcally reacted quantty of ons Tme of mmerson a) month, b) 2 months, c) 4 months, d) months Fg. llustrate the change of the dffuson coeffcent. The shft n tme of the sosurface of D eff to the external nterface cеment stone/soluton s due partlly to the capllary fllng wth products of the chemcal reacton and partally to the decrease of the sulfate ons concentraton wthn the volume. The results shown n Fg. 8 Fg. also llustrate the effect of nert fllers of the ons transfer, and the capabltes of the numercal algorthm when treatng a specmen wth a complex shape. Fg.. Isosurfaces of the effectve dffuson coeffcent Tme of mmerson a) month b) 2 months c) 4 months, d) months
10 Conclusons The relaton for the effectve dffuson coeffcent used allows also to follow how the current sulfate concentraton wthn the volume affects the rate of ons transfer. The comparson of the theoretcal results wth the expermental data shows qualtatve agreement. It may be concluded that modelng the ons transfer as a dffuson process gves plausble quanttatve and qualtatve descrpton of the phenomena. The results found can be used to both assess the sulfate corroson n saturated systems and predct and estmate damage of structures bult of cement-based mneral compostes. References Gospodnov P. (25), Numercal smulaton of 3D sulfate on dffuson and lqud push out of the materal capllares n cement compostes, Cement and Concrete Research, 35 (3), Gospodnov P., Kaandjev R., Partaln T., Mronova M., (999), Dffuson of sulfate ons nto cement stone regardng smultaneous chemcal reactons and resultng effects, Cement and Concrete Research. 29 (), Kaandjev R., Gospodnov P., Mronova M., (25), Assessment of the mechancal characterstcs of cement stone subjected to sulfate attack of varous ntensty, Proceedngs of the -th Nat. Congress on Theor. and Appl. Mechancs, Varna 25,, Marchand J., Samson E. and Maltas Y., (2), Modelng onc dffuson mechansms n saturated cement-based materals an overvew, Materal Scence of Concrete Ion and Mass Transport n Cement-Based Materals, Amercan Ceram. Socety (USA), D.Hooton et al. eds., 97- Marchand J., Samson E., Beaudon J.J., (22), Modelng on transport mechansms n unsaturated porous meda, Encyclopeda of Surface and Colod Scence, New York, USA, M. Dekker Mronova M., Gospodnov P., Kaandjev R., (22), The effect of lqud push out of the materal capllares under sulfate on dffuson n cement compostes, Cement and Concrete Research, 32 (), 9-5 Samson E., Lemare G., Marchand J. and Beaudon J.J, (999a), Modelng chemcal actvty effects n strong onc solutons, Computatonal Materal Scence 5, Samson E. and Marchand J., (999), Numercal soluton of the extended Nernst Planck model, Journal of Collod amd Interface Scence, 25, -8 Samson E., Marchand J., Beaudon J.J., (999b), Descrbng on dffuson mechansms n cementbased materals usng the homogenaton technque, Cement and Concrete Research, 29 (), Samson E., Marchand J., Robert J.-L., Bournael J.-P., (999c), Modellng on dffuson mechansms n porous meda, Int. J. Numer.Mech. Engng. 46, Stansh K., Hooton R.D., Thomas M.D.A., (24), A novel method for descrbng chlorde on transport due to an electrcal gradent n concrete: Part. Theoretcal descrpton, Cement and Concrete Research 34 (), 43 49
Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationPhysics 181. Particle Systems
Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationmodeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products
modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory
More information( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationAmplification and Relaxation of Electron Spin Polarization in Semiconductor Devices
Amplfcaton and Relaxaton of Electron Spn Polarzaton n Semconductor Devces Yury V. Pershn and Vladmr Prvman Center for Quantum Devce Technology, Clarkson Unversty, Potsdam, New York 13699-570, USA Spn Relaxaton
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationMathematical Preparations
1 Introducton Mathematcal Preparatons The theory of relatvty was developed to explan experments whch studed the propagaton of electromagnetc radaton n movng coordnate systems. Wthn expermental error the
More informationCHEMICAL ENGINEERING
Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton
More informationDiffusion Mass Transfer
Dffuson Mass Transfer General onsderatons Mass transfer refers to mass n transt due to a speces concentraton gradent n a mture. Must have a mture of two or more speces for mass transfer to occur. The speces
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationTowards the modeling of microgalvanic coupling in aluminum alloys : the choice of boundary conditions
Presented at the COMSOL Conference 2008 Boston COMSOL Conference BOSTON November 9-11 2008 Towards the modelng of mcrogalvanc couplng n alumnum alloys : the choce of boundary condtons Ncolas Murer *1,
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More informationArmy Ants Tunneling for Classical Simulations
Electronc Supplementary Materal (ESI) for Chemcal Scence. Ths journal s The Royal Socety of Chemstry 2014 electronc supplementary nformaton (ESI) for Chemcal Scence Army Ants Tunnelng for Classcal Smulatons
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationUnderstanding Electrophoretic Displays: Transient Current Characteristics of Dispersed Charges in a Non-Polar Medium
Understandng Electrophoretc Dsplays: Transent Current Characterstcs of Dspersed Charges n a Non-Polar Medum Yoocharn Jeon, Pavel Kornlovtch, Patrca Beck, Zhang-Ln Zhou, Rchard Henze, Tm Koch HP Laboratores
More informationAn identification algorithm of model kinetic parameters of the interfacial layer growth in fiber composites
IOP Conference Seres: Materals Scence and Engneerng PAPER OPE ACCESS An dentfcaton algorthm of model knetc parameters of the nterfacal layer growth n fber compostes o cte ths artcle: V Zubov et al 216
More informationA NUMERICAL COMPARISON OF LANGRANGE AND KANE S METHODS OF AN ARM SEGMENT
Internatonal Conference Mathematcal and Computatonal ology 0 Internatonal Journal of Modern Physcs: Conference Seres Vol. 9 0 68 75 World Scentfc Publshng Company DOI: 0.4/S009450059 A NUMERICAL COMPARISON
More informationOn the correction of the h-index for career length
1 On the correcton of the h-ndex for career length by L. Egghe Unverstet Hasselt (UHasselt), Campus Depenbeek, Agoralaan, B-3590 Depenbeek, Belgum 1 and Unverstet Antwerpen (UA), IBW, Stadscampus, Venusstraat
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationModule 1 : The equation of continuity. Lecture 1: Equation of Continuity
1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum
More informationMass Transfer Processes
Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.
More informationNumerical Simulation of ph-sensitive Hydrogel Response in Different Conditions
Numercal Smulaton of ph-senstve Hydrogel Response n Dfferent Condtons Bran O. Asmba, Andrew K. Shgol, Kamlesh J. Suthar *, Muraldhar K. Ghantasala, and Derrck. C. Mancn * Department of Mechancal and Aeronautcal
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationEntropy generation in a chemical reaction
Entropy generaton n a chemcal reacton E Mranda Área de Cencas Exactas COICET CCT Mendoza 5500 Mendoza, rgentna and Departamento de Físca Unversdad aconal de San Lus 5700 San Lus, rgentna bstract: Entropy
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationEVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES
EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge
More informationGouy-Chapman model (1910) The double layer is not as compact as in Helmholtz rigid layer.
CHE465/865, 6-3, Lecture 1, 7 nd Sep., 6 Gouy-Chapman model (191) The double layer s not as compact as n Helmholtz rgd layer. Consder thermal motons of ons: Tendency to ncrease the entropy and make the
More informationTemperature. Chapter Heat Engine
Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationFORCED CONVECTION HEAT TRANSFER FROM A RECTANGULAR CYLINDER: EFFECT OF ASPECT RATIO
ISTP-,, PRAGUE TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA FORCED CONVECTION HEAT TRANSFER FROM A RECTANGULAR CYLINDER: EFFECT OF ASPECT RATIO Mohammad Rahnama*, Seyed-Mad Hasheman*, Mousa Farhad**
More informationChapter 2. Electrode/electrolyte interface: ----Structure and properties
Chapter 2 Electrode/electrolyte nterface: ----Structure and propertes Electrochemcal reactons are nterfacal reactons, the structure and propertes of electrode / electrolytc soluton nterface greatly nfluences
More informationPORE STRUCTURE AND THERMAL CONDUCTIVITY OF BURNT CLAY BRICKS INTRODUCTION
PORE STRUCTURE AND THERMAL CONDUCTIVITY OF BURNT CLAY BRICKS Olga Koronthalyova, Peter Matasovsky Insttute of Constructon and Archtecture, Slovak Academy of Scences, Dubravska 9, 845 43 Bratslava, Slovaka.
More informationOne Dimensional Axial Deformations
One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The -as s taken as the
More informationProblem adapted reduced models based on Reaction-Diffusion Manifolds (REDIMs)
Problem adapted reduced models based on Reacton-Dffuson Manfolds (REDIMs) V Bykov, U Maas Thrty-Second Internatonal Symposum on ombuston, Montreal, anada, 3-8 August, 8 Problem Statement: Smulaton of reactng
More informationTotal Strain Behavior of Mortar under Freeze-Thaw Cycles in Consideration of the in Coefficient of Thermal Expansion of Frost Damaged Mortar
Total Stran Behavor of Mortar under Freeze-Thaw Cycles n Consderaton of the n Coeffcent of Thermal Expanson of Frost Damaged Mortar Evdon Scat 1, Fuyuan Gong 1*, Ueda Tamon 2 and Zhang Dawe 3 1 Graduate
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationOn the symmetric character of the thermal conductivity tensor
On the symmetrc character of the thermal conductvty tensor Al R. Hadjesfandar Department of Mechancal and Aerospace Engneerng Unversty at Buffalo, State Unversty of New York Buffalo, NY 146 USA ah@buffalo.edu
More informationApplied Nuclear Physics (Fall 2004) Lecture 23 (12/3/04) Nuclear Reactions: Energetics and Compound Nucleus
.101 Appled Nuclear Physcs (Fall 004) Lecture 3 (1/3/04) Nuclear Reactons: Energetcs and Compound Nucleus References: W. E. Meyerhof, Elements of Nuclear Physcs (McGraw-Hll, New York, 1967), Chap 5. Among
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationThermodynamics General
Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationMATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018
MATH 5630: Dscrete Tme-Space Model Hung Phan, UMass Lowell March, 08 Newton s Law of Coolng Consder the coolng of a well strred coffee so that the temperature does not depend on space Newton s law of collng
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More informationComparative Studies of Law of Conservation of Energy. and Law Clusters of Conservation of Generalized Energy
Comparatve Studes of Law of Conservaton of Energy and Law Clusters of Conservaton of Generalzed Energy No.3 of Comparatve Physcs Seres Papers Fu Yuhua (CNOOC Research Insttute, E-mal:fuyh1945@sna.com)
More informationA PROCEDURE FOR SIMULATING THE NONLINEAR CONDUCTION HEAT TRANSFER IN A BODY WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY.
Proceedngs of the th Brazlan Congress of Thermal Scences and Engneerng -- ENCIT 006 Braz. Soc. of Mechancal Scences and Engneerng -- ABCM, Curtba, Brazl,- Dec. 5-8, 006 A PROCEDURE FOR SIMULATING THE NONLINEAR
More informationNUMERICAL RESULTS QUALITY IN DEPENDENCE ON ABAQUS PLANE STRESS ELEMENTS TYPE IN BIG DISPLACEMENTS COMPRESSION TEST
Appled Computer Scence, vol. 13, no. 4, pp. 56 64 do: 10.23743/acs-2017-29 Submtted: 2017-10-30 Revsed: 2017-11-15 Accepted: 2017-12-06 Abaqus Fnte Elements, Plane Stress, Orthotropc Materal Bartosz KAWECKI
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationA comprehensive study: Boundary conditions for representative volume elements (RVE) of composites
Insttute of Structural Mechancs A comprehensve study: Boundary condtons for representatve volume elements (RVE) of compostes Srhar Kurukur A techncal report on homogenzaton technques A comprehensve study:
More informationAirflow and Contaminant Simulation with CONTAM
Arflow and Contamnant Smulaton wth CONTAM George Walton, NIST CHAMPS Developers Workshop Syracuse Unversty June 19, 2006 Network Analogy Electrc Ppe, Duct & Ar Wre Ppe, Duct, or Openng Juncton Juncton
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY
Proceedngs: Indoor Ar 2005 ERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY S Lu, J Lu *, N Zhu School of Envronmental Scence and Technology, Tanjn
More informationTurbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH
Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant
More information1 Matrix representations of canonical matrices
1 Matrx representatons of canoncal matrces 2-d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3-d rotaton around the x-axs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3-d rotaton around the y-axs:
More informationSo far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More informationA particle in a state of uniform motion remain in that state of motion unless acted upon by external force.
The fundamental prncples of classcal mechancs were lad down by Galleo and Newton n the 16th and 17th centures. In 1686, Newton wrote the Prncpa where he gave us three laws of moton, one law of gravty,
More informationInternational Power, Electronics and Materials Engineering Conference (IPEMEC 2015)
Internatonal Power, Electroncs and Materals Engneerng Conference (IPEMEC 2015) Dynamc Model of Wnd Speed Dstrbuton n Wnd Farm Consderng the Impact of Wnd Drecton and Interference Effects Zhe Dong 1, a,
More informationPh.D. Qualifying Examination in Kinetics and Reactor Design
Knetcs and Reactor Desgn Ph.D.Qualfyng Examnaton January 2006 Instructons Ph.D. Qualfyng Examnaton n Knetcs and Reactor Desgn January 2006 Unversty of Texas at Austn Department of Chemcal Engneerng 1.
More informationSIMULATION OF WAVE PROPAGATION IN AN HETEROGENEOUS ELASTIC ROD
SIMUATION OF WAVE POPAGATION IN AN HETEOGENEOUS EASTIC OD ogéro M Saldanha da Gama Unversdade do Estado do o de Janero ua Sào Francsco Xaver 54, sala 5 A 559-9, o de Janero, Brasl e-mal: rsgama@domancombr
More informationModeling of Dynamic Systems
Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how
More informationChapter 12. Ordinary Differential Equation Boundary Value (BV) Problems
Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(
More informationCHAPTER II THEORETICAL BACKGROUND
3 CHAPTER II THEORETICAL BACKGROUND.1. Lght Propagaton nsde the Photonc Crystal The frst person that studes the one dmenson photonc crystal s Lord Raylegh n 1887. He showed that the lght propagaton depend
More informationHomework 4. 1 Electromagnetic surface waves (55 pts.) Nano Optics, Fall Semester 2015 Photonics Laboratory, ETH Zürich
Homework 4 Contact: frmmerm@ethz.ch Due date: December 04, 015 Nano Optcs, Fall Semester 015 Photoncs Laboratory, ETH Zürch www.photoncs.ethz.ch The goal of ths problem set s to understand how surface
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationFundamental loop-current method using virtual voltage sources technique for special cases
Fundamental loop-current method usng vrtual voltage sources technque for specal cases George E. Chatzaraks, 1 Marna D. Tortorel 1 and Anastasos D. Tzolas 1 Electrcal and Electroncs Engneerng Departments,
More informationNUMERICAL MODEL FOR NON-DARCY FLOW THROUGH COARSE POROUS MEDIA USING THE MOVING PARTICLE SIMULATION METHOD
THERMAL SCIENCE: Year 2018, Vol. 22, No. 5, pp. 1955-1962 1955 NUMERICAL MODEL FOR NON-DARCY FLOW THROUGH COARSE POROUS MEDIA USING THE MOVING PARTICLE SIMULATION METHOD Introducton by Tomok IZUMI a* and
More informationThe non-negativity of probabilities and the collapse of state
The non-negatvty of probabltes and the collapse of state Slobodan Prvanovć Insttute of Physcs, P.O. Box 57, 11080 Belgrade, Serba Abstract The dynamcal equaton, beng the combnaton of Schrödnger and Louvlle
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationNormally, in one phase reservoir simulation we would deal with one of the following fluid systems:
TPG4160 Reservor Smulaton 2017 page 1 of 9 ONE-DIMENSIONAL, ONE-PHASE RESERVOIR SIMULATION Flud systems The term sngle phase apples to any system wth only one phase present n the reservor In some cases
More informationThermal-Fluids I. Chapter 18 Transient heat conduction. Dr. Primal Fernando Ph: (850)
hermal-fluds I Chapter 18 ransent heat conducton Dr. Prmal Fernando prmal@eng.fsu.edu Ph: (850) 410-6323 1 ransent heat conducton In general, he temperature of a body vares wth tme as well as poston. In
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationGrid Generation around a Cylinder by Complex Potential Functions
Research Journal of Appled Scences, Engneerng and Technolog 4(): 53-535, 0 ISSN: 040-7467 Mawell Scentfc Organzaton, 0 Submtted: December 0, 0 Accepted: Januar, 0 Publshed: June 0, 0 Grd Generaton around
More informationComputational Fluid Dynamics. Smoothed Particle Hydrodynamics. Simulations. Smoothing Kernels and Basis of SPH
Computatonal Flud Dynamcs If you want to learn a bt more of the math behnd flud dynamcs, read my prevous post about the Naver- Stokes equatons and Newtonan fluds. The equatons derved n the post are the
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationInterconnect Modeling
Interconnect Modelng Modelng of Interconnects Interconnect R, C and computaton Interconnect models umped RC model Dstrbuted crcut models Hgher-order waveform n dstrbuted RC trees Accuracy and fdelty Prepared
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More information