Mô phỏng một số hệ vật lý trên máy tính

MO PHONG MOT SO HE VAT LY TREN MAY TINH MAS6:QT.01.33 CHL' TRI DE TAI: PGS.TS Lc Vici Du KliLTons: CAC CAN BO PHOl HOP: TS Vii Due Minh ThS Nguyen Van Hal ThS Nguyen Thi Thanh Nhan CN Nsuven Tien Cuano CN Tran Trung Dure CN Ngu\en Thi Hien CN NsuN'en Tien Quanc [• BAG CAO TOM TAT a Ten 66 tai: Mo phong mot so he vat ly tren may tfnh Mas6:QT.0I '^3 b Chii iri de tai: PG.S.T.S Le Viet Du Khuang c Ciic can bo tham gia: T.S Vu Due Minh ThS Nouvin Van Hal ThS Nguyt^n Thi Thanh Nhan CN Ngu\en Tien CiFcyng CN Tran Trung Dae CN Nguyen Thi Hien CN NguN'dn Tien Quang d Muc lieu \a npi dung nghien ciru: Phuong phap mo phong may Imh vat ly' da duo'c sir dung rong rai xa CO hieu qua a cac nuoc lien lien iren the gioi nhimg rat moi me doi \'6i Viet nam \ \'ay can phai nghien ciru \'a du'a phu'o'ng phap hien dai \ao noi dung dao lao \ nghien ciru \'at ly' a niroc ta Vai muc tieu tren d^ tai xac dinh cho mmh nhiem \u ph; lam chu cac phu'ong phap mo phong va lu 66 iir lap lay cac chuong trlnh de mo phon cac he \'at ly' tren ma\' ifnh c Cac ket qua thu du'oc - Xa\' dung du*oc mot he g6m nhi6j chu*ang trlnh chu yeu viel brmg Matlab c mo phong mot so he \'at ly' thuoc mot so ITnh \\xc nhu*: ca nhiet dien til qu'sical training and research contents in our country With such a purpose, the task of the project is orientec to master simulation methods, and after that to form computer simulation programs in physical matters e Research results: A packet of programs has been obtained by using Matlab for the simulation of some physical systems in some areas such as: Mechanics Thermodynamics Electrodynamics Optics Modern Physics and Geophysics The project has contributed to the success of one PhD two Master and four Bachelors Two scientific articles have been published CHU TRI DE TAI XAC NHAN CIA BAN CHU NHIEM KHOA pGS.TS Le Viei Du Khuang XAC NHAN CL A TRU&NG ••HO HI^U TRUOMO ?^s.i2.3jrd3L'.fAa/yiv MUC LUC PHAN I PHUONG PHAP M PHONG TRONG CO HOC THONG KE >?• M6DAU >? CHUONG 1: GI61 THIEU VE MATLAB \ArSa hxgc v6 Matlab 1.2 Dae di^m cua Matlab 1.3 Cac ham Matlab dung m6 phong 1.3 L Nhom cac ham ca ban 1.3.2.Nh6m cac ham d6 hoa L3.3.Nh6m cac ham tfnh toan ' CHUONG 2: CO S6 LY THUYET VE THUYET D O N G HOC PHAN TlT 2.1 Cac trang thai nhiet d6ng 2.1.1 Trang thai vi m6 2.1.2 Trang thai vT m6 2.1.3 Trang thai cSn b^ng nhiet d6ng 2.2 Th6' nang giira cac phan tu 2.2.1 The nang 2.2.2 Luc tirong tac 2.3 Dcmvi 2.4 Thuat toan 2.4.1 Phuong trinh Newton 2.4.2 Thuat toan Verlet 2.5 Di^u kien bi6n tuSn hoan 2.6 Khi ly tuong 2.6.1 Khai niem ve ly tuong 2.6.2 Ham the cua ly tuong 2.6.3 Thuat toan tim thoi gian vacham CHltiNG 3: MO PHONG DONG HOC PHAN TU! 3.1 Nang luong va d6ng luong 3.2 Trang thai can bang Nhifet d6ng 3.2.L Tfnh kh6ng phu thu6c ti^n six cua trang thai can bang, 3.2.2 anh huomg cua mat d6 3.2.3 anh huomg cua ca'u hinh ban d^u 3.3 van d6 d6i chi^u van t6'c 3.4 van dl d6i chi^u thod gian 3.5 Cac dai luong nhiSt d6ng luc hoc 3.5.L Nhiet d6 3.5.2 ap suat 3.6 Ham phan b6 van t6c 3.7 Nhiet dung ding tfch 3.8 Ham phan h6 xuytn tarn 3.9 M6 phong khf ly tuong A 3.9.1 Cac dai luong nhiet d6ng 3.9.2 Quang ducmg tu trung binh 3.9.3 Thod gian va cham KET LUAN PHAN IL PHUONG PHAP MO PHONG TRONG CO HOC LUONG TlT M6DAU CHUONG 1: CAC PHUONG PHAP GL\I TICH SO l.l.Giai phuong trinh Schrodinger m6t chiSu kh6ng phu thu6c thoi gian 1.1.1 Giai phuong trinh Schrodinger bang phuong phap ban 1.1.2 Giai phuong trinh Schrodinger bang phuong phap sai phan huu han 1.2 Giai phuong trinh schrodinger m6t chi^u phu thu6c thcfi gian 1.2.1 Giai phuong trinh Schrodinger bang phuong phap nua budc 2.2.2 Giai phuong trinh Schrodinger bang phuong phap gia ph6 1.3 Giai phuong trinh Schrodinger hai chi6u bang phuong phap phSn tu huu han 1.4 Giai phuong trinh schrodinger ba chi6u de m6 phong nguyen tu hydro CHUONG 2: CAC PHUONG PHAP MONTE CARLO 2.1 Phuong phap monte Carlo bie'n phan 2.2 Hiuong phap monte Carlo luong tir each di ngiu nhien 2.3 Phuong phap monte Carlo khue'ch tan luong t i 2.4 Hiuong phap monte Carlo luong tu tfch phan dudng CHUONG 3: KET QUA VA NHAN XET A-Phdn dp dung cac phuang phap giai tick so 3.1.Giai phuong trinh Schrodinger dufng m6t chi^u 3.1.1.Phuong phap ban 3.1.2.Phuong phap sai phan huu han 3.2.Giai phuong trinh schrodinger m6t chi6u phu thu6c thod gian 3.2.I.S1J tiSn tri^n theo thod gian cua'mOt goi song Gaussian tu 3.2.2.SU ehuy^n d6ng cua m6t goi song tod m6t the bac thang 3.2.3.SU chuy^n d6ng cua m6t goi song tod m6t hang rao the 3.2.4.Sir chuyen d6ng cua m6t goi song h6' the cao huu han., 3.2.5.SU chuyen d6ng cua m6t goi song h6' the' cao vo han 3.2.6.SU tien trien theo thod gian cua hai goi song Gaussian tu 3.3 Phuong phap phdn ttr huu han 3.3.1,Giai phuong trinh schrodinger diing hai chieu 3.3.2.Giai phuong trinh schrodinger hai chieu phu thu6c thod gian 3.4 M6 phong cac orbital cua nguyen tu hydro B-Phdn dp dung cdc phiccmg phap Monte Carlo 3.5.Phuong phap monte Carlo bie'n phan 3.5.1.Dao d6ng tudieu hoa 3.5.2.Nguyen tu hydro 3.5.3.Chuyen d6ng trucmg the Yukawa 3.6 Phuong phap monte Carlo luong tij each di nglu nhien 3.6.1.Dao d6ng tudieu hoa 3.6.2.Dao d6ng tu phi dieu hoa 3.6.3.H6'the'vu6ng goe 3.6.4.H6 the'hinh tru 3.7 Phuong phap monte Carlo khue'ch tan luong tit 3.7.1.Daod6ngtirdi^uhoa 3.7.2.Dao d6ng tir phi didu hoa 3.7.3.Nguyen tu hydro 3.8 Phuong phap monte Carlo luong tii tfch phan dudng KET LUAN TAI LI|:U THAM KHAO PHU LUC PHAN PHUONG PHAP MO PHONG TRONG CO HOC THONG KE MCI DAU Ngay nay, c6ng nghe thdng tin phat trien rat manh me, no anh huong rat 16n de'n moi ITnh vuc ciia cu6c s6'ng M6t s6' nganh s6m ling dung c6ng nghe th6ng tin va da thu duoc nhCmg qua lorn lao nhu: nganh ngan hang, buu chinh, quan ly hanh chinh nha nuofc Trudc xu huomg khoa hoc va giao due khdng th^ diing ngoai cu6c, C6ng nghe th6ng tin noi chung va tfnh toan bang may tfnh noi rieng duoc danh gia la m6t c6ng cu kh6ng the' thie'u ciia n6n khoa hoc va giao due hien dai M6 phong bang may tfnh la m6t nhung ling dung cua c6ng nghe thdng tin vao khoa hpc va giao due Vdd khoa hoe, m6 phong bang mdy tfnh giup cho cac nha khoa hoc c6 m6t c6ng eu tfnh toan thuan tien hon va thu duoc nhung hinh anh true quan hon ve cac sir vat^hien tuong cSn nghien cuu Vdi giao due, no giiip cho giao vien c6 them c6ng cu true quan, h6 tro cho bai giang cua minh D6ng then no cung la tai lieu tham khao hiiu fch cho ngucd hoc, tru6c xu the kh6'i luong tri thu:c cang tang nhanh va triiru tuong Trong cu6c s6'ng hang ngay, cac he vat ly ma chung ta thudng tiep xuc nhu: kh6ng khf, nude, kim loai la cac he bao gom nhieu hat, e6 nhieu phuong phap de tie'p can vdi he nhieu hat nhu: dung Co hoc c6 dien (thuyet d6ng hoc phan tu), Co hoc lucmg tir Tuy nhien, cac phuong phap tren deu c6 nhiing han che' nha't dinh Co m6t each khac de tiep can vdi he nhieu hat da thu duoc ke't qua t6't, la phuong phap tie'p can cua Co hoc th6'ng ke Co hoc th6'ng ke nghien cim he nhieu hat dua tren viec tfnh trung binh th6'ng ke cua tat ca cac hat rieng le tao he Do s6' hat he la ra't I6n (~10" hat) nen dung toan hoc de tfnh gap ft nhieu kho khan Tuy nhien, kho khan c6 the duoc khlc phuc dua tren sire manh tfnh toan ciia may tfnh PtrOi^*^ ^ ° "^^^" "^^" "^"^ ^^^ ^^^"^ ^^^^ ^^ ^^^^ ^^ "^° phong va tfnh toan nhu: Foxtran, Mathematic^, Pascal, M6i phdn mem deu c6 nhirng diem manh cung nhu han che riengt Trong de t^i tac gia sir dung phdn mem MATLAB Po dr = B.I Rabinovich |3] di xua't them mdt cap cue phat A2B2 dat ben ngoai he cue bdn cue dd'i xung AiMNB, dung cho VES, d mdi vi tri eua he cue lin lugt phat hai ddng dien // va l] de' hai hieu xhtAUi (khi phat A,B,, he sd' he cue K^,) va AU2 (khi phat A2B2, he sd he circ AT,-,) giua cap cue thu Sau dd phat d6ng thdi hai ddng nguac chieu de'do hieu i\\tA(AU) {hinh J) M M '^1 Hien nhien, ngoai rtudng cong pp phuong phap sau kha'u trir trudng lai mdi vi irt cua he cue edn cho phep ddng ihdi thu duac mdt gia tn p.Mfi'i) va mdt gia tr; p,:(r2} tuang ung vdi hai he cue dd'i xung-A,.MNB, va A^MNB: • tu ta thu dugc cac dudng cong psiii'i) "^'^Ps2(>'2'>' (2) d{rlp,) N Bi B2/ *•• Q c tac giii Lam Quang Tliiep va Le Vict Du Khuang [5] da de nghi quy trinh sau dicn mdi vdi y tudng la cd' ging tang mdt each hop ly sd lugng tin hieu dien trudng d thuc dia de qua su tong hop cac fin hieu dd thu duoc cac dudng cong cd mat dd thdng tin Idn hon phan anh lai cii chinh xae hon Dien trd sua't bie'u kie'n vi phan Pp thu dugc bang each thuc don gian hon so vdi phuang phap sau kha'u tru trudng Do la phuong phap sau dien dd'i xung ludng cue hop nha't (CSDES - Combined Symmetrical Dipole Electric Sounding) Vdi mdt he thiet bi trinh bay tren hinh bao gom mdt cap cue phat AB va hai cap cue thu M|Ni, M2N2 bd tri dd'i xung qua tam sau, cap cue phat dugc bd tri ben cac cap cue thu (ta CO he cue lan lugt la MiM,ABN,N.) Hinh y So dd he thie't bi sau kha'u-tru trudng cua Rabinovich Dien trd sua't bie'u kie'n pp dugc tiiih theo cdng thuc (2) cd dang : \] AU cIr Pr d{rl AUr- p,) (3) (^2 ^ Ps2)-i^\ K MJ,.MJ }\ MAU) Rabinovich ggi phuang phap la phuang phap sau kha'u tru trudng Mdt yeu cau quan ciia phuang phap 60 sau kha'u tru trudng la phai dam bao cho Idn ciia hai ddng phat tuan theo mdt he thuc xac dinh: (4) VI Dai lugng pp dugc bie'u diin phtj thude vao khoang each trung binh : / • /• 218 = AU< ^ Ps^) i\ - / • K, Aur, (5) /// \\\ /// M- \\\ /// \\\ /// \\\ M- Hinh So he thie't bi sau dien dd'i xung va luong cue hap nha't mdi vi tri he cue chi phat mdt ddng / va hieu dien iht AUsi (giua M/N|) zl6^:(giua M7N2) AUri {Z\^'di N/N2) AUri (giiJa M/M2) Tu dd tinh duoc duowz cong dien trd sua't bie'u kie'npv/- Ps2 (tuong ung vdi sau dd'i xung) va, p,r, p,-i {tuong ung vdi sau luong cue true canh phai \a canh irai) theo cdng ihirc (1) va cac gia tri trung binh : Ps = ^Ps\-Ps2 ' PrF ^ Prr Suyra: pp Ps = (6) (7) ^ - Ps a c dai lugng Psx^Ps2^PrT^PrF^Pr^Pp^^^ dugc bi^u dien phu thude vao khoang each trung binh : r = ^^AN,AN^BN,BN (8) Nhu vay, ngoai dudng cong pp, phuong phap sau dien dd'i xung ludng cue hgp nha't cdn cho phep thu dugc cac dudng cong p^^, / j ^ , Ps^Pn> PrF^PrVdi cac he ciic tren, ta cd mdt sd' nhan xet: 1) Dd'i vdi phuong phap sau khau trir trudng, gia tri A(AU) thudng ra't be nen ddi hoi phai theo doi ra't cln than, mat khac edn phai c6 cac nguon phat ddng Idn mdi chinh xac 2) Viec dung hai mach phat ddng d phuang phap sau kha'u trir trudng lam tang kha nang dd dien, ddi hoi ty sd ddng tuan theo he thirc (///A) ^ (r/Zri)"' se lam cho Pp mdc sai sd Idn r/ /": pham sai sd khdng Idn idm 3) Muc dich chuye'n ddi tir dudng cong Ps sang dudng cong Pp theo cdng thire (2) khdng phai la mgi trudng hgp deu dat dugc vi co chira dao ham la mdt phep tinh khdng dn dinh nen mac phai sai sd Trong edng trinh [2] da chimg minh dieu nay, 4) Vdi he cue ciia phuang phap sau dien dd'i xung ludng cue hgp nha't da phin nao khiie phuc dugc nhirng nhugc diem tren Tuy nhien he cue van cdn phuc tap nen cho de'n vin ehua dugc ap dung vao san xua't d Viet Nam Hon the nira, chua cd nghT de'n viec thu nghiem hoac cai tie'n chimg de' ap dung cho phuong phap sau dien trd dat hieu qua hon • Mud'n tang tinh hieu qua eiia phucmg phap sau dien, mdt sd cac vah de dugc dat la lam the nao de' dugc nhieu tin hieu tang lugng thdng tin xuat phat, nhung khdng lam phirc tap qua nhi^u quy trinh thuc dia Ddng thdi tir cac thdng tin di^cc phai xay dung dugc nhieu loai dudng cong ung vdi cac he cue khac lira ehgn dugc loai dudng cong phan anh gdn nha't vdi lat cat dia dien thuc te giup cho qua trinh xii ly phan tich dat hieu qua* nha't Bang viec bd \i\ he cue nhu the rwio de' tai moi diem khao sat chi cdn sir dung mdt he cue CO ban thdng dung nao dd, giam thie'u e;ic phep ma ta vin cd dugc ca thdng tin ve dudng cong sau dd'i xiJmg p,y dudng cong ludng cue true p^ va dudng cong Petrovski Pp (thu dugc tir cac dudng cong p, p,-) thi lugng thdng tin ve diem khao sat dd se dugc tang len ga'p bdi Ta't ca nhirng thdng tin ne'u dugc khai thac triet de' u-ong mdt chuang trinh xu ly phan tich tdng hop ehdc ehdn se tao dieu kien cho ta hieu bie't mdt each chinh xac va tin cay han v^ dd'i tugng dia chat cdn tie'p can Dd chinh la ndi dung ciia cac phuong phap sau dien sii dung td hgp he circ hgp !y mdi chiing tdi d^ xua't Td hgp he cue do chiing tdi de xua't bao gom; I He circ sau dien dd'i xung cai tie'n (KM-01) .2.Hecuc sau dien ludng cue cai tie'n (KM-02) Tuong irng vdi vjec su dung nai he cue ta CO hai phuong phap sau mdi, la : phuong phap sau Jien ddi xirng cni tieh va phuang phap sau dien ludng cue mdt canh cai lien Tuy vay bang cac phep ciia mdt hai phuong phap cai tie'n neu tren ke't hcTp voi indt sd phep bie'n ddi don gian ta deu co ;1K ihu Jir'-'c ra'i c;i caL loai dudng cong >.au dien l.hac irong co ca nhung dudng cong co dO sau khao sat va dd phan giai k'm hon ma khdng phai true tie'p ngoai thuc dia nhung qua trinh t!i; cong don gian hieu sua't cjo va ::ia ihanh / Phuang: phap sau dien d6'i xung cai tien a) Md ta he cue sau dien ddi xung cai t'en (KM-01) Phuang phap sau dien dd'i xung eai tie'n diing he cue ddi ximg cai tien ma v^ hinh thire gid'ng nhu he cue dd'i ximg thdng thudng He cue bao gom hai dien cue phat A, B nam d vA hai dien circ fnu M, N nam d ngoai ddi ximg vdi qua tam eiia he cue Cac dien cue dugc bd tri cho (kich thude r, va he sd* he cue K, duoc cac tac gia tinh trude 12]) de tir cac phep ta thu dugc dudng cong p^i va p^z gdi 219 len nhuu tai mgi kich thude he cue irij kich thuac he cue ddu tien va eud'i cimg Qua trinh a thuc dla dugc tie'n hinh gid'ng nhu ddi vol phucmg phap sau dien dd'i ximg thdng thudng He cue sau dien dd'i xiimg cai tie'n it hon he cue sau dd'i ximg va luong cue hgp nha't dien cue Ung vdi mdi kich thude he cue se it hon phep de' xac dinh trirc tie'p hai phdn sau dien trd ludng cue pfi va p,/., Vi vay phuong phap sau dd'i xung cai tie'n cd nang sua't cao va chi phi dac thire dia tha'p hon phuang phap sau dd'i ximg va ludng cue hgp nha't Cac gia tri sau dien trd pxt va /j^-? da dugc ngoai thuc dia Tir cac gia tri p^i va ps2 ta tinh gia tri trung binh : = ylp.U'Ps2 (9) Khac vdi phuong phap sau dien dd'i xirng va ludng cue hgp nha't, phuang phap sau khdng true tie'p dudng cong p,r va prr, nhung ta hoan toan cd the de dang tinh dugc dudng cong trung binh psr ciia cac dudng cong pn va pri- tu cac dudng cong ps/ va p^2 bang cac phep tinh dai sd'don gian Xua't phat tir md'i lien he giira cac phdn hieu dien the dugc he cue sau dd'i xirng va ludng cue hgp nha't ta ed : AUnI AUr, ^ I ^ ' ^^S2 I ^^.vi I = SI K, P , ^.S2 (10) ^S I y dd: K,- la he sd he ludng cue true mdt canh cai tie'n (da dugc cac tac gia tinh trude |21), Ar 1^ dien trd sua't bie'u kie'n tuong img vdi dung he ludng cue true thu dugc tir bie'n ddi cac gia n-i A thuc te'bang he cue ddi xirng cai tie'n Tir cac gia tri A , tinh dugc bang cdng thirc tren, theo edng thuc (7) ta cd the xac dinh cac gia tri dien trd sua't Petrovski p^s,- ti/ang ung vdi dung he ludng cue true thu dugc tir bie'n ddi cac gia tri A thuc te'bang he cue dd'i xirng cai tie'n : 220 (H) Pr P 2, Phuong phap siu diin luang cue cai tiih Phuang phap sau dien ludng cue cai tie'n su dung mdt td hgp he cue KM-02 bao gdm : * He ludng cue true mdt canh cai tie'n, * Ket hgp them mdt phep bang he ludng cue xich dao tai kich thude eud'i ciia he cue sau ludng cue true mdt canh eai tieh He cue sau dien ludng cue true mdt canh cai tie'n (kich thude r/^v va he sd he cue K,- duoc cac tac gia tinh trude [2|) v6 hinh thire gid'ng nhu he cue ludng cue true mdt canh thdng thudng He cue bao gdm mdt ludng cue phat AB CO tam cd dinh va mdt ludng cue thu MN ndm tren true AB keo dai cd tam dich chuye'n ddn ve mdt phia dd'i vdi ludng cue phat Qua trinh dac ngoai thue dia dugc tie'n hanh gid'ng nhu dd'i vdi phuang phap sau ludng cue true mdt canh b) Md ta he cue sau dien ludng cue xich dao He cue sau dien ludng cue xich dao (kich thude r/cvJ va he sd he cue Ky:^a dugc cac tac gia tinh trude |21) ve hinh thirc gid'ng nhu he cue ludng cue xich dao thdng thudng He cue bao gdm mdt ludng cue phat AB cd tam cd dinh va mdt ludng cue thu MN cd tam O' ma AB va MN deu vudng gdc vdi 0 ' va ke't hgp vdi cdng thirc (1) ta cd : Psr Ps a) Md ta he cue sau dien ludng cgc true mot canh cai tien b) Tinh cac gia tri p^ Psr va pp^, Ps psr c) Quy trinh dac ngoai thgc dja bang td hgp he cue sau dien ludng cue cai tie'n KM-02 Trude het tai mdi die'm sau ta tie'n hanh quy trinh sau dien bdng he ludng cue true mdt canh cai tie'n gidng nhu phucmg phap sau ludng cue true mdt canh thdng thudng vdi kich thude va he sd he cue da dugc tinh trude 12] Thu or theo timg canh (do xong canh trai mdi canh phai) Sau xong bdng he ludng cue true mdt canh cai tie'n, tai kich thude eud'i tuong img vdi gia tri AB max (AB Idn eud'i ciing dd'i vdi he cue sau dien ludng cue true mdt canh cai tie'n) ta ke't hgp them mOt phep bdng he cue sau ludng cue xich dao (da md ta d tren) nhu sau : Xoay AB vudng gdc tai die'm gifl-a AB Xo^y MN vudng gdc tai vj tri cue thu eud'i cung (cue N) eiia phep sau ludng cue true mdt canh cai tie'n Tuong iirig vdi kich thude ON ciia phep sau ludng cue true mdt canh cai tie'n, vdi ricxd = ON ndi tren, ta cd kich thude ciia AB, MN va he sd rhung ta xic dinh eae gia Vr\ sau dien trd tuong img vdi he cue ddi ximg p^ khdng phai bdng each Uire tie'p the hieu eua eiie dien cue thu vdi he cue dd'i ximg, ma bing each bie'n ddi cac gia tri p^ vdi p^j^ qua eae phep u'nh don gian Chimg ta hay khao sat he cue cue gdm I ludng cue phat va dien e\ic Moo vi Noo Bing he cue ta cd the' thu dugc eae gia tri dien U-d sua't bie'u kie'n cua cac he cue cue nhu sau : Ps\ he c u t Krxd' Sau xong, ta da cd cac gia tn ciia sau ludng cue true mdt canh cai tie'n, mdt gia tri sau ludng cue xich dao ung vdi AB max ^ Khi so sanh vdi phuong phap sau dien dd'i xung va ludng cue hgp nha't, chung ta nhan tha'y phuang phap sau ludng cue cai tie'n don gian hon nhi6u : * He cue mdi it hon he cue sau dd'i xirng va ludng cue hgp nha't dien cue va irng vdi mdi kich thude he cue se it hon phep de xac dinh true tie'p phdn ddi xirng va mdt phdn lai .Y2 = ^Jl = KJ2 AU Af« I AU iVoo dd : AUMCO, AU^ao la hieu dien the'giua cac diem M N so vdi oo, K^i, Ks2 la eke he sd' he cue cue tuong img, / la cudng dd cua ddrig phat Tir tinh cha't the ciia trudng dien dimg ta cd : AUrr n hav AU = AU Moo AU Sx AU rt I = AU SM AU I [p Pn ^ * Ngoai \ iee iheo phuang phap ludng cue su>' : p^ K VI (12) true met canh cai tieh, cdn phai them phep U.v: f^r] bdng he cue sau ludng cue xich dact nhung kich \ thude ciia he cue chi bdng mdt n«a kich thuoc [p -\ ^ ^ •03) K he circ sau dd'i xirng va ludng cue hgp nha't l^,v r J Chinh nhd viec them mdt gia tri ta co the tinh dugc eae gia tri ciia dudng cong sau ludng Nhu the ne'u bie't gia tri A?* PrT ^^^^ Ps2^ Prf cue xich dao va tir dd co the tinh dugc dudng cong tai mdt kich thude he cue nao dd ta co the xac sau Petrovski dinh duoc gia tri A J ^^' ^'^h thude he cue gdn ke trude dd ds tie'p tue nhu vOy va tir dd ta ed cac Vi vay, phuang phap sau ludng cue cai tien gia tri A ^^^^ ^dng thirc (6) cho nang sua't cao va chi phi dac thuc dia tha'p hon nhieu so vdi phuang phap sau dien ddi ximg va ludng cue hgp nha't d) Tfnh cac gia tri p^ p^ va Pp^ > Cac gia tri AT, Prf ^o dugc ngoai thirc dia bdng he cue ludng cue true canh trai va canh phai Cac gia tri trung binh A ^^Pc tinh theo edng thirc (6) > Do dugc gia tri pnc^M^max)^ PrxdFi^meJ he ludng cue xich dao canh trai va canh phai tai kich thude eud'i cua he cue ludng cue true mdt canh cai tien > Khac vdi phuong phap sau dien dd'i ximg va ludng cue hgp nha't, phuong phap sau Nhu chiing ta da bie't, gia tri Psir^) bdng he dd'i xirng tuong duong vdi PncJ^'n) = iPrxdi^^n) + PrxdF {rn))/2 bdng he ludng cue xich dao tuong irng, nghla la : PszO'n) ^ Pr.xd^^''^ (14) Do dd, CO the ta ehi cdn mdt phep prxd bdng he cue ludng cue xich dad tai kich thude eud'i cua he cue ludng cue true mdt canh cai t)^ng tie'n va su dung edng thire gdn diing (14) de' thay the'cho gia tri ps2 tai kich thude eud'i eua he cue cdng thirc (12) hoac (13) ta cd the tinh dugc toan bd cac gia tri pj/, p^j tuong img vdi he cue dd'i ximg cai tie'n 221 ' Vide su dung edng thue gin dting (14) cho phep ehung ta khdng edn phai tie'n hanh dac bang he cue cue de' xae dinh ps^ ra't tdn kem va khd thirc hien kich thude he cue Idn ma vdn dam bao dt chinh xae edn thie't Cu the': Ne'u them mdt phdp picxJnj) bang he ludng cue xiehdaotai kich thude eud'i ciia he ludng cue true mdt canh cai tie'n ben canh trai ta se cd : (15) f^rxJ^ni) Kr{r„) gia tri ciia dudng cong sau dien trd Petrov^^ dd'i vdi he cue tuong irng theo edng thirc : Prsxd jjr^xd { P, V Prsxd (16 -1 ) Q c phuong phap gidi thieu d tren da dugc tie'i hanh thu nghiem tren viing Tan Dan - Hoanl Bd - Quang Ninh va tuye'n SI viing Dak.song - Ci Lai Vdi cac chuong trinh lap bdng ngdn ngi Matlab 11 ], chung tdi da tinh toan va bie'u dien ea ke't qua thu dugc Dudi day chiing tdi chi trinh bd; mdt vi du tai die'm 22 ciia tuye'n SII viini Daksong - Gia Lai tren cac hinh nghla la ta da xac djnh dugc gia trj PnxJii^n-x) "^^ Prsjufli^n) = PkxtMTtd = PicxOrifmax) ben canh De' kie'm nghiem tinh dimg dan eua phuont trai Cir tie'p tuc tinh theo cdng thirc truy hoi (12) phap, ehiing tdi da dac ngoai thuc dia bdng ta cho ca2 canh, ta se cd toan bd cac gia tri ciia dudng ca cac loai he cue gidi thieu d tren, nghla la ta cong sau dien trd d canh, eud'i cung thay vao die'm ehiing tdi tieh hanh thir tu theo quy trinh : cdng thirc (9) ta nhan dugc cac gia tri dien trd sua't • Do bang he cue ddi xirng eai tie'n ta cd dudnt bie'u kie'n pr^xj (tuong ung vdi dung he dd'i xirng cong A (ros) cai tie'n) thu dugc tir bie'n ddi cac gia tri p,- thue te bdng he ludng cue true cai tie'n va gia tri • Do bdng he cue ludng cue true mdt canh cai Prsxji''ma\) hoan toan gid'ng nhu cac he cue e(T ban thdiii: thudng (ehi khac o kich thuoc va he sd he cue) vdi qu\ trinh dac khdng co gi khac nhieu do hoan toan Je dang co the' su dung nga\ \'ao san xuat Mat khac dd sau nghien ciai cua phuone: phap na> Ion hon nhieu so vdi cac phu(Tng phap trude da\ n^n gia ihanh : cho phep ihu du(K- 223 nhi^u thdng tin khac dang tin cay nen cac nha dja vat 1^ vin siir dung dugc toan bd nhirng hie'u bie't v i kinh nghiem tich luy dugc qua trinh dae, xu ly v i phan tich tai lieu De' dam bao it sai pham v6 tinh ludng cue nen viee b6 tri he cue ed khac so vdi thuc te san xua't hien Cac tac gia da tie'p tuc nghien ciru de' cd the' thu nghiem va ap dung rdng rai vac san xua't theo dimg phuang phap thuc le'dang sii dung d nude ta hien la sau mat cdt bdng he cue ludng cue true each deu Dong thdi cac tac gia cung da nghien cuu de ap dung cho phuang phap sau phan cue kich thich Hy vong se dugc gidi thieu cac ke't qua nghien ciru dd cac sd bao tie'p theo Ldi earn on : tap the tac gia tran cam an Gs Tskh Ngd Van Buu da gdp nhieu y kie'n quy bau qua trinh hoan chinh bai bao .Xin tran cam on Ts Nguyen Tai Thinh trudng phdng Ke'hoach - Ky thuat va cac can bd xi nghiep Dja Vat ly mat dat thude Lien doan Vat ly - Dia cha't da ling hd va giiip dd nhiet tinh chiing tdi qua trinh dac thu nghiem ngoai thue dia TAI U$U THAM KHAO | | D M ETTER 1999 : Engineering Prcblem Solving with Matlab, Prentice [niemational Inc University of Colorado Boulder 423 p | | LE VIET DU KHUONG, VU OU'C MLNH va nnk, 1996 : Hoan thien va phat trie'n cac phuong phap dac xii ly va phan tich cac phuong phap sau dien tir De tai nghien ciai c;Vp Bd Giao due va Dao tao Ma sd': B93-05-79 n^ 24 | | B.I RABINOVICH, 1965 : Ve cac nguyen ly CO ban cua phuang phap kha'u trir trudng Dia Vat ly irng dung Tap 43,47-59 (Nga van) | | LAM QU/V^G THIER 1983 : Vd nguyen ly tuong ho tham dd dien Thdng bao Khoa hoc ciia Trudng Dai hoc Qud'c gia Moskva, Phdn Dia chat 75-78 (Nga van) [5] LAM QU.ANG THJEP LE VIET DU' KHL^ONG 1984) : Cac phuong phap sau va mat cdt dien bdng thie't bi dd'i xirng va ludng cue hirp nhat Tapcninuirh:!!, 24(167) 1-4 SUMMARY A new method for Resistivity Sounding by using the reasonable comoination of electrode array Many studies have been undertaken to transfer pjr) and p,- (r) curves that obtained in the field to Pp (r) curve that reflects the geo-eiectncal slice better Apart from this trend, some differentia; Resistivity Sounding Methods by using the different electrode array are suggested All research trends mentioned have the same purpose that is to raise the effectiveness of Resistivity Sounding Method nevertheless, good results is not frequen* achieved At the same time, the electrode array and measurements are still very complicated In this article, the authors's suggestion is a nev method for Resistivity Sounding by using the reasonable combination of electrode array, ir which curves are transferred easily with highei reliaoiiity Besides, the performance is simple bu* effective and the price is low N^dy nhon bai : 19-8-2001 Tiuang Dai hoc Khoa hoc 11( nliU'ii-DUOCiUN VNU JOURNAL OF SCIENCE Mathematics - Physics T.XIX NQA - 2003 BUILDING POTENTIALS OF ONE DIMENSION QUANTUM MECHANICS PROBLEMS BASED ON EXPERIMENTAL DATA Le V i e t D u K h u o n g , N g u y e n H o a n g O a n h Department of Physics, College of Science - \?\'U A b s t r a c t Potential plays a crucial role in studying quantum mechanics problems Common potentials such as harmonic potential, Lennard-Jones potential (LJ) Morse poremial etc., were built according to physical nature analysis of problems, their magnitude were only qualitative Quantities gained when apply these potennals in quantum mechanics problems not agree with experimental data in quantitative sense This paper presents a method to define potential promoted by the authors in efforr ;o get calculated values agreeing with experimental data at high accuracy This rw^'hoz \\?.^ rested in (al^-Idling vibrat,ion energies of Hydrogen molecule Moreover, results r.lsn p,,int cut m unicjue property of potential in this quantum mechanics inverse problen- I n t r o d u c t i o n Consider the problem of calculating vibration energies of a molecule A mrtiecule is a system consisting of two nuclei bound together by the elecTrons that orbit ahout them Since the nuclei are much heavier than the electrons v.-e can assume ihh: tinlatter move fast enough to readjust instantaneously to the chcs.ziv.z position of the r/,:rle: (Born-Oppenheimer approximation) The problem is therefore reduced to one in which the motion of the two nuclei is governed by a potential V, depending only upon r the distance between them The potential of this problem is attractive at large r reaches minimum, passes and becomes strongly repulsion at shorter distance The repulsion at short distance has physical origin related to the Pauli principle: when the electronic clouds surrounding the atoms start to overlap, the energy of the system increase abruptly The attraction at long distance is originated by van der Waals dispersion forces, originated by dipole-dipole interactions in turn due to fluctuating dipoles This term gives cohesion to the system The distance between the nuclei oscillates periodically between inner and outer points (Points at which kinetic energy of relative motion equals zero) The most common potential is the LJ potential given by the expression {'f-i^ The term t h a t is proportional with ( l / ^ y ^ dominating at short distance, models the repulsion between atoms when they are brought very close to each other The term that is proportional with (1/r)^, dominating at large scale, constitutes the attractive part The parameters VQ and a are chosen to fit physical properties in each specific problem In T>-pesef b> -4.vs^T£;X E;O BuUd^n, ,o.nUats of one dimension quantum mechanics ,roUems fact, on physical ground an exponential behavior woulH h common potential is Morse potential expressed^ '"°'" appropriate An other KwW = Vo / J• (2) experimental data show that there are 15 vXe^^lf \ " " ' ° ' ""''°''-' ™ ' - " - 'Oe - e can get only values of energ,, m l Mo^Xt7^'T" """"'^ ' ' ' ' * " " " ' ^ ' - i are not coincident with e x p e r i ^ L , data as e l a d T ' " M ° " " ' " ' " = ' ' • " "ô> of bnJding potentials These potential w e ^ T ^ T l I " " ' "iginated in the way problenr They have analytic L m s nd ca, b e T ? f """'""' '*-"''^^' - " - °f are only