VISCOUS FLUID FLOWS Mechanical Engineering
|
|
- Κλωθώ Δημητρίου
- 6 χρόνια πριν
- Προβολές:
Transcript
1 NEER ENGI STRUCTURE PRESERVING FORMULATION OF HIGH VISCOUS FLUID FLOWS Mechanical Engineering Technical Report ME-TR-9 grad curl div constitutive div curl grad
2 DATA SHEET Titel: Structure preserving formulation of high viscous fluid flows. Subtitle: Mechanical Engineering Series title and no.: Technical Report ME-TR-9 Author: Kennet Olesen Department of Engineering Mechanical Engineering, Aarhus University Internet version: The report is available in electronic format (pdf) at the Department of Engineering website Publisher: Aarhus University URL: Year of publication: 2014 Pages: 31 Editing completed: November 2014 Abstract: This report contains the progress status of the PhD project titled Structure preserving formulation of high viscous fluid flows. It describes the first ideas to a numerical scheme, which conserves mass and momentum in a discrete sense. It is based on spectral expansion polynomials, and it is thought to be applicable to arbitrary constitutive fluid models. Keywords: Computer aided engineering, Continuum mechanics, Numerical Modelling, Fluid mechanics, Non- Newtonian fluids, Spectral methods, Structure preserving methods Referee/Supervisor: Bo Gervang (main supervisor), Henrik Myhre Jensen and Marc Gerritsma Please cite as: Kennet Olesen, Structure preserving formulation of high viscous fluid flows. Department of Engineering, Aarhus University. Denmark. 31 pp. - Technical report ME-TR-9 Cover image: Kennet Olesen ISSN: Reproduction permitted provided the source is explicitly acknowledged
3 STRUCTURE PRESERVING FORMULATION OF HIGH VISCOUS FLUID FLOWS Kennet Olesen, Aarhus University Abstract This report contains the progress status of the PhD project titled Structure preserving formulation of high viscous fluid flows. It describes the first ideas to a numerical scheme, which conserves mass and momentum in a discrete sense. It is based on spectral expansion polynomials, and it is thought to be applicable to arbitrary constitutive fluid models.
4 t ts Pr tr t 2 t s r t s r t r2 ts t t s t t 1 r r t s r r t t r2 t r2 r 1 t t s s t r r r t t 1 r t r 2 ss r2
5
6 tr t r t s s r t rt t2 s s rt rs t t q t s r t s r t t t st t t r t t r s t r st t t t st t t r t s 2 r t s P r t s t r r str t r r s r r t t t s q t r r tr r2 r ss r ss t r r s r t r s s t s t q t s r s t r ss r s s str ss s t st t t r t r t s s s r t q t r s r t t st t t q t s s t s t s2st s t t2 ts t r ss r t s s str ss ts r s2st s st ts t t2 ts t r ss r r s r t s ts s t t t s2st ss r 2 s s t 2 t t r t s 2 t 1 r ss r t str ss s s t r t s t s t r tr r2 st t t s r r t r t s t r t t r r t t s r s t st s s t t s t s r s 2 t s t t s r t r s r t s s t t t t r2 s t r 2s tr rr r s t t r t r r t t s 1t s 2 r 2 r t tr2 s t s r t 2 t s r rt s t s t 2 t t r2 t r t t r r t t t r s s r r ss r rt s str t r s s rst r 2 s 1 1 s r t 2 s st r 2 t ss t s r 1 1t t t r2 t r r t s 1 r 1 s t s t s r r r t t r str t r r s r r s 1 r rt s s 2 s t r r s t
7 2 t r 2 s t t t s t r 2s s r t t s tt r 2s r s s r 2 t t s r t t ss s r t (ρu) t + (ρuu) = Π+f ext, ρ t + (ρu) = 0 s st t t q t s r s t r t t str ss s r t 2 s t st 2 s r t s ρ s t s t2 t u s t t2 t r Π s t t t str ss t s r f ext s r t r s r t 1t r 2 r s r t2 2 f ext = ρg r g s t r t t r t t r r 2 t t t ss r tr r2 1 s r t r s r q t t t t r tr t s t t str ss t s r Π s t t 1 r t r s t r tr r2 t s t rts Π = pi +τ. t r 2 r ss r p s r t t t s t2 t r t r t t r q t st t t s s s str ss t s r τ t t r s r t t t r t r t t s 3 r t s st t r2 r s t r s t s s r q r t s r t s r t t r r 2 st t t r t s r t t t r t r t t t r r 2 t r r s t t 2 ss t t t s2st s s t r s s st t r t 1 t2 t t r st t s q t s r ss t2 ss t tr t t s t rr rs s s t q t st t r t s t s t2 s st t s r s t ( ) (u) ρ +u u = Π+f ext, t u = 0. s t q t s r r ss s t r s t 2 t t t s r t s r t s r t r2 t s t t t s t s s str ss str r t r t r t tt r q t t s r s s t2 t t r st r t r2 ts r s t t s r r s ss s r r t t t s s str ss t r t r t s r t s t s t s r t s r t s s r2 t s t 2 t t t r t r st t s 2
8 τ = 2µ γ. γ γ = 1 2 ( u+( u) T). µ η( γ) = m γ n 1, n m η η η 0 η = (1+(λ γ) a ) n 1 a. γ η
9 r2 ts r n s t t r t s t 1 t r η 0 s t s s t2 t t s r r t s η s t s s t2 t t s r r t s a s t r t r t t t tr s t r λ t r s t s r r t r t tr s t st rts t s s r t t t r s r t s s t 0 < n < 1 s r t s r t n > 1 r t rr s 0 < n < 1 s r t s s t η 0 > η r s r t η 0 < η t s r r r r r s r t t r s t 2 rr s s t t t t t r r r ts t t s t r t 2 r 1 r t t r2 ts s s r t 2 s t s s ts t s t t t r 2 s ss t r r s t r r r t s r st 2 s s st ts r rt t str ss s t r r r t s s s s ts t ss r t s s r s s r ss r t s s r st q s st rr t t 2 ss t t t tr r s t 2 r s t t s s r t t t s t s st 1 r t t s s t 1 r s t rs s t s str t r r sq 3 t s s t t r r r s s s t r s t s s t s s s s r st 1 ts r t r s t st str ss s r r s t q str r s s t r 2 t r r t st str ss s t s s st s t t t s s s t2 t s s s t2 s r r tt t r r t s t t 1 3 r t t tt t s st t r2 t t s t2 V s r s s str ss s r τ yx.visc = µ du dy = µ γ yx(t), r u s t 1 t t t2 t r st s r str ss s 2 s r s s ts τ yx.elas = G dd dy = Gγ yx(t ref,t), Power law Newtonian λ = 0 λ = 0.01 λ = 0.1 λ = 1 λ = 10 λ = Power law Newtonian λ = 0 λ = 0.01 λ = 0.1 λ = 1 λ = 10 λ = 100 viscosity 10 4 viscosity strain-rate strain-rate r r s t r t rr s r s r t P r n = 0.1 m = rr s n = 0.1 η 0 = η = 10 a = 2 r r s t r t rr s r s r t P r n = 2 m = rr s n = 0.1 η 0 = 10 η = a = 2
10 G D γyx (tref, t) t tref ˆt γij (tref, t) = γ ij (t ) dt tref τyx + µ τyx = µγ yx (t ), G t τyx t τyx t = Gγ yx τyx (t) = G t 0 τyx t τyx γ yx (t ) dt = Gγyx (tref, t) tref f = GDspring, Dspring f = µ dddash, dt Ddash Dtotal = Dspring + Ddash. u=v Initial state Dtotal y Final state x u=0 f
11 t t s t t 1 t t r t s rt s f + µ df G dt = µdd total, dt t r r t s t 1 r 1 t t s s λ = µ G s r s t st ts r r s t t r t r 1 t t 2 s s ts r r s t t r r r r r t s r tt t s t t G µ t λ t s2st 2s t 2 st ts G µ t λ 0 t s2st r s st st t st st t s 2 r r t r s r s t s2st s t t r q t s t t s t 2 rt s r s r 2 rt ss t s r 2 1 r s 2 r t s r q t t s str ss str r t s t t s r q t t s τ +λ τ t = η 0 γ. r s s t r rs t s r s t t r 2 e λ t λ t r t r st t s t t t t r st t 2 r q r t t t str ss s t t t = t t r r t 1 s t τ(t) = ˆt [ η0 e (t t ) λ λ ] γ(t ) dt, r t t r t sq r r ts r t r r tt t γ(t ) s t str r t t st t s t s s t t t t 1 t t r r s 3 r t t t t str ss s s r s r t r r tt t r s s str rs 2 τ(t) = ˆt [ η0 2e (t t ) λ λ ] γ(t,t ) dt, t t s t t 1 s r 2 st t t t t r q r ts t t r st r 2 t s t t t s r r t s t r t s t s r r ss t r t r t s2st rt s r r t t t 1 s t t s s t s t r t 1 r t r t r s s 2 t t t st s t r tt s r 2 s s s 1 t r t r t t t st t r t2 Ω 2 ss t t t s s r 2 t 1 2 t t str r t t str ss r t t r r rt s s t r r r t s r t r r r s r t r rr s t t t r s t t t t 123 r t s2st t t r r rt s r t Ω s t s s t s s t 1 s st t t t t s s t r s t s str r t s st r t t r s t tr s r t t s r q t t t t s r q t r s t t t t s str t s r t t s r rs s t tr s r r t 2 r st t r2 r r r t r t t 2 2 t rt r t t τ t q t s r r t q t
12 2 y y x y 0 r r t s x 0 r str t t t r t 1 x t r 1 s t t t s s t t s str t s r s t s r t r 2 r t t r t r t r t s 2 s str s r r r 2 2 t r 2 t s s t r t s t r s t t r st t s t t 2 t s r A r rs A 1 1 sts s t q s t s A = R U = V R, r U =(A T A) 1 2 V =(A A T ) 1 2 A R = (A T A) 1 2 = A U 1. R s r r t t t s r t s t r t r tr r2 t r t t s t ts t s s t t U V t t str t r t A t 2 r r t t 2 r str t t s rs r s t 2 t t r t str t t s r r t t t s r s s r r tr r2 t r u s tr s r t v 2 t t s r A t s t s r s s t r t t rt R str t rt U t U tr s r s u t w R r t t s w t r v w v q t str t r t U r t t rs r u t w s t r t s t r t r t str t t s r s tt r r t t s t s t U V r t tr s r t s r r t r r t U r 2 ts t rs ξ i t s r t t t t r r t V 2 ts t rs ζ i U V r t str t r tr r2 t r t 2 t s λ U s s t rr s s t t s t r r rst t str t s r 2 U t t r t t s 2 R s V s t s s t t s r 2 rst 2 t r t t 2 R t str t t 2 t s V s r 2 r r t s r r t st t t r tr r2 ts r s r t t st s t r t t t t r 2 ts 1 r t t t t t t s 2 dr = dr r r.
13 r r t s t s r r r s t r t r t t s r F(t,t ) = r r. t r t 2 dr = dr r r, r r r s t rs r t r t t s r F 1 (t,t ) = r r. r t s r t t r 2 r s t t t t r 2 r t t s r s t s 2 s t s C = F F T C 1 = (F 1 ) T F 1, r C s t 2 str t s r C 1 s t r str t s r t t s str t s r s t t r str rs t r 1 s r s t str r st t s t t rr t t t t t s str t s r γ s r t t r str t s r C 1 τ(t) = ˆt [ η0 2e (t t ) λ λ ] C 1 (t,t ) dt, s s t q t s t s t st t2 s s r rr t 2 t t r s r r ts r t r s 2 r t t t r s t t t 2 t r t 2 rts s t r t r r t t s rt 2 s ] τ λ + [ dτ dt ( u)t τ τ u = η 0 λ I, r u s t t2 t r I s t t t2 t s r r t s t ss t s r t r s s str ss s r t r ss r r t s ts r s t r s s str ss r 3 r s r s τ s t r r 2 t s tr st t s 2 str ss t s r t ς = τ + η 0 λ I, u U R U R A w v i i R V r P r s t r t t r t str t t s rs
14 2 P At time t' dr' Q z r' r P dr At time t Q y x r 2 r r t t q t s [ ] dτ τ +λ dt ( u)t τ τ u = τ +λ τ= η 0 γ. r t 1 r ss t r ts s t r t r t t str ss t s r r t r t str ss t s r t s t 2 τ q t s t r t 1 t r t s r t s s t r s t r t s q t t 2 2 t s st t r r 2 s s t r t st s t 2 s t ˆx 1ˆx 2ˆx 3 r t s2st tt t t r s t t 2 t t t = t t t r r s t t st t r2 xyz r t s2st t t s t r ts P Q S t s t r t r r t s t t s s ê 1 ê 2 ê 3 r t t r r 1 r ss s ts r t s 2 r = ˆx 1 ê 1 + ˆx 2 ê 2 + ˆx 3 ê 3, dr = r ˆx 1dˆx1 + r ˆx 2dˆx2 + r ˆx 3dˆx3. s s t r r t t r t s2st s 2 g (i) = r ˆx i s t s s s t rs t 1 r ss t s s str ss t s r r t t t t rt s r t s2st rr s t Material grid at time t' dˆτ dt = dτ dt [ τ u+( u) T τ ]. S P ^x 2 Q y, ^x 2 Material grid at time t Q P x^ 1 S x, ^x 1 r t r r s r t r t st s t
15 r r t s s t s s str ss t ˆx 1ˆx 2ˆx 3 r t s2st r t t t r s t t t t s s t t t s t r t str ss t s r τ t t rr s t t s t r t r 2 t r t r r t rr s r r s r t r s r 1t s s t t 1 s t s rt 2 t ❼ r t r 2s r r 2 τ +λ 1 τ= η0 ( γ +λ 2 γ ) r 2s t s t str r t t r r t s t t st t λ 2 s t r t r t t s r s t s r t str ss ❼ t t3 r τ + η( γ) G 0 τ= η( γ) γ t t3 r t s s r t t t t 2 r t s s t2 t r G 0 s st t s r t r ❼ r 2 st t 1 τ +λ 1 τ + 2 (λ 1 µ 1 )( γ τ +τ γ)+ 1 2 µ 0(tr(τ)) γ ν 1(τ : γ)i [ = η 0 γ +λ 2 γ +(λ2 µ 2 )( γ γ)+ 1 ] 2 ν 2( γ : γ)i s r s 2 r 2 t r t s 2 r2 t st ts λ 1 λ 2 µ 0 µ 1 µ 2 ν 1 ν 2 r s r s t r st t t s ❼ s s τ +λ τ + αλ τ τ = η 0 γ η 0 s s r r t s r str ss t r s r r ts
16 r r t t r2 s t r s r s t ts s r r r s tr s s tr t t r t tr t s 2 t s t r ss str t r r s r t Pr rt r P t r q t s r t t r t r r 1 s s t s s 2 t s ts t s t r s2st q t s t s s s r2 2s r r t q r q t s r t t r tr r2 rt s t t t r s t r t r t t r st r rt r r t s t r t r r t t ss r t r t r t q t s r tr t s r t t r r 2 r s 1t r r s r r 2 t t t t t s 2 s s r t t t s st rt s t rt t2 s t t r q t s r t t rt r s r 2 t s t t t s t r r t t r q t s s r tr r2 t st r t t s rr s s t r t 2 r q t t s t r s r 33 r ss t st t s r s r t t2 r ss r t t t r s s r t t s t t r t t r t st s s r 1 r s tt rs3 r s t t t r2 s t t r s tr t s t r s q t t t r t r t s t s 2 r s r ø q st r s s tr t s s s r r r r t s r s t t s r t tr t t r2 tt s r P rt r t q t P L(u(x)) = f(x), r u s t f s t t t t s t r t s s2 s 2 t s t t r x P tt t s r t r 2 t 2 t t t t rt t r v(x) t r t r t Ω ˆ ˆ (L(u(x)),v(x)) = (f(x),v(x)). Ω Ω
17 t r2 t r r t r L t q t r r tt t r r u(x) v(x) r r s t s s r s 1 s u(x) = a i φ i (x) i=0 v(x) = b i ψ i (x), i=0 r a i b i r ts φ i ψ i r s s t s r 1 t s r tr 2 tr t t s t t s s N u(x) u N (x) = a i φ i (x) i=0 N v(x) v N (x) = b i ψ i (x), i=0 r t s t s t t t t r tr t r t tt r r 1 t r 2 r t s r t t r r s r r t s tr t s t s t r 1 t t 1 t t t s s s t t s t s s r s r s t s t t r s r t r 1 t s s tr t s r 2 t s t r s t t r s s t r t s t ts t t t r s t 1 s t r r 2 r t s r t t b i r t rs s t s r r r t r 3 r t 2 t r r t s s r t ts a i s s r r 2 s r t 1 s 2 s ψ i (x) r s t r st ❼ t t s 2 s tt ψ i (x) = δ(x x j ) r δ(x x j ) s t r t t q s t t t t x j t t 3 r r2 r s ❼ st sq r s t s s t (R,R) r R = f(x) L(u(x)) s t r s r 1 t s t s 3 r s s 2 s tt ψ i (x) = R a i ❼ r t s ts t 1 s 2 r t t st t t q t t 1 s 2 r t ψ i (x) = φ i (x) ❼ P tr r t s s 2 t r 1 s 2 t t 1 s 2 r t ψ i (x) φ i (x) t s t r r s t t st r s s t t t t t r t t t r s t t r r s t t r t t t t a i q s t s r t t u N (x) t t t t t t r t s s t st r r tt rs3 st sq r s t s t r rt2 t t t r ts t s t t t t s s2 tr tr 1 r t t r t r t r t s t2 s t s2 tr s s r t t t s t s t q t s2st s s t r 1 t r s s N t t 1 s 2 s r r r t t 2 t t st t s r t t t r s s t 2 r r r t r t t t t t s t s r r s ts s t s r t t s r rt t 2 r r 2 t t r s t s s r s t r t 2 r s s s t s2st q t s t t 2 s s t s r s t s t
18 r r t t r2 P 2 s r s t rt t r [a,b] ˆb a w(x)p m (x)p n (x)dx = δ mn c n, r w(x) s t t δ mn s t r r t c n s st t rt 2 s s s s s t 2 2 s t s r r r 3 r t r r r r s ss s 2 s t t s r rt2 t 2 r t2 2 t s t t t t r r t q t t st 2 s 2 s r t 2s t r 2 s t r t r t r t t r [ 1,1] t t 2s 2 s w(x) = 1 1 x 2 c n = r t r 2 s w(x) = 1 c n = 2 2n+1 { π r π 2 t r s 1 r t s r r s r r r s t s r t s t r t r tt t r q t s2st (v N,u N ) = (v N,f), Ma = b, r t ss tr 1 s 2 M pq = (φ p,φ q ) t r t s s 2 b p = (φ p,f) s t s 2 t 2 t t rs M r r t 1 s 2 s r r t t r [ 1, 1] ❼ t 1 s s 2 r s s t r r x s s t t t s t r r P t s s ts r r r X P 1 X P s X 2 = {1,x,x 2 } t X 3 = {1,x,x 2,x 3 } = X 2 {x 3 } ss tr 1 s 2 M pq = ˆ1 1 x p x q dx = { 2 p+q+1 r q 0 r q. ❼ 1 s s 1 2 r 2 s s sts P 2 s r r P 1 r r r (X P 1 X P ) s s t s 2 φ p (x q ) = δ pq s r s s t t t t t t r st t t t t t t t q t s r s 1 t 2 t t ts t 1 s t ts r r s t r 1 t s t r s 1 t r t ss tr 1 s t s t s r t r t t r q s s r t s tr 1 ❼ 1 s s r 2 s s s 1 r ss r t ss tr 1 M pq = ˆ1 1 L p (x)l q (x)dx = 2 2p+1 δ pq, s s s tr 1 s r2 s2 t rt s r t tr 1 s s t t r r t r t r t r t t tr 1 s r s s t t t r t 1 s 2 s t t r s r t L2 r κ 2 t r r r s2 tr tr 1 t L2 r s t r t t t 1 s r t r 2 1 s t r r P t s s κ 2 = 2 2 = 2P +1 2 r s s t t r t s t rs ss tr 1 s 2P+1
19 r 1 r t t r t t tt r t 1 s 2 t r t r rs r t r r 1 s r s t 2 t r t t t r s t s t t 2 r r r r s r r t t t r 2 1 s s t t r r s r t 2 s t 2 r r s r s s s r r r κ 2 10 P r t r 2 s rst st rts t s tr t r P 5 2 s rt 1 s s t ss t s r r r 1 t s t st t s2st s r t r s rt 2 s s t t t r r r r t s t t r rs t ts r t s s rr r t s r r t r t 2 s t t t t t r rr r t r 2 s s nl n (x) = (2n 1)xL n 1 (x) (n 1)L n 2 (x), L 0 (x) = 1, L 1 (x) = x (1 x 2 )L n(x) = nxl n (x)+nl n 1 (x) = (n+1)xl n (x) (n+1)l n+1 (x). r rr r t 2s 2 s s T n (x) = 2xT n 1 (x) T n 2 (x), T 0 (x) = 1, T 1 (x) = x (1 x 2 )T n(x) = nxt n (x) nt n+1 (x). r 1 r t s r r r r t s tr t s r t s s t t s t st s s t s r s 1 s 2 s t st s s d 2 u dx 2 +2du +10u = f(x) r x = [ 1,1] dx u( 1)+ du dx = 3 x= 1 u(1)+ du dx = 1. x=1 r f(x) = sin(x) t s t s t t r r r t s r r r t t2 r t s r t t t r t s s r r t t r t s t r t s r r r t t r t s 1 t
20 r r t t r Linear interpolation, Varying elements Quadratic interpolation, Varying elements Cubic interpolation, Varying elements Varing interpolation, One element Varing interpolation, Two element u uex u x DOFs r P t t st s t f(x) = sin(x) r r s r r t s r r t t f(x) = sin(x) r r t s t t s tr t s s t r r r s t t s f(x) s s t t t s st t 0 r 1 1 f(x) = H(x) = 2 r 1 1 r 1 r s t s s r t s r2 s r t t s t s r t t r r t r t s t r2 t r t t s r 2 t r r t s s r t s s s t t r2 t r t t ts st 1 t r s s t t t t t t s t t2 t r t s t t r t ts Linear interpolation, Varying elements Quadratic interpolation, Varying elements Cubic interpolation, Varying elements Varing interpolation, One element Varing interpolation, Two element u 2 1 uex u x DOFs r P t t st s r r s r r t s r r t
21 t t s s s t s r s t t r str t r r s r t s t r t r2 s t r t r r t rr t s st t str t r r s r r t s r s t q r q t s r t2 2 r 2 s r r tr r2 t t t 1t r t r tr t s s 2s q t t2 r s r 2 ss t r t q t s r t 2 2 t r s t r t r t r t t 1t r tr t s s r s t t t t tt t s 3 t r t s r s t s t t tr ss t s r st t q r r q t s s st s t s 2 s t 2 ts s 2 str t r r s r t s t t t t r s s r t s s t t t q t s r s t s t r s t 2 t r s r t s t r t s r t t st t t q t s r r r t s r s s r t s P r t t t s r 1t s 2 1 t tt r r r t t s r r t s s r t s t r P r t P r t s ts t t s q t r (p)+µ u = f, t t rt t2 ω = r (u) s s rt r (p)+µ r (ω) = f, s t ss t 2s q t t2 t tr t t t s t 1 t r t s 1 sts t r tr r2 tr ts t r r s 2 t t t r t r s ˆb a r (f) ds = f(b) f(a), t t s t r r (F) n ds = F ds, S t r t r (F) dω = F n ds. Ω Ω S r f s s r F s t r s s s S s s r s t t t r t r n Ω s s s s r s t s s r t 1 s r r t t 2s q t t2 st t t t r t t s r s 2s q t t2 s ss t t tr t 2s q t t2 ss t t
22 t t s u topological - intrinsically discrete inner oriented grad curl div 3 v constitutive outer oriented div curl grad topological - intrinsically discrete r s r t 1 r tr ss t s t t2 rt t2 s r r st r ss t s r t 1 r r t t r r t r t r t t t t s r t 1 t r r t r t r t t s s r r t s s s r t t t st t t q t s r t t t t r t t s P r t s sts t r q t s 2 ω = r (u) q t t r ss t t2 q t (u) = 0. r r s t ss t t s t tr ts s t t 1 t s r t r t s st s t rt t t t t2 q t t t s s r s t ss 1 r t s r s t s t s r ss t s t2 1 r s r 2 ū = u n ds r 2 t t 2 s r t t2 Ω 1 ss t t s r s s t t t t2 q t t s r 2 s s r 1 s t Ω N S (u) dω = ū i, r ū i s t t2 1 r s r t N S s t r s r s t s s t s s t t t t2 q t 2s s t s t s s s 2 s t t t2 1 ss t t t r s t s s s s q t ω = r (u) s s t s 1 t s r t 2 r s s t t s r t t2 1 ts ū v r s rt t2 s t r t t t s t t t2 1 s r r t t r ss t s r s t r t t s r t s st ss t t t t t s r s s r t rt t2 t r t r t s t s s s s ω = ω ds t t r t t s t r t t2 1 S s r 2 s t rt t2 t r s r ts s Ω S i=1 N s ū = u n ds = r (ω) n ds = ω i, r ω i s t rt t2 t r s r t s r N s s t r s t s r t s t ss t 2 2 t t r s t s 2 t t 1 t s r t r t s t s t s q t s t r t t s t s t s r t s s s rt t r 1 t s s rt t s t t q t s t t s t s tt r s 3 s t s t s r t t i=1
23 s s r 2 t t s q t t r t r r (p)+ (τ) = 0, t r ss t t2 q t t s s s t t r t q t s r t t t r s t s s r 1 t r s s s s s r t s st t t q t r s s t t s s s t2 t q t s r s r t r st t t q t s r s t t τ s s r r t s r t r t s st t t 1 r 2 s r s t r t t s r s t r s 2 2s t 2s q t t s r s r t 1 t r t r t q t s r r 2 t t r r tr r2 r t t s q t t rt t r s t t r s r τ p r 1t r tr t s t s r t r t r f s t 2 r t t s s s t t 3 r t s r t s s t r s s r s t s s str ss t r t r t ss t s r s r s r r r s t 1 t s r r ss r s r r r t t s r t s t s s tr t s 3 t r r 2 t t r t s r t s s t s t t t t s 3 s t s st t r ss r s r r t t ss t t t t s tr s r s s rr s s t t s t r r t r ts s rs s r t ss s r 2 t t ss r tr r2 t 2 ss r ss t2 t 2 tr t s t ss 1 r ts r s s s t tr t r r t t t t2 r t t t s s t 2 t t str r t s st t t s str r t s t r t s t t t r tr r2 ts r s str r t s tr 2 ss t t s t ts t2 s t r r t r 2 ss t t t ts t str r t r r r t tr t r r t t r t t2 s t r ss t t t s s t t r r t r t t t2 q t t r 2 ts t rs r s s t t t s r t s r 1 r r str t r s s t t t t t2 ts r tr 2 s r t t t t 2 s t t2 1 s r t s r s t s t s r t q r r ss r s s r s s s s r t r t 1 r t r t r t 2 r t r t r t t s r t s r s r 2 r r r r s t s ss tt r ts r t s t r t str t r r s str t s ss r ts r t r s t r t str t r s s r r P r t r q t s r s r r s t t t r t r st t t r t s r s s r r s t t t 2s q t t s r t t t r t r t t t t t r s ss t t t 1 t r 2 t t 1 t2 ts t r s ss t t t 2 t r 2 t t 2 t2 ts t t s s t st t t r t s s s t s st t t t 2s r r str ss s s t s s s t str r t s s t r t t t2 t str ss s r r r t t t2 t sq r tr 1 s2st t q t s r t t r t r t t t r t t2 q t s s t t s s s t r ss r t t
24 & & + $ $ $ +, $ + $ +, ++, + $ ① + & / & & 0 & & & & &② & & & / & +& & & 0 & + + & & & + + / & &/ & / / & / / & ++ & + / & / + / & & / &② & +& + & + + / + & & + &② / + / & & / + & + + & ② / / + / / + / & + +& & / & & & / & + & + + / + + & + + / & ② & + + / & & & &② & +&/ ++ &② + & + & + & &② + + /& ② ① / 0 / & / & & + / & & +&/ / & + 0 &② ++ & & & / & +&/ / & & + / & & + & / & & &② & &② + & 0 +&/ / & & + + & & + / & + & + & & / & +&/ / & + ② / / &② + & &② / &/ /② & + + / & & ② & / & & + / / 0 / & & & && / & / & & & & + + & & / + & + & & & &② / 0 / & + / 0 / & + + & ②+ + & + / & & + &② / ++ / / & / & +&/ ++ + & + / / + & &② / 0 / & & + / & / & & + & + + & / & / ③③ + ② & & & / ++ / / ① & + +& + / & & &② / ① & + ② S & / & + + & & / + &/ &+ & / ++ / / ① & + + PN 2 & &② / ① & + + PN +&/ & / / + / & & + / 0 / & & & +&/ ++ + / + / + & &② & +&/ ++ &② + / 0 / // &+ S + & & &② / 0 / &+ / & &② S/ ++ / &/ ++ S / & + +& & &② / ++ / / 0 / & +& + ② S & / & &② +&/ ++ / 0 / & + & & & & / ① & + & +&/ ++ +! $! & + + ③ + & &② / 0 & /& & & +&/ / & & &② & // & +& & + & / & // & & & ++ & &②
25 1e e y y e e e Streamlines, N p = e x e 05 1e Streamlines, N p = e e x e e e 05 y Inifinite norm of flux balance e e e e e e x 1e x 10 7 mass x momentum 6 y momentum Streamlines, N p = 12 1e 05 1e N p e 05 1e 05 1e e 05 1e r tr ts t r t 2 r r t st str t s s t ss t s r t t ss t s r s t 2 t t t t2 r s t s r r s r t str ss t 2 1tr str ss r2 t s t s r t t t str t r s r s r s st r s r t s t t r t r s rt t s t r t s r t r ts t st t s t t s ss t r r ss r rt r s s rt t t r t t s r rt
26 t t s P t s r r rr ts str t s r s r s s r t ss t t s t r s 2 s t s s t s r r t r t ss t r 1 t 2 s r t L r t s t t r t2 r tr t s r t s st t t q t s 2 r2 st t r s 2s s s r t s 1 r ss t r t s t s t s r t r s r s st t t q t s r r s t r s r t s r t r ss s t t r s s r t s r t r r t rs st t t q t s t r t rs r t r 3 t t r r st 2 r r st s r t t s r t s 1 t 2 r r s t t t s r t t r r 1 t rs t st t t q t s t s r t t 1t t s s t t r s r t s s s s r t r t t s r r t s t s 2 s r t ss 1 t 2 t t s r t t t2 s s st r s r t t s 2 r t s st r t t s s r s t t s t r t2 ts r r 2 t t r2 t t t t2 ts r s st ts s s t s s s q s r t t q t r t s r s t t r str ss ts r tr t r t 2 r t s r str ss t t r t r s t t t s tr s s t s t tr t t r2 t s tr s ts t s s tr s t r t s t r t2 s s t r r r s ss t r t t s r t t Ω t s t3 r2 Ω t t r ss t s t r t t s s r 2 t t q t σ = r (p)+ τ = 0 Ω, t t r t s r t ss r r ss u = 0 Ω, s t 2 s st t t s t str r t t t str ss t s r t s s s t2 s s τ = 2µ D. t s r s rs t2 rt t r s r s r r r s rs t2 rt t r s r s r s r rr ts t rs t2 2 t2 r s r 2 r t t r s rr ts t t
27 r p s t r ss r u s t t2 τ s t s r r s s str ss t s r µ s t st t s s t2 t t D s t s2 tr rt t str r t t s r D = 1 2 ( ) r T u+ r u. s s t 2 t r2 t s u = 0 Ω. r r r t s tr t t s r t s str t r t rr ts s t rt t2 t2 r ss r P r t t s r P r t s 2 r st t s s t2 ts s t s r s r t r t s r st s s t t2 r ss r str ss r t s r st t s s t2 ts s r t s r q r s r r s s r s t t r s r t t r s r t s tr t t rr ts P s 1 t2 r ss r str ss r t s r r r t s r s r r s t s t 2 t L( v,q,σ) = 1 (σ : σ) b(σ, v)+(q, v), 4µ r q L 2 (Ω) v H(div;Ω) σ [H(div;Ω)] 2 2 s s t s s2 tr 2 t s rs t sq r t r ts ts r s sq r t r t t t s r σ 2 ( σξξ σ σ = σ σ ηη ), t t r v = (u,v) T t t r r b(σ, v)) s 2 ˆ ( b(σ, v)) := σ ( ξξ u ξ u+σ η + v ) σ ) ηη ξ η v dω. Ω st t r2 t ( u, p, τ) t r s t s t s 2 t r t r t ( v,p) b(τ, v) = 0 v H(div;Ω) ( u,q) = 0 q L 2 (Ω) b(σ, u) + 1 2µ (τ : σ) = 0 σ [H(div;Ω)]2 2 s s s2st st t t s s2 tr 2 str 1 r t s rr ts P s r s ss t r s t s s t s t s 2 r r t s t s t s r t s tt s t t s s s s Q L 2 (Ω) V H(div;Ω) T [H(div;Ω)] 2 2 s r t r t st t t r s ( u h,p h,τ h ) V Q T s t t ( v h,p h ) b(τ h, v h ) = 0 v h V ( u h,q h ) = 0 q h Q b(σ h, u h ) + 1 2µ (τh : σ h ) = 0 σ h T s s r t s s t s t s 2 t t2 t s t s r q s t t Z V V t s s r t t r s v h s t s 2 v h = 0 t ZV Q s t 2 ss s r s ZV s t r 2 r 1 t ss s r t ZV s t s s r s r ss r s t s r s t t s s s V Q s t s 2 ZV Q st str t r t rr ts s t s r
28 t t s r 2 t s t t t s t2 s s V T t s s r t s Z T V s st t r s v h r t s2 tr rt t t2 r t s s Z T = { v h V v h + T v h = 0} { v h V b(σ, v h ) = 0, σ [H(div;Ω)] 2 2 s } t t t Z T s t s s 2 t s tr s t s r t t s t t2 r q r s t t ZT T Z T s t r s t s 2 s r t t 2 t s r s t2 s ZT s t s t 2 r 1 t s r t t s r s r t r t t r2 t s r t t2 s t s r t t t s 2 t s Z T = tr t s s t s t s r s s s t s t ξ i i = 0,...,N t ss tt r ts 2 r N ξ i i = 1,...,N t ss r ts t t t ξ i 1 < ξ i < ξ i r i = 1,...,N rt r r tr t 1t ss r ts ( ξ 0 = 1, ξ i, ξ N+1 = 1) t ss r ts s t ts 1 1 r 2 s ss t t t ts t 2 h i (ξ) t r 2 s ss t t t ts t 2 h i (ξ) t r 2 s ss t t t ts r rr t s h e (ξ) r t r 2 s str t t 2 t s 2 rr ts i 1 e i (ξ) = dh k (ξ), i = 1,...,N k=0 i 1 ẽ i = d h e (ξ), i = 1,...,N +1. e i (ξ) s 2 r N 1 ẽ i (ξ) s 2 r N t t s s s t s 1 r ss t t2 s tr t s k=0 N N N N u h (ξ,η) = u i,j h i (ξ) h j (η)+ v i,j hi (ξ)h j (η). i=0 j=1 i=1 j=0 t t t t ξ t t t2 s 2 r N t ξ r t 2 r N 1 t η r t u P N,N 1 r 2 t η t t t2 v P N 1,N t s t t u P N 1,N 1 t r r t r ss r 1 s N N p h (ξ,η) = p i,j e i (ξ)e j (η). i=1 j=1 s t t2 r ss r 1 s r t s t t ZV Q t r r 1 t ss s r t t t s r s r ss r s 2 s r t r ss r s t 2s s r st t s t t t r ss r s t r t st t r t s 2 s 1 1tr str ss ts s τ h ξξ(ξ,η) = ˆ N+1 Ω i=0 j=1 p h (ξ,η)dξdη = 0 N i=1 j=1 N N τ ξξi,j he i (ξ)e j (η), τηη(ξ,η) h = N p i,j = 0. N+1 i=1 j=0 τ ηηi,j e i (ξ) h e j(η), N N τξη(ξ,η) h = τηξ(ξ,η) h = τ ξηi,j h i (ξ)h j (η). i=0 j=0
29 t t s 1 s s t t τξξ h N+1 ξ = i=1 j=1 i=1 j=1 N (τ ξξi,j τ ξξi 1,j )ẽ i (ξ)e j (η) P N,N 1, τηη h N η = N+1 (τ ηηi,j τ ηηi,j 1 )e i (ξ)ẽ j (η) P N 1,N. t r s 2 r τξξ h/ ξ s t s s s t ξ t uh τ ηη / η s t s 2 s s t η t u h r s u s t 3 r t t r t r2 t str τξξ h 2 s tt τ h ξξ ξ = 0 r ξ = ±1. r 2 s τ h ηη η = 0 r η = ±1. t t s t str ts s r t t τξξ h / ξ 1 r ss s t s r t u t2 s rs r2 u 1 r ss t r s t s τξξ h r t s s s r τξξ h / ξ v r t r t t s r str ss t s r t 3 t s r r t s u/ η v/ ξ s r 2 N u η = i=0 j=0 v N ξ = i=0 j=0 N (u i,j+1 u i,j )h i (ξ)ẽ j (η), N (v i+1,j v i,j )ẽ i (ξ)h j (η), t t t tr 1 s ts r t t t2 1 s s t ts r s t s rt t r s r t t t2 ts t r2 r r r t u i,0 r u i,n+1 r t 2 t t t t2 r r r t v 0,j v N+1,j r t s s 2 t r s r t t t2 t t t r t r2 r s t 2 t t t u/ η v/ ξ r t s 2 s s t s r str ss r r s t t
30 s t t t s r r ss r rt r ts t rr t st t s t s P r t r t2 t t s r s t s t r rst t t r2 r 2 r r t s t t t s s t t r q r ts rs s str t r r s r r t t t s r s s st t t r s r ss t r r tr r2 st t t s 2 s t t r2 r 2 s r s t t s r rt r t s s s st t rt t t r r t s s t t t r r t s r r t s s s r r t r r t s s t t s r t t r 2 r r t s ss t s t t s t t t t r t ts s t r r t s t r s s r t s r r ss r rt r r s t t s ss ss t t r r t s r s r t s t rst t ss t t r P r t s s r s r t s s s r r rr ts t 1t s 2 r s r t tr2 r t 2 s tt t s r rt t r t2 r t s r r s r s ss t t r s t t r s t t s t s s s t r t2 t st s r s t2 s t s r s r t tr t t s t s t t2 t t t2 str ss s 2 s r r t r 1 t s s r t str ss rt t 2 t str ss s s t s r t t t2 s r s s t s r s t t t s t r t t r str t r r s r t s st r t s t s s t s t r q r ts s rr t 2 r
31 t r r s s t s t t s r t r t t P r t t s t s t r s t s 2 t r t rt 1 r t rt t rt r r t s s t s rr s s t t r r t t 2 1 t t r t r t r s t r2 t t t r st s t t r t s st t 2 t t st t t s s r s r s t r t 1 s r t s t t t t r2 s t ss t s st s r t r s r st t t s t s r t s s t s r ss t t 1 t 1 r ss s r t str ss s t r 1 r ss s r q r t r t t s rr t s t s r s s r2 t s t t s t r t r s t 2 r t rs r 2 t s t r t s t s r tt r s r s t s r t t t t r t r t tr t r r t s s r2 r s t ts r st ss r s t st s s r t r r r t s 2 t t2 t r r t rr t tt r s r s t r r t r r t s r t r t t s 1 r t q Pr ss r r r r s s t s r tr t t r t r t q s 2 r rr t 2 t r t s rs t r s rt t 1 r t r s t r r ts t r r ts s s r 1 r 1 s s q s t r 2 2 s r r s r s s r t r s s tr t t s s s t s s q s r t t r r t 2 r 1 t r t r t s s s tr s s r r s s st t q s r r s t q s t s s t r rt s t t r st t t r t s r rt s s t tr s r r s t 2 2 r r t st t t tt s r t r tt t r tt tt q
32 t r r r s r 1 r s st r r t t s s t s s
33 r 2 t t t t r t rs r t r 2r r str rt ss r 2 s P 2 r q s s r 2 t 2 s r 33 r t 1 st q ss r 1 t s t r s r s r r t rs rt s P s tt rt ts t s t t 2s s r 4 t t 2 s rr ts r t s r s tr t t s tr r r t s r rt r t q t s t r t s t t s r rr ts r P s t 2 t s tr r 1 t s r t t2 r ss r str ss r t t st s r tt rs3 t r 2s s tr t s r2 t s str s s s s é rr ts r r r tr t s t 1 t s r t r rt s r t t P 2s s r s r r r tr t t s r r 2 t 1 r rs t2 Pr ss r s r t st r r 2s t t r r ss s r t t P 2s s r t s r rr ts r 1 t s tr t t r st s t s r r s t r t t P 2s s r t s r s t tr t t s r t 3 t tr2 P 2s s P t s s r t 2 P t r t 2 tr t t s r t r ss r st s q t s t t t rt s r 2s t t s s rr s t rst 2 r 1 st t 1 r rs t2 Pr ss
34 r 2 r 2 s t r t r q t s st t Pr s t 2 t2 P rt r r r t s r t 3 t t t t t r s r tr r2 q r t r s P t s s r t ø q st r t tr t t s r t st 2 r s r ss r t s q t s P t s s r ss s tts st t t 2 s s s s é rr ts r tr r t r s t s r t t r t s t t r t r s t t st t P 1t s r 2 s r t r st r t r s s s t
35 ss r2 t t P P P s r t t t 2 s t r t t t t t t ss r ss tt r P rt r t q t Pr rt r tr t t rt t2 t2 Pr ss r
36 Olesen, Kennet. Structure preserving formulation of high viscous fluid flows, 2014 Department of Engineering Aarhus University Inge Lehmanns Gade Aarhus Denmark
Alterazioni del sistema cardiovascolare nel volo spaziale
POLITECNICO DI TORINO Corso di Laurea in Ingegneria Aerospaziale Alterazioni del sistema cardiovascolare nel volo spaziale Relatore Ing. Stefania Scarsoglio Studente Marco Enea Anno accademico 2015 2016
Διαβάστε περισσότεραLEM. Non-linear externalities in firm localization. Giulio Bottazzi Ugo Gragnolati * Fabio Vanni
LEM WORKING PAPER SERIES Non-linear externalities in firm localization Giulio Bottazzi Ugo Gragnolati * Fabio Vanni Institute of Economics, Scuola Superiore Sant'Anna, Pisa, Italy * University of Paris
Διαβάστε περισσότεραr r t r r t t r t P s r t r P s r s r r rs tr t r r t s ss r P s s t r t t tr r r t t r t r r t t s r t rr t Ü rs t 3 r r r 3 rträ 3 röÿ r t
r t t r t ts r3 s r r t r r t t r t P s r t r P s r s r P s r 1 s r rs tr t r r t s ss r P s s t r t t tr r 2s s r t t r t r r t t s r t rr t Ü rs t 3 r t r 3 s3 Ü rs t 3 r r r 3 rträ 3 röÿ r t r r r rs
Διαβάστε περισσότεραAnalysis of a discrete element method and coupling with a compressible fluid flow method
Analysis of a discrete element method and coupling with a compressible fluid flow method Laurent Monasse To cite this version: Laurent Monasse. Analysis of a discrete element method and coupling with a
Διαβάστε περισσότεραMulti-GPU numerical simulation of electromagnetic waves
Multi-GPU numerical simulation of electromagnetic waves Philippe Helluy, Thomas Strub To cite this version: Philippe Helluy, Thomas Strub. Multi-GPU numerical simulation of electromagnetic waves. ESAIM:
Διαβάστε περισσότεραAssessment of otoacoustic emission probe fit at the workfloor
Assessment of otoacoustic emission probe fit at the workfloor t s st tt r st s s r r t rs t2 t P t rs str t t r 1 t s ér r tr st tr r2 t r r t s t t t r t s r ss r rr t 2 s r r 1 s r r t s s s r t s t
Διαβάστε περισσότεραP P Ó P. r r t r r r s 1. r r ó t t ó rr r rr r rí st s t s. Pr s t P r s rr. r t r s s s é 3 ñ
P P Ó P r r t r r r s 1 r r ó t t ó rr r rr r rí st s t s Pr s t P r s rr r t r s s s é 3 ñ í sé 3 ñ 3 é1 r P P Ó P str r r r t é t r r r s 1 t r P r s rr 1 1 s t r r ó s r s st rr t s r t s rr s r q s
Διαβάστε περισσότεραQBER DISCUSSION PAPER No. 8/2013. On Assortative and Disassortative Mixing in Scale-Free Networks: The Case of Interbank Credit Networks
QBER DISCUSSION PAPER No. 8/2013 On Assortative and Disassortative Mixing in Scale-Free Networks: The Case of Interbank Credit Networks Karl Finger, Daniel Fricke and Thomas Lux ss rt t s ss rt t 1 r t
Διαβάστε περισσότεραCoupling strategies for compressible - low Mach number flows
Coupling strategies for compressible - low Mach number flows Yohan Penel, Stéphane Dellacherie, Bruno Després To cite this version: Yohan Penel, Stéphane Dellacherie, Bruno Després. Coupling strategies
Διαβάστε περισσότεραr t t r t t à ré ér t é r t st é é t r s s2stè s t rs ts t s
r t r r é té tr q tr t q t t q t r t t rrêté stér ût Prés té r ré ér ès r é r r st P t ré r t érô t 2r ré ré s r t r tr q t s s r t t s t r tr q tr t q t t q t r t t r t t r t t à ré ér t é r t st é é
Διαβάστε περισσότεραMesh Parameterization: Theory and Practice
Mesh Parameterization: Theory and Practice Kai Hormann, Bruno Lévy, Alla Sheffer To cite this version: Kai Hormann, Bruno Lévy, Alla Sheffer. Mesh Parameterization: Theory and Practice. This document is
Διαβάστε περισσότεραts s ts tr s t tr r n s s q t r t rs d n i : X n X n 1 r n 1 0 i n s t s 2 d n i dn+1 j = d n j dn+1 i+1 r 2 s s s s ts
r s r t r t t tr t t 2 t2 str t s s t2 s r PP rs t P r s r t r2 s r r s ts t 2 t2 str t s s s ts t2 t r2 r s ts r t t t2 s s r ss s q st r s t t s 2 r t t s t t st t t t 2 tr t s s s t r t s t s 2 s ts
Διαβάστε περισσότεραAx = b. 7x = 21. x = 21 7 = 3.
3 s st 3 r 3 t r 3 3 t s st t 3t s 3 3 r 3 3 st t t r 3 s t t r r r t st t rr 3t r t 3 3 rt3 3 t 3 3 r st 3 t 3 tr 3 r t3 t 3 s st t Ax = b. s t 3 t 3 3 r r t n r A tr 3 rr t 3 t n ts b 3 t t r r t x 3
Διαβάστε περισσότεραNetwork Neutrality Debate and ISP Inter-Relations: Traffi c Exchange, Revenue Sharing, and Disconnection Threat
Network Neutrality Debate and ISP Inter-Relations: Traffi c Exchange, Revenue Sharing, and Disconnection Threat Pierre Coucheney, Patrick Maillé, runo Tuffin To cite this version: Pierre Coucheney, Patrick
Διαβάστε περισσότεραConsommation marchande et contraintes non monétaires au Canada ( )
Consommation marchande et contraintes non monétaires au Canada (1969-2008) Julien Boelaert, François Gardes To cite this version: Julien Boelaert, François Gardes. Consommation marchande et contraintes
Διαβάστε περισσότεραŁs t r t rs tø r P r s tø PrØ rø rs tø P r s r t t r s t Ø t q s P r s tr. 2stŁ s q t q s t rt r s t s t ss s Ø r s t r t. Łs t r t t Ø t q s
Łs t r t rs tø r P r s tø PrØ rø rs tø P r s r t t r s t Ø t q s P r s tr st t t t Ø t q s ss P r s P 2stŁ s q t q s t rt r s t s t ss s Ø r s t r t P r røs r Łs t r t t Ø t q s r Ø r t t r t q t rs tø
Διαβάστε περισσότεραP r s r r t. tr t. r P
P r s r r t tr t r P r t s rés t t rs s r s r r t é ér s r q s t r r r r t str t q q s r s P rs t s r st r q r P P r s r r t t s rés t t r t s rés t t é ér s r q s t r r r r t r st r q rs s r s r r t str
Διαβάστε περισσότεραrs r r â t át r st tíst Ó P ã t r r r â
rs r r â t át r st tíst P Ó P ã t r r r â ã t r r P Ó P r sã rs r s t à r çã rs r st tíst r q s t r r t çã r r st tíst r t r ú r s r ú r â rs r r â t át r çã rs r st tíst 1 r r 1 ss rt q çã st tr sã
Διαβάστε περισσότεραON THE MEASUREMENT OF
ON THE MEASUREMENT OF INVESTMENT TYPES: HETEROGENEITY IN CORPORATE TAX ELASTICITIES HENDRIK JUNGMANN, SIMON LORETZ WORKING PAPER NO. 2016-01 t s r t st t t2 s t r t2 r r t t 1 st t s r r t3 str t s r ts
Διαβάστε περισσότεραE fficient computational tools for the statistical analysis of shape and asymmetryof 3D point sets
E fficient computational tools for the statistical analysis of shape and asymmetryof 3D point sets Benoît Combès To cite this version: Benoît Combès. E fficient computational tools for the statistical
Διαβάστε περισσότεραRésolution de problème inverse et propagation d incertitudes : application à la dynamique des gaz compressibles
Résolution de problème inverse et propagation d incertitudes : application à la dynamique des gaz compressibles Alexandre Birolleau To cite this version: Alexandre Birolleau. Résolution de problème inverse
Διαβάστε περισσότεραRobust Segmentation of Focal Lesions on Multi-Sequence MRI in Multiple Sclerosis
Robust Segmentation of Focal Lesions on Multi-Sequence MRI in Multiple Sclerosis Daniel García-Lorenzo To cite this version: Daniel García-Lorenzo. Robust Segmentation of Focal Lesions on Multi-Sequence
Διαβάστε περισσότεραss rt çã r s t Pr r Pós r çã ê t çã st t t ê s 1 t s r s r s r s r q s t r r t çã r str ê t çã r t r r r t r s
P P P P ss rt çã r s t Pr r Pós r çã ê t çã st t t ê s 1 t s r s r s r s r q s t r r t çã r str ê t çã r t r r r t r s r t r 3 2 r r r 3 t r ér t r s s r t s r s r s ér t r r t t q s t s sã s s s ér t
Διαβάστε περισσότεραγ 1 6 M = 0.05 F M = 0.05 F M = 0.2 F M = 0.2 F M = 0.05 F M = 0.05 F M = 0.05 F M = 0.2 F M = 0.05 F 2 2 λ τ M = 6000 M = 10000 M = 15000 M = 6000 M = 10000 M = 15000 1 6 τ = 36 1 6 τ = 102 1 6 M = 5000
Διαβάστε περισσότεραHigh order interpolation function for surface contact problem
3 016 5 Journal of East China Normal University Natural Science No 3 May 016 : 1000-564101603-0009-1 1 1 1 00444; E- 00030 : Lagrange Lobatto Matlab : ; Lagrange; : O41 : A DOI: 103969/jissn1000-56410160300
Διαβάστε περισσότεραPhysique des réacteurs à eau lourde ou légère en cycle thorium : étude par simulation des performances de conversion et de sûreté
Physique des réacteurs à eau lourde ou légère en cycle thorium : étude par simulation des performances de conversion et de sûreté Alexis Nuttin To cite this version: Alexis Nuttin. Physique des réacteurs
Διαβάστε περισσότεραss rt t r s t t t rs r ç s s rt t r t Pr r r q r ts P 2s s r r t t t t t st r t
Ô P ss rt t r s t t t rs r ç s s rt t r t Pr r r q r ts P 2s s r r t t t t t st r t FichaCatalografica :: Fichacatalografica https://www3.dti.ufv.br/bbt/ficha/cadastrarficha/visua... Ficha catalográfica
Διαβάστε περισσότεραÉmergence des représentations perceptives de la parole : Des transformations verbales sensorielles à des éléments de modélisation computationnelle
Émergence des représentations perceptives de la parole : Des transformations verbales sensorielles à des éléments de modélisation computationnelle Anahita Basirat To cite this version: Anahita Basirat.
Διαβάστε περισσότεραJeux d inondation dans les graphes
Jeux d inondation dans les graphes Aurélie Lagoutte To cite this version: Aurélie Lagoutte. Jeux d inondation dans les graphes. 2010. HAL Id: hal-00509488 https://hal.archives-ouvertes.fr/hal-00509488
Διαβάστε περισσότεραTransfert sécurisé d Images par combinaison de techniques de compression, cryptage et de marquage
Transfert sécurisé d Images par combinaison de techniques de compression, cryptage et de marquage José Marconi Rodrigues To cite this version: José Marconi Rodrigues. Transfert sécurisé d Images par combinaison
Διαβάστε περισσότεραΠ Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α
Α Ρ Χ Α Ι Α Ι Σ Τ Ο Ρ Ι Α Π Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α Σ η µ ε ί ω σ η : σ υ ν ά δ ε λ φ ο ι, ν α µ ο υ σ υ γ χ ω ρ ή σ ε τ ε τ ο γ ρ ή γ ο ρ ο κ α ι α τ η µ έ λ η τ ο ύ
Διαβάστε περισσότεραCouplage dans les applications interactives de grande taille
Couplage dans les applications interactives de grande taille Jean-Denis Lesage To cite this version: Jean-Denis Lesage. Couplage dans les applications interactives de grande taille. Réseaux et télécommunications
Διαβάστε περισσότεραACI sécurité informatique KAA (Key Authentification Ambient)
ACI sécurité informatique KAA (Key Authentification Ambient) Samuel Galice, Veronique Legrand, Frédéric Le Mouël, Marine Minier, Stéphane Ubéda, Michel Morvan, Sylvain Sené, Laurent Guihéry, Agnès Rabagny,
Διαβάστε περισσότεραModèles de représentation multi-résolution pour le rendu photo-réaliste de matériaux complexes
Modèles de représentation multi-résolution pour le rendu photo-réaliste de matériaux complexes Jérôme Baril To cite this version: Jérôme Baril. Modèles de représentation multi-résolution pour le rendu
Διαβάστε περισσότεραUNIVERSITE DE PERPIGNAN VIA DOMITIA
Délivré par UNIVERSITE DE PERPIGNAN VIA DOMITIA Préparée au sein de l école doctorale Energie et Environnement Et de l unité de recherche Procédés, Matériaux et Énergie Solaire (PROMES-CNRS, UPR 8521)
Διαβάστε περισσότεραMeasurement-driven mobile data traffic modeling in a large metropolitan area
Measurement-driven mobile data traffic modeling in a large metropolitan area Eduardo Mucelli Rezende Oliveira, Aline Carneiro Viana, Kolar Purushothama Naveen, Carlos Sarraute To cite this version: Eduardo
Διαβάστε περισσότεραRadio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes.
Radio détection des rayons cosmiques d ultra-haute énergie : mise en oeuvre et analyse des données d un réseau de stations autonomes. Diego Torres Machado To cite this version: Diego Torres Machado. Radio
Διαβάστε περισσότεραLangages dédiés au développement de services de communications
Langages dédiés au développement de services de communications Nicolas Palix To cite this version: Nicolas Palix. Langages dédiés au développement de services de communications. Réseaux et télécommunications
Διαβάστε περισσότεραForêts aléatoires : aspects théoriques, sélection de variables et applications
Forêts aléatoires : aspects théoriques, sélection de variables et applications Robin Genuer To cite this version: Robin Genuer. Forêts aléatoires : aspects théoriques, sélection de variables et applications.
Διαβάστε περισσότεραThree essays on trade and transfers: country heterogeneity, preferential treatment and habit formation
Three essays on trade and transfers: country heterogeneity, preferential treatment and habit formation Jean-Marc Malambwe Kilolo To cite this version: Jean-Marc Malambwe Kilolo. Three essays on trade and
Διαβάστε περισσότεραSolving an Air Conditioning System Problem in an Embodiment Design Context Using Constraint Satisfaction Techniques
Solving an Air Conditioning System Problem in an Embodiment Design Context Using Constraint Satisfaction Techniques Raphael Chenouard, Patrick Sébastian, Laurent Granvilliers To cite this version: Raphael
Διαβάστε περισσότεραFourier Analysis of Waves
Exercises for the Feynman Lectures on Physics by Richard Feynman, Et Al. Chapter 36 Fourier Analysis of Waves Detailed Work by James Pate Williams, Jr. BA, BS, MSwE, PhD From Exercises for the Feynman
Διαβάστε περισσότεραTransformations d Arbres XML avec des Modèles Probabilistes pour l Annotation
Transformations d Arbres XML avec des Modèles Probabilistes pour l Annotation Florent Jousse To cite this version: Florent Jousse. Transformations d Arbres XML avec des Modèles Probabilistes pour l Annotation.
Διαβάστε περισσότεραADVANCED STRUCTURAL MECHANICS
VSB TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING ADVANCED STRUCTURAL MECHANICS Lecture 1 Jiří Brožovský Office: LP H 406/3 Phone: 597 321 321 E-mail: jiri.brozovsky@vsb.cz WWW: http://fast10.vsb.cz/brozovsky/
Διαβάστε περισσότεραVers un assistant à la preuve en langue naturelle
Vers un assistant à la preuve en langue naturelle Thévenon Patrick To cite this version: Thévenon Patrick. Vers un assistant à la preuve en langue naturelle. Autre [cs.oh]. Université de Savoie, 2006.
Διαβάστε περισσότεραP t s st t t t t2 t s st t t rt t t tt s t t ä ör tt r t r 2ö r t ts t t t t t t st t t t s r s s s t är ä t t t 2ö r t ts rt t t 2 r äärä t r s Pr r
r s s s t t P t s st t t t t2 t s st t t rt t t tt s t t ä ör tt r t r 2ö r t ts t t t t t t st t t t s r s s s t är ä t t t 2ö r t ts rt t t 2 r äärä t r s Pr r t t s st ä r t str t st t tt2 t s s t st
Διαβάστε περισσότεραAnnulations de la dette extérieure et croissance. Une application au cas des pays pauvres très endettés (PPTE)
Annulations de la dette extérieure et croissance. Une application au cas des pays pauvres très endettés (PPTE) Khadija Idlemouden To cite this version: Khadija Idlemouden. Annulations de la dette extérieure
Διαβάστε περισσότεραMolekulare Ebene (biochemische Messungen) Zelluläre Ebene (Elektrophysiologie, Imaging-Verfahren) Netzwerk Ebene (Multielektrodensysteme) Areale (MRT, EEG...) Gene Neuronen Synaptische Kopplung kleine
Διαβάστε περισσότεραHomework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
Διαβάστε περισσότεραTraitement STAP en environnement hétérogène. Application à la détection radar et implémentation sur GPU
Traitement STAP en environnement hétérogène. Application à la détection radar et implémentation sur GPU Jean-François Degurse To cite this version: Jean-François Degurse. Traitement STAP en environnement
Διαβάστε περισσότεραΚεφάλαιο 1 Πραγματικοί Αριθμοί 1.1 Σύνολα
x + = 0 N = {,, 3....}, Z Q, b, b N c, d c, d N + b = c, b = d. N = =. < > P n P (n) P () n = P (n) P (n + ) n n + P (n) n P (n) n P n P (n) P (m) P (n) n m P (n + ) P (n) n m P n P (n) P () P (), P (),...,
Διαβάστε περισσότερα❷ s é 2s é í t é Pr 3
❷ s é 2s é í t é Pr 3 t tr t á t r í í t 2 ➄ P á r í3 í str t s tr t r t r s 3 í rá P r t P P á í 2 rá í s é rá P r t P 3 é r 2 í r 3 t é str á 2 rá rt 3 3 t str 3 str ýr t ý í r t t2 str s í P á í t
Διαβάστε περισσότεραA Probabilistic Numerical Method for Fully Non-linear Parabolic Partial Differential Equations
A Probabilistic Numerical Metod for Fully Non-linear Parabolic Partial Differential Equations Aras Faim To cite tis version: Aras Faim. A Probabilistic Numerical Metod for Fully Non-linear Parabolic Partial
Διαβάστε περισσότεραP P Ô. ss rt çã r s t à rs r ç s rt s 1 ê s Pr r Pós r çã ís r t çã tít st r t
P P Ô P ss rt çã r s t à rs r ç s rt s 1 ê s Pr r Pós r çã ís r t çã tít st r t FELIPE ANDRADE APOLÔNIO UM MODELO PARA DEFEITOS ESTRUTURAIS EM NANOMAGNETOS Dissertação apresentada à Universidade Federal
Διαβάστε περισσότεραContribution à l évolution des méthodologies de caractérisation et d amélioration des voies ferrées
Contribution à l évolution des méthodologies de caractérisation et d amélioration des voies ferrées Noureddine Rhayma To cite this version: Noureddine Rhayma. Contribution à l évolution des méthodologies
Διαβάστε περισσότεραStratégies Efficaces et Modèles d Implantation pour les Langages Fonctionnels.
Stratégies Efficaces et Modèles d Implantation pour les Langages Fonctionnels. François-Régis Sinot To cite this version: François-Régis Sinot. Stratégies Efficaces et Modèles d Implantation pour les Langages
Διαβάστε περισσότεραSecond Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
Διαβάστε περισσότεραAppendix A. Curvilinear coordinates. A.1 Lamé coefficients. Consider set of equations. ξ i = ξ i (x 1,x 2,x 3 ), i = 1,2,3
Appendix A Curvilinear coordinates A. Lamé coefficients Consider set of equations ξ i = ξ i x,x 2,x 3, i =,2,3 where ξ,ξ 2,ξ 3 independent, single-valued and continuous x,x 2,x 3 : coordinates of point
Διαβάστε περισσότεραPoints de torsion des courbes elliptiques et équations diophantiennes
Points de torsion des courbes elliptiques et équations diophantiennes Nicolas Billerey To cite this version: Nicolas Billerey. Points de torsion des courbes elliptiques et équations diophantiennes. Mathématiques
Διαβάστε περισσότερα1. (a) (5 points) Find the unit tangent and unit normal vectors T and N to the curve. r(t) = 3cost, 4t, 3sint
1. a) 5 points) Find the unit tangent and unit normal vectors T and N to the curve at the point P, π, rt) cost, t, sint ). b) 5 points) Find curvature of the curve at the point P. Solution: a) r t) sint,,
Διαβάστε περισσότεραA 1 A 2 A 3 B 1 B 2 B 3
16 0 17 0 17 0 18 0 18 0 19 0 20 A A = A 1 î + A 2 ĵ + A 3ˆk A (x, y, z) r = xî + yĵ + zˆk A B A B B A = A 1 B 1 + A 2 B 2 + A 3 B 3 = A B θ θ A B = ˆn A B θ A B î ĵ ˆk = A 1 A 2 A 3 B 1 B 2 B 3 W = F
Διαβάστε περισσότεραAuthor : Πιθανώς έχει κάποιο λάθος Supervisor : Πιθανώς έχει καποιο λάθος.
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ Τμήμα Φυσικής 1ο Σετ Ασκήσεων Γενικών Μαθηματικών ΙΙ Author : Βρετινάρης Γεώργιος Πιθανώς έχει κάποιο λάθος Supervisor : Χ.Τσάγκας 19 Φεβρουαρίου 217 ΑΕΜ: 14638 Πιθανώς
Διαβάστε περισσότεραAboa Centre for Economics. Discussion paper No. 122 Turku 2018
Joonas Ollonqvist Accounting for the role of tax-benefit changes in shaping income inequality: A new method, with application to income inequality in Finland Aboa Centre for Economics Discussion paper
Διαβάστε περισσότεραΑ Ρ Ι Θ Μ Ο Σ : 6.913
Α Ρ Ι Θ Μ Ο Σ : 6.913 ΠΡΑΞΗ ΚΑΤΑΘΕΣΗΣ ΟΡΩΝ ΔΙΑΓΩΝΙΣΜΟΥ Σ τ η ν Π ά τ ρ α σ ή μ ε ρ α σ τ ι ς δ ε κ α τ έ σ σ ε ρ ι ς ( 1 4 ) τ ο υ μ ή ν α Ο κ τ ω β ρ ί ο υ, η μ έ ρ α Τ ε τ ά ρ τ η, τ ο υ έ τ ο υ ς δ
Διαβάστε περισσότεραEulerian Simulation of Large Deformations
Eulerian Simulation of Large Deformations Shayan Hoshyari April, 2018 Some Applications 1 Biomechanical Engineering 2 / 11 Some Applications 1 Biomechanical Engineering 2 Muscle Animation 2 / 11 Some Applications
Διαβάστε περισσότεραLa naissance de la cohomologie des groupes
La naissance de la cohomologie des groupes Nicolas Basbois To cite this version: Nicolas Basbois. La naissance de la cohomologie des groupes. Mathématiques [math]. Université Nice Sophia Antipolis, 2009.
Διαβάστε περισσότεραD Alembert s Solution to the Wave Equation
D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique
Διαβάστε περισσότεραt ts P ALEPlot t t P rt P ts r P ts t r P ts
t ts P ALEPlot 2 2 2 t t P rt P ts r P ts t r P ts t t r 1 t2 1 s r s r s r 1 1 tr s r t r s s rt t r s 2 s t t r r r t s s r t r t 2 t t r r t t2 t s s t t t s t t st 2 t t r t r t r s s t t r t s r t
Διαβάστε περισσότεραUNIVtrRSITA DEGLI STUDI DI TRIESTE
UNIVtrRSITA DEGLI STUDI DI TRIESTE XXVNI CICLO DEL DOTTORATO DI RICERCA IN ASSICURAZIONE E FINANZA: MATEMATICA E GESTIONE PRICING AND HEDGING GLWB AND GMWB IN THE HESTON AND IN THE BLACK-SCHOLES \MITH
Διαβάστε περισσότεραγ n ϑ n n ψ T 8 Q 6 j, k, m, n, p, r, r t, x, y f m (x) (f(x)) m / a/b (f g)(x) = f(g(x)) n f f n I J α β I = α + βj N, Z, Q ϕ Εὐκλείδης ὁ Ἀλεξανδρεύς Στοιχεῖα ἄκρος καὶ μέσος λόγος ὕδωρ αἰθήρ ϕ φ Φ τ
Διαβάστε περισσότεραThis is a repository copy of Persistent poverty and children's cognitive development: Evidence from the UK Millennium Cohort Study.
This is a repository copy of Persistent poverty and children's cognitive development: Evidence from the UK Millennium Cohort Study. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/43513/
Διαβάστε περισσότεραThree Essays on Canadian Housing Markets and Electricity Market
Three Essays on Canadian Housing Markets and Electricity Market by Yuan Zhang A Thesis presented to The University of Guelph In partial fulfilment of requirements for the degree of Doctor of Philosophy
Διαβάστε περισσότεραTeor imov r. ta matem. statist. Vip. 94, 2016, stor
eor imov r. ta matem. statist. Vip. 94, 6, stor. 93 5 Abstract. e article is devoted to models of financial markets wit stocastic volatility, wic is defined by a functional of Ornstein-Ulenbeck process
Διαβάστε περισσότεραk k ΚΕΦΑΛΑΙΟ 1 G = (V, E) V E V V V G E G e = {v, u} E v u e v u G G V (G) E(G) n(g) = V (G) m(g) = E(G) G S V (G) S G N G (S) = {u V (G)\S v S : {v, u} E(G)} G v S v V (G) N G (v) = N G ({v}) x V (G)
Διαβάστε περισσότερα1 String with massive end-points
1 String with massive end-points Πρόβλημα 5.11:Θεωρείστε μια χορδή μήκους, τάσης T, με δύο σημειακά σωματίδια στα άκρα της, το ένα μάζας m, και το άλλο μάζας m. α) Μελετώντας την κίνηση των άκρων βρείτε
Διαβάστε περισσότεραΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. «Προστασία ηλεκτροδίων γείωσης από τη διάβρωση»
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «Προστασία ηλεκτροδίων
Διαβάστε περισσότεραss rt çã r s t à rs r ç s rt s 1 ê s Pr r Pós r çã ís r t çã tít st r t
ss rt çã r s t à rs r ç s rt s 1 ê s Pr r Pós r çã ís r t çã tít st r t FichaCatalografica :: Fichacatalografica https://www3.dti.ufv.br/bbt/ficha/cadastrarficha/visua... Ficha catalográfica preparada
Διαβάστε περισσότεραDevelopment and Verification of Multi-Level Sub- Meshing Techniques of PEEC to Model High- Speed Power and Ground Plane-Pairs of PFBS
Rose-Hulman Institute of Technology Rose-Hulman Scholar Graduate Theses - Electrical and Computer Engineering Graduate Theses Spring 5-2015 Development and Verification of Multi-Level Sub- Meshing Techniques
Διαβάστε περισσότεραA hybrid PSTD/DG method to solve the linearized Euler equations
A hybrid PSTD/ method to solve the linearized Euler equations ú P á ñ 3 rt r 1 rt t t t r t rs t2 2 t r s r2 r r Ps s tr r r P t s s t t 2 r t r r P s s r r 2s s s2 t s s t t t s t r t s t r q t r r t
Διαβάστε περισσότεραDefects in Hard-Sphere Colloidal Crystals
Defects in Hard-Sphere Colloidal Crystals The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Accessed Citable Link Terms
Διαβάστε περισσότεραΚεθάιαην Επηθακπύιηα θαη Επηθαλεηαθά Οινθιεξώκαηα
Δπηθακπύιηα Οινθιεξώκαηα Κεθάιαην Επηθακπύιηα θαη Επηθαλεηαθά Οινθιεξώκαηα Επηθακπύιηα Οινθιεξώκαηα θαη εθαξκνγέο. Επηθακπύιην Οινθιήξωκα. Έζηω όηη ε βαζκωηή ζπλάξηεζε f(x,y,z) είλαη νξηζκέλε πάλω ζε κία
Διαβάστε περισσότεραFinite difference method for 2-D heat equation
Finite difference method for 2-D heat equation Praveen. C praveen@math.tifrbng.res.in Tata Institute of Fundamental Research Center for Applicable Mathematics Bangalore 560065 http://math.tifrbng.res.in/~praveen
Διαβάστε περισσότεραAVERTISSEMENT. D'autre part, toute contrefaçon, plagiat, reproduction encourt une poursuite pénale. LIENS
AVERTISSEMENT Ce document est le fruit d'un long travail approuvé par le jury de soutenance et mis à disposition de l'ensemble de la communauté universitaire élargie. Il est soumis à la propriété intellectuelle
Διαβάστε περισσότεραDiscretization of the Convection Term
FMIA F. Moukalled L. Mangani M. Darwish An Advanced Introduction with OpenFOAM and Matlab This textbook explores both the theoretical oundation o the Finite Volume Method (FVM) and its applications in
Διαβάστε περισσότεραJ. of Math. (PRC) Banach, , X = N(T ) R(T + ), Y = R(T ) N(T + ). Vol. 37 ( 2017 ) No. 5
Vol. 37 ( 2017 ) No. 5 J. of Math. (PRC) 1,2, 1, 1 (1., 225002) (2., 225009) :. I +AT +, T + = T + (I +AT + ) 1, T +. Banach Hilbert Moore-Penrose.. : ; ; Moore-Penrose ; ; MR(2010) : 47L05; 46A32 : O177.2
Διαβάστε περισσότεραConditions aux bords dans des theories conformes non unitaires
Conditions aux bords dans des theories conformes non unitaires Jerome Dubail To cite this version: Jerome Dubail. Conditions aux bords dans des theories conformes non unitaires. Physique mathématique [math-ph].
Διαβάστε περισσότεραTransformation automatique de la parole - Etude des transformations acoustiques
Transformation automatique de la parole - Etude des transformations acoustiques Larbi Mesbahi To cite this version: Larbi Mesbahi. Transformation automatique de la parole - Etude des transformations acoustiques.
Διαβάστε περισσότεραSOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM
SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM Solutions to Question 1 a) The cumulative distribution function of T conditional on N n is Pr T t N n) Pr max X 1,..., X N ) t N n) Pr max
Διαβάστε περισσότεραMulti-scale method for modeling thin sheet buckling under residual stress : In the context of cold strip rolling
Multi-scale method for modeling thin sheet buckling under residual stress : In the context of cold strip rolling Rebecca Nakhoul To cite this version: Rebecca Nakhoul. Multi-scale method for modeling thin
Διαβάστε περισσότερα2. Α ν ά λ υ σ η Π ε ρ ι ο χ ή ς. 3. Α π α ι τ ή σ ε ι ς Ε ρ γ ο δ ό τ η. 4. Τ υ π ο λ ο γ ί α κ τ ι ρ ί ω ν. 5. Π ρ ό τ α σ η. 6.
Π Ε Ρ Ι Ε Χ Ο Μ Ε Ν Α 1. Ε ι σ α γ ω γ ή 2. Α ν ά λ υ σ η Π ε ρ ι ο χ ή ς 3. Α π α ι τ ή σ ε ι ς Ε ρ γ ο δ ό τ η 4. Τ υ π ο λ ο γ ί α κ τ ι ρ ί ω ν 5. Π ρ ό τ α σ η 6. Τ ο γ ρ α φ ε ί ο 1. Ε ι σ α γ ω
Διαβάστε περισσότεραDéformation et quantification par groupoïde des variétés toriques
Défomation et uantification pa goupoïde de vaiété toiue Fédéic Cadet To cite thi veion: Fédéic Cadet. Défomation et uantification pa goupoïde de vaiété toiue. Mathématiue [math]. Univeité d Oléan, 200.
Διαβάστε περισσότεραCoupled Fluid Flow and Elastoplastic Damage Analysis of Acid. Stimulated Chalk Reservoirs
Nazanin Jahani Coupled Fluid Flow and Elastoplastic Damage Analysis of Acid Stimulated Chalk Reservoirs Thesis for the degree of Philosophiae Doctor Trondheim, October 2015 Norwegian University of Science
Διαβάστε περισσότεραConstitutive Relations in Chiral Media
Constitutive Relations in Chiral Media Covariance and Chirality Coefficients in Biisotropic Materials Roger Scott Montana State University, Department of Physics March 2 nd, 2010 Optical Activity Polarization
Διαβάστε περισσότεραF (x) = kx. F (x )dx. F = kx. U(x) = U(0) kx2
F (x) = kx x k F = F (x) U(0) U(x) = x F = kx 0 F (x )dx U(x) = U(0) + 1 2 kx2 x U(0) = 0 U(x) = 1 2 kx2 U(x) x 0 = 0 x 1 U(x) U(0) + U (0) x + 1 2 U (0) x 2 U (0) = 0 U(x) U(0) + 1 2 U (0) x 2 U(0) =
Διαβάστε περισσότεραDissertation for the degree philosophiae doctor (PhD) at the University of Bergen
Dissertation for the degree philosophiae doctor (PhD) at the University of Bergen Dissertation date: GF F GF F SLE GF F D Ĉ = C { } Ĉ \ D D D = {z : z < 1} f : D D D D = D D, D = D D f f : D D
Διαβάστε περισσότεραJ. of Math. (PRC) 6 n (nt ) + n V = 0, (1.1) n t + div. div(n T ) = n τ (T L(x) T ), (1.2) n)xx (nt ) x + nv x = J 0, (1.4) n. 6 n
Vol. 35 ( 215 ) No. 5 J. of Math. (PRC) a, b, a ( a. ; b., 4515) :., [3]. : ; ; MR(21) : 35Q4 : O175. : A : 255-7797(215)5-15-7 1 [1] : [ ( ) ] ε 2 n n t + div 6 n (nt ) + n V =, (1.1) n div(n T ) = n
Διαβάστε περισσότεραQ π (/) ^ ^ ^ Η φ. <f) c>o. ^ ο. ö ê ω Q. Ο. o 'c. _o _) o U 03. ,,, ω ^ ^ -g'^ ο 0) f ο. Ε. ιη ο Φ. ο 0) κ. ο 03.,Ο. g 2< οο"" ο φ.
II 4»» «i p û»7'' s V -Ζ G -7 y 1 X s? ' (/) Ζ L. - =! i- Ζ ) Η f) " i L. Û - 1 1 Ι û ( - " - ' t - ' t/î " ι-8. Ι -. : wî ' j 1 Τ J en " il-' - - ö ê., t= ' -; '9 ',,, ) Τ '.,/,. - ϊζ L - (- - s.1 ai
Διαβάστε περισσότεραΑπειροστικός Λογισμός ΙΙ, εαρινό εξάμηνο Φυλλάδιο ασκήσεων επανάληψης.
Απειροστικός Λογισμός ΙΙ, εαρινό εξάμηνο 2016-17. Φυλλάδιο ασκήσεων επανάληψης. 1. Για καθεμία από τις παρακάτω συναρτήσεις ελέγξτε βάσει του ορισμού της παραγωγισιμότητας αν είναι παραγωγίσιμη στο αντίστοιχο
Διαβάστε περισσότεραm i N 1 F i = j i F ij + F x
N m i i = 1,..., N m i Fi x N 1 F ij, j = 1, 2,... i 1, i + 1,..., N m i F i = j i F ij + F x i mi Fi j Fj i mj O P i = F i = j i F ij + F x i, i = 1,..., N P = i F i = N F ij + i j i N i F x i, i = 1,...,
Διαβάστε περισσότεραy(t) S x(t) S dy dx E, E E T1 T2 T1 T2 1 T 1 T 2 2 T 2 1 T 2 2 3 T 3 1 T 3 2... V o R R R T V CC P F A P g h V ext V sin 2 S f S t V 1 V 2 V out sin 2 f S t x 1 F k q K x q K k F d F x d V
Διαβάστε περισσότερα