materials sciencecontinuum mechanicsscrew dislocationselastic stressestensile stresscompressive stressedge dislocation/ A0340D Mathematical theory of elasticity A4630C Elasticity A6170 Defects in crystalsThe convention for the sign of the Bergers vector are discussed. One convention leads to stresses that are...
because macroscopically the Burgers vector is characterized by the tensor field (Burgers, 1939; Kröner, 1960)G=curlHp(Gij=εirqHjq,rp),a field that necessarily involves Wp, sincecurlHp=curlEp+curlWp.(We prefer to phrase the theory in terms of a Burgers vector, which is a precisely defin...
The vector field (2.6)X=ξ1(t,u,x)∂∂t+ξ2(t,u,x)∂∂x+η(t,u,x)∂∂uX=ξ1(t,u,x)∂∂t+ξ2(t,u,x)∂∂x+η(t,u,x)∂∂u is a Lie point symmetry of (1.5) if and only if (2.7)X[3](ut+αu2ux+ωuxx−βutxx)∣∣(1.5)=0,X[3](ut+...
vector predictionBurgers problemThe Aitken's Δ 2 -prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is ...
Fluid dynamics cooperating with nonlinear science could describe many natural phenomena, e.g., the Boussinesq-Burgers-type equations for the shallow water waves. In this paper, as for the shallow water waves in a lake or near an ocean beach, we study a Boussinesq-Burgers system. Via the Hiro...
Analytic solutions of vector Burgers equation, Quart - Nerney, Schmahl, et al. - 1996 () Citation Context ... Burgers equation to more interesting physical situations is strongly limited.2 1. Introduction We solved Burgers equation in three dimensions for arbitrary orthogonal curvilinear coordinate ...
Burgers equation vs. large N limit in TT-deformed O(N) vector model - ScienceDirectJunichi Haruna aKatsuta Sakai bKentaroh Yoshida aNuclear Physics B
The effect of establishing a preferred Burgers vector orientation by cold-working, on the SIPA creep rate of an otherwise isotropic material is examined. A modest increase only in the SIPA creep rate parallel to the notional cold-working direction is predicted, followed by a decline to zero ...
state vectormaterial phasematerial phase trackingIn this Letter we describe the classification of symmetric integrable coupled Burgers type equations. Restricting our attention to the systems that cannot be decoupled by a change of dependent variables, we obtain two previously unknown classes of integrable...
Under this form, the velocity vector 𝒘(𝑧,𝑡)w(z,t) fulfills the continuity equation. We also suppose that the extra-stress tensor 𝑻𝑒Te, as well as the fluid velocity 𝑤(𝑧,𝑡)w(z,t), is a function of z and t only. If the fluid has been at rest at the ...