摘要:

AbstractTruncated Newton minimization methods are combined with Peskin's immersed boundary method to facilitate investigation of the dynamic interaction between a viscous, incompressible fluid and immersed elastic objects of complex structure. Applications to aquatic animal locomotion and platelet aggregation during blood clotting are presented. © 1993 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160460602

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractI t is well known that ap‐periodic potentialQ(x)can be reconstructed from spectral data of the corresponding Hill operator −(d2/dx2) + Q(x)in terms of a Riemann θ‐function. We regard the periodic potentialQ(x)as the pointwise limit of a scattering potentialQN,c(x)(defined to equalQ(x) when −Np≦x≦Np, to equal zero whenx(Np) asN→ ∞ andc2→ ∞. The scattering potentialQN,c(x)can be recovered from the scattering data of the corresponding Schrödinger operator in terms of a Dyson determinant according to a well known‐theory. We derive the Riemann θ‐function corresponding to the periodic potentialQ(x) by taking the above limit of the Dyson determinant for the scattering potential.We first calculate the scattering data of the potentialQN,c(x) through recursive formulas in terms of the left transmission and reflection coefficientsTandRof the potential which is equal toQ(x) when 0 ≦x≦pand equal to zero otherwise. We use these data to express the Dyson determinant ofQN,c(x). We then expand the Dyson determinant into a Fredholm series and compute the main contributions to the expansion in the asymptotic limitN→ ∞ andc2→ ∞ using a method developed by Lax, Levermore, and Venakides in their study of the small dispersion limit of the initial value problem of Korteweg‐de Vries equation. The computation of the leading order contributions reduces to a quadratic functional maximization problem constrained by a positivity condition and by a mass quantization condition. The solutions to this maximization problem constitute the differentials on a Riemann surface, the main ingredients for the Riemann θ‐function corresponding to the periodic potential. The limit of the Dyson determinant forQN,c(x) asN→ ∞ andc2→ ∞ is shown to equal the exact Riemann θ‐function corresponding to the periodic potentialQ(x) times an exponential function with exponent being a quadratic polynomial in x. Our calculation includes the correct phase

ISSN:0010-3640    

DOI:10.1002/cpa.3160460603

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractWe consider the stability of multi‐ orn‐soliton solutions to the Korteweg‐de Vries equation (KdV) posed on the real line. It is shown that in the standard variational characterization of KdV multi‐solitons as critical points, then‐solitons actually realize non‐isolated constrained minimizers. (The casen= 1 was already known to Benjamin; see [6].) From this fact a precise dynamic stability result for multi‐solitons follows, namely, that initial data close to a givenn‐soliton evolves in time so as to remain close (in theHn(

ISSN:0010-3640    

DOI:10.1002/cpa.3160460604

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractWe consider the Cauchy problem for a generalN×Nsystem of conservation laws. Existence of solutions was proved by Glimm using his celebrated random choice scheme. In this paper, we obtain a third‐order interaction estimate analagous to that obtained by Glimm for 2×2 systems. By using this estimate, and identifying a global cancellation effect, we obtainL∞‐stability for solutions generated by Glimm's scheme. As an immediate consequence we haveL1‐stability andL∞‐decay, obtained by Temple for 2×2 systems. © 1993 John

ISSN:0010-3640    

DOI:10.1002/cpa.3160460605

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460601

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY