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The behavior of solutions of the finite-genus Whitham equations for the weak dispersion limit of the defocusing nonlinear
Schrodinger equation is investigated analytically and numerically for piecewise-constant initial data. In particular, the
dynamics of constant-amplitude initial conditions with one or more frequency jumps (i.e., piecewise linear phase) are considered.
It is shown analytically and numerically that, for finite times, regions of arbitrarily high genus can be produced; asymptotically
with time, however, the solution can be divided into expanding regions which are either of genus-zero, genus-one, or genus-two
type, their precise arrangement depending on the specifics of the initial datum given. This behavior should be compared to
that of the Korteweg-de Vries equation,
where the solution is divided into regions which are either genus-zero or genus-one asymptotically. Finally, the potential
application of these results to the generation of short optical pulses is discussed: The method proposed takes advantage of
nonlinear compression via appropriate frequency modulation, and allows control of both the pulse amplitude and its width,
as well as the distance along the fiber at which the pulse is produced 相似文献
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Kai Kamada Shintaro Udo Shuichi Yamashita Yuko Tsutsumi Yasumichi Matsumoto 《Solid State Ionics》2003,160(3-4):389-394
Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al2O3 (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al2O3 and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi2Sr2CaCu2Oy (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm−2). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm−2). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount. 相似文献
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Fumie Takei Daisuke Kodama Sugiko Nakamura Kiyotaka Onitsuka Shigetoshi Takahashi 《Journal of polymer science. Part A, Polymer chemistry》2006,44(1):585-595
Aryl isocyanides bearing free‐base and metallo‐porphyrins were prepared and polymerized with a Pd–Pt μ‐ethynediyl complex as the initiator to give polymers with narrow polydispersity indices. The molecular weights of the resulting polymers were precisely controlled by the initial feed ratio of the porphyrin monomer to the initiator. The UV–VIS spectra suggested that the porphyrin pendants are regularly arranged to form stacked columns. Metallo‐porphyrin polymers were also prepared by reacting free‐base porphyrin polymers with metal salts. The successive reactions of free‐base and zinc‐porphyrin monomers resulted in the formation of diblock polymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 585–595, 2006 相似文献
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Let m be an integer with m3. Let K and K be perfect fields of characteristic p and p such that (p,m)=1 and (p,m)=1, respectively. Moreover let A and A be algebraic function fields over K and K defined by xm+ym=a(0, ak) and xm+ym=a(a0 ak), respectively. Put g=(m–1)(m–2)/2. Denote by M(K,p,a) and M(K,p,a) the Hasse-Witt matrices of A and A with respect to the canonical bases of holomorphic differentials. Then we show that if p+p0(mod.m) then rank M(K,p,a)+rank M(K,p,a)=g and if pp1 (mod.m) then rank M(K,p,a)=rank M(K,p,a). 相似文献
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