Space-time L^2-estimates and life-span of the Klainerman-Machedon radial solutions to some semi-linear wave equations

We consider the Cauchy problem for some semi-linear wave equations in three space dimensions and prove global or almost global existence of the Klainerman-Machedon radial solutions. The proof is carried out by a contraction-mapping argument based on a refined version of the Keel-Smith-Sogge estimate, together with the Morawetz-type inequality

Generation of Alfven Waves by Magnetic Reconnection

In this paper, results of 2.5-dimensional magnetohydrodynamical simulations are reported for the magnetic reconnection of non-perfectly antiparallel magnetic fields. The magnetic field has a component perpendicular to the computational plane, that is, guide field. The angle theta between magnetic field lines in two half regions is a key parameter in our simulations whereas the initial distribution of the plasma is assumed to be simple; density and pressure are uniform except for the current sheet region. Alfven waves are generated at the reconnection point and propagate along the reconnected field line. The energy fluxes of the Alfven waves and magneto-acoustic waves (slow mode and fast mode) generated by the magnetic reconnection are measured. Each flux shows the similar time evolution independent of theta. The percentage of the energies (time integral of energy fluxes) carried by the Alfven waves and magneto-acoustic waves to the released magnetic energy are calculated. The Alfven waves carry 38.9%, 36.0%, and 29.5% of the released magnetic energy at the maximum (theta=80^\circ) in the case of beta=0.1, 1, and 20 respectively, where beta is the plasma beta (the ratio of gas pressure to magnetic pressure). The magneto-acoustic waves carry 16.2% (theta=70^\circ), 25.9% (theta=60^\circ), and 75.0% (theta=180^\circ) of the energy at the maximum. Implications of these results for solar coronal heating and acceleration of high-speed solar wind are discussed.Comment: Accepted for publication in PASJ. 24 pages, 11 figure

A remark on the almost global existence theorems of Keel, Smith and Sogge

We shall give a new proof of temporally global existence of small solutions for systems of semi-linear wave equations. Our proof uses the Klainerman-Sideris inequality and a space-time L^2-estimate. We shall also discuss whether the scale-invariant version of the space-time L^2-estimates can hold, and obtain some related estimates. Among other things, we prove that the Keel-Smith-Sogge estimate actually holds in all space dimensions

Shape evolution of electrodeposited copper bumps with high peclet numbers

We report the shape evolution of initial copper bumps at Peclet numbers higher than a hundred. The role of vortices and of penetration flow within the cavity was discussed with numerical fluid dynamics computation to obtain a bump with a single hump at the center. The current distributions, or flux profiles, were calculated at the diffusion controlled overpotential and were compared with the electrodeposited bump shapes. For the 100 mu m cavity width, the vortices increase at the upstream corners with Peclet numbers 1410 and 7311. The vortices are the local resistance of mass transfer to the cathode. These vortices cause the hollows in flux profiles at the upstream corner with these Peclet numbers. The penetration flow collides with the photoresist sidewall and the vortices decrease at downstream corners. These decreased vortices cause the increase in flux profile at downstream corners. For a 30 pm cavity width a single large vortex forms for the higher Peclet number 44,500 and a single hump in flux is achieved.</p

Morphology Control of Aromatic Polymers during Polymerization

Morphology and formation mechanism of poly (4'-oxy-4-biphenylcarbonyl) (POBP) crystals obtained by solution polymerization were firstly treated. It was concluded that the formation mechanism of the bundlelike aggregates of fibrillar crystals in POBP was fundamentally simillar to that in POB whiskers. Secondly the copolymerization effects of m-acetoxybenzoic acid and 4-(4-acetoxyphenyl) benzoic acid on the morphology of POB whiskers were studied. The experimental results strongly supported our proposal for the formation mechanism of whiskers which was consisted of crystallization of oligomers with a critical length as lamellae from solution and solid state polymerizationof oligomers between lamellae. Finally, the formation mechanism of poly (p-oxycinnamoyl) spherical products during solution polymerization was treated. The formation of these spherical products could be understood by overlapped phase diagram of melting depression curve and consolute curve of oligomers-solvent system

Structure and magnetic properties of the single-molecule magnet [Mn11CrO12(O2CCH3)(16)(H2O)(4)]center dot 2CH(3)COOH center dot 4H(2)O: magnetization manipulation and dipolar-biased tunneling in a Mn11Cr/Mn-12 mixed crystal

The structural and magnetic properties of the single-molecule magnet [Mn11CrO12(O2CCH3)(16)(H2O)(4)].2CH(3)COOH.4H(2)O (Mn11Cr) are studied through the analysis of a Mn11Cr/Mn-12 (approximate to1:1) mixed crystal, where Mn-12 is [Mn12O12(O2CCH3)(16)(H2O)(4)].2CH(3)COOH.4H(2)O. X-ray absorption spectra reveal that the Cr ion in Mn11Cr is in the +3 valence state and occupies a specific Mn3+ site in the Mn-12 skeleton. High-frequency electron paramagnetic resonance (EPR) spectra are well explained by assuming that Mn11Cr is in a ground spin-state of S=19/2 with nearly the same EPR parameter set as for Mn-12. The lower spin quantum number results in lower barrier height (56.8 K) compared to Mn-12. The magnetization curves indicate a coercive field of 0.95 T for Mn11Cr at 1.8 K, nearly half that for Mn-12. Quantum tunneling of magnetization (QTM) in Mn11Cr is observed below the blocking temperature T-B, with the same field interval as for Mn-12. The magnetization of Mn11Cr and Mn-12 in the mixed crystal can be independently manipulated by utilizing the difference between their coercive fields. The resonance fields of QTM in Mn11Cr are significantly affected by the magnetization direction of Mn-12, suggesting the effect of dipolar-biased tunneling.</p