Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a $Q$-Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution.     

Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves

This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp–Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander. Supported in part by the JSPS Grant (B)(1)14340029     

Resonance states in 12C and α-particle condensation

The states with J^π = 0⁺, 2⁺, and 4⁺ of ¹²C with excitation energies less than about 15 MeV are investigated with the alpha condensate wave function with spatial deformation and by using the method of ACCC (analytic continuation in the coupling constant) which is necessary for a proper treatment of resonance states. The calculated energy and width of the recently observed 2₂⁺ state are found to be well reproduced. The obtained 2₂⁺ wave function has a large overlap with a single condensate wave function of 3α gas-like structure. The density distribution is shown to be almost the same as that of the 0₂⁺ state that is regarded as a 3α Bose-condensed state, if the energy of the 2₂⁺ state is scaled down to the same value as the one of the 0₂⁺ state. Furthermore, the kinetic energy, nuclear interaction energy, and Coulomb interaction energy of the calculated 2₂⁺ state are shown to be very similar to those of the 0₂⁺ state. We conclude that the 2₂⁺ state has a structure similar to the 0₂⁺ state of Bose-condensate character with a dilute 3α gas-like structure. In addition, the resonance states, 0₃⁺, 0₄⁺, 4₂⁺, are also discussed.     

Inelastic form factors to alpha-particle condensate states in 12C and 16O: What can we learn?

In order to discuss the spatial extention of the 0₂ ⁺-state of ¹²C (Hoyle state), we analyze the inelastic form factor of electron scattering to the Hoyle state, which our 3α-condensate wave function reproduces very well like previous 3α RGM/GCM models. The analysis is made by varying the size of the Hoyle state artificially. As a result, we find that only the maximum value of the form factor sensitively depends on its size, while the positions of maximum and minimum are almost unchanged. This size dependence is found to come from a characteristic feature of the transition density from the ground state to the Hoyle state. We further show the theoretical predictions of the inelastic form factor to the 2₂ ⁺-state of ¹²C, which was recently observed above the Hoyle state, and of the inelastic form factor to the calculated 0₃ ⁺-state of ¹⁶O, which was conjectured to correspond to the 4α condensed state in previous theoretical work by the present authors.     

Motion by Mean Curvature from the Ginzburg-Landau Interface Model

We consider the scalar field φ _t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ _t -field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the -field. Received: 1 February 1996 / Accepted: 2 July 1996     

Tetrataenite in metallic grains of the Antarctic L6 chondrite ALHA 76009

Mössbauer X-ray diffraction and electron microscopy studies revealed that segregation and ordering occurred in the metal particles of the Antarctic L6 chondrite ALHA 76009. The ordered crystal structure of AuCu type (tetrataenite) was detected coexisting with the disordered 50-50 taenite.     

Circular Dichroism Study of the Inclusion-Dissociation Behavior of Complexes between a Molecular Nanotube and Azobenzene Substituted Linear Polymers

We have investigated the inclusion properties of molecular nanotubes composed ofcrosslinked -cyclodextrin. Induced circular dichroism was used to probe theformation and dissociation of complexes between the nanotubes and azobenzenemodified linear polymers. The polymer was poly(ethylene glycol) (PEG), either withor without a hydrophobic alkyl chain.It was found that the inclusion complex betweenthe nanotubes and polymers formed at room temperature, and that the polymers dissociated from the nanotubes with increasing temperature. Further, the polymer with hydrophobic alkyl chain was bound inside the nanotube more strongly and dissociated more abruptly with increasing temperature than its hydrophilic counterpart as expected theoretically.     

Laser ablation-induced gas and flyer ejection from composite films applied to regulation of a liquid micro-stream

We have developed laser-ignitable gas generating films to control a liquid stream for use in micro processing that can be ignited with both continous wave (CW) and pulsed lasers. Films of 100 m thick polyethylene terephthalate (PET) were coated with mixtures of nitrocellulose, trimethylolethanetrinitrate, and carbon black. A light beam from a Nd:YAG laser diode, or an Ar⁺ laser was focused onto the nitrocellulose layer through the PET substrate to ignite the layer. In the case of CW irradiation the delay time between the onset of irradiation and the ignition of the films was established by measuring the transmission of the laser light passing through the films. Gas generation dynamics were studied as a function of film thickness and irradiation conditions. In the case of pulsed laser irradiation, the dynamics were followed by imaging using a conventional double pulse pump-probe technique, with which it was possible to observe material ejection and the transient disturbance of a micro liquid stream in the path of emitted debris.PACS 79.20.Ds; 41.75.Jv; 61.80.Ba     

Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels

The propagation of curved detonation waves of gaseous explosives stabilized in rectangular-cross-section curved channels is investigated. Three types of stoichiometric test gases, C₂H₄ + 3O₂, 2H₂ + O₂, and 2C₂H₂ + 5O₂ + 7Ar, are evaluated. The ratio of the inner radius of the curved channel (r_i) to the normal detonation cell width (λ) is an important factor in stabilizing curved detonation waves. The lower boundary of stabilization is around r_i/λ = 23, regardless of the test gas. The stabilized curved detonation waves eventually attain a specific curved shape as they propagate through the curved channels. The specific curved shapes of stabilized curved detonation waves are approximately formulated, and the normal detonation velocity (D_n)?curvature (κ) relations are evaluated. The D_n nondimensionalized by the Chapman–Jouguet (CJ) detonation velocity (D_CJ) is a function of the κ nondimensionalized by λ. The D_n/D_CJ?λκ relation does not depend on the type of test gas. The propagation behavior of the stabilized curved detonation waves is controlled by the D_n/D_CJ?λκ relation. Due to this propagation characteristic, the fully-developed, stabilized curved detonation waves propagate through the curved channels while maintaining a specific curved shape with a constant angular velocity. Self-similarity is seen in the front shock shapes of the stabilized curved detonation waves with the same r_i/λ, regardless of the curved channel and test gas.