Surface induced dissociations of protonated ethanol monomer, dimer and trimer ions: Trimer break-down graph from the collision energy dependence of projectile fragmentation
An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. A hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented. PACS number: 02.03.Ik
IntroductionIn recent years, research in the dispersionless hierarchies has become quite active (see, for example, [1-11] and references therein). Dispersionless hierarchies arise as the quasiclassical limit of the original dispersionful hierarchies [2]. The operators in the Lax equations for dispersionful hierarchy are replaced by phase functions for dispersionless hierarchy; commutators are replaced by Poisson brackets and the role of Lax pair equations by dispersionless Lax pair equations. The dispersionless hierarchies have Hamiltonian formulation [1, 3] and many other aspects [4][5][6], and several methods of solutions of dispersionless hierarchies have been formulated [7-11].The soliton equations with self-consistent sources (SESCS) are another type of integrable models and have important physical applications [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. There are some ways to derive the SESCS, for example, the Mel'nikov way [12,18,19,21,30] and the Leon approach [13][14][15]. In recent years, SESCS were studied based on the constrained flows of soliton equations which are just the stationary equations of SESCSs [16,17]. There are several methods for solving the SESCSs, for example, the inverse scattering method [18][19][20], the matrix theory [21], thē ∂ method and gauge transformation [22,23], and the Darboux transformation [17,[24][25][26]. By treating the variable x as the evolution parameter and t as the 'spatial' variable, and by introducing Jacobi-Ostrogradiski coordinates, the SESCS has a t-type Hamiltonian formulation [27,28].
The piezoresistive mechanisms of composite thick films based on RuO 2 particles and both calcium-borosilicate and bismuth-borosilicate glass matrices were investigated by chemical and electrical microanalyses. The resistor based on bismuthborosilicate glass showed higher sensitivity than that based on calcium-borosilicate glass. It was confirmed that the diffusion of ruthenium into glass affects the binding state of RuO 2 at the interface of the glass. Furthermore, an intermediate resistive layer is detected around the RuO 2 particle. These results suggest that the piezoresistive effect is related to a change in the electrical conductivity of the interfacial reaction layer caused by the diffusion of ruthenium into glass.
Diffusion pairs of RuO2 and glass were prepared as model specimens for composite thick‐film resistors and chemical and electrical microanalyses were carried out at the interface to clarify the piezoresistive mechanism of the resistors. The diffusion of ruthenium into glass was examined with SIMS and the chemical structure was analyzed with EELS. In situ measurement of resistance change was conducted as a function of applied load with a microprobe on the RuO2–glass interfaces locally by conductive AFM. The glass with higher piezoresistive sensitivity was found to have larger amount of diffused ruthenium, which has trivalent and tetravalent states in the glass. The originally insulative glass showed electrical conductivity by the diffusion of ruthenium. Furthermore, load‐dependent conductivity change was observed near the interface. The analysis suggests that the conduction mechanism is variable range hopping and that the strain‐derived electronic state changes must be the origin of the piezoresistive effect of the thick film resistors.
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