POSITIVE SOLUTIONS FOR NONHOMOGENEOUS ELLIPTIC EQUATIONSWITH CRITICAL GROWTH ON R~(2)

1IntroductionIntillspaper,weare(follccrlledwitlltileexistellccofPositly(tsollltiollsoftilefollowillgnonhonlogelleousellipticProblclll:whereg(x)EL'(R'),g(:v)Z0alldg(x)t0,f(x,t)=h(x,t).hi=withb>0,h(x,t)EC(R=xR,R)alldtilefollowing(CI)-(C3)11old:(CI)sliphillM0.linljfl- x,h(T,t)(t--if-=011llif'orllllyforxeR2.hill}t:l-:,t)(axle(~ltJ')= lx,11lliforllllyl'Ora:6RZ.ltl~la(C3)ThereexistM>0,aE(0,1]sucllthatFOllowing[1,5],wesaythatf(x,t)=h(x,f…     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

CALCULUS OF VARIATIONS WITH DIRICHLET BOUNDARY VALUE PROBLEM FOR PERTURBED SECOND-ORDER DIFFERENTIAL EQUATIONS ON A HALF-LINE

Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

Fabrication of patterned gold electrodes with spin-coated-and-fired Au(1 1 1) film by the soft lithography

We prepared high quality Au(1 1 1) film on Si wafer through the spin coating and thermal decomposition of a gold ink, spin-coated-and-fired (SCAF) Au film. The X-ray measurements, XRD and pole-figure analysis, showed that the SCAF Au film has a (1 1 1) out-of-plane orientation with a random in-plane orientation. In order to confirm the chemical activity of the SCAF Au film, we demonstrate the formation of patterned structures with the film by using soft lithography technique. The chemical activities of this physically stable SCAF Au film to the alkanethiols were at least equivalent those of physically deposited the Au films. The possibility of the mass production of micro patterned structure with the SCAF Au film was also demonstrated over the wide region on Si wafer by the microcontact lithography. These suggest that the Au film will help the easy fabrication of various nanosized devices on Si wafer and other substrates.     

Novel methods and universal software for HRXRD, XRR and GISAXS data interpretation

Several novel methods for evaluation and interpretation of X-ray data from modern nanostructures are presented along with their applications. The background of methods and their relations to fundamental problems of X-ray analysis is shortly described. The key features of LEPTOS software, which is designed for the analysis of X-ray data measured with various geometries and setups and implements all discussed techniques, are discussed.     

Contact angle hysteresis of liquid drops as means to measure adhesive energy of zein on solid substrates

Adhesion of zein to solid substrates has been studied using surface energy profiles as indices and by adhesion mapping using atomic force microscopy (AFM). Different plasticizers like glycerol and sorbitol have been used to form mixed films with zein and properties of these films are studied using surface energy profiles. Comparison of the results from the different mixed samples with those from the pure zein films showed that force mapping could identify areas rich in protein. The adhesion maps produced were deconvoluted from sample topography and contrasted with the data obtained from contact angle measurements. A comparison of the two methods shows that the extent of contact angle hysteresis is indicative of both hydrophobicity of the surface as well as the force of adhesion. Mechanical properties and microstructure of zein films prepared by casting from solutions and using Langmuir-Blodgett film technique have been investigated. Pure zein seemed brittle and exhibited an essentially linear relationship between stress and strain. Films with plasticizer were tougher than these films. In general, mixed films showed better mechanical properties than pure films and had higher ultimate tensile strength and increased per cent elongation. Further, the mixed films of zein showed a higher force of adhesion compared to the pure films.     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.