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61.
On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls
N. I. Pogodaev 《Siberian Mathematical Journal》2007,48(5):897-912
We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints. 相似文献
62.
M. Dubé C. Daneault V. Vuorinen M. Alava M. Rost 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):15-26
We investigate the structure and dynamics of the interface between
two immiscible liquids in a three-dimensional disordered porous
medium. We apply a phase-field model that includes explicitly
disorder and discuss both spontaneous and forced imbibition.
The structure of the interface is dominated by a length scale
ξ× which arises from liquid conservation. We further show
that disorder in the capillary and permeability act on different
length scales and give rise to different scalings and
structures of the interface properties. We conclude with a
range of applications. 相似文献
63.
Scott T. Knauert Jack F. Douglas Francis W. Starr 《Journal of Polymer Science.Polymer Physics》2007,45(14):1882-1897
Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007 相似文献
64.
T. Ramanathan S. Stankovich D. A. Dikin H. Liu H. Shen S. T. Nguyen L. C. Brinson 《Journal of Polymer Science.Polymer Physics》2007,45(15):2097-2112
Mechanical, thermal, and electrical properties of graphite/PMMA composites have been evaluated as functions of particle size and dispersion of the graphitic nanofiller components via the use of three different graphitic nanofillers: “as received graphite” (ARG), “expanded graphite,” (EG) and “graphite nanoplatelets” (GNPs) EG, a graphitic materials with much lower density than ARG, was prepared from ARG flakes via an acid intercalation and thermal expansion. Subsequent sonication of EG in a liquid yielded GNPs as thin stacks of graphitic platelets with thicknesses of ~10 nm. Solution‐based processing was used to prepare PMMA composites with these three fillers. Dynamic mechanical analysis, thermal analysis, and electrical impedance measurements were carried out on the resulting composites, demonstrating that reduced particle size, high surface area, and increased surface roughness can significantly alter the graphite/polymer interface and enhance the mechanical, thermal, and electrical properties of the polymer matrix. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2097–2112, 2007 相似文献
65.
Jie-Fang Zhang 《Acta Mechanica Solida Sinica》1991,4(2):139-151
Based on D'Alembert's principle of a mechanical system relative to non-inertial frame and by introducing the concept of the generalized inertial potential, new forms of differential equations of motion of a mechanical system with holonomic and the non-holonomic constraints relative to the non-inertial frame are obtained. The merits and demerits between our method and the Newtonian dynamic method as well as the analytic dynamic method are discussed comparatively. Finally, two examples are given to illustrate the application of the motive differential equations in the new forms. 相似文献
66.
The fixed point property for multivalued nonexpansive mappings 总被引:1,自引:0,他引:1
T. Domínguez Benavides 《Journal of Mathematical Analysis and Applications》2007,328(2):1471-1483
We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties. 相似文献
67.
Yi Lin 《Advances in Mathematics》2007,208(2):699-709
In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces. 相似文献
68.
Wengu Chen Yixin Lai 《分析论及其应用》2006,22(2):195-200
Let μ be a Borel measure on Rd which may be non doubling. The only condition that μ must satisfy is μ(Q) ≤ col(Q)n for any cube Q () Rd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1 (μ). 相似文献
69.
Mitre C. Dourado Fábio Protti Jayme L. Szwarcfiter 《Discrete Applied Mathematics》2007,155(18):2435-2443
Let p?1 and q?0 be integers. A family of sets F is (p,q)-intersecting when every subfamily F′⊆F formed by p or less members has total intersection of cardinality at least q. A family of sets F is (p,q)-Helly when every (p,q)-intersecting subfamily F′⊆F has total intersection of cardinality at least q. A graph G is a (p,q)-clique-Helly graph when its family of (maximal) cliques is (p,q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p=2,q=1. In this work we present a characterization for (p,q)-clique-Helly graphs. For fixed p,q, this characterization leads to a polynomial-time recognition algorithm. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard. 相似文献
70.
利用微分方程的级数求解方法,分析了两端简支的有限长功能梯度圆筒的轴对称稳态热弹性问题,推导出了稳态温度场与应力场的解析解。分析中采用指数函数模型来描述FGM圆筒中材料性能在厚度方向的连续变化,同时忽略温度对材料性能的影响。另外,论文以金属钼和多铝红柱石制成的功能梯度圆筒为例,给出了稳态温度场和应力场的数值结果。 相似文献