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61.
We use the methods of statistical mechanics to describe the interaction of N compressible gas bubbles in an incompressible, inviscid and irrotational liquid. The governing equations for bubble positions, radii and corresponding momenta form a Hamiltonian system depending on the virtual mass matrix. An explicit expression of the virtual mass matrix is presented, which is calculated with accuracy (b/d)3, where b and d are respectively the mean bubble radius and the mean inter-bubble distance. We study two limit cases: the limit of moving rigid spheres and the limit of immobile oscillating bubbles. In each case, we construct a canonical ensemble partition function. In the limit of rigid spheres, we improve results by Yurkovetsky and Brady (phys Fluids 8(4): 881–895, 1996). In particular, we derive an analytic expression for the “attractive” potential which may be responsible for the clustering effect, and show why the accuracy (b/d)3 is not sufficient to characterize the “repulsive potential” . In the limit of immobile oscillating bubbles, we prove the existence of a long range repulsive potential. 相似文献
62.
We study the amply regular diameter d graphs Γ such that for some vertex a the set of vertices at distance d from a is the set of points of a 2-design whose set of blocks consists of the intersections of the neighborhoods of points with the set of vertices at distance d-1 from a. We prove that the subgraph induced by the set of points is a clique, a coclique, or a strongly regular diameter 2 graph. For diameter 3 graphs we establish that this construction is a 2-design for each vertex a if and only if the graph is distance-regular and for each vertex a the subgraph Γ3(a) is a clique, a coclique, or a strongly regular graph. We obtain the list of admissible parameters for designs and diameter 3 graphs under the assumption that the subgraph induced by the set of points is a Seidel graph. We show that some of the parameters found cannot correspond to distance-regular graphs. 相似文献
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Ivan P. Gavrilyuk Wolfgang Hackbusch Boris N. Khoromskij. 《Mathematics of Computation》2004,73(247):1297-1324
In previous papers the arithmetic of hierarchical matrices has been described, which allows us to compute the inverse, for instance, of finite element stiffness matrices discretising an elliptic operator The required computing time is up to logarithmic factors linear in the dimension of the matrix. In particular, this technique can be used for the computation of the discrete analogue of a resolvent
In the present paper, we consider various operator functions, the operator exponential negative fractional powers , the cosine operator function and, finally, the solution operator of the Lyapunov equation. Using the Dunford-Cauchy representation, we get integrals which can be discretised by a quadrature formula which involves the resolvents mentioned above. We give error estimates which are partly exponentially, partly polynomially decreasing.
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Linear and nonlinear fluid sloshing problems in a circular conical tank are studied in a curvilinear coordinate system. The linear sloshing modes are approximated by a series of the solid spheric harmonics. These modes are used to derive a new nonlinear modal theory based on the Moiseyev asymptotics. The theory makes it possible to both classify steady-state waves occurring due to horizontal resonant excitation and visualise nonlinear wave patterns. Secondary (internal) resonances and shallow fluid sloshing (predicted for the semi-apex angles >60) are extensively discussed. 相似文献
69.
A. E. Ershov A. P. Gavrilyuk S. V. Karpov P. N. Semina 《Applied physics. B, Lasers and optics》2014,115(4):547-560
We propose an optodynamical model of interaction of pulsed laser radiation with aggregates of spherical metallic nanoparticles embedded into host media. The model takes into account polydispersity of particles, pair interactions between the particles, dissipation of absorbed energy, heating and melting of the metallic core of particles and of their polymer adsorption layers, and heat exchange between electron and ion components of the particle material as well as heat exchange with the interparticle medium. Temperature dependence of the electron relaxation constant of the particle material and the effect of this dependence on interaction of nanoparticles with laser radiation are first taken into consideration. We study in detail light-induced processes in the simplest resonant domains of multiparticle aggregates consisting of two particles of an arbitrary size in aqueous medium. Optical interparticle forces are realized due to the light-induced dipole interaction. The dipole moment of each particle is calculated by the coupled dipole method (with correction for the effect of higher multipoles). We determined the role of various interrelated factors leading to photomodification of resonant domains and found an essential difference in the photomodification mechanisms between polydisperse and monodisperse nanostructures. 相似文献
70.
A. A. Gavrilyuk 《Mathematical Notes》2014,95(5-6):625-633
Given any parallelohedron P, its affine class A (P), i.e., the set of all parallelohedra affinely equivalent to it, is considered. Does this affine class contain at least one Voronoi parallelohedron, i.e., a parallelohedron which is a Dirichlet domain for some lattice? This question, more commonly known as Voronoi’s conjecture, has remained unanswered for more than a hundred years. It is shown that, in the case where the subset of Voronoi parallelohedra in A (P) is nonempty, this subset is an orbifold, and its dimension (as a real manifold with singularities) is completely determined by its combinatorial type; namely, it is equal to the number of connected components of the so-called Venkov subgraph of the given parallelohedron. Nevertheless, the structure of this orbifold depends not only on the combinatorial properties of the parallelohedron but also on its affine properties. 相似文献