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Geometric ergodicity for dissipative particle dynamics
No full textDissipative particle dynamics is a model of multi-phase fluid flows described by a system of stochastic differential equations. We consider the problem of N particles evolving on the one-dimensional periodic domain of length L and, if the density of particles is large, prove geometric convergence to a unique invariant measure. The proof uses minorization and drift arguments, but allows elements of the drift and diffusion matrix to have compact support, in which case hypoellipticity arguments are not directly availabl
Level of repair analysis and minimum cost homomorphisms of graphs
No full textLevel of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize overall life-cycle costs. For a LORA problem with two levels of indenture with three possible repair decisions, which is of interest in UK and US military and which we call LORA-BR, Barros (1998) and Barros and Riley (2001) developed certain branch-and-bound heuristics. The surprising result of this paper is that LORA-BR is, in fact, polynomial-time solvable. To obtain this result, we formulate the general LORA problem as an optimization homomorphism problem on bipartite graphs, and reduce a generalization of LORA-BR, LORA-M, to the maximum weight independent set problem on a bipartite graph. We prove that the general LORA problem is NP-hard by using an important result on list homomorphisms of graphs. We introduce the minimum cost graph homomorphism problem and provide partial results. Finally, we show that our result for LORA-BR can be applied to prove that an extension of the maximum weight independent set problem on bipartite graphs is polynomial time solvable
Convolution roots and embedding of probability measures on Lie groups
No full textWe show that for a large class of connected Lie groups , viz. from \emph{class} described below, given a probability measure μ on and a natural number , for any sequence of th convolution roots of μ there exists a sequence of elements of G, centralising the support of μ, and such that \{z_i \nu_i \z_i^{-1}\} is relatively compact; thus the set of roots is relatively compact ‘modulo’ the conjugation action of the centraliser of supp μ. We also analyse the dependence of the sequence \{z_i\}n$. The results yield a simpler and more transparent proof of the embedding theorem for infinitely divisible probability measures on the Lie groups as above, proved in [S.G. Dani, M. McCrudden, Embeddability of infinitely divisible distributions on linear Lie groups, Invent. Math. 110 (1992) 237–261]
Particle-size segregation and diffusive remixing in shallow granular avalanches
Get PDFSegregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the size-distribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particle-size segregation and diffusive remixing of large and small particles in shallow gravity-driven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation–remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation–remixing equation reduces to a logistic type equation and the ‘S’-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation–remixing equation to Burgers equation and using the Cole–Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent two-dimensional solutions are also constructed for plug-flow in a semi-infinite chute
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
Get PDFMany applications give rise to nonlinear eigenvalue problems
with an underlying structured matrix polynomial.
In this paper several useful classes of structured polynomial
(e.g., palindromic, even, odd) are identified
and the relationships between them explored.
A special class of linearizations
that reflect the structure of these polynomials,
and therefore preserve symmetries in their spectra,
is introduced and investigated.
We analyze the existence and uniqueness of such linearizations,
and show how they may be systematically constructed
An exact analytical solution for discrete barrier options
No full textIn the present paper we provide an analytical solution for pricing discrete
barrier options in the Black-Scholes framework.We reduce the valuation problem
to a Wiener-Hopf equation that can be solved analytically. We are able to give
explicit expressions for the Greeks of the contract. The results from our formulae
are compared with those from other numerical methods available in the literature.
Very good agreement is obtained, although evaluation using the present method is
substantially quicker than the alternative methods presented
Electrodynamics of the atmosphere (in Russian)
Get PDFThe textbook is based on a selection of problems with detailed solutions, which have been taught over a number of years as part of the Theoretical Physics module to students at the Moscow Institute of Physics and Technology. All the problems are related to various electromagnetic phenomena in the Earth's ionosphere, including the scattering of the sunlight, transmission of EM waves and interaction of the solar wind with the Earth's magnetosphere
Palindromic Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
Get PDFMany applications give rise to nonlinear eigenvalue problems
with an underlying structured matrix polynomial.
In this paper several useful classes of structured polynomial
(e.g., palindromic, even, odd) are identified
and the relationships between them explored.
A special class of linearizations
that reflect the structure of these polynomials,
and therefore preserve symmetries in their spectra,
is introduced and investigated.
We analyze the existence and uniqueness of such linearizations,
and show how they may be systematically constructed
Directions and equidistribution in homology for periodic orbits
Get PDFWe discuss the asymptotic distribution of the directions in homology of periodic orbits of Anosov flows. We obtain a limiting measure which is either a Dirac measure on a single point or is fully supported. In the latter case , we relate the result to a more general equidistribution problem