5,843 research outputs found
Problems on electrorheological fluid flows
We develop a model of an electrorheological fluid such that the fluid is
considered as an anisotropic one with the viscosity depending on the second
invariant of the rate of strain tensor, on the module of the vector of electric
field strength, and on the angle between the vectors of velocity and electric
field. We study general problems on the flow of such fluids at nonhomogeneous
mixed boundary conditions, wherein values of velocities and surface forces are
given on different parts of the boundary. We consider the cases where the
viscosity function is continuous and singular, equal to infinity, when the
second invariant of the rate of strain tensor is equal to zero. In the second
case the problem is reduced to a variational inequality. By using the methods
of a fixed point, monotonicity, and compactness, we prove existence results for
the problems under consideration. Some efficient methods for numerical solution
of the problems are examined.Comment: Presented to the journal "Discrete and Continuous Dynamical Systems,
Series
Diffeomorphism Invariant Integrable Field Theories and Hypersurface Motions in Riemannian Manifolds
We discuss hypersurface motions in Riemannian manifolds whose normal velocity
is a function of the induced hypersurface volume element and derive a second
order partial differential equation for the corresponding time function
at which the hypersurface passes the point . Equivalently, these
motions may be described in a Hamiltonian formulation as the singlet sector of
certain diffeomorphism invariant field theories. At least in some (infinite
class of) cases, which could be viewed as a large-volume limit of Euclidean
-branesmoving in an arbitrary -dimensional Riemannian manifold, the
models are integrable: In the time-function formulation the equation becomes
linear (with a harmonic function on the embedding Riemannian
manifold). We explicitly compute solutions to the large volume limit of
Euclidean membrane dynamics in \Real^3 by methods used in electrostatics and
point out an additional gradient flow structure in \Real^n. In the
Hamiltonian formulation we discover infinitely many hierarchies of integrable,
multidimensional, -component theories possessing infinitely many
diffeomorphism invariant, Poisson commuting, conserved charges.Comment: 15 pages, LATE
Mutual selection in time-varying networks
Copyright @ 2013 American Physical SocietyTime-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment
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Extensive microscale N isotopic heterogeneity in chondritic organic matter
Introduction: H and N isotopic anomalies (mainly excesses of D and 15N) in organic matter from primitive meteorites and IDPs suggest preservation of presolar molecular cloud material [1-3]. However, there have been very few spatially correlated H and N studies for either chondrites or IDPs [4, 5]. We report C and N isotopic imaging data for organic matter from four meteorites and three IDPs. D/H imaging data for many of the same samples are presented in [6, 7] and bulk organic isotope data in [8]
Network growth model with intrinsic vertex fitness
© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions
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