991 research outputs found
The mathematics of functional differentiation under conservation constraint
The mathematics of K-conserving functional differentiation, with K being the
integral of some invertible function of the functional variable, is clarified.
The most general form for constrained functional derivatives is derived from
the requirement that two functionals that are equal over a restricted domain
have equal derivatives over that domain. It is shown that the K-conserving
derivative formula is the one that yields no effect of K-conservation on the
differentiation of K-independent functionals, which gives the basis for its
generalization for multiple constraints. Connections with the derivative with
respect to the shape of the functional variable and with the shape-conserving
derivative, together with their use in the density-functional theory of
many-electron systems, are discussed. Yielding an intuitive interpretation of
K-conserving functional derivatives, it is also shown that K-conserving
derivatives emerge as directional derivatives along K-conserving paths, which
is achieved via a generalization of the Gateaux derivative for that kind of
paths. These results constitute the background for the practical application of
K-conserving differentiation.Comment: final version, published in J Math Chem; with an Appendix with the
proof of (17) added, and some errata to [1] inserte
Properties of nanostructured diamond-silicon carbide composites sintered by high pressure infiltration technique
A high-pressure silicon infiltration technique was applied to sinter diamond–SiC composites with different diamond crystal sizes. Composite samples were sintered at pressure 8 GPa and temperature 2170 K. The structure of composites was studied by evaluating x-ray diffraction peak profiles using Fourier coefficients of ab initio theoretical size and strain profiles. The composite samples have pronounced nanocrystalline structure: the volume-weighted mean crystallite size is 41–106 nm for the diamond phase and 17–37 nm for the SiC phase. The decrease of diamond crystal size leads to increased dislocation density in the diamond phase, lowers average crystallite sizes in both phases, decreases composite hardness, and improves fracture toughness
Universality in active chaos
Many examples of chemical and biological processes take place in large-scale
environmental flows. Such flows generate filamental patterns which are often
fractal due to the presence of chaos in the underlying advection dynamics. In
such processes, hydrodynamical stirring strongly couples into the reactivity of
the advected species and might thus make the traditional treatment of the
problem through partial differential equations difficult. Here we present a
simple approach for the activity in in-homogeneously stirred flows. We show
that the fractal patterns serving as skeletons and catalysts lead to a rate
equation with a universal form that is independent of the flow, of the particle
properties, and of the details of the active process. One aspect of the
universality of our appraoch is that it also applies to reactions among
particles of finite size (so-called inertial particles).Comment: 10 page
Additive decomposability of functions over abelian groups
Abelian groups are classified by the existence of certain additive
decompositions of group-valued functions of several variables with arity gap 2.Comment: 17 page
Approximating Nearest Neighbor Distances
Several researchers proposed using non-Euclidean metrics on point sets in
Euclidean space for clustering noisy data. Almost always, a distance function
is desired that recognizes the closeness of the points in the same cluster,
even if the Euclidean cluster diameter is large. Therefore, it is preferred to
assign smaller costs to the paths that stay close to the input points.
In this paper, we consider the most natural metric with this property, which
we call the nearest neighbor metric. Given a point set P and a path ,
our metric charges each point of with its distance to P. The total
charge along determines its nearest neighbor length, which is formally
defined as the integral of the distance to the input points along the curve. We
describe a -approximation algorithm and a
-approximation algorithm to compute the nearest neighbor
metric. Both approximation algorithms work in near-linear time. The former uses
shortest paths on a sparse graph using only the input points. The latter uses a
sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam
Frictional coupling between sliding and spinning motion
We show that the friction force and torque, acting at a dry contact of two
objects moving and rotating relative to each other, are inherently coupled. As
a simple test system, a sliding and spinning disk on a horizontal flat surface
is considered. We calculate, and also measure, how the disk is slowing down,
and find that it always stops its sliding and spinning motion at the same
moment. We discuss the impact of this coupling between friction force and
torque on the physics of granular materials.Comment: 4 pages, 5 figures; submitte
Reverse engineering of linking preferences from network restructuring
We provide a method to deduce the preferences governing the restructuring
dynamics of a network from the observed rewiring of the edges. Our approach is
applicable for systems in which the preferences can be formulated in terms of a
single-vertex energy function with f(k) being the contribution of a node of
degree k to the total energy, and the dynamics obeys the detailed balance. The
method is first tested by Monte-Carlo simulations of restructuring graphs with
known energies, then it is used to study variations of real network systems
ranging from the co-authorship network of scientific publications to the asset
graphs of the New York Stock Exchange. The empirical energies obtained from the
restructuring can be described by a universal function f(k) -k ln(k), which is
consistent with and justifies the validity of the preferential attachment rule
proposed for growing networks.Comment: 7 pages, 6 figures, submitted to PR
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