1,512 research outputs found
Macroscopic network circulation for planar graphs
The analysis of networks, aimed at suitably defined functionality, often
focuses on partitions into subnetworks that capture desired features. Chief
among the relevant concepts is a 2-partition, that underlies the classical
Cheeger inequality, and highlights a constriction (bottleneck) that limits
accessibility between the respective parts of the network. In a similar spirit,
the purpose of the present work is to introduce a new concept of maximal global
circulation and to explore 3-partitions that expose this type of macroscopic
feature of networks. Herein, graph circulation is motivated by transportation
networks and probabilistic flows (Markov chains) on graphs. Our goal is to
quantify the large-scale imbalance of network flows and delineate key parts
that mediate such global features. While we introduce and propose these notions
in a general setting, in this paper, we only work out the case of planar
graphs. We explain that a scalar potential can be identified to encapsulate the
concept of circulation, quite similarly as in the case of the curl of planar
vector fields. Beyond planar graphs, in the general case, the problem to
determine global circulation remains at present a combinatorial problem
Thermodynamic Bond Graphs and the Problem of Thermal Inertance
It is shown that an isolated thermal inertance does not obey the second law of thermodynamics. Consequently, such an element should not be used in physical systems theory. To eliminate the structural gap in the thermal domain of current physical systems theory, a new framework is introduced using Bond Graph concepts. These Thermodynamic Bond Graphs are the result of synthesis of methods used in thermodynamics and in mechanics
The Conformal Window from the Worldline Formalism
We use the worldline formalism to derive a universal relation for the lower
boundary of the conformal window in non-supersymmetric QCD-like theories. The
derivation relies on the convergence of the expansion of the fermionic
determinant in terms of Wilson loops. The expansion shares a similarity with
the lattice strong coupling expansion and the genus expansion in string theory.
Our result relates the lower boundary of the conformal window in theories with
different representations and different gauge groups. Finally, we use SQCD to
estimate the boundary of the conformal window in QCD-like theories and compare
it with other approaches.Comment: 14 pages. 4 eps figures. v2: refs. added. To appear in Nuclear
Physics
Guarded Second-Order Logic, Spanning Trees, and Network Flows
According to a theorem of Courcelle monadic second-order logic and guarded
second-order logic (where one can also quantify over sets of edges) have the
same expressive power over the class of all countable -sparse hypergraphs.
In the first part of the present paper we extend this result to hypergraphs of
arbitrary cardinality. In the second part, we present a generalisation dealing
with methods to encode sets of vertices by single vertices
Negative magnetic eddy diffusivities from test-field method and multiscale stability theory
The generation of large-scale magnetic field in the kinematic regime in the
absence of an alpha-effect is investigated by following two different
approaches, namely the test-field method and multiscale stability theory
relying on the homogenisation technique. We show analytically that the former,
applied for the evaluation of magnetic eddy diffusivities, yields results that
fully agree with the latter. Our computations of the magnetic eddy diffusivity
tensor for the specific instances of the parity-invariant flow-IV of G.O.
Roberts and the modified Taylor-Green flow in a suitable range of parameter
values confirm the findings of previous studies, and also explain some of their
apparent contradictions. The two flows have large symmetry groups; this is used
to considerably simplify the eddy diffusivity tensor. Finally, a new analytic
result is presented: upon expressing the eddy diffusivity tensor in terms of
solutions to auxiliary problems for the adjoint operator, we derive relations
between magnetic eddy diffusivity tensors that arise for opposite small-scale
flows v(x) and -v(x).Comment: 29 pp., 19 figures, 42 reference
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