439 research outputs found
Acyclic orientations with path constraints
Many well-known combinatorial optimization problems can be stated over the
set of acyclic orientations of an undirected graph. For example, acyclic
orientations with certain diameter constraints are closely related to the
optimal solutions of the vertex coloring and frequency assignment problems. In
this paper we introduce a linear programming formulation of acyclic
orientations with path constraints, and discuss its use in the solution of the
vertex coloring problem and some versions of the frequency assignment problem.
A study of the polytope associated with the formulation is presented, including
proofs of which constraints of the formulation are facet-defining and the
introduction of new classes of valid inequalities
Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph
Traffic grooming is a major issue in optical networks. It refers to grouping
low rate signals into higher speed streams, in order to reduce the equipment
cost. In SONET WDM networks, this cost is mostly given by the number of
electronic terminations, namely ADMs. We consider the case when the topology is
a unidirectional ring. In graph-theoretical terms, the traffic grooming problem
in this case consists in partitioning the edges of a request graph into
subgraphs with a maximum number of edges, while minimizing the total number of
vertices of the decomposition. We consider the case when the request graph has
bounded maximum degree , and our aim is to design a network being able
to support any request graph satisfying the degree constraints. The existing
theoretical models in the literature are much more rigid, and do not allow such
adaptability. We formalize the problem, and solve the cases (for all
values of ) and (except the case C=4). We also provide lower
and upper bounds for the general case
Equilibrium crystal shapes in the Potts model
The three-dimensional -state Potts model, forced into coexistence by
fixing the density of one state, is studied for , 3, 4, and 6. As a
function of temperature and number of states, we studied the resulting
equilibrium droplet shapes. A theoretical discussion is given of the interface
properties at large values of . We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
, but increase when measured as a fraction of the melting temperature. We
also found equilibrium shapes closely approaching a sphere near the melting
point, even though the three-dimensional Potts model with three or more states
does not have a phase transition with a diverging length scale at the melting
point.Comment: 6 pages, 3 figures, submitted to PR
Intercomparison of Permittivity Measurement Techniques for Ferroelectric Thin Layers
International audienceThe dielectric properties of a KTa0.65Nb0.35O3 (KTN) ferroelectric composition for a submicronic thin layer were measured in the microwave domain using different electromagnetic characterization methods. Complementary experimental techniques (broadband methods versus resonant techniques, waveguide versus transmission line) and complementary data processing procedures (quasi-static theoretical approaches versus full-wave analysis) were selected to investigate the best way to characterize ferroelectric thin films. The measured data obtained from the cylindrical resonant cavity method, the experimental method that showed the least sources of uncertainty, were taken as reference values for comparisons with results obtained using broadband techniques. The error analysis on the methods used is discussed with regard to the respective domains of validity for each method; this enabled us to identify the best experimental approach for obtaining an accurate determination of the microwave dielectric properties of ferroelectric thin layers
Giant quantum oscillations in thermal transport in low-density metals via electron absorption of phonons
Oscillations of conductance observed in strong magnetic fields are a striking
manifestation of the quantum dynamics of charge carriers in solids. The large
charge carrier density in typical metals sets the scale of oscillations in both
electrical and thermal conductivity, which characterize the Fermi surface. In
semimetals, thermal transport at low-charge carrier density is expected to be
phonon dominated, yet several experiments observe giant quantum oscillations in
thermal transport. This raises the question of whether there is an overarching
mechanism leading to sizable oscillations that survives in phonon-dominated
semimetals. In this work, we show that such a mechanism exists. It relies on
the peculiar phase-space allowed for phonon scattering by electrons when only a
few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe5
support this counter-intuitive mechanism through observation of pronounced
thermal quantum oscillations, since they occur in similar magnitude and phase
in directions parallel and transverse to the magnetic field. Our phase-space
argument applies to all low-density semimetals, topological or not, including
graphene and bismuth. Our work illustrates that phonon absorption can be
leveraged to reveal degrees of freedom through their imprint on longitudinal
thermal transport
Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances
A history is given of the applications of the simple expression generalized
from the surmise by Wigner and also by Ibach to extract the strength of the
interaction between steps on a vicinal surface, via the terrace width
distribution (TWD). A concise guide for use with experiments and a summary of
some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed
paper for special issue of Applied Physics A entitled "From Surface Science
to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof.
H. L\"ut
- âŠ