2,514 research outputs found
Hierarchy of boundary driven phase transitions in multi-species particle systems
Interacting systems with driven particle species on a open chain or
chains which are coupled at the ends to boundary reservoirs with fixed particle
densities are considered. We classify discontinuous and continuous phase
transitions which are driven by adiabatic change of boundary conditions. We
build minimal paths along which any given boundary driven phase transition
(BDPT) is observed and reveal kinetic mechanisms governing these transitions.
Combining minimal paths, we can drive the system from a stationary state with
all positive characteristic speeds to a state with all negative characteristic
speeds, by means of adiabatic changes of the boundary conditions. We show that
along such composite paths one generically encounters discontinuous and
continuous BDPTs with taking values depending on
the path. As model examples we consider solvable exclusion processes with
product measure states and particle species and a non-solvable
two-way traffic model. Our findings are confirmed by numerical integration of
hydrodynamic limit equations and by Monte Carlo simulations. Results extend
straightforwardly to a wide class of driven diffusive systems with several
conserved particle species.Comment: 12 pages, 11 figure
Discriminants, symmetrized graph monomials, and sums of squares
Motivated by the necessities of the invariant theory of binary forms J. J.
Sylvester constructed in 1878 for each graph with possible multiple edges but
without loops its symmetrized graph monomial which is a polynomial in the
vertex labels of the original graph. In the 20-th century this construction was
studied by several authors. We pose the question for which graphs this
polynomial is a non-negative resp. a sum of squares. This problem is motivated
by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the
derivative of a univariate polynomial, and an interesting example of P. and A.
Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative
but not a sum of squares. We present detailed information about symmetrized
graph monomials for graphs with four and six edges, obtained by computer
calculations
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems
We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with integrable derivatives
on by an -parametric analytic family better than order
of .
Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of .Comment: 40 page
A Note on Fuzzy Set--Valued Brownian Motion
In this paper, we prove that a fuzzy set--valued Brownian motion , as
defined in [1], can be handle by an --valued Wiener process , in the
sense that B_t =\indicator{b_t}; i.e. it is actually the indicator function
of a Wiener process
Odd Parity and Line Nodes in Non-Symmorphic Superconductors
Group theory arguments have been invoked to argue that odd parity order
parameters cannot have line nodes in the presence of spin-orbit coupling. In
this paper we show that these arguments do not hold for certain non-symmorphic
superconductors. Specifically, we demonstrate that when the underlying crystal
has a twofold screw axis, half of the odd parity representations vanish on the
Brillouin zone face perpendicular to this axis. Many unconventional
superconductors have non-symmorphic space groups, and we discuss implications
for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.Comment: 4 page
``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields
We present some consequences of non-anomalous propagation requirements on
various massless fields. Among the models of nonlinear electrodynamics we show
that only Maxwell and Born-Infeld also obey duality invariance. Separately we
show that, for actions depending only on the F_\mn^2 invariant, the permitted
models have . We also characterize acceptable
vector-scalar systems. Finally we find that wide classes of gravity models
share with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure
Threat of taxation, stagnation and social unrest: Evidence from 19th century sicily
Taxation may trigger social unrest, as highlighted by historical examples. At the same time, tax income could boost state capacity which may, in turn, foster political stability. Under-standing the a priori ambiguous taxation-turmoil nexus is particularly relevant for low-income countries today - yet causal evidence on the topic is very scarce. Using a regres-sion discontinuity design, we exploit a unique policy experiment in 19th century Sicily to identify the effect of taxation on social unrest. It turns out that it is mostly the threat of taxation that may distort economic investment and ultimately result in greater political turmoil. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/
The Gigabit Optical Transmitters for the LHCb Calorimeters
This report presents the boards developed for the optical data transmission of the calorimeter system of the LHCb experiment and test results. We developed two types of transmission boards: the single-channel and the multi-channel ones. Multi-channel boards can be equipped with a variable number of transmitters, depending on the need, with a maximum allowed of 12 channels. Each optical channel allows transmitting 32 bit data at 40.08 MHz. The boards have been designed and built using radiation hard devices produced at CERN. The optical links have been qualified using the eye diagram and the BERT at 1.6Gbps
Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires
We report on a theoretical study of the electronic structures of InSb and
GaSb nanowires oriented along the [001] and [111] crystallographic directions.
The nanowires are described by atomistic, spin-orbit inteaction included,
tight-binding models, and the band structures and the wave functions of the
nanowires are calculated by means of a Lanczos iteration algorithm. For the
[001]-oriented InSb and GaSb nanowires, the systems with both square and
rectangular cross sections are considered. Here, it is found that all the
energy bands are double degenerate. Furthermore, although the lowest conduction
bands in these nanowires show good parabolic dispersions, the top valence bands
show rich and complex structures. In particular, the topmost valence bands of
these nanowires with a square cross section show a double maximum structure. In
the nanowires with a rectangular cross section, this double maximum structure
is suppressed and top valence bands gradually develop into parabolic bands as
the aspect ratio of the cross section is increased. For the [111]-oriented InSb
and GaSb nanowires, the systems with hexagonal cross sections are considered.
It is found that all the bands at the \Gamma-point are again double degenerate.
However, some of them will split into non-degenerate bands when the wave vector
moves away from the \Gamma-point. Furthermore, although the lowest conduction
bands again show good parabolic dispersions, the topmost valence bands do not
show the double maximum structure but, instead, a single maximum structure with
its maximum at a wave vector slightly away from the \Gamma-point. We also
investigate the effects of quantum confinement on the band structures of the
[001]- and [111]-oriented InSb and GaSb nanowires and present an empirical
formula for the description of quantization energies of the band edge states in
the nanowires.Comment: 17 pages, 19 figure
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