5,097 research outputs found
Discrete Approximations of a Controlled Sweeping Process
The paper is devoted to the study of a new class of optimal control problems
governed by the classical Moreau sweeping process with the new feature that the polyhe-
dral moving set is not fixed while controlled by time-dependent functions. The dynamics of
such problems is described by dissipative non-Lipschitzian differential inclusions with state
constraints of equality and inequality types. It makes challenging and difficult their anal-
ysis and optimization. In this paper we establish some existence results for the sweeping
process under consideration and develop the method of discrete approximations that allows
us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type
sweeping process by their discrete counterparts
Origin of the structural phase transition in Li7La3Zr2O12
Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a
low-conductivity tetragonal and a high-conductivity cubic phase. Using
density-functional theory and variable cell shape molecular dynamics
simulations, we show that the tetragonal phase stability is dependent on a
simultaneous ordering of the Li ions on the Li sublattice and a
volume-preserving tetragonal distortion that relieves internal structural
strain. Supervalent doping introduces vacancies into the Li sublattice,
increasing the overall entropy and reducing the free energy gain from ordering,
eventually stabilizing the cubic phase. We show that the critical temperature
for cubic phase stability is lowered as Li vacancy concentration (dopant level)
is raised and that an activated hop of Li ions from one crystallographic site
to another always accompanies the transition. By identifying the relevant
mechanism and critical concentrations for achieving the high conductivity
phase, this work shows how targeted synthesis could be used to improve
electrolytic performance
Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential
Using the nonrelativistic effective field theory vNRQCD, we determine the
contribution to the next-to-leading logarithmic (NLL) running of the effective
quark-antiquark potential at order v (1/mk) from diagrams with one potential
and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame.
The results are numerically important and complete the description of ultrasoft
next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair
production and annihilation close to threshold.Comment: 25 pages, 7 figures, 3 tables; minor modifications, typos corrected,
references added, footnote adde
Charm mass corrections to the bottomonium mass spectrum
The one-loop corrections to the bottomonium mass spectrum due to the finite
charm mass are evaluated in the framework of the relativistic quark model. The
obtained corrections are compared with the results of perturbative QCD.Comment: 6 pages, references added, version to be published in Phys. Rev.
Quarkonium spectroscopy and perturbative QCD: massive quark-loop effects
We study the spectra of the bottomonium and B_c states within perturbative
QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between
the static potential and the pole mass is performed in the epsilon-expansion
scheme. We extend our previous analysis by including the (dominant) effects of
non-zero charm-quark mass in loops up to the next-to-leading non-vanishing
order epsilon^3. We fix the b-quark MSbar mass on Upsilon(1S) and compute the higher levels. The
effect of the charm mass decreases by about 11 MeV and increases
the n=2 and n=3 levels by about 70--100 MeV and 240--280 MeV, respectively. We
provide an extensive quantitative analysis. The size of non-perturbative and
higher order contributions is discussed by comparing the obtained predictions
with the experimental data. An agreement of the perturbative predictions and
the experimental data depends crucially on the precise value (inside the
present error) of alpha_s(M_Z). We obtain .Comment: 33 pages, 21 figures; v2: Abstract modified; Table7 (summary of
errors) added; Version to appear in Phys.Rev.
Improved Perturbative QCD Approach to the Bottomonium Spectrum
Recently it has been shown that the gross structure of the bottomonium
spectrum is reproduced reasonably well within the non-relativistic boundstate
theory based on perturbative QCD. In that calculation, however, the fine
splittings and the S-P level splittings are predicted to be considerably
narrower than the corresponding experimental values. We investigate the
bottomonium spectrum within a specific framework based on perturbative QCD,
which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4
m_b), respectively, in the computations of the fine splittings and the S-P
splittings. We find that the agreement with the experimental data for the fine
splittings improves drastically due to an enhancement of the wave functions
close to the origin as compared to the Coulomb wave functions. The agreement of
the S-P splittings with the experimental data also becomes better. We find that
natural scales of the fine splittings and the S-P splittings are larger than
those of the boundstates themselves. On the other hand, the predictions of the
level spacings between consecutive principal quantum numbers depend rather
strongly on the scale mu of the operator \propto C_A/(m_b r^2). The agreement
of the whole spectrum with the experimental data is much better than the
previous predictions when mu \simeq 3-4 GeV for alpha_S(M_Z)=0.1181. There
seems to be a phenomenological preference for some suppression mechanism for
the above operator.Comment: 26 pages, 16 figures. Minor changes, to be published in PR
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