357,368 research outputs found
Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media
Solitary waves bifurcated from edges of Bloch bands in two-dimensional
periodic media are determined both analytically and numerically in the context
of a two-dimensional nonlinear Schr\"odinger equation with a periodic
potential. Using multi-scale perturbation methods, envelope equations of
solitary waves near Bloch bands are analytically derived. These envelope
equations reveal that solitary waves can bifurcate from edges of Bloch bands
under either focusing or defocusing nonlinearity, depending on the signs of
second-order dispersion coefficients at the edge points. Interestingly, at edge
points with two linearly independent Bloch modes, the envelope equations lead
to a host of solitary wave structures including reduced-symmetry solitons,
dipole-array solitons, vortex-cell solitons, and so on -- many of which have
never been reported before. It is also shown analytically that the centers of
envelope solutions can only be positioned at four possible locations at or
between potential peaks. Numerically, families of these solitary waves are
directly computed both near and far away from band edges. Near the band edges,
the numerical solutions spread over many lattice sites, and they fully agree
with the analytical solutions obtained from envelope equations. Far away from
the band edges, solitary waves are strongly localized with intensity and phase
profiles characteristic of individual families.Comment: 23 pages, 15 figures. To appear in Phys. Rev.
Do we know how to count powers in pionless and pionful effective field theory?
In this article I summarize recent progress in the effective field theory
approach to low energy nuclear systems, with a focus on the power counting
issue. In the pionless sector, where the power counting is quite well
understood at the nucleon-nucleon (NN) level, I discuss some recent
developments toward few- and many-body calculations. In the pionful sector, I
focus on the actively debated issue of power counting in the NN sector and some
recent developments toward a model-independent NN interaction. Finally, the
scenario that the power counting might depend on the number of particles is
discussed.Comment: 19 pages, 1 figure. Contributions to the EPJA topical issue: The
tower of effective (field) theories and the emergence of nuclear phenomena.
Published versio
On the bound of first excursion probability
Method has been developed to improve the lower bound of the first excursion probability that can apply to the problem with either constant or time-dependent barriers. The method requires knowledge of the joint density function of the random process at two arbitrary instants
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Reaction Mechanisms for Long-Life Rechargeable Zn/MnO 2 Batteries
Rechargeable aqueous Zn-ion batteries (ZIBs) are very promising for large-scale grid energy storage applications owing to their low cost, environmentally benign constituents, excellent safety, and relatively high energy density. Their usage, however, is largely hampered by the fast capacity fade. The complexity of the reactions has resulted in long-standing ambiguities of the chemical pathways of Zn/MnO 2 system. In this study, we find that both H + /Zn 2+ intercalation and conversion reactions occur at different voltages and that the rapid capacity fading can clearly be ascribed to the rate-limiting and irreversible conversion reactions at a lower voltage. By limiting the irreversible conversion reactions at â1.26 V, we successfully demonstrate ultrahigh power and long life that are superior to most of the reported ZIBs or even some lithium-ion batteries
A nonperturbative parametrization and scenario for EFT renormalization
We present a universal form of the -matrices renormalized in
nonperturbative regime and the ensuing notions and properties that fail
conventional wisdoms. A universal scale is identified and shown to be
renormalization group invariant. The effective range parameters are derived in
a nonperturbative scenario with some new predictions within the realm of
contact potentials. Some controversies are shown to be due to the failure of
conventional wisdoms.Comment: 5 pages, no figure, to appear in Europhys. Let
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