Atomic electron tomography in three and four dimensions

Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. Here, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution

Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite power series in the auxiliary metric given by ref. \cite{s14}, but just picks out the first term from the series formally. New effective interactions of the theories are revealed. That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinite terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite power series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This non-linearity is inevitable to the requirement the two dual actions are equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions added; v3: concision made; v4: minor modification mad

New Born-Infeld and DpDp-Brane Actions under 2-Metric and 3-Metric Prescriptions

The parent action method is utilized to the Born-Infeld and $Dp$-brane theories. Various new forms of Born-Infeld and $Dp$-brane actions are derived by using this systematic approach, in which both the already known 2-metric and newly proposed 3-metric prescriptions are considered. An auxiliary worldvolume tensor field, denoted by ${\omega}_{{\mu}{\nu}}$, is introduced and treated probably as an additional worldvolume metric because it plays a similar role to that of the auxiliary worldvolume (also called {\em intrinsic}) metric ${\gamma}_{{\mu}{\nu}}$. Some properties, such as duality, permutation and Weyl invariance as a local worldvolume symmetry of the new forms are analyzed. In particular, a new symmetry, i.e. the double Weyl invariance is discovered in 3-metric forms.Comment: v1: 30 pages, 4 figures; v2: 31 pages, 4 figures, final version with some modifications to appear in Phys. Rev.