Long-Lived Non-Equilibrium Interstitial-Solid-Solutions in Binary Mixtures

We perform particle resolved experimental studies on the heterogeneous crystallisation process of two compo- nent mixtures of hard spheres. The components have a size ratio of 0.39. We compared these with molecular dynamics simulations of homogenous nucleation. We find for both experiments and simulations that the final assemblies are interstitial solid solutions, where the large particles form crystalline close-packed lattices, whereas the small particles occupy random interstitial sites. This interstitial solution resembles that found at equilibrium when the size ratios are 0.3 [Filion et al., Phys. Rev. Lett. 107, 168302 (2011)] and 0.4 [Filion, PhD Thesis, Utrecht University (2011)]. However, unlike these previous studies, for our system sim- ulations showed that the small particles are trapped in the octahedral holes of the ordered structure formed by the large particles, leading to long-lived non-equilibrium structures in the time scales studied and not the equilibrium interstitial solutions found earlier. Interestingly, the percentage of small particles in the crystal formed by the large ones rapidly reaches a maximum of around 14% for most of the packing fractions tested, unlike previous predictions where the occupancy of the interstitial sites increases with the system concentration. Finally, no further hopping of the small particles was observed

Orphans of the Motherland: Puerto Rican Images of Spain in Jacobo Morales\u27s Linda Sara

Puerto Rican identity has been confounded by Puerto Rico\u27s prolonged colonial relationship to Spain (nearly 80 years longer than that of most other Latin American colonies) and its abrupt change in status to that of United States protectorate in 1898 after the Spanish American War. Increasingly, Puerto Rican identity has been theorized in sole reference to the political relationship with the United States. The residual presence of Spain and Spaniards in the construction of the new Puerto Rican collective, and the denial or nostalgia that might still be elicited by the former empire, have gradually receded into the background. Perhaps surprisingly, the presence of Spain and reactions to it find their widest outlet in popular culture. This article analyzes the complex portrayal of the continuing substratum of the Spanish heritage in Puerto Rico in one example from Puerto Rican popular culture—Jacobo Morales\u27s 1994 film Linda Sara. The film\u27s characters either willingly or unknowingly falsify their Spanish past, recounting their (hi)story according to their present needs

Trajectory-dependent energy loss for swift He atoms axially scattered off a silver surface

Angle- and energy-loss- resolved distributions of helium atoms grazingly scattered from a Ag(110) surface along low indexed crystallographic directions are investigated considering impact energies in the few keV range. Final projectile distributions are evaluated within a semi-classical formalism that includes dissipative effects due to electron-hole excitations through a friction force. For mono-energetic beams impinging along the $[1\bar{1}0]$, $[1\bar{1}2]$ and $[1\bar{1}0]$ directions, the model predicts the presence of multiple peak structures in energy-loss spectra. Such structures provide detailed information about the trajectory-dependent energy loss. However, when the experimental dispersion of the incident beam is taken into account, these energy-loss peaks are completely washed out, giving rise to a smooth energy-loss distribution, in fairly good agreement with available experimental data

Controlling the nature of a charged impurity in a bath of Feshbach dimers

We theoretically study the dynamics of a trapped ion that is immersed in an ultracold gas of weakly bound atomic dimers created by a Feshbach resonance. Using quasi-classical simulations, we find a crossover from dimer dissociation to molecular ion formation depending on the binding energy of the dimers. The location of the crossover strongly depends on the collision energy and the time-dependent fields of the Paul trap. Deeply bound dimers lead to fast molecular ion formation, with rates approaching the Langevin collision rate $\Gamma'_\text{L}\approx4.8\times10^{-9}\,$cm$^3$s$^{-1}$. The kinetic energies of the created molecular ions have a median below $1\,$mK, such that they will stay confined in the ion trap. We conclude that interacting ions and Feshbach molecules may provide a novel approach towards the creation of ultracold molecular ions with applications in precision spectroscopy and quantum chemistry.Comment: 9 pages and 12 figures including appendice

Three Observations on Commutators of Singular Integral Operators with BMO Functions

Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely \[\frac{1}{|Q|}\left|\left\{x\in Q\, : \, |[b,T](f\chi_Q)(x)|>M^2f(x)t\right\}\right|\leq c e^{-\sqrt{ct\|b\|_{BMO}}}\] is sharp, since it cannot be better than subgaussian. 2 - It is not possible to obtain a pointwise control of the commutator by a finite sum of sparse operators defined by $L\log L$ averages. 3 - Motivated by the conjugation method for commutators, it is shown the failure of the following endpoint estimate, if $w\in A_p\setminus A_1$ then $$\left\| wM\left(\frac{f}{w}\right)\right\|_{L^1(\mathbb{R}^n)\rightarrow L^{1,\infty}(\mathbb{R}^n)}=\infty.$$MTM2012-3074

Classical-quantum localization in one dimensional systems: The kicked rotor

This work explores the origin of dynamical localization in one-dimensional systems using the kicked rotor as an example. In particular, we propose the fractal dimension of the phase space as a robust indicator to characterize the onset of classical chaos. As a result, we find that the system crosses the stability border when the fractal dimension ≥1.81, and we obtain a functional form for the fractal dimension as a function of the kick strength. At the same time, dynamical localization is explored in the quantum realm by looking into the energy–localization relationship across the classical stability border, thus finding a correlation between the classical chaos and the presence of dynamical localization

Borderline Weighted Estimates for Commutators of Singular Integrals

In this paper we establish the following estimate $$w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\frac{|f(x)|}{\lambda}\right)M_{L(\log L)^{1+\varepsilon}}w(x)dx$$ where $w\geq0, \, 0<\varepsilon<1$ and $\Phi(t)=t(1+\log^+(t))$. This inequality relies upon the following sharp $L^p$ estimate $$\|[b,T]f\|_{L^{p}(w)}\leq c_{T}\left(p'\right)^{2}p^{2}\left(\frac{p-1}{\delta}\right)^{\frac{1}{p'}} \|b\|_{BMO} \, \|f \|_{L^{p}(M_{L(\log L)^{2p-1+\delta}}w)}$$where $1<p<\infty, w\geq0 \text{ and } 0<\delta<1.$ As a consequence we recover the following estimate essentially contained in \cite{MR3008263}: $$w\left(\{x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| >\lambda\}\right)\leq c_T\,[w]_{A_{\infty}}\left(1+\log^{+}[w]_{A_{\infty}}\right)^{2}\int_{\mathbb{R}^{n}} \Phi\left(\|b\|_{BMO}\frac{|f(x)|}{\lambda}\right)Mw(x)dx$$ We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols