Planar vector field versions of Carathéodory's and Loewner's conjectures

Let r = 3, 4, . . . ,∞, ω. The Cr-Carathéodory's Conjecture states that every Cr convex embedding of a 2-sphere into R3 must have at least two umbilics. The Cr-Loewner's conjecture (stronger thanthe one of Carathéodory) states that there are no umbilics of index bigger than one. We show that these two conjectures are equivalent to others about planar vector fields. For instance, if r = ω, Cr-Carath'eodory's Conjecture is equivalent to the following one: Let ρ > 0 and β : U ⊂ R2 → R, be of class Cr, where U is a neighborhood of the compact disc D(0, ρ) ⊂ R2 of radius ρ centered at 0. If β restricted to a neighborhood of the circle ∂D(0, ρ) has the form β(x, y) = (ax2 + by2)/(x2 + y2), where a < b < 0, then the vector field (defined in U) that takes (x, y) to (βxx(x, y) − βyy(x, y), 2βxy(x, y)) has at least two singularities in D(0, ρ

Triatomic continuum resonances for large negative scattering lengths

We study triatomic systems in the regime of large negative scattering lengths which may be more favorable for the formation of condensed trimers in trapped ultracold monoatomic gases as the competition with the weakly bound dimers is absent. The manipulation of the scattering length can turn an excited weakly bound Efimov trimer into a continuum resonance. Its energy and width are described by universal scaling functions written in terms of the scattering length and the binding energy, $B_3$, of the shallowest triatomic molecule. For $a^{-1}<-0.0297 \sqrt{m B_3/\hbar^2}$ the excited Efimov state turns into a continuum resonance.Comment: 4 pages, 4 figure

Ligand Binding Rate Constants in Heme Proteins Using Markov State Models and Molecular Dynamics Simulations

Computer simulation studies of the molecular basis for ligand migration in proteins allow the description and quantification of the key events implicated in this process as, such as the transition between docking sites, displacements of existing ligands and solvent molecules, and open/closure of specific 'gates', among other factors. In heme proteins, especially in globins, these phenomena are related to the regulation of protein function, since ligand migration from the solvent to the active site preludes ligand binding to the iron in the distal cavity, which in turn triggers the different globin functions. In this work, a combination of molecular dynamics simulations with a Markov-state model of ligand migration is used to the study the migration of O2 and ·NO in two truncated hemoglobins of Mycobacterium tuberculosis (truncated hemoglobin N -Mt-TrHbN- and O -Mt-TrHbO). The results indicate that the proposed model provides trends in kinetic association constants in agreement with experimental data. In particular, for Mt-TrHbN, we show that the difference in the association constant in the oxy and deoxy states relies mainly in the displacement of water molecules anchored in the distal cavity by O2 in the deoxy form, whereas the conformational transition of PheE15 between open and closed states plays a minor role. On the other hand, the results also show the relevant effect played by easily diffusive tunnels, as the ones present in Mt-TrHbN, compared to the more impeded passage in Mt-TrHbO, which contributes to justify the different .NO dioxygenation rates in these proteins. Altogether, the results in this work provide a valuable approach to study ligand migration in globins using molecular dynamics simulations and Markov-state model analysis

Structure of exotic three-body systems

The classification of large halos formed by two identical particles and a core is systematically addressed according to interparticle distances. The root-mean-square distances between the constituents are described by universal scaling functions obtained from a renormalized zero-range model. Applications for halo nuclei, $^{11}$Li and $^{14}$Be, and for atomic $^4$He$_3$ are briefly discussed. The generalization to four-body systems is proposed.Comment: Contribution to the International workshop "Critical Stability of Few-Body Quantum Systems". To be published in "Few-Body Systems

Treatment of congenital atypical haemangiosarcoma in a foal

Haemangiosarcoma is a rare vascular tumour in horses, usually originating from blood vessel endothelial cells. We present the case of an 8-day-old foal, referred for an atypical large subcutaneous mass on the left side since birth. Ultrasonographically, it showed multiple cavities with hypoechoic content, marked vascularisation and fluid movement between cavities. As the nature of the mass suggested that surgery could result in profuse bleeding, we decided to perform an initial arteriography to identify the pattern and calibre of the main vessels and embolisation of this vascular supply, which allowed surgical removal with less bleeding than expected. This approach, with pre-surgical transarterial embolisation of the tumour, is not commonly used in equine surgery. Histology established a diagnosis of cutaneous haemangiosarcoma. During 1-year post-surgery, clinical and ultrasound examinations were carried out without any signs of recurrence or metastasis. One year later, the foal was euthanised due to a limb fracture. No macroscopic signs of metastasis were observed at necropsy. Histology showed no signs of recurrence. Cutaneous haemangiosarcomas, though rare, should be included in the differential of masses and growths with compatible ultrasound or cytological findings. Transcatheter arterial embolisation of highly vascularised neoplasms can reduce bleeding and facilitate subsequent surgical resection

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.Comment: Accepted for publication in special issue of Few-Body Systems devoted to the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, October 2011, Erice, Sicily, Ital

Evidence for Efimov quantum states in an ultracold gas of cesium atoms

Systems of three interacting particles are notorious for their complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.Comment: 18 pages, 3 figure