The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure

Resonance phenomena in ultracold dipole-dipole scattering

Elastic scattering resonances occurring in ultracold collisions of either bosonic or fermionic polar molecules are investigated. The Born-Oppenheimer adiabatic representation of the two-bodydynamics provides both a qualitative classification scheme and a quantitative WKB quantization condition that predicts several sequences of resonant states. It is found that the near-threshold energy dependence of ultracold collision cross sections varies significantly with the particle exchange symmetry, with bosonic systems showing much smoother energy variations than their fermionic counterparts. Resonant variations of the angular distributions in ultracold collisions are also described.Comment: 19 pages, 6 figures, revtex4, submitted to J. Phys.

Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions

We present a unique theoretical description of the physics of the spherically trapped $N$-atom degenerate Fermi gas (DFG) at zero temperature based on an ordinary Schr\"{o}dinger equation with a microscopic, two body interaction potential. With a careful choice of coordinates and a variational wavefunction, the many body Schr\"{o}dinger equation can be accurately described by a \emph{linear}, one dimensional effective Schr\"{o}dinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius and peak density of ground state energy are made to those predicted by Hartree-Fock (HF). Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction

Quantum Simulations of Extended Hubbard Models with Dipolar Crystals

In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.Comment: 44 pages, 14 figure

Low energy atomic collision with dipole interactions

We apply quantum defect theory to study low energy ground state atomic collisions including aligned dipole interactions such as those induced by an electric field. Our results show that coupled even ($l$) relative orbital angular momentum partial wave channels exhibit shape resonance structures while odd ($l$) channels do not. We analyze and interpret these resonances within the framework of multichannel quantum defect theory (MQDT).Comment: 27 pages, 17 figures, an inadvertent typo correcte

Solution of three-dimensional Faddeev equations: ultracold Helium trimer calculations with a public quantum three-body code

Abstract. We present an illustration of using a quantum three-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform highly-accurate calculations of quantum three-body systems. The previously known results for He 3 ground state are well reproduced by the code

The weight of water

Leonardo da Vinci’s pioneering work on hydrostatics combined traditional knowledge and innovative empiricism in an attempt to understand an object fraught with paradox: the water-filled container

Optimization of Supercritical Carbon Dioxide Extraction of Rice Bran Oil and γ-Oryzanol Using Multi-Factorial Design of Experiment

After rice harvesting, the milling processes generate many by-products including husk, bran, germs, and broken rice representing around 40% of the total grain. Bran, one of the external cereal layers, contains proteins, dietary fibers, minerals, and lipids. One of the most common rice bran utilization is the extraction of rice bran oil (RBO). Among all vegetable oils, RBO presents a unique chemical composition rich in antioxidant compounds such as γ-oryzanol that provide several beneficial properties. RBO is generally extracted by exploiting hexane, a solvent toxic to the environment and human health. The growing demand for this oil has led researchers to look for more sustainable extraction techniques. Supercritical carbon dioxide (SC-CO2) has been successfully applied to extract oil and functional compounds from several matrices. In this work, the SC-CO2 extraction of RBO was optimized using a Design of Experiment (DoE) on a pilot scale. "The DoE approach involving multilinear regression allowed modelling the yield in RBO and gamma oryzanol as a function of temperature and pressure, keeping the extraction time constant, as decided by the company. This approach made it possible to optimize the extraction yield and to identify the best temperature (40 °C), while also highlighting that pressure did not play any influential role in the process, at least concerning the analyzed experimental domain on this industrial plant. A model for computing the extraction yield as a function of temperature and pressure was obtained. This study shows that it is possible to obtain good quality RBO, rich in γ-oryzanol and essential fatty acids, using low temperatures and pressures, starting from a rice milling by-product. Graphical Abstract: [Figure not available: see fulltext.

Unfolding Simulations of Holomyoglobin from Four Mammals: Identification of Intermediates and β-Sheet Formation from Partially Unfolded States

Myoglobin (Mb) is a centrally important, widely studied mammalian protein. While much work has investigated multi-step unfolding of apoMb using acid or denaturant, holomyoglobin unfolding is poorly understood despite its biological relevance. We present here the first systematic unfolding simulations of holoMb and the first comparative study of unfolding of protein orthologs from different species (sperm whale, pig, horse, and harbor seal). We also provide new interpretations of experimental mean molecular ellipticities of myoglobin intermediates, notably correcting for random coil and number of helices in intermediates. The simulated holoproteins at 310 K displayed structures and dynamics in agreement with crystal structures (R g ~1.48-1.51 nm, helicity ~75%). At 400 K, heme was not lost, but some helix loss was observed in pig and horse, suggesting that these helices are less stable in terrestrial species. At 500 K, heme was lost within 1.0-3.7 ns. All four proteins displayed exponentially decaying helix structure within 20 ns. The C- and F-helices were lost quickly in all cases. Heme delayed helix loss, and sperm whale myoglobin exhibited highest retention of heme and D/E helices. Persistence of conformation (RMSD), secondary structure, and ellipticity between 2-11 ns was interpreted as intermediates of holoMb unfolding in all four species. The intermediates resemble those of apoMb notably in A and H helices, but differ substantially in the D-, E- and F-helices, which interact with heme. The identified mechanisms cast light on the role of metal/cofactor in poorly understood holoMb unfolding. We also observed β-sheet formation of several myoglobins at 500 K as seen experimentally, occurring after disruption of helices to a partially unfolded, globally disordered state; heme reduced this tendency and sperm-whale did not display any sheet propensity during the simulations