Fragmented metastable states exist in an attractive bose-einstein condensate for atom numbers well above the critical number of the Gross-Pitaevskii theory

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number N(cr)(GP) of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above N(cr)(GP). The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.     

'Lock and key' control of optical properties in a push-pull system

We report the modulation of the absorbance of a flavin push-pull derivative through specific recognition by a complementary diamidopyridine (DAP), shifting the flavin intramolecular charge transfer band by approximately 30 nm.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.     

A graph-theoretic approach for comparing dimensions of components in simply-graded algebras

Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that in a digraph without parallel edges, the number of pairs of vertices having a common in-neighbor or a common out-neighbor is at least the number of edges. We deduce that for any simple group-grading, the dimension of the trivial component is maximal.     

Novel boracycles from 2-amino-2-methylpropan-1-ol and borane methyl sulfide: Synthesis and X-ray crystal structures

On reacting the simple 1,2-amino alcohol: 2-amino-2-methylpropan-1-ol, with borane methyl sulfide (BMS), the expected five member oxazaborolidine ring is not obtained. Instead, two polycyclic structures with trigonal boron atoms 6 and 7 were obtained, and their structure were determined by X-ray crystallography. Compound 6 was obtained in 39% yield and compound 7 was obtained in 7% yield.     

Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

A study of the 1,2-addition of group IV metallacycles derived from 1-alkynylphosphonates to conjugated enones

Addition of group IV cyclopropenemetallocycles to conjugated enones indicates that the reaction course is mostly dependent on the metallocyle and the enone moiety. The zirconacycle affords the unrearranged products 3. On the other hand, some rearranged products, 1,3-butadienylphosphonates, are obtained when titanacycles are used.     

Demixing of bosonic mixtures in optical lattices from macroscopic to microscopic scales

Mixtures of cold bosonic atoms in optical lattices undergo demixing on different length scales with increasing interspecies repulsion. As a general rule, the stronger the intraspecies interactions, the shorter is this length scale. The wealth of phenomena is documented by illustrative examples on both superfluids and Mott insulators.