Stress analysis of a doubly-curved skin with a flared nozzle port, phase v annual summary report

Computer method for stress and deflection calculation of nozzle flow openings in large pressure vessels

Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions

We study few-body problems in mixed dimensions with $N \ge 2$ heavy atoms trapped individually in parallel one-dimensional tubes or two-dimensional disks, and a single light atom travels freely in three dimensions. By using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad region of heavy-light atom scattering length combinations. Specifically, the existence of trimer and tetramer states persist to negative scattering lengths regime, where no two-body bound state is present. These few-body bound states are analogous to the Efimov states in three dimensions, but are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps. This resonant behavior is a unique feature for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure

Zero dimensional area law in a gapless fermion system

The entanglement entropy of a gapless fermion subsystem coupled to a gapless bulk by a "weak link" is considered. It is demonstrated numerically that each independent weak link contributes an entropy proportional to lnL, where L is linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio

Exchange and Correlation in Open Systems of Fluctuating Electron Number

While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semi-local density functional approximations curves upward and the exact-exchange-only or Hartree-Fock energy downward. As a result, semi-local density functionals fail for separated open systems of fluctuating electron number, as in stretched molecular ions A$_2^{+}$ and in solid transition metal oxides. We develop an exact-exchange theory and an exchange-hole sum rule that explain these failures and we propose a way to correct them via a local hybrid functional.Comment: 4 pages, 2 figure

What is a crystal?

Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean ``any solid having an essentially discrete diffraction diagram.'' Have we learned enough about crystallinity in the last 25 years, or do we need more time to explore additional physical systems? There is much confusion and contradiction in the literature in using the term crystal. Are we ready now to propose a permanent definition for crystal to be used by all? I argue that time has come to put a sense of order in all the confusion.Comment: Submitted to Zeitschrift fuer Kristallographi

Wave Mechanics of a Two Wire Atomic Beamsplitter

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to non-adiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three dimensional structure of the beam splitter, gathering quantitative information about mode-mixing, splitting ratios,and reflection and transmission probabilities

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

A unified electrostatic and cavitation model for first-principles molecular dynamics in solution

The electrostatic continuum solvent model developed by Fattebert and Gygi is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. Our model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution, and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon