12,082 research outputs found

### 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

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