35,985 research outputs found
Complex Bifurcation from Real Paths
A new bifurcation phenomenon, called complex bifurcation, is studied. The basic idea is simply that real solution paths of real analytic problems frequently have complex paths bifurcating from them. It is shown that this phenomenon occurs at fold points, at pitchfork bifurcation points, and at isola centers. It is also shown that perturbed bifurcations can yield two disjoint real solution branches that are connected by complex paths bifurcating from the perturbed solution paths. This may be useful in finding new real solutions.
A discussion of how existing codes for computing real solution paths may be trivially modified to compute complex paths is included, and examples of numerically computed complex solution paths for a nonlinear two point boundary value problem, and a problem from fluid mechanics are given
A dual-beam actinic light source for photosynthesis research
Simulation of photosynthetic process in plants is accomplished by using two separate and identical optical channels that provide independently adjustable wavelengths (filters), shutter sequencing, and control intensity of illumination. In addition to experiments using electron paramagnetic resonance spectroscopy, system may be applicable to other types of research in photosynthetic field
Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
The past several years have seen renewed interest in the use of
symmetry-projected Hartree-Fock for the description of strong correlations.
Unfortunately, these symmetry-projected mean-field methods do not adequately
account for dynamic correlation. Presumably, this shortcoming could be
addressed if one could combine symmetry-projected Hartree-Fock with a many-body
method such as coupled cluster theory, but this is by no means straightforward
because the two techniques are formulated in very different ways. However, we
have recently shown that the singlet -projected unrestricted Hartree-Fock
wave function can in fact be written in a coupled cluster-like wave function:
that is, the spin-projected unrestricted Hartree-Fock wave function can be
written as a polynomial of a double-excitation operator acting on some
closed-shell reference determinant. Here, we extend this result and show that
the spin-projected generalized Hartree-Fock wave function (which has both
and projection) is likewise a polynomial of low-order excitation
operators acting on a closed-shell determinant, and provide a closed-form
expression for the resulting polynomial coefficients. We include a few
preliminary applications of the combination of this spin-projected Hartree-Fock
and coupled cluster theory to the Hubbard Hamiltonian, and comment on
generalizations of the methodology. Results here are not for production level,
but a similarity transformed theory that combines the two offers the promise of
being accurate for both weak and strong correlation, and particularly may offer
significant improvements in the intermediate correlation regime where neither
projected Hartree-Fock nor coupled cluster is particularly accurate.Comment: accepted by Phys. Rev.
Gas chromatograph injection system
An injection system for a gas chromatograph is described which uses a small injector chamber (available in various configurations). The sample is placed in the chamber while the chamber is not under pressure and is not heated, and there is no chance of leakage caused by either pressure or heat. It is injected into the apparatus by changing the position of a valve and heating the chamber, and is volatilized and swept by a carrier gas into the analysis apparatus
Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
Spin-projected Hartree-Fock is introduced as a particle-hole excitation
ansatz over a symmetry-adapted reference determinant. Remarkably, this
expansion has an analytic expression that we were able to decipher. While the
form of the polynomial expansion is universal, the excitation amplitudes need
to be optimized. This is equivalent to the optimization of orbitals in the
conventional projected Hartree-Fock framework of non-orthogonal determinants.
Using the inverse of the particle-hole expansion, we similarity transform the
Hamiltonian in a coupled-cluster style theory. The left eigenvector of the
non-hermitian Hamiltonian is constructed in a similar particle-hole expansion
fashion, and we show that to numerically reproduce variational projected
Hartree-Fock results, one needs as many pair excitations in the bra as the
number of strongly correlated entangled pairs in the system. This
single-excitation polynomial similarity transformation theory is an alternative
to our recently presented double excitation theory, but supports projected
Hartree-Fock and coupled cluster simultaneously rather than interpolating
between them
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