2,018 research outputs found
Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow
The appearance of travelling-wave-type solutions in pipe Poiseuille flow that
are disconnected from the basic parabolic profile is numerically studied in
detail. We focus on solutions in the 2-fold azimuthally-periodic subspace
because of their special stability properties, but relate our findings to other
solutions as well. Using time-stepping, an adapted Krylov-Newton method and
Arnoldi iteration for the computation and stability analysis of relative
equilibria, and a robust pseudo-arclength continuation scheme we unfold a
double-zero (Takens-Bogdanov) bifurcating scenario as a function of Reynolds
number (Re) and wavenumber (k). This scenario is extended, by the inclusion of
higher order terms in the normal form, to account for the appearance of
supercritical modulated waves emanating from the upper branch of solutions at a
degenerate Hopf bifurcation. These waves are expected to disappear in
saddle-loop bifurcations upon collision with lower-branch solutions, thereby
leaving stable upper-branch solutions whose subsequent secondary bifurcations
could contribute to the formation of the phase space structures that are
required for turbulent dynamics at higher Re.Comment: 26 pages, 15 figures (pdf and png). Submitted to J. Fluid Mec
Advantages of Unfair Quantum Ground-State Sampling
The debate around the potential superiority of quantum annealers over their
classical counterparts has been ongoing since the inception of the field by
Kadowaki and Nishimori close to two decades ago. Recent technological
breakthroughs in the field, which have led to the manufacture of experimental
prototypes of quantum annealing optimizers with sizes approaching the practical
regime, have reignited this discussion. However, the demonstration of quantum
annealing speedups remains to this day an elusive albeit coveted goal. Here, we
examine the power of quantum annealers to provide a different type of quantum
enhancement of practical relevance, namely, their ability to serve as useful
samplers from the ground-state manifolds of combinatorial optimization
problems. We study, both numerically by simulating ideal stoquastic and
non-stoquastic quantum annealing processes, and experimentally, using a
commercially available quantum annealing processor, the ability of quantum
annealers to sample the ground-states of spin glasses differently than
classical thermal samplers. We demonstrate that i) quantum annealers in general
sample the ground-state manifolds of spin glasses very differently than thermal
optimizers, ii) the nature of the quantum fluctuations driving the annealing
process has a decisive effect on the final distribution over ground-states, and
iii) the experimental quantum annealer samples ground-state manifolds
significantly differently than thermal and ideal quantum annealers. We
illustrate how quantum annealers may serve as powerful tools when complementing
standard sampling algorithms.Comment: 13 pages, 11 figure
Fracton topological order via coupled layers
In this work, we develop a coupled layer construction of fracton topological
orders in spatial dimensions. These topological phases have sub-extensive
topological ground-state degeneracy and possess excitations whose movement is
restricted in interesting ways. Our coupled layer approach is used to construct
several different fracton topological phases, both from stacked layers of
simple topological phases and from stacks of fracton topological
phases. This perspective allows us to shed light on the physics of the X-cube
model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be
obtained as the strong-coupling limit of a coupled three-dimensional stack of
toric codes. We also construct two new models of fracton topological order: a
semionic generalization of the X-cube model, and a model obtained by coupling
together four interpenetrating X-cube models, which we dub the "Four Color Cube
model." The couplings considered lead to fracton topological orders via
mechanisms we dub "p-string condensation" and "p-membrane condensation," in
which strings or membranes built from particle excitations are driven to
condense. This allows the fusion properties, braiding statistics, and
ground-state degeneracy of the phases we construct to be easily studied in
terms of more familiar degrees of freedom. Our work raises the possibility of
studying fracton topological phases from within the framework of topological
quantum field theory, which may be useful for obtaining a more complete
understanding of such phases.Comment: 20 pages, 18 figures, published versio
Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory
We reconsider the time-dependent Born-Oppenheimer theory with the goal to
carefully separate between the adiabatic decoupling of a given group of energy
bands from their orthogonal subspace and the semiclassics within the energy
bands. Band crossings are allowed and our results are local in the sense that
they hold up to the first time when a band crossing is encountered. The
adiabatic decoupling leads to an effective Schroedinger equation for the
nuclei, including contributions from the Berry connection.Comment: Revised version. 19 pages, 2 figure
Degenerate perturbation theory in thermoacoustics: High-order sensitivities and exceptional points
In this study, we connect concepts that have been recently developed in
thermoacoustics, specifically, (i) high-order spectral perturbation theory,
(ii) symmetry induced degenerate thermoacoustic modes, (iii) intrinsic
thermoacoustic modes, and (iv) exceptional points. Their connection helps gain
physical insight into the behaviour of the thermoacoustic spectrum when
parameters of the system are varied. First, we extend high-order adjoint-based
perturbation theory of thermoacoustic modes to the degenerate case. We provide
explicit formulae for the calculation of the eigenvalue corrections to any
order. These formulae are valid for self-adjoint, non-self-adjoint or even
non-normal systems; therefore, they can be applied to a large range of
problems, including fluid dynamics. Second, by analysing the expansion
coefficients of the eigenvalue corrections as a function of a parameter of
interest, we accurately estimate the radius of convergence of the power series.
Third, we connect the existence of a finite radius of convergence to the
existence of singularities in parameter space. We identify these singularities
as exceptional points, which correspond to defective thermoacoustic
eigenvalues, with infinite sensitivity to infinitesimal changes in the
parameters. At an exceptional point, two eigenvalues and their associated
eigenvectors coalesce. Close to an exceptional point, strong veering of the
eigenvalue trajectories is observed. As demonstrated in recent work,
exceptional points naturally arise in thermoacoustic systems due to the
interaction between modes of acoustic and intrinsic origin. The role of
exceptional points in thermoacoustic systems sheds new light on the physics and
sensitivity of thermoacoustic stability, which can be leveraged for passive
control by small design modifications
Reconstructing ellipsoids from projections
Caption title.Includes bibliographical references (p. 23-25).Supported by the National Science Foundation. MIP-9015281 Supported by the Army Office of Sponsored Research. DAAL03-92-G-0115 Supported by the Office of Naval Research. N00014-91-J-1004William C. Karl, George C. Verghese, Alan S. Willsky
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