18,325 research outputs found
Frequency tuning, nonlinearities and mode coupling in circular graphene resonators
We study circular nanomechanical graphene resonators by means of continuum
elasticity theory, treating them as membranes. We derive dynamic equations for
the flexural mode amplitudes. Due to geometrical nonlinearity these can be
modeled by coupled Duffing equations. By solving the Airy stress problem we
obtain analytic expressions for eigenfrequencies and nonlinear coefficients as
functions of radius, suspension height, initial tension, back-gate voltage and
elastic constants, which we compare with finite element simulations. Using
perturbation theory, we show that it is necessary to include the effects of the
non-uniform stress distribution for finite deflections. This correctly
reproduces the spectrum and frequency tuning of the resonator, including
frequency crossings.Comment: 21 pages, 7 figures, 3 table
Pseudo-digital quantum bits
Quantum computers are analog devices; thus they are highly susceptible to
accumulative errors arising from classical control electronics. Fast
operation--as necessitated by decoherence--makes gating errors very likely. In
most current designs for scalable quantum computers it is not possible to
satisfy both the requirements of low decoherence errors and low gating errors.
Here we introduce a hardware-based technique for pseudo-digital gate operation.
We perform self-consistent simulations of semiconductor quantum dots, finding
that pseudo-digital techniques reduce operational error rates by more than two
orders of magnitude, thus facilitating fast operation.Comment: 4 pages, 3 figure
Sample genealogies and genetic variation in populations of variable size
We consider neutral evolution of a large population subject to changes in its
population size. For a population with a time-variable carrying capacity we
have computed the distributions of the total branch lengths of its sample
genealogies. Within the coalescent approximation we have obtained a general
expression, Eq. (27), for the moments of these distributions for an arbitrary
smooth dependence of the population size on time. We investigate how the
frequency of population-size variations alters the distributions. This allows
us to discuss their influence on the distribution of the number of mutations,
and on the population homozygosity in populations with variable size.Comment: 19 pages, 8 figures, 1 tabl
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