3,829 research outputs found
Blast Those Stuumps!
You can get rid of troublesome stumps around your farm by blasting with dynamite. The coast isn\u27t large, but there are precautions to take
Wavelet solution of variable order pseudodifferential equations
Sobolev spaces H m(x)(I) of variable order 0<m(x)<1 on an interval I⊂ℝ arise as domains of Dirichlet forms for certain quadratic, pure jump Feller processes X t∈ℝ with unbounded, state-dependent intensity of small jumps. For spline wavelets with complementary boundary conditions, we establish multilevel norm equivalences in H m(x)(I) and prove preconditioning and wavelet matrix compression results for the variable order pseudodifferential generators A of X. Sufficient conditions on A to satisfy a Gårding inequality in H m(x)(I) and time-analyticity of the semigroup T t associated with the Feller process X t are established. As application, wavelet-based algorithms of log-linear complexity are obtained for the valuation of contingent claims on pure jump Feller-Lévy processes X t with state-dependent jump intensity by numerical solution of the corresponding Kolmogoroff equation
Cooling a mechanical resonator via coupling to a tunable double quantum dot
We study the cooling of a mechanical resonator (MR) that is capacitively
coupled to a double quantum dot (DQD). The MR is cooled by the dynamical
backaction induced by the capacitive coupling between the DQD and the MR. The
DQD is excited by a microwave field and afterwards a tunneling event results in
the decay of the excited state of the DQD. An important advantage of this
system is that both the energy level splitting and the decay rate of the DQD
can be well tuned by varying the gate voltage. We find that the steady average
occupancy, below unity, of the MR can be achieved by changing both the decay
rate of the excited state and the detuning between the transition frequency of
the DQD and the microwave frequency, in analogy to the laser sideband cooling
of an atom or trapped ion in atomic physics. Our results show that the cooling
of the MR to the ground state is experimentally implementable.Comment: 10 pages, 5 figure
Probing tiny motions of nanomechanical resonators: classical or quantum mechanical?
We propose a spectroscopic approach to probe tiny vibrations of a
nanomechanical resonator (NAMR), which may reveal classical or quantum behavior
depending on the decoherence-inducing environment. Our proposal is based on the
detection of the voltage-fluctuation spectrum in a superconducting transmission
line resonator (TLR), which is {\it indirectly} coupled to the NAMR via a
controllable Josephson qubit acting as a quantum transducer. The classical
(quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark
shifts of the qubit levels, which can be measured by the voltage fluctuations
in the TLR. Thus, the motion of the NAMR, including if it is quantum mechanical
or not, could be probed by detecting the voltage-fluctuation spectrum of the
TLR.Comment: 4 pages, 3 figures. to appear in Physical Review Letter
Multiresolution kernel matrix algebra
We propose a sparse arithmetic for kernel matrices, enabling efficient
scattered data analysis. The compression of kernel matrices by means of
samplets yields sparse matrices such that assembly, addition, and
multiplication of these matrices can be performed with essentially linear cost.
Since the inverse of a kernel matrix is compressible, too, we have also fast
access to the inverse kernel matrix by employing exact sparse selected
inversion techniques. As a consequence, we can rapidly evaluate series
expansions and contour integrals to access, numerically and approximately in a
data-sparse format, more complicated matrix functions such as and
. By exploiting the matrix arithmetic, also efficient Gaussian process
learning algorithms for spatial statistics can be realized. Numerical results
are presented to quantify and quality our findings
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