4,489 research outputs found
Throughput and Delay Scaling in Supportive Two-Tier Networks
Consider a wireless network that has two tiers with different priorities: a
primary tier vs. a secondary tier, which is an emerging network scenario with
the advancement of cognitive radio technologies. The primary tier consists of
randomly distributed legacy nodes of density , which have an absolute
priority to access the spectrum. The secondary tier consists of randomly
distributed cognitive nodes of density with , which
can only access the spectrum opportunistically to limit the interference to the
primary tier. Based on the assumption that the secondary tier is allowed to
route the packets for the primary tier, we investigate the throughput and delay
scaling laws of the two tiers in the following two scenarios: i) the primary
and secondary nodes are all static; ii) the primary nodes are static while the
secondary nodes are mobile. With the proposed protocols for the two tiers, we
show that the primary tier can achieve a per-node throughput scaling of
in the above two scenarios. In the associated
delay analysis for the first scenario, we show that the primary tier can
achieve a delay scaling of
with . In the second scenario, with two mobility
models considered for the secondary nodes: an i.i.d. mobility model and a
random walk model, we show that the primary tier can achieve delay scaling laws
of and , respectively, where is the random walk
step size. The throughput and delay scaling laws for the secondary tier are
also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC
201
RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure
models continue to play important roles in industrial flow simulations.
However, the commonly used linear eddy viscosity models are intrinsically
unable to handle flows with non-equilibrium turbulence. Reynolds stress models,
on the other hand, are plagued by their lack of robustness. Recent studies in
plane channel flows found that even substituting Reynolds stresses with errors
below 0.5% from direct numerical simulation (DNS) databases into RANS equations
leads to velocities with large errors (up to 35%). While such an observation
may have only marginal relevance to traditional Reynolds stress models, it is
disturbing for the recently emerging data-driven models that treat the Reynolds
stress as an explicit source term in the RANS equations, as it suggests that
the RANS equations with such models can be ill-conditioned. So far, a rigorous
analysis of the condition of such models is still lacking. As such, in this
work we propose a metric based on local condition number function for a priori
evaluation of the conditioning of the RANS equations. We further show that the
ill-conditioning cannot be explained by the global matrix condition number of
the discretized RANS equations. Comprehensive numerical tests are performed on
turbulent channel flows at various Reynolds numbers and additionally on two
complex flows, i.e., flow over periodic hills and flow in a square duct.
Results suggest that the proposed metric can adequately explain observations in
previous studies, i.e., deteriorated model conditioning with increasing
Reynolds number and better conditioning of the implicit treatment of Reynolds
stress compared to the explicit treatment. This metric can play critical roles
in the future development of data-driven turbulence models by enforcing the
conditioning as a requirement on these models.Comment: 35 pages, 18 figure
Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble
In diamond, the mechanical vibration induced strain can lead to interaction
between the mechanical mode and the nitrogen-vecancy (NV) centers. In this
work, we propose to utilize the strain induced coupling for the quantum
non-demolition (QND) single phonon measurement and memory in diamond. The
single phonon in a diamond mechanical resonator can be perfectly absorbed and
emitted by the NV centers ensemble (NVE) with adiabatically tuning the
microwave driving. An optical laser drives the NVE to the excited states, which
have much larger coupling strength to the mechanical mode. By adiabatically
eliminating the excited states under large detuning limit, the effective
coupling between the mechanical mode and the NVE can be used for QND
measurement of the single phonon state. Under realistic experimental
conditions, we numerically simulate the scheme. It is found that the fidelity
of the absorbing and emitting process can reach a much high value. The overlap
between the input and the output phonon shapes can reach .Comment: 7 pages, 3 figure
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