42,963 research outputs found
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
Density-functional investigation of the rhombohedral to simple cubic phase transition of arsenic
We report on our investigation of the crystal structure of arsenic under
compression, focusing primarily on the pressure-induced A7 to simple cubic (sc)
phase transition. The two-atom rhombohedral unit cell is subjected to pressures
ranging from 0 GPa to 200 GPa; for each given pressure, cell lengths and
angles, as well as atomic positions, are allowed to vary until the fully
relaxed structure is obtained. We find that the nearest and next-nearest
neighbor distances give the clearest indication of the occurrence of a
structural phase transition. Calculations are performed using the local density
approximation (LDA) and the PBE and PW91 generalized gradient approximations
(GGA-PBE and GGA-PW91) for the exchange-correlation functional. The A7 to sc
transition is found to occur at 21+/-1 GPa in the LDA, at 28+/-1 GPa in the
GGA-PBE and at 29+/-1 GPa in the GGA-PW91; no volume discontinuity is observed
across the transition in any of the three cases. We use k-point grids as dense
as 66X66X66 to enable us to present reliably converged results for the A7 to sc
transition of arsenic.Comment: To be published in Physical Review B; material supplementary to this
article is available at arXiv:0810.169
Time-dependent universal conductance fluctuations in mesoscopic Au wires: implications
In cold, mesoscopic conductors, two-level fluctuators lead to time-dependent
universal conductance fluctuations (TDUCF) manifested as noise. In Au
nanowires, we measure the magnetic field dependence of TDUCF, weak localization
(WL), and magnetic field-driven (MF) UCF before and after treatments that alter
magnetic scattering and passivate surface fluctuators. Inconsistencies between
and strongly suggest either that the
theory of these mesoscopic phenomena in weakly disordered, highly pure Au is
incomplete, or that the assumption that the TDUCF frequency dependence remains
to very high frequencies is incorrect. In the latter case, TDUCF in
excess of expectations may have implications for decoherence in
solid-state qubits.Comment: 8 pages, 9 figures, accepted to PR
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Energy and CO2 implications of decarbonization strategies for China beyond efficiency: Modeling 2050 maximum renewable resources and accelerated electrification impacts
Energy efficiency has played an important role in helping China achieve its domestic and international energy and climate change mitigation targets, but more significant near-term actions to decarbonize are needed to help China and the world meet the Paris Agreement goals. Accelerating electrification and maximizing supply-side and demand-side renewable adoption are two recent strategies being considered in China, but few bottom-up modeling studies have evaluated the potential near-term impacts of these strategies across multiple sectors. To fill this research gap, we use a bottom-up national end-use model that integrates energy supply and demand systems and conduct scenario analysis to evaluate even lower CO2 emissions strategies and subsequent pathways for China to go beyond cost-effective efficiency and fuel switching. We find that maximizing non-conventional electric and renewable technologies can help China peak its national CO2 emissions as early as 2025, with significant additional CO2 emission reductions on the order of 7 Gt CO2 annually by 2050. Beyond potential CO2 reductions from power sector decarbonization, significant potential lies in fossil fuel displaced by renewable heat in industry. These results suggest accelerating the utilization of non-conventional electric and renewable technologies present additional CO2 reduction opportunities for China, but new policies and strategies are needed to change technology choices in the demand sectors. Managing the pace of electrification in tandem with the pace of decarbonization of the power sector will also be crucial to achieving CO2 reductions from the power sector in a scenario of increased electrification
Information Erasure and Recover in Quantum Memory
We show that information in quantum memory can be erased and recovered
perfectly if it is necessary. That the final states of environment are
completely determined by the initial states of the system allows that an easure
operation can be realized by a swap operation between system and an ancilla.
Therefore, the erased information can be recoverd. When there is an
irreversible process, e.g. an irreversible operation or a decoherence process,
in the erasure process, the information would be erased perpetually. We present
that quantum erasure will also give heat dissipation in environment. And a
classical limit of quantum erasure is given which coincides with Landauer's
erasure principle.Comment: PACS: 0365.Bz. 03.67.Hk;3page
Cavity QED treatment of scattering-induced efficient free-space excitation and collection in high-Q whispering-gallery microcavities
Whispering-gallery microcavity laser possesses ultralow threshold, whereas
convenient free-space optical excitation and collection suffer from low
efficiencies due to its rotational symmetry. Here we analytically study a
three-dimensional microsphere coupled to a nano-sized scatterer in the
framework of quantum optics. It is found that the scatterer is capable of
coupling light in and out of the whispering-gallery modes (WGMs) without
seriously degrading their high-Q properties, while the microsphere itself plays
the role of a lens to focus the input beam on the scatterer and vice versa. Our
analytical results show that (1) the high-Q WGMs can be excited in free space,
and (2) over 50% of the microcavity laser emission can be collected within less
than . This coupling system holds great potential for low
threshold microlasers free of external couplers.Comment: 10 pages, 8 figure
Building stock dynamics and its impacts on materials and energy demand in China
China hosts a large amount of building stocks, which is nearly 50 billion square meters. Moreover, annual new construction is growing fast, representing half of the world's total. The trend is expected to continue through the year 2050. Impressive demand for new residential and commercial construction, relative shorter average building lifetime, and higher material intensities have driven massive domestic production of energy intensive building materials such as cement and steel. This paper developed a bottom-up building stock turnover model to project the growths, retrofits and retirements of China's residential and commercial building floor space from 2010 to 2050. It also applied typical material intensities and energy intensities to estimate building materials demand and energy consumed to produce these building materials. By conducting scenario analyses of building lifetime, it identified significant potentials of building materials and energy demand conservation. This study underscored the importance of addressing building material efficiency, improving building lifetime and quality, and promoting compact urban development to reduce energy and environment consequences in China
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