The effects of the model errors generated by discretization of 'on-off'' processes on VDA

Through an idealized model of a partial differential equation with discontinuous 'on-off'' switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical 'on-off'' processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with 'on-off'' switches is also examined. The theoretical analyses illustrate that in the analytic case, the gradient of the associated cost function (CF) with respect to an initial condition (IC) exists provided that the IC does not trigger the threshold condition. But in the discrete case, if the on switches (or off switches) in the forward model are straightforwardly assigned the nearest time level after the threshold condition is (or is not) exceeded as the usual treatment, the discrete CF gradients (even the one-sided gradient of CF) with respect to some ICs do not exist due to the model error, which is the difference between the analytic and numerical solutions to the governing equation. Besides, the solution of the corresponding tangent linear model (TLM) obtained by the conventional approach would not be a good first-order linear approximation to the nonlinear perturbation solution of the governing equation. Consequently, the validity of the adjoint approach in VDA with parameterized physical processes could not be guaranteed. Identical twin numerical experiments are conducted to illustrate the influences of these problems on VDA when using adjoint method. The results show that the VDA outcome is quite sensitive to the first guess of the IC, and the minimization processes in the optimization algorithm often fail to converge and poor optimization retrievals would be generated as well. Furthermore, the intermediate interpolation treatment at the switch times of the forward model, which reduces greatly the model error brought by the traditional discretization of 'on-off'' processes, is employed in this study to demonstrate that when the 'on-off'' switches in governing equations are properly numerically treated, the validity of the adjoint approach in VDA with discontinuous physical 'on-off'' processes can still be guaranteed

The effects of the model errors generated by discretization of "on-off'' processes on VDA

International audienceThrough an idealized model of a partial differential equation with discontinuous "on-off'' switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical "on-off'' processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with "on-off'' switches is also examined. The theoretical analyses illustrate that in the analytic case, the gradient of the associated cost function (CF) with respect to an initial condition (IC) exists provided that the IC does not trigger the threshold condition. But in the discrete case, if the on switches (or off switches) in the forward model are straightforwardly assigned the nearest time level after the threshold condition is (or is not) exceeded as the usual treatment, the discrete CF gradients (even the one-sided gradient of CF) with respect to some ICs do not exist due to the model error, which is the difference between the analytic and numerical solutions to the governing equation. Besides, the solution of the corresponding tangent linear model (TLM) obtained by the conventional approach would not be a good first-order linear approximation to the nonlinear perturbation solution of the governing equation. Consequently, the validity of the adjoint approach in VDA with parameterized physical processes could not be guaranteed. Identical twin numerical experiments are conducted to illustrate the influences of these problems on VDA when using adjoint method. The results show that the VDA outcome is quite sensitive to the first guess of the IC, and the minimization processes in the optimization algorithm often fail to converge and poor optimization retrievals would be generated as well. Furthermore, the intermediate interpolation treatment at the switch times of the forward model, which reduces greatly the model error brought by the traditional discretization of "on-off'' processes, is employed in this study to demonstrate that when the "on-off'' switches in governing equations are properly numerically treated, the validity of the adjoint approach in VDA with discontinuous physical "on-off'' processes can still be guaranteed

Macroscopical Entangled Coherent State Generator in V configuration atom system

In this paper, we propose a scheme to produce pure and macroscopical entangled coherent state. When a three-level ''V'' configuration atom interacts with a doubly reasonant cavity, under the strong classical driven condition, entangled coherent state can be generated from vacuum fields. An analytical solution for this system under the presence of cavity losses is also given

Mechanism of cellular uptake of genotoxic silica nanoparticles.

Mechanisms for cellular uptake of nanoparticles have important implications for nanoparticulate drug delivery and toxicity. We have explored the mechanism of uptake of amorphous silica nanoparticles of 14 nm diameter, which agglomerate in culture medium to hydrodynamic diameters around 500 nm. In HT29, HaCat and A549 cells, cytotoxicity was observed at nanoparticle concentrations ≥ 1 μg/ml, but DNA damage was evident at 0.1 μg/ml and above. Transmission electron microscopy (TEM) combined with energy-dispersive X-ray spectroscopy confirmed entry of the silica particles into A549 cells exposed to 10 μg/ml of nanoparticles. The particles were observed in the cytoplasm but not within membrane bound vesicles or in the nucleus. TEM of cells exposed to nanoparticles at 4°C for 30 minutes showed particles enter cells when activity is low, suggesting a passive mode of entry. Plasma lipid membrane models identified physical interactions between the membrane and the silica NPs. Quartz crystal microbalance experiments on tethered bilayer lipid membrane systems show that the nanoparticles strongly bind to lipid membranes, forming an adherent monolayer on the membrane. Leakage assays on large unilamellar vesicles (400 nm diameter) indicate that binding of the silica NPs transiently disrupts the vesicles which rapidly self-seal. We suggest that an adhesive interaction between silica nanoparticles and lipid membranes could cause passive cellular uptake of the particles

Офорт Олени Кульчицької “За море” і тема еміграції

Illustrators of the Ukrainian press at the 2nd half ХІХ to еarly XX c. and an artist Olena Kul’chitska is known consider the theme of еmigration and expressed it in the form of social satire

Hawking Radiation of an Arbitrarily Accelerating Kinnersley Black Hole: Spin-Acceleration Coupling Effect

The Hawking radiation of Weyl neutrinos in an arbitrarily accelerating Kinnersley black hole is investigated by using a method of the generalized tortoise coordinate transformation. Both the location and temperature of the event horizon depend on the time and on the angles. They coincide with previous results, but the thermal radiation spectrum of massless spinor particles displays a kind of spin-acceleration coupling effect.Comment: 8 pages, no figure, revtex 4.0, revisted version with typesetting errors and misprint correcte

Tissue-specific Accumulation of Flavonoids in Grape Berries is Related to Transcriptional Expression of VvF3′H and VvF3′5′H

The products and the related gene expression of flavonoid metabolism were examined in the skin and pulpof Yan73 (Vitis vinifera L. cv.) grapes, a teinturier variety cultivated in China, and the data were comparedwith those in the skin and pulp of Cabernet Sauvignon (Vitis vinifera L. cv.) grapes, a well-known redvariety. The results showed that, in comparison with the skins of Cabernet Sauvignon, the skins of Yan73berries were characterised by fewer types of flavonols and anthocyanins, a higher level of flavonoids,and a much lower percentage of 3′-hydroxylated flavonols. Flavonoid metabolism was also present in thepulp of Yan73, and the percentages of 3′-hydroxylated flavonols and 3′-hydroxylated flavan-3-ols weresignificantly higher than the percentages of their corresponding 3′,5′-hydroxylated forms. Only flavan-3-ols were found in the pulp of Cabernet Sauvignon. The expression of VvmybA1 exhibited a co-ordinationwith the accumulation of anthocyanins in the pulp of the teinturier cultivar, which showed great similarityto that in the skin. A good correlation was found between the expression of VvF3′H and 3′-hydroxylatedflavonoids, as well as between the expression of VvF3′5′H and 3′,5′-hydroxylated flavonoids in the skin andpulp of the grape berries. It is suggested that tissue-specific accumulation of flavonoids in grape berries isrelated to the transcriptional expression of VvF3′H and VvF3′5′H