Study of the microscopic characteristics of a repetitive microsecond barrier discharge

Results are presented from investigations of the electric, optical, and spatial characteristics of a microsecond barrier discharge in atmospheric-pressure air in a uniform electric field. The currents in individual microscopic channels were measured by using sectioned electrodes. It is found that the first series of microscopic discharges is characterized by a relatively low current density (lower than 280 A/cm²). In the subsequent series, the microscopic discharges have a pronounced channel structure with a high current density. The prints of the channels on the metal anode have the form of microscopic craters 4 μm in diameter and 0.5 μm in depth.     

COMPOSITION OF INDOOR AEROSOLS AT EMPEROR QIN''''S TERRA-COTTA MUSEUM, XI''''AN, CHINA, DURING SUMMER, 2004

Particle samples were collected in August 2004 both inside and outside Emperor Qin's Terra-Cotta Museum in Xi'an, China. Mass and chemical composition of total suspended particles (JSP, particles with aerodynamic diameter less than-30μm), PM2.5(particles with aerodynamic diameter <2.5μm) were determined. The average levels of indoor PM2.5 and TSP were 108.4 and 172.4 μg·m-3, respectively, with PM2.5 constituting 62.9% of the TSP mass. Sulfate ((32.4±6.2)%), organics ((27.7±8.0)%), and geological material ((12.5±3.4)%) dominated indoor PM2.5, followed by ammonium ((8.9±2.8)%), nitrate ((7.0±2.9)%), and elemental carbon (EC, (3.9±1.5)%). Particle size distribution varied with the number of tourists in the museum. The size of sulfate, organics, EC, nitrate, and ammonium was found to vary in the range of 0.43 to 3.3 μm in fraction. Ion balance indicated that the aerosol was acidic, with insufficient ammonium ions to neutralize the sulfuric and nitric acids. High concentrations of acidic aerosols will erode the Terra-cotta warriors and horses especially in the summer season with high temperature (30℃) and relative humidity (70%) and undesirable solar radiation inside the museum. More attention should be paid to protecting these precious antiques made 2000 years ago.     

Local a posteriori estimates for the Stokes problem

We obtain computable estimates of the difference between an exact solution of the Stokes problem and an approximation from a respective energy class. The estimates are presented in terms of local norms and linear functionals. Certain generalizations to some nonlinear problems are discussed. Bibliography: 17 titles. Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 233–245.     

To the 75th birthday of Vsevolod Alekseevich Solonnikov

Bibliography: 45 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 5–14. Original article submitted November 27, 2008.     

A Posteriori Estimates in Local Norms

We derive a posteriori estimates for the difference between exact solutions and approximate solutions to boundary-value problems in terms of local norms. The diffusion problem, linear elasticity and generalizations to other boundary-value elliptic problems are considered. Computable estimates for the deviation from the exact solution are also obtained in terms of linear functionals. Unlike published works of other authors, the construction of such estimates is not connected with any analysis of the adjoint boundary-value problem. On the basis of multiplicative inequalities, local estimates in certain norms subject to the energy norm are derived. Bibliography: 10 titles.     

On a posteriori error estimates for the stationary Navier-Stokes problem

We obtain a computable upper bound for the difference between a solution to the stationary Navier-Stokes problem and any solenoidal vector-valued function satisfying the boundary condition and possessing necessary differentiability properties. For sufficiently small velocities this estimate implies an estimate of the deviation from exact solution in the energy norm and the uniqueness of a weak solution. Bibliography: 3 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 89–92.     

Functional a posteriori error estimates for the reaction-convection-diffusion problem

In this paper, a general form of functional type a posteriori error estimates for linear reaction-convection-diffusion problems is presented. It is derived by purely functional arguments without attracting specific properties of the approximation method. The estimate provides a guaranteed upper bound of the difference between the exact solution and any conforming approximation from the energy functional class. It is also proved that the derived error majorants give computable quantities, which are equivalent to the error evaluated in the energy and combined primal-dual norms. Bibliography: 14 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 127–146.