Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

Diagnostics of accelerating plasma Semiannual progress report, 1 Sep. 1968 - 28 Feb. 1969

Accelerating plasma diagnostics - validity of local thermal equilibrium assumption in electromagnetic shock tubes, and current-sheet velocity in coaxial plasma accelerato

Diagnostics of accelerating plasma Semiannual progress report, 1 Mar. - 31 Aug. 1968

Plasma diagnostics in electromagnetically driven shock tubes using laser scattering methods as compared to spectroscopic technique

Exchange coupling between two ferromagnetic electrodes separated by a graphene nanoribbon

In this study, based on the self-energy method and the total energy calculation, the indirect exchange coupling between two semi-infinite ferromagnetic strips (FM electrodes) separated by metallic graphene nanoribbons (GNRs) is investigated. In order to form a FM/GNR/FM junction, a graphitic region of finite length is coupled to the FM electrodes along graphitic zigzag or armchair interfaces of width $N$. The numerical results show that, the exchange coupling strength which can be obtained from the difference between the total energies of electrons in the ferromagnetic and antiferromagnetic couplings, has an oscillatory behavior, and depends on the Fermi energy and the length of the central region.Comment: 4 pages, 6 figures, International Conference on Theoretical Physics 'Dubna-Nano2008

AC and DC House Wiring Efficiency Estimations Using a Fast Extensive Measurements Approach

DC-based appliances are exponentially increasing in the present market. This scenario opens the opportunity to utilize the DC electricity produced by the PV panels directly without going through the conversion stages. Due to high penetration of DC electricity sources, it is timely to utilize DC electricity directly. Several research works have been reported in the literature to experimentally test and compare AC and DC wiring options. Accurate and precise experimental measurements are vital to establish a sound theoretical basis. However, this is difficult due to cost and time constraints. Therefore, to avoid costly measurements, this paper develops a mathematical model based on measurements on selected AC and DC wiring at four voltage levels (12 V DC, 24 V DC, 48 V DC, and 230 V AC). A digital simulation calibration using DigSilent is conducted to validate the proposed mathematical model. This paper proposed to utilize the simulation calibration approach that is a cost-effective and timesaving option to perform extensive measurements accurately

New reduction factor for Cracked Square hollow section K-joints

Cracks are commonly observed at the hot spot stress location of tubular joints and it can be due to fatigue, accidental damage or corrosion. As a consequence, the plastic collapse load (Pc) of the tubular joints is reduced, and hence it is necessary to produce design guidance which can safely be used to estimate the static residual strength of cracked tubular structures in practice. This paper proposes a new expression for determining the reduction factor (FAR) of cracked square hollow section (SHS) K-joints. A completely new and robust finite element mesh generator which is validated using the full scale experimental test results is used for the parametric study to propose the new FAR expressions for cracked SHS K-joints. The crack area and the brace to chord width ratio (β) are shown to have the most profound effect on the Pc load of cracked SHS K-joints. For a given value of crack area, the variation of the FAR values is up to 3.6% for different values of β. Furthermore, the FAR values calculated using the existing equation given in the latest BS 7910:2013 + A1:2015 for circular hollow section (CHS) joints are revealed to be conservative up to 23.5%

Meridional Transport in the Stratosphere of Jupiter

The Cassini measurements of C$_2$H$_2$ and C$_2$H$_6$ at $\sim$5 mbar provide a constraint on meridional transport in the stratosphere of Jupiter. We performed a two-dimensional photochemical calculation coupled with mass transport due to vertical and meridional mixing. The modeled profile of C$_2$H$_2$ at latitudes less than 70$^\circ$ follows the latitude dependence of the solar insolation, while that of C$_2$H$_6$ shows little latitude dependence, consistent with the measurements. In general, our model study suggests that the meridional transport timescale above 5-10 mbar altitude level is $\gtrsim$1000 years and the time could be as short as 10 years below 10 mbar level, in order to fit the Cassini measurements. The derived meridional transport timescale above the 5 mbar level is a hundred times longer than that obtained from the spreading of gas-phase molecules deposited after the impact of Shoemaker-Levy 9 comet. There is no explanation at this time for this discrepancy.Comment: 11 pages, 3 figures, 1 table. ApJL in pres

The Energy of a Plasma in the Classical Limit

When \lambda_{T} << d_{T}, where \lambda_{T} is the de Broglie wavelength and d_{T}, the distance of closest approach of thermal electrons, a classical analysis of the energy of a plasma can be made. In all the classical analysis made until now, it was assumed that the frequency of the fluctuations \omega << T (k_{B}=\hbar=1). Using the fluctuation-dissipation theorem, we evaluate the energy of a plasma, allowing the frequency of the fluctuations to be arbitrary. We find that the energy density is appreciably larger than previously thought for many interesting plasmas, such as the plasma of the Universe before the recombination era.Comment: 10 pages, 2 figures, accepted for publication in Phys.Rev.Let

Морфологические изменения в нижнеальвеолярном нерве на экспериментальной модели его травмы разной степени тяжести

У роботі на 40 лабораторних щурах досліджено закономірності та патоморфологічні зміни у нижньоальвеолярному нерві й параневральных тканинах у різний термін після операції, що викликані різним ступенем дії травмуючого фактору.During the experiments on 40 laboratory rodents we have studied the regularities and pathomorphological changes in lower dental nerve and paraneural tissues induced by disturbing factor of varying influence intensity observed at different postoperative periods

A simulation study on the abatement of CO2 emissions by de-absorption with monoethanolamine

Because of the adverse effect of CO2 from fossil fuel combustion on the earth's ecosystems, the most cost-effective method for CO2 capture is an important area of research. The predominant process for CO2 capture currently employed by industry is chemical absorption in amine solutions. A dynamic model for the de-absorption process was developed with monoethanolamine (MEA) solution. Henry's law was used for modelling the vapour phase equilibrium of the CO2, and fugacity ratios calculated by the Peng-Robinson equation of state (EOS) were used for H2O, MEA, N-2 and O-2. Chemical reactions between CO2 and MEA were included in the model along with the enhancement factor for chemical absorption. Liquid and vapour energy balances were developed to calculate the liquid and vapour temperature, respectively