Post-Newtonian Kozai–Lidov mechanism and its effect on cumulative shift of periastron time of binary pulsar

ABSTRACT We study the Kozai–Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post-Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai–Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai–Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

Method of double averaging for optimum accounting of non-certainty of results of measurements greenhouse gases low gases concentrations at the ground distributed systems of atmospheric measurements

To increase effectiveness of measurements of concentration of greenhouse gases questions on optimum accounting of non-certainty of results of measurements of low gases concentrations at the ground distributed nets of atmospheric measurements are considered. It is noted that temporal and structural non-stability of atmospheric aerosol leads to occurrence of non-certainty of carried out measurements. It is suggested to use the method of non-conditional variation optimization to determine the optimum interrelation between cost functions of researched atmospheric gas and aerosol which provides best metrological support for carried out measurements. In order to form the functional of optimization the newly suggested method of double averaging is used. The matter of suggested method of double averaging is that two following different averaging operations should be carried out sequentially: geometrical weighted averaging and algebraic averaging. To form the target functional of optimization the limitation condition should be adopted which is imposed to searched for optimum function. Solution of the formulated optimization task of non-conditional variation optimization does show that upon presence of linear interrelation between scalar cost functions of gas and aerosol the target functional could reach its maximum that is the uttermost value of non-certainty of measurements results are reached. On the base of aforesaid the heuristically recommendations on necessity to form the inverse interrelation between scalar values of cost functions of researched gas and atmospheric aerosol are formulated.

Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution

A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the 18O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

Turbulent kinetic energy flux and budget in a water-worked gravel bed

Turbulent flow over a water-worked gravel bed (WGB) was investigated using the double-averaging methodology (DAM). The flow measurements were carried out by the particle image velocimetry (PIV) technique. The double-averaged (DA) turbulent characteristics (DA Turbulent kinetic energy (TKE) components, form-induced TKE components, DA TKE fluxes, form-induced TKE fluxes, DA TKE budget) were analyzed for the WGB. To understand the effect of changed bed topography on the turbulent characteristics, the flow measurements were carried out over a screeded gravel bed (SGB), keeping the flow Froude number same as in case of WGB. Owing to water work, the bed topography of WGB was dissimilar to that of SGB, resulting in higher roughness size for the former than that for the latter. Comparative study of the DA turbulent characteristics of both the beds infers that especially in the near-bed flow zone, the flow parameters of the WGB are attaining higher values than those of the SGB. However, they are almost alike for both the beds in the flow outer layer.

Stress balance for a viscous flow with a single rolling particle

One of the most important aspects in hydraulic engineering is to describe flows over mobile porous media in a continuum sense to derive models for sediment transport. This remains a challenging task due to the complex coupling of the particle and the fluid phase. Computational Fluid Dynamics can provide the data needed to understand the coupling of the two phases. To this end, we carry out grain-resolving Direct Numerical Simulations of multiphase flow. The particle phase is introduced by the Immersed Boundary Method and the particle-particle interaction is described by a sophisticated Discrete Element Method. We derive the stress budgets of the fluid and the particle phases separately through a rigorous analysis of the governing equations using the Double Averaging Methodology and the Coarse-Graining Method. As a next step, we perform a simple simulation of a heavy particle exposed to a Poiseuille flow rolling along a wall to understand the physical implications of the fluid-particle coupling. All terms of the stress balances can be computed in a straightforward manner allowing to close the budgets for the two phases separately. However, we encounter problems when attempting to combine the fluid-resolved local stresses with the coarse-grained particle stresses into a single balance for the fluid-particle mixture.

Velocity field and drag force measurements of a cube and a hemisphere mounted on an artificial bed surface roughness

Quantification of the resistance in complex roughness situations, when both bed surface and form roughnesses contribute to the total resistance, as well as partitioning of the two contributions is still unsolved. Studies about form resistance of single elements focused on obstacles mounted on smooth bed surfaces, and only few considered a rough bed surface. In order to define an approach for shear stress partitioning in open channel flows, the effect of flow conditions, the geometrical characteristics of the obstacle, and the effect of the bed surface need to be studied. This paper contributes to the topic presenting results of experiments investigating the flow field around a cube and a hemisphere mounted on a bed surface with wake interference roughness. The velocity field and the drag force exerted on the obstacles were measured with a 3D Laser Doppler Anemometer and a drag force sensor, respectively. The double averaging methodology (DAM) was applied to define the characteristic region influenced by the cube and the hemisphere, and to analyse the streamwise velocities. DAM was developed for canopy flow, thus, the methodology needed to be adapted for isolated obstacle situations. A dependency of the drag coefficient on the relative submergence is observed and analysed.

A Numerical Investigation to Study Roughness Effects in Oscillatory Flows

Effects of roughness on the near-bed turbulence characteristics in oscillatory flows are studied by means of particle-resolved direct numerical simulations (DNS). Two particle sizes of diameter 375 and 125 in wall units corresponding to the large size gravel and the small size sand particle, respectively, in a very rough turbulent flow regime are reported. A double-averaging technique is employed to study the nature of the wake field, i.e., the spatial inhomogeneities at the roughness length scale. This introduced additional production and transport terms in double-averaged Reynolds stress budget, indicating alternate pathways of turbulent energy transfer mechanisms. Budgets of normal components of Reynolds stress reveal redistribution of energy from streamwise component to other two components and is attributed to the work of pressure in both flow cases. It is shown that the large diameter gravel particles significantly modulate the near-bed flow structures, leading to pronounced isotropization of the near-bed flow; while in the sand case, elongated horseshoe structures are found as a result of high shear rate. Effect of mean shear rate on the near-bed anisotropy is significant in the sand case, while it is minimal for the gravel-bed. Redistribution of energy in the gravel case showed reduced dependence on the flow oscillations, while for the sand particle it is more pronounced towards the end of an acceleration cycle.