MODELING AND ANALYSIS OF PARAMETRIC OPTIMIZATION OF THE MASS OF A CLOSED PLANETARY MECHANISM FORMED BY TWO SIMPLE PLANETARY MECHANISMS OF JAMES

The mathematical model of estimation of a design mass of the closed planetary mechanism formed from two simple planetary mechanisms of James (mechanism of type ), taking into account their structural diagrams and design constraints, determined by the conditions of contact and bending strengths of external gearing of sun gears and satellites, is offered. A model is a dimensionless function (analogue of mass) of two variables – transmission relations of simple planetary mechanisms, and set of numerical parameters. As parameters of analogue of mass coefficients are chosen, characterizing the models of mass of gear wheels and carriers, structural and strength limitations of the external gearing of simple planetary mechanisms of the type , and also structure of these mechanisms. In the program Mathcad differential properties of the offered model and influence on position of minimum of analogue of mass are investigational depending on the numerical values of his parameters. Documents of the Mathcad program are presented that implement computer modeling of algorithms for parametric optimization of mass closed planetary mechanism, where the function of the analogue of the mass of the given mechanism is used as the objective function. A comparative analysis of minimizing the design mass of two kinematic schemes of planetary mechanisms is considered – closed planetary mechanism and in-line planetary of the type . Keywords: simple planetary mechanism of James, simple planetary mechanism type ; closed planetary mechanism; in-line planetary mechanism; mass of closed planetary mechanism; contact strength of gearing; bending strength of gearing; parametric optimization; parametric optimization of mass of planetary mechanism

Counterexamples to the Maximum Force Conjecture

Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity F*=c4/GN with the dimensions of force (equivalently, tension). Then in any physical situation we must have Fphysical=fF*, where the quantity f is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields f=O(1), and quite often f≤1/4. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.

Irreversibility in dynamical phases and transitions

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a measure of irreversibility we term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales. We use this scalar, dimensionless function to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We measure the total energetic cost of establishing synchronized biochemical oscillations while simultaneously quantifying the distribution of irreversibility across spatiotemporal frequencies.

Analytical stability in the Caledonian Symmetric Five-Body Problem

In this paper, we develop an analytical stability criterion for a five-body symmetrical system, called the Caledonian Symmetric Five-Body Problem (CS5BP), which has two pairs of equal masses and a fifth mass located at the centre of mass. The CS5BP is a planar problem that is configured to utilise past–future symmetry and dynamical symmetry. The introduction of symmetries greatly reduces the dimensions of the five-body problem. Sundman’s inequality is applied to derive boundary surfaces to the allowed real motion of the system. This enables the derivation of a stability criterion valid for all time for the hierarchical stability of the CS5BP. We show that the hierarchical stability depends solely on the Szebehely constant $$C_0$$ C 0 which is a dimensionless function involving the total energy and angular momentum. We then explore the effect on the stability of the whole system of varying the relative sizes of the masses. The CS5BP is hierarchically stable for $$C_0 > 0.065946$$ C 0 > 0.065946 . This criterion can be applied in the investigation of the stability of quintuple hierarchical stellar systems and symmetrical planetary systems.

Effective modules of two-phase construction composites with grain filler

In the book of R.M. Christensen, “Introduction to the Mechanics of Composites” (1982), a calculation formula is given for the bulk module of polydisperse composites with spherical inclusions. This formula has been known to the Russianspeaking reader for almost 40 years, but unfortunately, it is not used in the practice of building materials science. To identify applied possibilities, R.M. Christensen's formula is modified and reduced to a dimensionless function k = k ( w , η, θ), which depends on three dimensionless parameters, i.e., it depends on three quantities: w is the volume fraction of the inclusion, η - the ratio of the shear modulus of the matrix material to the volume modulus of the same matrix, θ is the ratio of the volume moduli of the matrix materials and inclusion. Numerical studies of this function reveal that in two-phase granular composites, the range of effective moduli is significantly narrowed compared to the region limited by Voigt and Reuss estimates (in the sense of the upper and lower bounds of real values). At the same time, the lower Christensen score is the same as the Reuss score. Numerical and graphically presented results are given on the examples of the study of two characteristic groups of composite materials. In addition, the dimensionless form of the effective module allows to construct a system of visual graphic dependencies of the functions k ( w ) in a flat space k - w . For different values of θ, the function k = k ( w , η) displays a bunch of curved segments, which sets the position of the plane figure in flat space. Examples of constructing figures for characteristic regions of the values of the function k (η, θ, w ) are given.

Experimental Validation of a Pore-Scale-Derived Dimensionless Capillary Pressure Function for Imbibition Under Mixed-Wet Conditions

Summary We validate experimentally a dimensionless capillary pressure function for imbibition at mixed-wet conditions that we developed recently on the basis of pore-scale modeling in rock images. The difference from Leverett's traditional J-function is that our dimensionless function accounts for wettability and initial water saturation after primary drainage through area-averaged, effective contact angles that depend on the wetting property and distribution of oil- and water-wet grain surfaces. In the present work, we adopt the dimensionless function to scale imbibition capillary pressure data measured on mixed-wet sandstone and chalk cores. The measured data practically collapse to a unique curve when subjected to the dimensionless capillary pressure function. For each rock material, we use the average dimensionless curve to reproduce the measured capillary pressure curves and obtain excellent agreement. We also demonstrate two approaches to generate different capillary pressure curves at other mixed-wettability states than that available from the data used to generate the dimensionless curve. The first approach changes the shape of the spontaneous- and forced-imbibition segments of the capillary pressure curve whereas the saturation at zero capillary pressure is constant. The second approach shifts the vertical level of the entire capillary pressure curve, such that the Amott wetting index (and the saturation at zero capillary pressure) changes accordingly. Thus, integrating these two approaches with the dimensionless function yields increased flexibility to account for different mixed-wettability states. The validated dimensionless function scales mixed-wet capillary pressure curves from core samples accurately, which demonstrates its applicability to describe variations of wettability and permeability with capillary pressure in reservoir-simulation models. This allows for improved use of core experiments in predicting reservoir performance. Reservoir-simulation models can also use the dimensionless function together with existing capillary pressure correlations.

Analysis of the effects of conical indentation variables on the indentation response of elastic–plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load–depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 26 was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/hmax, n, θ, E, and hmax. The dimensional variables E and hmax were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/hmax was obtained with two different hmax values. A set of dimensionless functions was defined to analyze the effect of the input variables: Π1 = Pl/Eh2, Π2 = hc/h, Π3 = H/Y, Π4= S/Ehmax, Π6 = hmax/hf, and Π7 = Wp/WT. These six functions were found to depend only on the dimensionless variables studied (Y/E, R/hmax, n, θ). Another dimensionless function, Π5 = β, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on β was θ. However, β showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that β is especially susceptible to the error in the calculation of the initial unloading slope.

Features of stable diffuse arcs observed by means of auroral tomography

In this paper we study the spatial distribution of optical volume emission rates and peculiarities of the luminosity intensity within weak diffuse auroral arcs recovered by means of auroral tomography. The tomographic images are obtained from sets of scanning multi-channel photometer data obtained in February 1999 on the Kola Peninsula in Russia at three sites of a chain extending 226 km along the geomagnetic meridian. The 427.8- and 557.7-nm emissions of a 15-s time resolution observed within one hour during low geomagnetic activity are analyzed. We found that the intensity profile of an individual arc along the geomagnetic meridian has an inverted-V-shape. The luminosity maximum altitude decrease by 4–14 km at about 140 km distance in the south-north direction can be observed during two or more diffuse arcs. The parameters of the precipitating electron flux are obtained from an integral equation, which determines the best relationship between the 427.8-nm intensity height profile and an arbitrary particle energy spectrum. A dimensionless function of the energy dissipation is used as the core in the integral equation. The estimated average energy of electron flux, which generated the isolated diffuse arc, is 1–2 keV higher in the central part of the arc in comparison to values at its borders.

Flashback Limit and Mechanism of Methane and Syngas Fuel

Flashback is one of the major problems in lean premixed combustion of gas turbine combustor. Due to the effulgent future of co-product system and IGCC, lean premixed combustion, one of the approaches to ultra low NOx for rich hydrogen syngas fuel need farther research on anti-flashback and low pressure drop combustor. Mechanism and characteristics of methane and syngas flashback for 2 types of flame holders, i.e. ring shape and rod shape have been researched through experiment as well as numerical simulation. The partial premix model has been selected to simulate premixed combustion flashback process since it combined the advantage of PDF model and TFC model. Experiments demonstrate that, the flashback velocity of different fuel compositions or flame holder size generally can be correlated to the same dimensionless function by using Peclet number model if the structures of flame holders are the same. Peclet function curves were used to compare the anti-flashback performance of the 2 types of flame holders mentioned above with swirl holder. Boundary coaxial jet can change flashback through the wall into flashback in the core flow and significantly improve the anti-flashback performance of the ring-type flame holder on condition that the velocity of the boundary coaxial jet is in an optimal range. As the result, ring shape holder shows the best while swirl holder the worst on anti-flashback performance.