Efficiency of gas cooling and accretion at the disc-corona interface

In star-forming galaxies, stellar feedback can have a dual effect on the circumgalactic medium both suppressing and stimulating gas accretion. The trigger of gas accretion can be caused by disc material ejected into the halo in the form of fountain clouds and by its interaction with the surrounding hot corona. Indeed, at the disc-corona interface, the mixing between the cold/metal-rich disc gas (T ~ 10^6 K) can dramatically reduce the cooling time of a portion of the corona and produce its condensation and accretion. We studied the interaction between fountain clouds and corona in different galactic environments through parsec-scale hydrodynamical simulations, including the presence of thermal conduction, a key mechanism that influences gas condensation. Our simulations showed that the coronal gas condensation strongly depends on the galactic environment, in particular it is less efficient for increasing virial temperature/mass of the haloes where galaxies reside and it is fully ineffective for objects with virial masses larger than 10^13 Msun. This result implies that the coronal gas cools down quickly in haloes with low-intermediate virial mass (Mvir <~ 3 x 10^12 Msun) but the ability to cool the corona decreases going from late-type to early-type disc galaxies, potentially leading to the switching off of accretion and the quenching of star formation in massive systems.Comment: 14 pages, 8 figures, accepted for publication in MNRA

Mixing of metals during star cluster formation: statistics and implications for chemical tagging

Ongoing surveys are in the process of measuring the chemical abundances in large numbers of stars, with the ultimate goal of reconstructing the formation history of the Milky Way using abundances as tracers. However, interpretation of these data requires that we understand the relationship between stellar distributions in chemical and physical space, i.e., how similar in chemical abundance do we expect a pair of stars to be as a function of the distance between their formation sites. We investigate this question by simulating the gravitational collapse of a turbulent molecular cloud extracted from a galaxy-scale simulation, seeded with chemical inhomogeneities with different initial spatial scales. We follow the collapse from galactic scales down to resolutions scales of $\approx 10^{-3}$ pc, and find that, during this process, turbulence mixes the metal patterns, reducing the abundance scatter initially present in the gas by an amount that depends on the initial scale of inhomogeneity of each metal field. However, we find that regardless of the initial spatial structure of the metals at the onset of collapse, the final stellar abundances are highly correlated on distances below a few pc, and nearly uncorrelated on larger distances. Consequently, the star formation process defines a natural size scale of $\sim 1$ pc for chemically-homogenous star clusters, suggesting that any clusters identified as homogenous in chemical space must have formed within $\sim 1$ pc of one another. However, in order to distinguish different star clusters in chemical space, observations across multiple elements will be required, and the elements that are likely to be most efficient at separating distinct clusters in chemical space are those whose correlation length in the ISM is of order tens of pc, comparable to the sizes of individual molecular clouds.Comment: 15 pages, 10 figures; submitted to MNRA

Tolerance Analysis Considering form Errors in Planar Datum Features

The paper investigates the role of planar datum features in tolerance analysis problems. Mating relations between datum planes are shown to involve translational and rotational errors, which are related to form tolerances and are usually neglected in tolerance analysis. To evaluate these errors, the contact between datum planes was simulated by a stochastic model, where two surface profiles are randomly generated and then registered to reproduce a mating condition. Concepts of fractal geometry were exploited to make the generation consistent with the autocorrelation properties of actual surfaces resulting from manufacturing processes. A simulation plan allowed to predict the amount of contact errors as a function of size, tolerance and process-related assumptions on the two features. An example of 3D tolerance chain is presented to demonstrate the relevance of form errors in the variation of assembly requirements

A static analogy for 2D tolerance analysis

Purpose - This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data. Design/methodology/approach - The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain into a corresponding static problem, which can be solved by common algebraic or graphical procedures. Findings - The static analogy leads to a correct treatment of tolerance chains, as the analysis of several examples has confirmed by comparison to alternative methods. Research limitations/implications - Currently, the method has only been tested on two-dimensional chains of linear dimensions for assemblies with nonredundant kinematic constraints among parts. Practical implications - The proposed method lends itself to ready application by using simple operations with minimal software assistance. This could make it complementary to current methods for calculating sensitivities, which are mathematically complex and require software implementation for deployment in industrial practice. Originality/value - Analogy with force analysis, which has not been previously highlighted in the literature, is a potentially interesting concept that could be extended to a wider range of tolerancing problems

Solving basic problems of compliant tolerance analysis by static analogy

Predicting the geometric variation of sheet metal assemblies is a complex task, because deformation during joining operations influences the propagation of initial part deviations. To consider this effect, the paper proposes a method that formulates tolerance analysis as an equivalent problem of static analysis. Previously proposed for rigid parts, the static analogy is extended to compliant parts and applied to two-dimensional problems modeled with straight beams under the assumptions of small displacements and normal distributions of errors. For such simple cases, the method solves the problem by linearization, avoiding the use of Monte Carlo simulation and the related computational burden. Compared to existing linearization methods, the static analogy is less efficient in the integration with a finite element solver. However, it features an especially simple procedure that does not require the calculation of deflections, thus allowing a streamlined solution and even manual calculations. The comparison with alternative methods provides a first verification of the feasibility of the method, in view of further developments with the aim of dealing with cases of realistic complexity

Allocation of geometric tolerances in one-dimensional stackup problems

Many tolerancing problems on mechanical assemblies involve a functional requirement depending on a chain of parallel dimensions on individual parts. In these one-dimensional cases, simple methods are available for the analysis and the allocation of dimensional tolerances. However, they are difficult to extend to geometric tolerances, which must be translated into equivalent dimensional tolerances; this allows the analysis but makes the allocation generally impossible without Monte Carlo simulation and complex search strategies. To overcome this difficulty, the paper proposes a way of dealing directly with geometric tolerances in the allocation problem. This consists in expressing the functional requirement as a linear model of geometric tolerances rather than equivalent dimensional tolerances; the coefficients of the model (sensitivities) are calculated considering both the dimension chain and the standard definition of the geometric tolerances. The approach can be combined with any constrained optimization method based on sensitivities. The optimal scaling method, previously proposed for dimensional tolerances, is extended to geometric tolerances and used in two examples to demonstrate the simplicity of the overall workflow and the quality of the optimal solution

Estimating the cost of functional requirements for tolerance allocation on mechanical assemblies

When allocating tolerances to geometric features of machine parts, a target variation must be specified for some functional requirements on the assembly. Such decision, however, is usually made from experience without consideration of its effect on manufacturing cost. To allow such an assessment, the paper describes a method for estimating the cost of a requirement as a function of its variation. The estimation can be done before solving a tolerance allocation problem, at the time the variation on the requirement is chosen as an optimization constraint. A simple expression for the cost of requirements of various types is obtained using the extended reciprocal-power function for the cost of part tolerances, and the optimal scaling method for tolerance allocation. As a result, the costs of both requirement variations and part tolerances can be treated in the same way; this allows a hierarchical approach to tolerance allocation, which can simplify the problem when dealing with complex dimension chains. Furthermore, simple calculations based on the proposed method suggest general cost reduction criteria in the design of assemblies

Technology Pooling Licensing Agreements: Promoting Patent Access Through Collaborative IP Mechanisms

In patent communities several patentees cooperate contractually to licence the respective patented technologies to third parties. In consideration of the rising relevance of this business practice, this book discusses crucial courses and strategic considerations, which are the basis for the establishment of patent communities, both in legal and empirical regard, in order to identify the optimal conditions for successful conversion in a competitive surrounding. Thus the best conditions for the promotion of innovation are to be created

Tolerance analysis by static analogy on 2D assemblies with fits and fasteners

In tolerance analysis, the effect of clearance fits is especially difficult to estimate because the mating parts are not necessarily in actual contact and can take an infinite number of relative positions. The treatment of these situations is allowed in most of the available methods, possibly introducing additional elements in the dimension chains with appropriate statistical assumptions. The paper provides a similar extension for the static analogy, a previously proposed method that converts the tolerance analysis problem into an equivalent problem of force analysis. The procedure represents each fit, possibly between patterns of features (e.g., fasteners and holes), with a proper constraint in the equivalent static model. The ability of the constraint to transmit forces and torques is determined according to the types and directions of misalignments allowed by the joint clearance. With simple rules, this avoids complications in the static model, which must include only the constraint between parts rather than the geometric details of the mating features. The extended method, currently limited to 2D dimension chains, is demonstrated on examples involving both dimensional and geometric tolerances. The comparison with existing methods shows the correctness of the proposed procedure. The simplicity of the workflow confirms the possibility, already demonstrated for the static analogy, of avoiding numerical simulations or even the use of computer-based tools

The survival of gas clouds in the Circumgalactic Medium of Milky Way-like galaxies

Observational evidence shows that low-redshift galaxies are surrounded by extended haloes of multiphase gas, the so-called 'circumgalactic medium' (CGM). To study the survival of relatively cool gas (T < 10^5 K) in the CGM, we performed a set of hydrodynamical simulations of cold (T = 10^4 K) neutral gas clouds travelling through a hot (T = 2x10^6 K) and low-density (n = 10^-4 cm^-3) coronal medium, typical of Milky Way-like galaxies at large galactocentric distances (~ 50-150 kpc). We explored the effects of different initial values of relative velocity and radius of the clouds. Our simulations were performed on a two-dimensional grid with constant mesh size (2 pc) and they include radiative cooling, photoionization heating and thermal conduction. We found that for large clouds (radii larger than 250 pc) the cool gas survives for very long time (larger than 250 Myr): despite that they are partially destroyed and fragmented into smaller cloudlets during their trajectory, the total mass of cool gas decreases at very low rates. We found that thermal conduction plays a significant role: its effect is to hinder formation of hydrodynamical instabilities at the cloud-corona interface, keeping the cloud compact and therefore more difficult to destroy. The distribution of column densities extracted from our simulations are compatible with those observed for low-temperature ions (e.g. SiII and SiIII) and for high-temperature ions (OVI) once we take into account that OVI covers much more extended regions than the cool gas and, therefore, it is more likely to be detected along a generic line of sight.Comment: 12 pages, 10 figures. Accepted for publication in MNRA