An approach to the Riemann problem in the light of a reformulation of the state equation for SPH inviscid ideal flows: a highlight on spiral hydrodynamics in accretion discs

In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations if flow discontinuities (the Riemann problem) are to be solved. A necessary dissipation is normally used in such cases. An explicit artificial viscosity contribution is normally adopted to smooth out spurious heating and to treat transport phenomena. Such a treatment of inviscid flows is also widely adopted in the Smooth Particle Hydrodynamics (SPH) finite volume free Lagrangian scheme. In other cases, the intrinsic dissipation of Godunov-type methods is implicitly useful. Instead "shock tracking" methods normally use the Rankine-Hugoniot jump conditions to solve such problems. A simple, effective solution of the Riemann problem in inviscid ideal gases is here proposed, based on an empirical reformulation of the equation of state (EoS) in the Euler equations in fluid dynamics, whose limit for a motionless gas coincides with the classical EoS of ideal gases. The application of such an effective solution to the Riemann problem excludes any dependence, in the transport phenomena, on particle smoothing resolution length $h$ in non viscous SPH flows. Results on 1D shock tube tests, as well as examples of application for 2D turbulence and 2D shear flows are here shown. As an astrophysical application, a much better identification of spiral structures in accretion discs in a close binary (CB), as a result of this reformulation is also shown here.Comment: 19 pages, 17 figure

An approach for solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries

In this work, we propose a SPH interpolating Kernel reformulation suitable also to treat free edge boundaries in the computational domain. Application to both inviscid and viscous stationary low compressibility accretion disc models in Close Binaries (CB) are shown. The investigation carried out in this paper is a consequence of the fact that a low compressibility modelling is crucial to check numerical reliability. Results show that physical viscosity supports a well-bound accretion disc formation, despite the low gas compressibility, when a Gaussian-derived Kernel (from the Error Function) is assumed, in extended particle range - whose Half Width at Half Maximum (HWHM) is fixed to a constant $h$ value - without any spatial restrictions on its radial interaction (hereinafter GASPHER). At the same time, GASPHER ensures adequate particle interpolations at the boundary free edges. Both SPH and adaptive SPH (hereinafter ASPH) methods lack accuracy if there are not constraints on the boundary conditions, in particular at the edge of the particle envelope: Free Edge (FE) conditions. In SPH, an inefficient particle interpolation involves a few neighbour particles; instead, in the second case, non-physical effects involve both the boundary layer particles themselves and the radial transport. Either in a regime where FE conditions involve the computational domain, or in a viscous fluid dynamics, or both, a GASPHER scheme can be rightly adopted in such troublesome physical regimes. Despite the applied low compressibiity condition, viscous GASPHER model shows clear spiral pattern profiles demonstrating the better quality of results compared to SPH viscous ones. Moreover a successful comparison of results concerning GASPHER 1D inviscid shock tube with analytical solution is also reported.Comment: 18 pages, 12 figure

Economic structure, technology diffusion and convergence - the case of the Italian regions

Over the years, Italy’s regional disparities have been the object of much investigation in the literature. Recent evidence points to a revival of the convergence process, which had come to a halt in the mid-1970s, and renews the interest in the subject. This paper aims at contributing to the debate. Endorsing the critiques of the neoclassical assumption of technology as a public good, we investigate the link between economies’ structural characteristics and their growth performance. Specifically, treating technology as sector-specific and modelling technological spillovers as a positive function of the degree of similarity between economies’ sectoral features, a modified version of the Solow model is put forward and used to derive an “extended” convergence equation. The latter is then estimated by means of Panel Data procedures and data on the Italian regions over the 1970-1995 period. The results bring empirical support to our approach. From a theoretical viewpoint, our model suggests that the effects of technology diffusion on the convergence process are twofold. Firstly, if technological progress is partly dependent on external innovations, the temporal evolution of each economy’s productivity level, and its speed of convergence to the steady state value, cannot be ascribed solely to the existence of diminishing returns to capital, as suggested by Neoclassical Growth Theory, but is affected by technology diffusion as well. The difficulty in disentangling the effects of the two factors on the convergence rate remains, but the “extended” convergence equation arrived at reveals that the size of technological spillovers will have a level effect on productivity. Secondly, treating technological progress as sector dependent, our model implies potential steady-state growth rate heterogeneity. Thus, the estimated convergence rate can be ascribed to the concept of “Weak Conditional Convergence” [Islam (2003)], with each economy converging to its own steady state growth rate, which is more likely to be different from the others the more diverse the steady state production structures. These arguments lend support to the concept of “Club Convergence”.

Water resource as a factor of production - water use and economic growth

Water is one of the most important natural resources that is necessary for the rise and development of any biological and human activity. Being water resource a necessary good for multiple uses, it generates a series of competitive demands whose degree of competitiveness becomes greater in the presence of relevant and increasing pressure factors. The paper sets out a logical scheme for the analysis of productive uses of water, with the purpose of understanding both the functioning of an economy in the presence of a technical constraint to the exploitation of water resources, and the possible policy instruments available to the public authority. Our starting point is the definition of productive uses of water in terms of the amount of resource that is activated to make the stock of physical capital productive. Water resource is not a pure public good, it is available at private and social costs, given the existence of an optimal ratio between physical capital and water resources needed by the economic system in order to be productive. A complementarity hypothesis between the two forms of capital considered (physical and water capital) arises, with the first coming from private investment and the second being defined as the amount of public investment in services and infrastructures for water resource exploitation. As public investment in water capital crowds out private saving eventually available for private physical capital accumulation, an allocation criterion is needed to maximize total production of the system, never falling behind the optimal physical capital-water capital ratio. The first section of the paper reviews the literature dealing with the relationship between natural resources use and economic growth; the second section is focused on the presentation of a Solow-type model that introduces water in a general production function. In developing the model, equilibrium conditions in a “water economy” are described and a parametrical device is set in order to identify optimal taxation policies to finance public water infrastructures investment. The last section shows the results of an empirical analysis that is carried out in order to test the existence of a significant relationship between the aggregate use of water and per capita income produced by an economy. A country-based panel data analysis is performed with the aim of estimating a “water” production function.

The People\u27s Republic of China\u27s Potential Growth Rate: The Long-Run Constraints

We estimate the People’s Republic of China’s (PRC’s) potential growth rate in 2012 at 8.7% and at 9.2% for the average of 2008–2012, about the same as the average actual growth rate for this period. This rate is the natural growth rate, that is, the rate consistent with a constant unemployment rate and stable inflation. The PRC’s natural growth rate displays a downward trend since 2006, when it peaked at 11.1%. Probably the Great Recession has been an important factor, although we argue that there are other factors. We show that the PRC’s potential growth rate is not demand constrained, in particular by the balance of payments. The PRC’s potential growth rate is determined by the supply side of the economy, in particular by: (i) changes in the structure of the economy, in particular in the share of industrial employment; (ii) the working-age population; (iii) the share of net exports in gross domestic product (GDP); (iv) export growth; (v) the share of foreign direct investment (FDI) in GDP; and (vi) human capital accumulation

The Declining Share of Agricultural Employment in the People\u27s Republic of China: How Fast?

From 1962 to 2013, the People’s Republic of China’s (PRC’s) agricultural employment share declined from 82% to 31%. The transfer of workers out of low-productivity agriculture is a fundamental pillar of the PRC’s aspirations to progress and eventually become a high-income economy. We hypothesize that the drivers of this decline have been the increase in income per capita, industrial value added, foreign direct investment, and domestic credit. We use an Autoregressive Distributed Lag Model to test the strong exogeneity of the regressors so that we can use it for forecasting. Results indicate that the share of employment in agriculture in the PRC will decline to about 24% by 2020, the end of the 13th Five-Year Plan (2016–2020). We also estimate that the PRC’s employment share will reach 5%, the share observed in today’s rich economies, by 2042–2048

Evidence of radius inflation in stars approaching the slow-rotator sequence

Average stellar radii in open clusters can be estimated from rotation periods and projected rotational velocities under the assumption of random orientation of the spin axis. Such estimates are independent of distance, interstellar absorption, and models, but their validity can be limited by missing data (truncation) or data that only represent upper/lower limits (censoring). We present a new statistical analysis method to estimate average stellar radii in the presence of censoring and truncation. We use theoretical distribution functions of the projected stellar radius $R \sin i$ to define a likelihood function in the presence of censoring and truncation. Average stellar radii in magnitude bins are then obtained by a maximum likelihood parametric estimation procedure. This method is capable of recovering the average stellar radius within a few percent with as few as $\approx$ 10 measurements. Here it is applied for the first time to the dataset available for the Pleiades. We find an agreement better than $\approx$ 10 percent between the observed $R$ vs $M_K$ relationship and current standard stellar models for 1.2 $\ge M/M_{\odot} \ge$ 0.85 with no evident bias. Evidence of a systematic deviation at $2\sigma$ level are found for stars with 0.8 $\ge M/M_{\odot} \ge$ 0.6 approaching the slow-rotator sequence. Fast-rotators ($P$ < 2 d) agree with standard models within 15 percent with no systematic deviations in the whole 1.2 $\ge M/M_{\odot} \ge$ 0.5 range. The evidence found of a possible radius inflation just below the lower mass limit of the slow-rotator sequence indicates a possible connection with the transition from the fast to the slow-rotator sequence.Comment: Accepted by Astronomy and Astrophysics, 11 pages, 6 figure