Exact solution of the van der Waals model in the critical region

The celebrated van der Waals model describes simple fluids in the thermodynamic limit and predicts the existence of a critical point associated to the gas-liquid phase transition. However the behaviour of critical isotherms according to the equation of state, where a gasliquid phase transition occurs, significantly departs from experimental observations. The correct critical isotherms are heuristically re-established via the Maxwell equal areas rule. A long standing open problem in mean field theory is concerned with the analytic description of van der Waals isotherms for a finite size system that is consistent, in the thermodynamic limit, with the Maxwell prescription. Inspired by the theory of nonlinear conservation laws, we propose a novel mean field approach, based on statistical mechanics, that allows to calculate the van der Waals partition function for a system of large but finite number of particles N. Our partition function naturally extends to the whole space of thermodynamic variables, reproduces, in the thermodynamic limit N ! 1, the classical results outside the critical region and automatically encodes Maxwell’s prescription. We show that isothermal curves evolve in the space of thermodynamic variables like nonlinear breaking waves and the criticality is explained as the mechanism of formation of a classical hydrodynamic shock

The structural transformation between manufacturing and services and the deline in the U.S. GDP volatility

For a single firm with a given volatility of total factor productivity at the gross output level (GTFP), the volatility of total factor productivity at the value added level (YTFP) increases with the share of intermediate goods in gross output. For a Cobb-Douglas production function in capital, labor and intermediate goods, YTFP volatility is equal to GTFP volatility divided by one minus the share of intermediate goods in gross output. In the U.S., this share is steadily around 0.6 for manufacturing and 0.38 for services during the 1960-2005 period. Thus, the same level of GTFP volatility in the two sectors implies a 55% larger YTFP volatility in manufacturing. This fact contributes to the higher measured YTFP volatility in manufacturing with respect to services. It follows that, as the services share in GDP increases from 0.53 in 1960 to 0.71 in 2005 in the U.S., GDP volatility is reduced. I construct a two-sector dynamic general equilibrium input-output model to quantify the role of the structural transformation between manufacturing and services in reducing the U.S. GDP volatility. Numerical results for the calibrated model economy suggest that the structural transformation can account for 32% of the GDP volatility reduction between the 1960-1983 and the 1984-2005 periods

Biased Technical Change, Intermediate Goods and Total Factor Productivity

Biased technical change can be defined as changes that affect the elasticity of output with respect to inputs. In this paper, I analyze the effect of biased technical change on total factor productivity (TFP). I construct an input-output economy in which firms produce gross output using capital, labor and intermediate goods. In equilibrium, biased technical change appears as an explicit part of TFP in the value added aggregate production function, where the latter is obtained through the aggregation of individual firms optimal decisions. A larger elasticity of gross output with respect to intermediates implies a smaller TFP level. I use the model to quantify the impact of biased technical change for measured TFP growth in Italy. The exercise shows that biased technical change can account for the productivity slowdown observed in Italy from 1994 to 2004

How robotic surgery is changing our understanding of anatomy

The most recent revolution in our understanding and knowledge of the human body is the introduction of new technologies allowing direct magnified vision of internal organs, as in laparoscopy and robotics. The possibility of viewing an anatomical detail, until now not directly visible during open surgical operations and only partially during dissections of cadavers, has created a 'new surgical anatomy'. Consequent refinements of operative techniques, combined with better views of the surgical field, have given rise to continual and significant decreases in complication rates and improved functional and oncological outcomes. The possibility of exploring new ways of approaching organs to be treated now allows us to reinforce our anatomical knowledge and plan novel surgical approaches. The present review aims to clarify some of these issues. \ua9 2017 Arab Association of Urology