Startup process in the Richtmyer-Meshkov instability

An analytical model for the initial growth period of the planar Richtmyer–Meshkov instability is presented for the case of a reflected shock, which corresponds in general to light-to-heavy interactions. The model captures the main features of the interfacial perturbation growth before the regime with linear growth in time is attained. The analysis provides a characteristic time scale τ for the startup phase of the instability, expressed explicitly as a function of the perturbation wavenumber k, the algebraic transmitted and reflected shock speeds U_(S1) 0 (defined in the frame of the accelerated interface), and the postshock Atwood number A^+: τ=[(1-A^+)/U_(S2)+(1+A^+)/(-U_(s1))]/(2k). Results are compared with computations obtained from two-dimensional highly resolved numerical simulations over a wide range of incident shock strengths S and preshock Atwood ratios A. An interesting observation shows that, within this model, the amplitude of small perturbations across a light-to-heavy interface evolves quadratically in time (and not linearly) in the limit A→1^−

An Economic-Psychological Model of Sustainable Food Consumption

This paper proposes a novel economic-psychological model of individual food consumption and food waste that recognizes individuals as social and moral beings who are boundedly rational and have limited capacity for self-control. The model identifies five components of individuals’ utility that correspond to five modes of being or selves: the hedonic agent, the social agent, the moral agent, the health-conscious agent and the habits-driven agent. In the model, individuals maximize this composite utility given their budget and effort constraints. We apply the model to analyze policies that can support the adoption of sustainable food consumption practices.bounded rationality, bounded self-control, habits, identity, social and moral norms, sustainable food consumption, Food Consumption/Nutrition/Food Safety, D03, D11, D12,

Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability

We first study the linear stability of an interface between two fluids following the passage of an imploding or exploding shock wave. Assuming incompressible flow between the refracted waves following shock impact, we derive an expression for the asymptotic growth rate for a three-dimensional combination of azimuthal and axial perturbations as a function of the Atwood ratio, the axial and azimuthal wave numbers, the initial radial position and perturbation amplitude of the interface, and the interface velocity gain due to the shock interaction. From the linearized theory, a unified expression for the impulsive asymptotic growth rate in plane, cylindrical, and spherical geometries is obtained which clearly delineates the effects of perturbation growth due to both geometry and baroclinic vorticity deposition. Several different limit cases are investigated, allowing recovery of Mikaelian's purely azimuthal theory and Richtmyer's plane model. We discuss the existence of three-dimensional perturbations with zero growth, typical of curvilinear geometries, as first observed by Mikaelian. The effect of shock proximity on the interface growth rate is studied in the case of a reflected shock. Analytical predictions of the effect of the incident shock strength and the perturbation wave numbers are then compared with results obtained from highly resolved numerical simulations of cylindrical imploding Richtmyer–Meshkov instability for ideal gases. A parallel is made with the instability growth in spherical and plane geometry. In particular, we propose a representation of the perturbation growth by considering the volume of the perturbed layer. This volume is found to grow faster in the plane case than in the imploding cylindrical geometry, among other results

Converging shocks in elastic-plastic solids

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e = e_(s)(I_1)+e_(h)(ρ,ς), where e_(s) accounts for shear through the first invariant of the Cauchy–Green tensor, and e_(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e_(h) = e_(h)(ρ), with a power-law dependence e_(h) ∝ ρ_(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M ∝ [log(1/R)]^α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M ∝ R^(−(s−1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R^(−(s−1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ−1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed

Essays on Economic Inequalities

This work relates to income inequalities studied from two different perspectives: ICT innovation (Chapter 1-2) and bargaining among social groups (Chapter 3-4). ICT innovation affects the number of jobs but also the structure of the labor market, with important consequences on income distribution. ICT innovation could destroy more jobs than it creates, for the first time since the beginning of industrialization; meanwhile the advanced ICT softwares are reducing that professions typically associated with the middle class, in favor of those that lies to the extremes of pays. On the other hand, the ability of each social group to attract resources is a second source of movements in income distribution; in particular, bargaining can take place within each company (firms versus trade-unions) and within the government (political parties competing to impose welfare regime). In Chapter 1 we estimate the effect of internet revolution on the number of jobs. The fourth industrial revolution, which began with the rise of internet technology, is now seeing the development of increasingly sophisticated artificial intelligence software. One consequence of such development is the ever-more serious risk posed for jobs. Chapter 1 shall examine this phenomenon in three steps; first, we shall empirically show that productivity growth over the last two decades was led by ICT; secondly, we shall discuss whether these productivity gains have affected the structure of employment by examining the data coming from 16 OECD countries and how such outcomes may be linked to innovation in ICT. Finally, a forecasting logistic model on the evolution of employment will be provided, projecting that by 2040-50 unemployment and atypical forms of work will affect 60% of the workforce in most of the countries observed. In Chapter 2 we observe the structure of job market over the last 25 years in order to find which professions have expanded and which ones have reduced and then we link this outcome to middle class thinning and the consequent income inequality growth. The underlying hypothesis is that ICT innovations are changing job structures, at least in the most industrialized countries. Firstly, this chapter takes the studies of Acemoglu and Autor (2010) and Goos et al. (2009) as a starting point and then updates their results for 16 European countries. The outcome we have found is an accentuation of the dynamics already observed in the literature. On the one hand, the number of non-routine jobs has increased while routine ones (both skilled and non-skilled) have become fewer; on the other hand, while the number of both low-paid and high-paid jobs has risen, those with average compensation have fallen almost everywhere. The consequence is a progressive thinning of the middle class and a change in income distribution among Western populations. Secondly, Chapter 2 links these findings with the recent intensification of the populist phenomenon. We shall be discussing an original theory, consistent both with the literature and with the empirical evidence, which describes the populist origins and its future prospects. In Chapter 3 shift our consideration to the social dynamic of inequalities. Income inequalities increase and decrease according to the capability of each social group in appropriating the national added value. The final outcome of this partition may be seen reflected on the price level. The lasting debate about the origins of inflation has determined two opposing approaches: monetarism and bargaining. The aim of Chapter 3 is to put these aspects together in an innovative synthesis. To investigate this item, we used an Input-Output (IO) approach and we developed an original mathematical process to define the real price index variations. After that, we tested this theoretical definition with an empirical study on Italian inflation over 30 years where we elaborated 31 official I-O tables compiled by the Italian statistics bureau (ISTAT). By this verified definition, inflation is strictly due to the level of wages and profits. This level, in turn, depends both on monetary government intervention (monetarist approach) and on collective bargaining among trade-unions and stakeholders (classic bargaining approach). Finally, by this model, theoretical implications are derived and summed up in six different settings ceteris paribus. Finally, in Chapter 4 we link income inequalities to Health Systems in a European perspective. With a sociological slant, we compare European countries in the context of neoliberal era, focusing on healthy life years for elderly (HLY65+). Firstly, we outline the theoretical state of the art in the literature on health inequalities, stressing the important relationship that links health inequalities to geographic area. In the second part of Chapter 4 we observe data relating to the changes of HLY65+ in the European member states and we correlate these results with the income inequality measured by the Gini index. The last part of Chapter 4 advance some comments on health inequalities in the context of the neoliberal era and in relation to geographic place and welfare policies

Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global ss-minimal surfaces

This article is divided into two parts. In the first part we show that a set E has locally finite s-perimeter if and only if it can be approximated in an appropriate sense by smooth open sets. In the second part we prove some elementary properties of local and global s-minimal sets, such as existence and compactness. We also compare the two notions of minimizer (i.e., local and global), showing that in bounded open sets with Lipschitz boundary they coincide. Conversely, in general this is not true in unbounded open sets, where a global s-minimal set may fail to exist (we provide an example in the case of a cylinder Omega x R)

The Role of the Public Municipality in Urban Regeneration: the Case of Genoa

The conditions why processes of urban regeneration can be developed in modern-day cities have changed enormously over the last decade. Unlike the recent past, where the reuse for urban uses of former industrial areas was only based on maximising the amount of space, after the housing bubble began in 2008 and the pandemic crisis, the profit margins for operators were reduced, and today, they faced to a sharp contraction in demand and a surplus of supply. Consequently, the framework within which we carry out the investment decisions is increasingly complex and is characterised by the opposition of a potential conflict between two forces. On the one hand, the public administration which seeks to take full advantage of the urban transformation processes to improve the quality of life for citizens; on the other, the private entity that has the aim of maximising the profits obtainable from the intervention and to minimise business risk. Therefore, to ensure the overall feasibility of an intervention, urban viability must correspond to economic and financial sustainability. The paper analyses the role of public strategies in urban regeneration interventions through the analysis of a case study in the city of Genoa. Currently, in the city some urban transformation interventions are being implemented; most of them (and the most relevant) are all aligned along the border between the city and the port. The role of the public administration is not limited to that of regulation, but the local municipality also acts as a financier (of public works) and as owner of the areas (which it makes available in concession). In this way, an attempt is made to make the city more competitive in the international real estate market. It is essential to reduce risk and cost factors compared to the private investor. The question then arises of how to evaluate the potential public benefits of these transformation operations