In this paper we study the causal relation between country Economic Fitness F c and its Gross Dom... more In this paper we study the causal relation between country Economic Fitness F c and its Gross Domestic Product per capita ( G D P ). Using the Takens’ theorem, as first suggested in (Sugihara, G. et al. 2012), we show that there exists a reasonable evidence of causal correlation between G D P and F c for relatively rich countries. This is not the case for relatively poor countries where F c and G D P do not show any significant causal relation. We also present some preliminary results to understand whether G D P or F c are driving factor for economic growth.
Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasi... more Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of traject...
We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Ra... more We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Rayleigh numbers using direct numerical simulations with polymers of different relaxation times. We find that heat flux is enhanced by polymers and the amount of heat enhancement first increases and then decreases with the Weissenberg number, which is the ratio of the polymer relaxation time to the typical time scale of the flow. We show that this nonmonotonic behavior of the heat flux enhancement is the combined effect of the decrease in the viscous energy dissipation rate due to the viscosity of the Newtonian fluid and the increase in the energy dissipation rate due to polymers when Weissenberg number is increased. We explain why the viscous energy dissipation rate decreases with the Weissenberg number. Then by carrying out a generalized boundary layer analysis supplemented by a space-dependent effective viscosity from the numerical simulations, we provide a theoretical understanding of ...
In this paper we study a one-dimensional, nonlinear stochastic differential equation when small a... more In this paper we study a one-dimensional, nonlinear stochastic differential equation when small amplitude, long-period forcing is applied. The equation arises in the theory of the climate of the earth. We find that the cooperative effect of the stochastic perturbation and periodic forcing lead to an amplification of the peak of the power spectrum, due to a mechanism that we call stochastic resonance. A heuristic analysis of the resonance condition is presented and our analytical findings are confirmed by numerical calculations.
Bacteria and plankton populations living in oceans and lakes reproduce and die under the in- flue... more Bacteria and plankton populations living in oceans and lakes reproduce and die under the in- fluence of turbulent currents. Turbulent transport interacts in a complex way with the dynamics of populations because the typical reproduction time of microorganism is within the inertial range of turbulent time scales. In the present manuscript we quantitatively investigate the effect of flow compressibility on the dynamics of populations. While a small compressibility can be induced by several physical mechanisms, like density mismatch or the finite size of microorganisms with respect to the fluid turbulence, its effect on the the carrying capacity of the ecosystem can be dramatic. We report, for the first time, how a small compressibility can produce a sizeable reduction in the carrying capacity, due to an integrated effect made possible by the long replication times of the organisms with respect to turbulent time scales. A full statistical quantification of the fluctuations of population concentration field leads to data collapse over a broad range in parameter space.
By high-resolution numerical integration of two-dimensional Navier-Stokes equations we show that ... more By high-resolution numerical integration of two-dimensional Navier-Stokes equations we show that the turbulent flow at high Reynolds number is dominated by a simple and weakly unstable Hamiltonian system of pointlike vortices. The large instabilities, typical of the turbulent flow, are found uniquely outside vortices, in the wide dissipative region which results to be only a small perturbation of the vortex
We propose an approach to study the old-standing problem of the anomaly of the scaling exponents ... more We propose an approach to study the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by ‘Statistically Preserved Structures’ which are associated with statistical conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations, and it demonstrates that the scaling exponents of these nonlinear models are indeed anomalous. In order to adress the universality of these nonlinear model we study the statistical properties of a semi-infinite chain of passive vectors advecting each other and study the scaling exponents at the fixed point of this chain.
In this paper, the basic elements of the theory of the Lattice Boltzmann equation are reviewed. R... more In this paper, the basic elements of the theory of the Lattice Boltzmann equation are reviewed. Representative applications, such as turbulent flows and low-Reynolds flows in porous media are presented, along with a qualitative discussion on the most recent advances of this recent tool for computational fluid dynamics.
In this paper we study the causal relation between country Economic Fitness F c and its Gross Dom... more In this paper we study the causal relation between country Economic Fitness F c and its Gross Domestic Product per capita ( G D P ). Using the Takens’ theorem, as first suggested in (Sugihara, G. et al. 2012), we show that there exists a reasonable evidence of causal correlation between G D P and F c for relatively rich countries. This is not the case for relatively poor countries where F c and G D P do not show any significant causal relation. We also present some preliminary results to understand whether G D P or F c are driving factor for economic growth.
Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasi... more Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of traject...
We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Ra... more We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Rayleigh numbers using direct numerical simulations with polymers of different relaxation times. We find that heat flux is enhanced by polymers and the amount of heat enhancement first increases and then decreases with the Weissenberg number, which is the ratio of the polymer relaxation time to the typical time scale of the flow. We show that this nonmonotonic behavior of the heat flux enhancement is the combined effect of the decrease in the viscous energy dissipation rate due to the viscosity of the Newtonian fluid and the increase in the energy dissipation rate due to polymers when Weissenberg number is increased. We explain why the viscous energy dissipation rate decreases with the Weissenberg number. Then by carrying out a generalized boundary layer analysis supplemented by a space-dependent effective viscosity from the numerical simulations, we provide a theoretical understanding of ...
In this paper we study a one-dimensional, nonlinear stochastic differential equation when small a... more In this paper we study a one-dimensional, nonlinear stochastic differential equation when small amplitude, long-period forcing is applied. The equation arises in the theory of the climate of the earth. We find that the cooperative effect of the stochastic perturbation and periodic forcing lead to an amplification of the peak of the power spectrum, due to a mechanism that we call stochastic resonance. A heuristic analysis of the resonance condition is presented and our analytical findings are confirmed by numerical calculations.
Bacteria and plankton populations living in oceans and lakes reproduce and die under the in- flue... more Bacteria and plankton populations living in oceans and lakes reproduce and die under the in- fluence of turbulent currents. Turbulent transport interacts in a complex way with the dynamics of populations because the typical reproduction time of microorganism is within the inertial range of turbulent time scales. In the present manuscript we quantitatively investigate the effect of flow compressibility on the dynamics of populations. While a small compressibility can be induced by several physical mechanisms, like density mismatch or the finite size of microorganisms with respect to the fluid turbulence, its effect on the the carrying capacity of the ecosystem can be dramatic. We report, for the first time, how a small compressibility can produce a sizeable reduction in the carrying capacity, due to an integrated effect made possible by the long replication times of the organisms with respect to turbulent time scales. A full statistical quantification of the fluctuations of population concentration field leads to data collapse over a broad range in parameter space.
By high-resolution numerical integration of two-dimensional Navier-Stokes equations we show that ... more By high-resolution numerical integration of two-dimensional Navier-Stokes equations we show that the turbulent flow at high Reynolds number is dominated by a simple and weakly unstable Hamiltonian system of pointlike vortices. The large instabilities, typical of the turbulent flow, are found uniquely outside vortices, in the wide dissipative region which results to be only a small perturbation of the vortex
We propose an approach to study the old-standing problem of the anomaly of the scaling exponents ... more We propose an approach to study the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by ‘Statistically Preserved Structures’ which are associated with statistical conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations, and it demonstrates that the scaling exponents of these nonlinear models are indeed anomalous. In order to adress the universality of these nonlinear model we study the statistical properties of a semi-infinite chain of passive vectors advecting each other and study the scaling exponents at the fixed point of this chain.
In this paper, the basic elements of the theory of the Lattice Boltzmann equation are reviewed. R... more In this paper, the basic elements of the theory of the Lattice Boltzmann equation are reviewed. Representative applications, such as turbulent flows and low-Reynolds flows in porous media are presented, along with a qualitative discussion on the most recent advances of this recent tool for computational fluid dynamics.
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Papers by Roberto Benzi