1,721,044 research outputs found
Multiphase partitions of lattice random walks
No full textConsidering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two lattice phases. In this letter we show that the hyperbolic hydrodynamic model obtained by enforcing the boundedness of lattice velocities derived in Giona M., Phys. Scr., 93 (2018) 095201 correctly describes the dynamics of the system and permits to derive easily the boundary condition at the interface, which, contrarily to the common belief, involves the lattice velocities in the two phases and not the phase diffusivities. The dispersion properties of independent particles moving on an infinite lattice composed by the periodic repetition of a multiphase unit cell are investigated. It is shown that the hyperbolic transport theory correctly predicts the effective diffusion coefficient over all the range of parameter values, while the corresponding continuous parabolic models deriving from Langevin equations for particle motion fail. The failure of parabolic transport models is shown via a simple numerical experiment
Generalized poisson–kac processes and the regularity of laws of nature
No full textThe meaning and the features of Generalized Poisson–Kac processes are analyzed in the light of their regularity properties in order to show how the finite propagation velocity, characterizing these models, permits to eliminate the occurrence of singularities in transport models. Apart from a brief overview on their spectral properties, on the regularization of boundary-value problems, and on their origin from simple Lattice Random Walk models, the article focuses on their application in the study of stochastic partial di erential equations, and how their use permits to eliminate the divergence of low-order moments that characterizes the corresponding field equations in the presence of spatially δ-correlated stochastic perturbations, and to ensure positivity whenever needed. A simple reaction-di usion system subjected to a stochastically intermitted flux and the Edwards–Wilkinson model are used to show these properties
Advection-diffusion in chaotic flows
No full textThe aim of these notes is to provide an overview of the different approaches used to address the advection-diffusion equation, viewed as the mathematical setting for studying mixing in laminar incompressible flows. In its beginnings1, i. e. starting from the paper by (1984), the field of laminar mixing was essentially a new playground for physicists, fluid dynamicists and engineers, where the tools of dynamical system theory could be applied
Relativistic Poisson-Kac processes and equilibrium Jüttner distribution
No full textIt is shown that relativistic Ornstein-Uhlenbeck processes driven by stochastic perturbations possessing finite propagation velocity, and specifically by Poisson-Kac processes, are consistent with the known equilibrium velocity distribution of a relativistic gas (Jüttner distribution). Some observations on the boundedness of acceleration are addressed from elementary quantum principles (quantization of the action variable)
Hydrodynamic Green functions: paradoxes in unsteady Stokes conditions and infinite propagation velocity in incompressible viscous models
No full textWe present a simple representation of the hydrodynamic Green functions grounded on the free propagation of a vector field without any constraints (such as incompressibility) coupled with a gradient gauge in order to enforce these constraints. This approach involves the solution of two scalar problems: a couple of Poisson equations in the case of the Stokes regime, and a system of diffusion/Poisson equations for unsteady Stokes flows. The explicit and closed-form expression of the Green function for unsteady Stokes flow is developed. The relevance of this approach resides in its conceptual simplicity and it enables us to focus on the intrinsic singularities (Stokesian paradoxes) associated with the propagation of the stresses in incompressible flows under unsteady Stokes conditions, determining the occurrence of power-law tails in the velocity profile arbitrarily far away from the location of the impulsive force
Time-series analysis approach for the identification of flooding/loading transition in gas-liquid stirred tank reactors
No full textThis work provides a simple method for the objective, quantitative and non-intrusive detection of flooding/loading transition in gas/liquid systems in agitated vessels starting from the time-series analysis of conductance fluctuations along a generic cross section of the vessel. The conductance probe is designed in order to introduce minimal perturbations of the flow field within the vessel. A thorough statistical characterization of the time series collected by the probe provides deeper insight into the fluid dynamics of gas-liquid systems in stirred vessels as well as a simple, objective way to detect flooding/loading transitions
Identification of two phase flow regimes via diffusional analysis of experimental time series
No full textThe problem of identifying different two phase flow regimes from experimental time series by employing the method of diffusional analysis is addressed. This technique, recently applied to the multiphase flow field, is described and compared with other techniques used to characterize multiphase flow regimes. Diffusional analysis is applied to experimental time-series obtained from both a γ-densitometer and capacitance probes. The choice of the appropriate experimental signal to be processed is also discussed. The experimental time series were obtained from a rig with air and light oil. The results obtained confirm the advantages of the method proposed in identifying the features of different flow regimes. The advantages are particularly evident when comparing diffusional analysis with the widely applied Rescaled Range technique
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