One-dimensional hyperbolic transport: Positivity and admissible boundary conditions derived from the wave formulation

Brasiello, Antonio; Crescitelli, Silvestro; Giona, Massimiliano

doi:10.1016/j.physa.2015.12.111

Cited by 20 publications

(24 citation statements)

References 30 publications

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“…(37) is valid for γ < 1. The extension to γ > 1 is discussed in [20], and therefore it is not repeated here. For the stochastic differential equation (33) the conditions at the boundary are simply reflection conditions, corresponding to the mirror simmetric reflection of the particle position at x = 0, 1, and to the switching of (−1) χ(t) → −(−1) χ(t) of the Poissonian perturbation.…”

Section: The Velocity Vield V(x) Is Given Bymentioning

confidence: 99%

On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

Giona¹,

Brasiello²,

Crescitelli³

2016

Physica A: Statistical Mechanics and its Applications

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We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time statistics. After addressing simple cases such as diffusion in a channel, and the switching statistics in the presence of a polarization potential, we thoroughly study Poisson-Kac diffusion in fractal domains. Diffusion in fractal spaces highlights neatly how the modification in the switching-time statistics associated with reflections against a complex and fractal boundary induces new emergent features of Poisson-Kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set.

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Section: The Velocity Vield V(x) Is Given Bymentioning

confidence: 99%

On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

Giona¹,

Brasiello²,

Crescitelli³

2016

Physica A: Statistical Mechanics and its Applications

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“…In food science, theories behind models, suitable for description of specific phenomena occurring at different time and length scales, are often borrowed from other research fields such as molecular dynamics (Frenkel & Smit, ; Nivelle, Beghin, Bosmans, & Delcour, ), computational chemistry, stochastic dynamics (Giona, Brasiello, & Crescitelli, , ; Helmroth, Varekamp, & Dekker, ), Monte Carlo methods (Defraeye, ), nonequilibrium mechanics and thermodynamics (Bird, Stewart, & Lightfoot, ; Datta, ). The synergistic use of different approaches can bridge together different spatio‐temporal scales (Brasiello, Crescitelli, & Giona, ; Defraeye, ; Giona, Brasiello, & Crescitelli, ).…”

Section: Introductionmentioning

confidence: 99%

“…The synergistic use of different approaches can bridge together different spatio-temporal scales (Brasiello, Crescitelli, & Giona, 2016;Defraeye, 2014;Giona, Brasiello, & Crescitelli, 2015).…”

Section: Introductionmentioning

confidence: 99%

A moving boundary model for food isothermal drying and shrinkage: One‐dimensional versus two‐dimensional approaches

Adrover

Brasiello

2019

J Food Process Engineering

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We investigate and quantify the error in the estimate of water diffusivity resulting from the adoption of one‐dimensional (1‐d) models to describe the drying process of thin discoidal or long‐thin cylindrical samples. Numerical results obtained with the 1‐d and the 2‐d moving boundary models recently proposed by Adrover, Brasiello, and Ponso (2019a, 2019b) are compared for different sample aspect ratios. The overestimate error of 1‐d model predictions of diffusivity falls below 5% for an aspect ratio radius‐over‐thickness R0/L0 > 10 for discoidal samples while, for cylindrical samples, the aspect ratio height‐to‐radius L0/R0 must be greater than 15 to get a similar level of accuracy. To overcome this issue we propose a modified 1‐d model able to take into account water flux from lateral surfaces (usually neglected in a 1‐d approach) thus reducing the overestimate error of water diffusivity below 2% even for low‐intermediate values of the aspect ratio. The 1‐d modified model is successfully applied to experimental data of convective drying of eggplant and chayote discoidal samples. Practical applications End consumer is increasingly demanding for ever more standardized and high quality food products. To meet these requirements, food industries are challenged to refine process design and control tools in order to be able to take into account the variability of both food matrices and operating conditions. This objective cannot be reached without the help of mathematical models based on first principles as the one here discussed and applied to food drying. The comparison between one‐ and two–dimensional approaches and the resulting quantification of errors in the adoption of simpler one‐dimensional models have a great practical interest for industrial applications as they provide reliable criteria to obtain good predictions even when the whole set of the needed experimental data are not available or too expensive. The developed method can be easily adopted to predict final food quality (moisture content, sample volume reduction, and deformation) and therefore to implement more refined control systems and to optimize process‐operating conditions, thus saving experimental and processing costs.

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“…Indeed, the Cattaneo equation, in spatial dimensions higher than one, does not even fulfil the requirement of positivity (i.e., the solution of this equation can attain negative values starting from non-negative initial conditions in the free-space propagation) [21]. In point of fact, positivity problems may arise also in the one-dimensional case, whenever bounded domains (intervals) are considered, depending on the way boundary conditions are set [22]. The statistical properties of stochastic processes possessing finite propagation velocity have been mathematically approached by Kolesnik in a brilliant way in a series of articles [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Generalized Poisson--Kac Processes and the Regularity of Laws of Nature

Giona¹

2018

Acta Phys. Pol. B

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The 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 differential 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-diffusion system subjected to a stochastically intermitted flux and the Edwards-Wilkinson model are used to show these properties.

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One-dimensional hyperbolic transport: Positivity and admissible boundary conditions derived from the wave formulation

Cited by 20 publications

References 30 publications

On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

A moving boundary model for food isothermal drying and shrinkage: One‐dimensional versus two‐dimensional approaches

Generalized Poisson--Kac Processes and the Regularity of Laws of Nature

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