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

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

Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes

We analyze some basic issues associated with Generalized Poisson-Kac (GPK) stochastic processes, starting from the extended notion of the Markovian condition. The extended Markovian nature of GPK processes is established, and the implications of this property derived: the associated adjoint formalism for GPK processes is developed essentially in an analogous way as for the Fokker-Planck operator associated with Langevin equations driven by Wiener processes. Subsequently, the regularity of trajectories is addressed: the occurrence of fractality in the realizations of GPK is a long-term emergent property, and its implication in thermodynamics is discussed. The concept of completeness in the stochastic description of GPK is also introduced. Finally, some observations on the role of correlation properties of noise sources and their influence on the dynamic properties of transport phenomena are addressed, using a Wiener model for comparison

Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory

This article introduces the notion of Generalized Poisson-Kac (GPK) processes which generalize the class of "telegrapher's noise dynamics" introduced by Marc Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the stochastic perturbation acts as a switching amongst a set of stochastic velocity vectors controlled by a Markov-chain dynamics. GPK processes possess trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the convergence towards Brownian motion (and to stochastic dynamics driven by Wiener perturbations), which characterizes also the long-term/long-distance properties of these processes. In this article we introduce the structural properties of GPK processes, leaving all the physical implications to part II and part III

Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part II Irreversibility, Norms and Entropies

In this second part, we analyze the dissipation properties of Generalized Poisson-Kac (GPK) processes, considering the decay of suitable $L^2$-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions $\{ p_\alpha({\bf x},t) \}_{\alpha=1}^N$, while the corresponding energy dissipation and entropy functions based on the overall probability density $p({\bf x},t)$ do not satisfy monotonicity requirements as a function of time. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations

A non-isothermal moving-boundary model for continuous and intermittent drying of pears

Abstract: A non-isothermal moving-boundary model for food dehydration, accounting for shrinkage and thermal effects, is proposed and applied to the analysis of intermittent dehydration in which air temperature, relative humidity, and velocity vary cyclically in time. The convection-diffusion heat transport equation, accounting for heat transfer, water evaporation, and shrinkage at the sample surface, is coupled to the convection-diffusion water transport equation. Volume shrinkage is not superimposed but predicted by the model through the introduction of a point-wise shrinkage velocity. Experimental dehydration curves, in continuous and intermittent conditions, are accurately predicted by the model with an effective water diffusivity Deff(T) that depends exclusively on the local temperature. The non-isothermal model is successfully applied to the large set of experimental data of continuous and intermittent drying of Rocha pears

Space-time inversion of stochastic dynamics

This article introduces the concept of space-time inversion of stochastic Langevin equations as a way of transforming the parametrization of the dynamics from time to a monotonically varying spatial coordinate. A typical physical problem in which this approach can be fruitfully used is the analysis of solute dispersion in long straight tubes (Taylor-Aris dispersion), where the time-parametrization of the dynamics is recast in that of the axial coordinate. This allows the connection between the analysis of the forward (in time) evolution of the process and that of its exit-time statistics. The derivation of the Fokker-Planck equation for the inverted dynamics requires attention: it can be deduced using a mollified approach of the Wiener perturbations “a-la Wong-Zakai” by considering a sequence of almost everywhere smooth stochastic processes (in the present case, Poisson-Kac processes), converging to the Wiener processes in some limit (the Kac limit). The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. Several examples ranging from stochastic thermodynamics and fractal-time models are also analyzed

A multiscale approach to triglycerides simulations: from atomistic to coarse-grained models and back

The aim of this paper is to provide a simulation strategy to study the liquid-solid transition of triglycerides. The strategy is based on a multiscale approach. A coarse-grained model, parameterized on the basis of reference atomistic simulations, has been used to model the liquid-solid transition. A reverse mapping procedure has been proposed to reconstruct atomistic models from coarse-grained configurations and validated against experimental structural properties. The nucleation and growth of the crystalline order have been analysed in terms of several properties

Valorisation of Olive Pomace for the Production of Bio-Composite Adsorbents Applied in as Removal from Drinking Waters

Arsenic is a toxic metalloid representing a serious threat to human health, reaching a concentration in drinking water above the limit of 10 µg/L in many regions of the world. Although adsorption technologies are available today to remove arsenic from water, the employed adsorbents are expensive, which severely hinders the possibility of water treatment in marginal and rural areas. In this study, a two-stage process is investigated in which an adsorbent for the removal of arsenic from water is produced by hydrothermal carbonization (HTC) of olive pomace followed by iron precipitation. In the first part of the study, the kinetics of solid mass variation during the HTC process were analyzed to derive indications about the mechanisms driving the thermochemical conversion of olive pomace to hydrochar. It was thus verified that a satisfactory hydrochar yield could be attained after 30 min through the polymerization of hydrolysis products released during the early stages of HTC. Adsorption isotherms were determined for the Fe-hydrochar and the Fe-biochar produced by iron precipitation onto the hydrochar and the pyrolyzed olive pomace (biochar). Fe hydrochar showed higher adsorption capacity (qmax=8.7 mg/g) compared to the Fe-biochar (qmax= 5.3 mg/g). Fe-hydrochar was finally tested in a fixed-bed adsorption column for As removal, evidencing the ability to maintain the arsenic concentration below the 10 µg/L limit when employed in the configuration conventionally adopted for water treatment. However, in this configuration, the apparent adsorption capacity was reduced, indicating the need for an optimization of the fixed bed-column desig

Molecular dynamics of triglycerides: atomistic and coarse-grained approaches

The objective of this thesis have been the development and the analysis of microscopic mathematical models to investigate the dependence of triglycerides conformations from environmental conditions. Triglycerides are important constituents of food products that show polymorphic solid transitions. Such behaviors influence greatly processes management involving fats mixtures. To investigate the relationship between macroscopic conditions and conformational induced properties, we dealt with microscopic mathematical models. The first part of the thesis regards the building of a united-atoms model from which physical properties and structural distribution functions of a liquid phase were derived. The second part regards the development of a coarse-grained model. The force field of such model was developed, by means of statistical tools, using suitable distribution functions derived from the atomistic one. The coarse-grained model was used to perform numerical experiments to highlight the dependence of molecules conformations from experimental conditions. The results of our simulations show a clear relationship between the conformational state of molecules and temperature annealing condition. Moreover, the improvement of order features through radial distribution functions was pointed out during several heating-cooling processes. The formation of small clusters of few planar molecules can be easily observed by means of visual inspection. The effect of simple flow conditions imposed on the system was also investigated. Imposed flows increase molecules mobility causing a raise of planar molecules and a greater uniform distribution of inter-molecular orientational order vector

3-D Modeling of dehydration kinetics and shrinkage of ellipsoidal fermented amazonian cocoa beans

recently proposed moving-boundary model for food isothermal dehydration was applied to analyze the dehydration kinetics of ellipsoidal cocoa beans, characterized by a moderate shrinkage and a non-uniform initial distribution of water content between the core and the shell of the bean. The aim is to predict the influence of air velocity and non-uniformity of the initial water distribution on the dehydration rates, as well as the temporal evolution of the water content in the core and in the shell and of the characteristic lengths of the ellipsoidal bean. The model proved capable of accurately describing the two-phases dehydration process: an initial fast dehydration of the shell, characterized by higher dehydration rates, followed by a slower dehydration of the core, characterized by a linear relationship jd = d(T)Xr between the dehydration rate jd and the moisture ratio Xr. A shortcut method to estimate the effective water diffusivity D is also proposed, deriving from the basic observation that the asymptotic exponential behaviour of the dehydration curve Xr(t) for an ellipsoidal bean coincides with that of an equivalent sphere, with the same surface-to-volume ratio