Particle-photon radiative interactions and thermalization.

We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation theorem is derived and the particle velocity distribution analyzed. It is shown analytically that, neglecting molecular collisions, the velocity distribution function cannot be Gaussian, as the equilibrium value for the kurtosis κ is different from κ=3. A Maxwellian velocity distribution can be recovered in the limit of small radiative friction.

A Covariant Non-Local Model of Bohm's Quantum Potential.

Assuming that the energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm's quantum potential and the Madelung equation are obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics do admit a classical interpretation based on non-locality. Here, we generalize this approach imposing a finite speed of propagation of any perturbation, thus determining a covariant formulation of the Madelung equation.

Taming Taylor-Aris dispersion through chaotic advection.

Taylor-Aris dispersion represents an undesired phenomenon in pressure-driven liquid chromatography, often responsible for the unchecked increase of the Height Equivalent of the Theoretical Plate (HETP) when high throughput operating conditions are sought. Previous work on the subject showed how it is possible to contain the augmented dispersion in empty microchannels by inducing cross-sectional velocity components yielding an overall helical structure of the flow streamlines. Here, we explore the possibility of further reducing axial dispersion by devising flow conditions that give rise to chaotic streamlines. A three-dimensional steady flow generated by the combination of a pressure-driven Poiseuille flow and an electroosmotically-induced spatially periodic flow is used as a case study. Brenner's macrotransport approach is used to predict the axial dispersion coefficient of a diffusing solute in flows possessing regular, partially chaotic and globally chaotic kinematic features. Accurate Lagrangian-stochastic simulations of particle ensembles are used to validate the predictions obtained through Brenner's paradigm. Our findings suggest that the Taylor-Aris phenomenon can be altogether suppressed in the limit of globally chaotic kinematics. A theoretical interpretation of this outcome is developed by combining macrotransport theory with established results of the spectral approach to mixing in advecting-diffusing chaotic flows.

Invariant manifold approach for quantifying the dynamics of highly inertial particles in steady and time-periodic incompressible flows.

The dynamics of finite-sized particles with large inertia are investigated in steady and time-dependent flows through the numerical solution of the invariance equation, describing the spatiotemporal evolution of the slow/inertial manifold representing the effective particle velocity field. This approach allows for an accurate reconstruction of the effective particle divergence field, controlling clustering/dispersion features of particles with large inertia for which a perturbative approach is either inaccurate or not even convergent. The effect of inertia on heavy and light particles is quantified in terms of the rate of contraction/expansion of volume elements along a particle trajectory and of the maximum Lyapunov exponent for systems exhibiting chaotic orbits, such as the time-periodic sine-flow on the 2D torus and the time-dependent 2D cavity flow.

Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity.

This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson-Kac processes and Lévy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower boundedness of the real part of the eigenvalue spectrum that corresponds to an upper limit of the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We also analyze Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there is a critical value for the wave vector, above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case, and in fact, it represents a simple and clear example of a sub-quantum dynamics with hidden variables.

Swelling and Drug Release in Polymers through the Theory of Poisson-Kac Stochastic Processes.

Experiments on swelling and solute transport in polymeric systems clearly indicate that the classical parabolic models fail to predict typical non-Fickian features of sorption kinetics. The formulation of moving-boundary transport models for solvent penetration and drug release in swelling polymeric systems is addressed hereby employing the theory of Poisson-Kac stochastic processes possessing finite propagation velocity. The hyperbolic continuous equations deriving from Poisson-Kac processes are extended to include the description of the temporal evolution of both the Glass-Gel and the Gel-Solvent interfaces. The influence of polymer relaxation time on sorption curves and drug release kinetics is addressed in detail.

Space-time-modulated stochastic processes.

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Relativistic analysis of stochastic kinematics.

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ(w)=(1-w^{2}/c^{2})^{-1/2}. Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ(w). The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Dispersion of overdamped diffusing particles in channel flows coupled to transverse acoustophoretic potentials: transport regimes and scaling anomalies.

We address the dispersion properties of overdamped Brownian particles migrating in a two-dimensional acoustophoretic microchannel, where a pressure-driven axial Stokes flow coexists with a transverse acoustophoretic potential. Depending on the number and symmetries of the stable nodal points of the acoustophoretic force with respect to the axial velocity profile, different convection-enhanced dispersion regimes can be observed. Among these regimes, an anomalous scaling, for which the axial dispersion increases exponentially with the particle Peclét number, is observed whenever two or more stable acoustophoretic nodes are associated with different axial velocities. A theoretical explanation of this regime is derived, based on exact moment homogenization. Attention is also focused on transient dispersion, which can exhibit superballistic behavior 〈(x-〈x〉)^{2}〉∼t^{3},x being the axial coordinate.

Convection-dominated dispersion regime in wide-bore chromatography: a transport-based approach to assess the occurrence of slip flows in microchannels.

This article develops the theoretical analysis of transport and dispersion phenomena in wide-bore chromatography at values of the Peclet number Pe beyond the upper bound of validity of the Taylor-Aris theory. It is shown that for Poiseuille flows in cylindrical capillaries the average residence time grows logarithmically with the Peclet number, while the variance of the outlet chromatogram scales as the power 1/3 of Pe. In the presence of slip boundary conditions, both the mean and the variance of the outlet chromatograms saturate at high Pe, and this phenomenon provides an indirect transport-based way to detect slip flow conditions at the solid walls and, more generally, flow distributions in channel flows.

Necrosis evolution during high-temperature hyperthermia through implanted heat sources.

A nonstationary model for high-temperature hyperthermic treatments is developed. The aim of this model is to describe the thermal propagation within a living tissue and to quantify its clinical effects as it regards the physiological status (necrosis) of a neoplastic body. Particular attention is turned to the description of the necrotic transition induced by heating. This leads to the introduction of a necrosis field and to an effective-medium approximation for the corresponding physiological status (vascularization, necrosis, etc.) of the exposed tissue. The resulting nonlinear, nonstationary model is applied to a multilayered spherical structure with a temperature-regulated implant, and to a clinical case of a solid liver tumor. Clinical data on the spatial extent of the necrotized region are in good agreement with model predictions.

Modified model for the regulation of the tryptophan operon in Escherichia coli.

This article proposes a modification of the model developed by Sinha (1988) and Sen and Liu (1990) for the regulation dynamics of the tryptophan operon in E. coli based on a consistent overall balance of the agent repressing the mRNA transcription. The dynamics of the model are analyzed by means of continuation techniques and the influence of periodic fluctuations in the intracellular demand for tryptophan is addressed. The analysis provides deeper insight into the dynamics of this operon system and the results obtained may be a useful starting point for the optimization of tryptophan yield in bacterial cultures.