Autocatalytic reaction-diffusion processes in restricted geometries

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of the system

Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics

We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout the sites of the lattice, updating the relevant spins. Since the walker is biased towards borders between clusters, the border-sites are more likely to be updated with respect to a non-diffusive dynamics and therefore, we expect the spin configurations to be affected. In particular, by means of the box-counting technique, we measure the fractal dimension of magnetic patterns emerging on the lattice, as the temperature is varied. Interestingly, our results provide a geometric signature of the phase transition and they also highlight some non-trivial, quantitative differences between the behaviors pertaining to the diffusive and non-diffusive dynamics

Universal features of information spreading efficiency on dd-dimensional lattices

A model for information spreading in a population of $N$ mobile agents is extended to $d$-dimensional regular lattices. This model, already studied on two-dimensional lattices, also takes into account the degeneration of information as it passes from one agent to the other. Here, we find that the structure of the underlying lattice strongly affects the time $\tau$ at which the whole population has been reached by information. By comparing numerical simulations with mean-field calculations, we show that dimension $d=2$ is marginal for this problem and mean-field calculations become exact for $d > 2$. Nevertheless, the striking nonmonotonic behavior exhibited by the final degree of information with respect to $N$ and the lattice size $L$ appears to be geometry independent.Comment: 8 pages, 9 figure

Autocatalytic reaction-diffusion processes in restricted geometries

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of the system

Two interacting diffusing particles on low-dimensional discrete structures

In this paper we study the motion of two particles diffusing on low-dimensional discrete structures in presence of a hard-core repulsive interaction. We show that the problem can be mapped in two decoupled problems of single particles diffusing on different graphs by a transformation we call 'diffusion graph transform'. This technique is applied to study two specific cases: the narrow comb and the ladder lattice. We focus on the determination of the long time probabilities for the contact between particles and their reciprocal crossing. We also obtain the mean square dispersion of the particles in the case of the narrow comb lattice. The case of a sticking potential and of 'vicious' particles are discussed.Comment: 9 pages, 6 postscript figures, to appear in 'Journal of Physics A',-January 200

Target annihilation by diffusing particles in inhomogeneous geometries

The survival probability of immobile targets, annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points, as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behaviour at large times can still be expressed in terms of the spectral dimension $\widetilde {d}$, and its exact analytical expression is given. The results show that the asymptotic survival probability is site independent on recurrent structures ($\widetilde{d}\leq2$), while on transient structures ($\widetilde{d}>2$) it can strongly depend on the target position, and such a dependence is explicitly calculated.Comment: To appear in Physical Review E - Rapid Communication

Salivary cytokines as biomarkers for oral squamous cell carcinoma: A systematic review

The prognosis of patients with oral squamous carcinoma (OSCC) largely depends on the stage at diagnosis, the 5-year survival rate being approximately 30% for advanced tumors. Early diagnosis, including the detection of lesions at risk for malignant transformation, is crucial for limiting the need for extensive surgery and for improving disease-free survival. Saliva has gained popularity as a readily available source of biomarkers (including cytokines) useful for diagnosing specific oral and systemic conditions. Particularly, the close interaction between oral dysplastic/neoplastic cells and saliva makes such fluid an ideal candidate for the development of non-invasive and highly accurate diagnostic tests. The present review has been designed to answer the question: “Is there evidence to support the role of specific salivary cytokines in the diagnosis of OSCC?” We retrieved 27 observational studies satisfying the inclusion and exclusion criteria. Among the most frequent cytokines investigated as candidates for OSCC biomarkers, IL-6, IL-8, TNF-α are present at higher concentration in the saliva of OSCC patients than in healthy controls and may therefore serve as basis for the development of rapid tests for early diagnosis of oral cancer