Survival time of random walk in random environment among soft obstacles

We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general d-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ""mixed"" probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE).

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

Dynamics of linear polymers in random media

We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian dynamics and estimate the diffusion constant of the center-of-mass of the chain in such disordered media. For internal dynamics of the chain, we estimate the dynamic exponents. We propose similar scaling theory for the reptation dynamics of the chain in the framework of Flory theory for the disordered medium. The modifications in the case of correlated disorders are also discussed. .

Analytical pyrolysis to study microplastics and other polymers in the environment

Synthetic polymers constitute a wide class of materials which has enhanced the quality of human life, providing comforts and innovations. Anyway, the increasing production and the incorrect waste management, are leading to the occurrence of polymers in the environment, generating concern. To understand the extent of this issue, analytical investigation holds an essential position. Standardised methods have not established yet, and additional studies are required to improve the present knowledge. The main aim of this thesis was to provide comprehensive information about the potential of pyrolysis coupled with gas-chromatography and mass spectrometry (Py-GC-MS) for polymers investigation, from their characterisation to their identification and quantification in complex matrices. Water-soluble (poly(dimethylsiloxanes), PDMS bearing poly(ethylene glycol), PEG, side chains) and water-insoluble polymers (microplastics, MPs, and bioplastics) were studied. The different studies revealed the possibility to identify heterogeneous classes of polymers, fingerprinting the presence of PDMS copolymers and distinguishing chemically different polyurethanes (PURs). The occurrence of secondary reactions in pyrolysis of polymer mixtures was observed as possible drawback. Pyrolysis products indicative of secondary reactions and their reaction mechanisms were identified. Py-GC-MS also revealed its fundamental role for the identification of polymers composing commercial bioplastics items based. The results aided to identify chemicals that have the potential to migrate in sea waters. Investigations of environmental samples demonstrated the capability of Py-GC-MS to provide reliable, reproducible and comparable results about polymers in complex matrices (PEG-PDMS in sewage sludges and PURs and other MPs in road dusts and spider webs). Criticisms were especially found in quantitation, such as the retrieval reference materials, the construction of reliable calibration protocols and the occurrence of bias due to interferences between pyrolysis products. This thesis pursues the greater purpose to develop harmonised and standardised methods for environmental investigations of polymers, that is fundamental to assess the real state of the environment.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

New method for measuring longitudinal fuctuations and directed flow in ultrarelativistic heavy ion reactions

It has been shown in recent ALICE@LHC measurements that the odd flow harmonics, in particular, a directed flow v1, occurred to be weak and dominated by random fluctuations. In this work we propose a new method, which makes the measurements more sensitive to the flow patterns showing global collective symmetries. We demonstrate how the longitudinal center of mass rapidity fluctuations can be identified, and then the collective flow analysis can be performed in the event-by-event center of mass frame. Such a method can be very effective in separating the flow patterns originating from random fluctuations, and the flow patterns originating from the global symmetry of the initial state.

On the recurrence of random walks in Lévy random environments

This thesis investigates one-dimensional random walks in random environment whose transition probabilities might have an infinite variance. The ergodicity of the dynamical system ''from the point of view of the particle'' is proved under the assumptions of transitivity and existence of an absolutely continuous steady state on the space of the environments. We show that, if the average of the local drift over the environments is summable and null, then the RWRE is recurrent. We provide an example satisfying all the hypotheses.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

Polygalacturonase-Mediated Solubilization and Depolymerization of Pectic Polymers in Tomato Fruit Cell Walls1 : Regulation by pH and Ionic Conditions

The hydrolysis of cell wall pectins by tomato (Lycopersicon esculentum) polygalacturonase (PG) in vitro is more extensive than the degradation affecting these polymers during ripening. We examined the hydrolysis of polygalacturonic acid and cell walls by PG isozyme 2 (PG2) under conditions widely adopted in the literature (pH 4.5 and containing Na+) and under conditions approximating the apoplastic environment of tomato fruit (pH 6.0 and K+ as the predominate cation). The pH optima for PG2 in the presence of K+ were 1.5 and 0.5 units higher for the hydrolysis of polygalacturonic acid and cell walls, respectively, compared with activity in the presence of Na+. Increasing K+ concentration stimulated pectin solubilization at pH 4.5 but had little influence at pH 6.0. Pectin depolymerization by PG2 was extensive at pH values from 4.0 to 5.0 and was further enhanced at high K+ levels. Oligomers were abundant products in in vitro reactions at pH 4.0 to 5.0, decreased sharply at pH 5.5, and were negligible at pH 6.0. EDTA stimulated PG-mediated pectin solubilization at pH 6.0 but did not promote oligomer production. Ca2+ suppressed PG-mediated pectin release at pH 4.5 yet had minimal influence on the proportional recovery of oligomers. Extensive pectin breakdown in processed tomato might be explained in part by cation- and low-pH-induced stimulation of PG and other wall-associated enzymes.

Molecular crowding effects of linear polymers in protein solutions

Measurement of protein-polymer second virial coefficients (B-AP) by sedimentation equilibrium studies of carbonic anhydrase and cytochrome c in the presence of dextrans (T10-T80) has revealed an inverse dependence of B-AP upon dextran molecular mass that conforms well with the behaviour predicted for the excluded-volume interaction between a spherical protein solute A and a random-flight representation of the polymeric cosolute P. That model of the protein-polymer interaction is also shown to provide a reasonable description of published gel chromatographic and equilibrium dialysis data on the effect of polymer molecular mass on BAP for human serum albumin in the presence of polyethylene glycols, a contrary finding from analysis of albumin solubility measurements being rejected on theoretical grounds. Inverse dependence upon polymer chainlength is also the predicted excluded-volume effect on the strength of several types of macromolecular equilibria-protein isomerization, protein dimerization, and 1 : 1 complex formation between dissimilar protein reactants. It is therefore concluded that published experimental observations of the reverse dependence, preferential reaction enhancement within DNA replication complexes by larger polyethylene glycols, must reflect the consequences of cosolute chemical interactions that outweigh those of thermodynamic nonideality arising from excluded-volume effects. (c) 2005 Elsevier B.V. All rights reserved.

Non-invasive methodology for the identification of plastic pieces in museum environment – a novel approach

The preservation of modern and contemporary art and costume collections in museums requires a complete understanding of their constituent materials which are often synthetic or semi-synthetic polymers. An extraordinary amount of quality information can be gained from instrumental techniques, but some of them have the disadvantage of being destructive. This paper presents a new totally integrated non-invasive methodology, for the identification of polymers and their additives, on plastic artefacts in museums. NMR (nuclear magnetic resonance) and in-situ FTIR-ATR (attenuated total reflection infrared spectroscopy) combination allowed the full characterization of the structure of thesematerials and correct identification of each one. The NMR technique applied to leached surface exudates identified unequivocally a great number of additives, exceeding the Py–GC–MS analysis of micro-fragments in number and efficiency. Additionally, in-situ FTIR-ATR provided exactly the same information of the destructive μ-FTIR about the polymer structure and confirmed the presence of some additives. Eight costume pieces (cosmetic boxes and purses), dating to the beginning of the 20th century and belonging to the Portuguese National Museum of Costume and Fashion, were correctly identified with this new integrated methodology, as beingmade of plastics derived fromcellulose acetate or cellulose nitrate polymers, contradicting the initial information that these pieces were made of Bakelite. The identification of a surprisingly large number of different additives forms an added value of this methodology and opens a perspective of a quick and better characterization of plastic artefacts in museum environments.