Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation

The Enskog kinetic theory is applied to compute the mean square displacement of impurities or intruders (modeled as smooth inelastic hard spheres) immersed in a granular gas of smooth inelastic hard spheres (grains). Both species (intruders and grains) are surrounded by an interstitial molecular gas (background) that plays the role of a thermal bath. The influence of the latter on the motion of intruders and grains is modeled via a standard viscous drag force supplemented by a stochastic Langevin-like force proportional to the background temperature. We solve the corresponding Enskog-Lorentz kinetic equation by means of the Chapman-Enskog expansion truncated to first order in the gradient of the intruder number density. The integral equation for the diffusion coefficient is solved by considering the first two Sonine approximations. To test these results, we also compute the diffusion coefficient from the numerical solution of the inelastic Enskog equation by means of the direct simulation Monte Carlo method. We find that the first Sonine approximation generally agrees well with the simulation results, although significant discrepancies arise when the intruders become lighter than the grains. Such discrepancies are largely mitigated by the use of the second Sonine approximation, in excellent agreement with computer simulations even for moderately strong inelasticities and/or dissimilar mass and diameter ratios. We invoke a random walk picture of the intruders' motion to shed light on the physics underlying the intricate dependence of the diffusion coefficient on the main system parameters. This approach, recently employed to study the case of an intruder immersed in a granular gas, also proves useful in the present case of a granular suspension. Finally, we discuss the applicability of our model to real systems in the self-diffusion case. We conclude that collisional effects may strongly impact the diffusion coefficient of the grains.

First-encounter time of two diffusing particles in two- and three-dimensional confinement

The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two- and three-dimensional domains with reflecting boundaries. Based on the outcome of the simulations, we give a comprehensive overview of the behavior of the survival probability S(t) and the associated first-encounter time probability density H(t) over a broad time range spanning several decades. In addition, we provide numerical estimates and empirical formulas for the mean first-encounter time 〈T〉, as well as for the decay time T characterizing the monoexponential long-time decay of the survival probability. Based on the distance between the boundary and the center of mass of two particles, we obtain an empirical lower bound t_{B} for the time at which S(t) starts to significantly deviate from its counterpart for the no boundary case. Surprisingly, for small-sized particles, the dominant contribution to T depends only on the total diffusivity D=D_{1}+D_{2}, in sharp contrast to the one-dimensional case. This contribution can be related to the Wiener sausage generated by a fictitious Brownian particle with diffusivity D. In two dimensions, the first subleading contribution to T is found to depend weakly on the ratio D_{1}/D_{2}. We also investigate the slow-diffusion limit when D_{2}≪D_{1}, and we discuss the transition to the limit when one particle is a fixed target. Finally, we give some indications to anticipate when T can be expected to be a good approximation for 〈T〉.

Pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres

We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted so that the particles do not levitate over the grid, resulting in quasi-two-dimensional dynamics. We show that the behavior of diffusion and correlations in this system is particularly rich. Noticeably as well (and related to the complex dynamical behavior), a variety of phases appear, with important peculiarities with respect to analogous setups. We observe gas, liquid, glass, and hexagonal crystal phases. Most notably, we show that the melting of the hexagonal crystal occurs in coexistence with a liquid phase. This strikingly differs from the corresponding transition in a purely two-dimensional systems of air-fluidized disks, for which no phase coexistence has been reported in the literature.

First-encounter time of two diffusing particles in confinement

We investigate how confinement may drastically change both the probability density of the first-encounter time and the associated survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density valid over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case with unequal diffusivities and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as the translational invariance of such systems is broken.

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking. Inhomogeneously growing domains are frequently encountered in biological phenomena involving stochastic transport, such as tumor growth and morphogen gradient formation. A method for constructing analytic expressions for short-time moments of the position of the particles is developed and moments calculated from this approach are shown to compare favorably with results from random walk simulations and numerical integration of the reaction transport equation. The results show the important role played by the initial condition. In particular, it strongly affects the time dependence of the moments in the short-time regime by introducing additional drift and diffusion terms. We also discuss how our reaction transport equation could be applied to study the spreading of a population on an evolving interface. From a more general perspective, our findings help to mitigate the scarcity of analytic results for reaction-diffusion problems in geometries displaying nonuniform growth. They are also expected to pave the way for further results, including the treatment of first-passage problems associated with encounter-controlled reactions in such domains.

Standard and fractional Ornstein-Uhlenbeck process on a growing domain

We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive continuous-time random walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the aging of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing or contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly self-similar as one goes from one generation of the family to the next. Under these circumstances, the total probability that the walker hits a trap is determined exactly as a function of the single-step survival probability q of the mortal walker. On the nth generation graph of the family, this probability is shown to be given by the nth iterate of a certain scaling function or map q→f(q). The properties of the map then determine, in each case, the behavior of the trapping probability, the mean time to trapping, the temporal scaling factor governing the random walk dimension on the graph, and other related properties. The formalism is illustrated for the cases of a linear hierarchical lattice and the Sierpinski graphs in two and three Euclidean dimensions. We find an effective reduction of the random walk dimensionality due to the ballistic behavior of the surviving particles induced by the mortality constraint. The relevance of this finding for experiments involving travel times of particles in diffusion-decay systems is discussed.

Long-term monitoring programme of polychlorinated dioxins and polychlorinated furans in ambient air of Catalonia, Spain (1994-2015)

Reductions in concentrations of persistent organic pollutants were observed for polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in a comparison of two consecutive decades ending in December 31, 2015 (n = 413) and compiled from a 48-station long-term air-monitoring network in Catalonia, Spain. Reductions were observed in geometric mean concentration of total PCDD/Fs, decreasing at a rate of 11% yr^-1. Results reflect the relative success of improved pollution control measures at industry and traffic locations. At traffic and industrial locations, PCDD/Fs were reduced by around 68% (from 70 to 22 fg I-TEQ/m³) and 66% (from 57 to 19 fg I-TEQ/m³), respectively. The highest concentration of 1196 fg I-TEQ/m³ was observed during the first decade at an industrial location. The highest concentration over the second decade was at a background location during winter (674 fg I-TEQ/m³). Winter observations are generally higher than those recorded in summer, as evident in an 8-year period of moderate PCDD/F levels (<250 fg I-TEQ/m³, n = 143). PCDD/F congener profiles were identified has having less chlorinated PCDD/F, indicating the presence of nearby combustion sources at selected locations. More long-term sampling campaigns, combined with network optimization and integration into a meteorological model, can offer a tool for future PCDD/Fs control measures in not only Catalonia - but also applicable to other areas.

Tuning the Electronic and Dynamical Properties of a Molecule by Atom Trapping Chemistry

The ability to trap adatoms with an organic molecule on a surface has been used to obtain a range of molecular functionalities controlled by the choice of the molecular trapping site and local deprotonation. The tetraphenylporphyrin molecule used in this study contains three types of trapping sites: two carbon rings (phenyl and pyrrole) and the center of a macrocycle. Catching a gold adatom on the carbon rings leads to an electronic doping of the molecule, whereas trapping the adatom at the macrocycle center with single deprotonation leads to a molecular rotor and a second deprotonation leads to a molecular jumper. We call "atom trapping chemistry" the control of the structure, electronic, and dynamical properties of a molecule achieved by trapping metallic atoms with a molecule on a surface. In addition to the examples previously described, we show that more complex structures can be envisaged.

Continuous-time random-walk model for anomalous diffusion in expanding media

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Analysis of polychlorinated dibenzo-p-dioxins and dibenzofurans in stack gas emissions by gas chromatography-atmospheric pressure chemical ionization-triple-quadrupole mass spectrometry

A gas chromatography coupled to triple-quadrupole mass spectrometry (GC-(QqQ)MS/MS) including a soft-ionization through an atmospheric pressure chemical ionization (APCI) source based method was compared with the high resolution mass spectrometry (HRMS) standard reference method EN1948, for the analysis of polychlorinated dibenzo-p-dioxins and furans (PCDD/Fs) in stack gas emissions. The stack emission samples were collected, both, by manual method sampling (from 6 to 8h) and by long-term sampling systems (sampling time of several weeks). This work presents the first comparison of GC-(QqQ)MS/MS with APCI source with the European Standard EN1948 technique for stack gas emissions. Sample concentrations ranged from 0.5 to 596pg I-TEQ/Nm³. Comparative results in all investigated samples showed relative errors that were within ±15%. These results make GC-(QqQ)MS/MS with APCI suitable for the quantitative analysis of dioxins in the studied samples and create a real alternative tool to the reference sector GC-HRMS instruments.

Conformational ensemble of human α-synuclein physiological form predicted by molecular simulations

We perform here enhanced sampling simulations of N-terminally acetylated human α-synuclein, an intrinsically disordered protein involved in Parkinson's disease. The calculations, consistent with experiments, suggest that the post-translational modification leads to the formation of a transient amphipathic α-helix. The latter, absent in the non-physiological form, alters protein dynamics at the N-terminal and intramolecular interactions.

A four-year survey in the farming region of Chile, occurrence and human exposure to polychlorinated dibenzo-p-dioxins and dibenzofurans, and dioxin -like polychlorinated biphenyls in different raw meats

For the first time in South America, a four-year survey (2011-2014) was conducted to assess the occurrence of polychlorinated dibenzo-p-dioxins and furans (PCDD/Fs) and dioxin-like polychlorinated biphenyls (dl-PCBs) in different raw meats (bovine, pork, ovine, chicken, and turkey) sampled from ten of the fifteen regions of Chile. When expressed as pg World Health Organization Toxic Equivalent (WHO-TEQ₂₀₀₅)g^-1 fat, the highest PCDD/F values for each species were 0.54 (bovine-2012), 0.27 (pork-2013), 0.23 (ovine-2011), 0.61 (chickens-2013), and 0.34 (turkey-2012). The highest mean dl-PCBs levels were 0.18 (bovine-2011), 0.05 (pork-2014), 0.13 (ovine-2011), 0.1 (chicken-2014), and 0.21 (turkey-2013). Penta- and tetra-chlorinated congeners dominated PCDD/F WHO-TEQ₂₀₀₅ profiles during the survey, while PCB 126 dominated dl-PCBs profiles. Statistically significant interspecies differences were found. Dietary intake was also estimated, and the highest total PCDD/F and dl-PCBs values, found in poultry meat, were 0.09pgWHO-TEQ₂₀₀₅kg^-1bwd^-1 (2013) for adults and 0.36pgWHO-TEQ₂₀₀₅kg^-1bwd^-1 (2013) for children. The concentrations and dietary intakes for the studied compounds in raw meat were below international and national maximum permitted limits.

Polychlorinated dibenzo-p-dioxins, dibenzofurans and dioxin-like PCBs in commercialized food products from Colombia

Polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs) and dioxin-like polychlorinated biphenyls (dl-PCBs) are commonly known as dioxins and are the most toxic members of persistent organic pollutants (POPs) because present a variety of health effects especially as promoting agent of growing and transformation of cancer cells. They are bio-accumulate in humans primarily via the diet, specifically by ingestion of foods that have high lipid content which are generally associated with foods of animal origin such as oils and fats and with fishery and dairy products. In Colombia the Ministry of Health and Social Protection which is the entity responsible for surveillance food conditions, has established maximum levels for dioxins and dl-PCBs in oils from animal and vegetable origins. Oils of vegetable and animal origin represent an appreciable intake in the country thus the presence of dioxins and dl-PCBs in these materials is a matter of concern because they can bioaccumulate in fat. In this contribution the levels of PCDD/Fs and dl-PCBs in olive, soybean, fish oil, butter and shrimp consumed in Colombia were determined using HRGC-HRMS and were compared with the maximum levels permitted in oil samples according to both the Colombian and European regulations. WHO-TEQ concentrations for PCDD/Fs and dioxin like PCBs ranged from 0.24 to 1.710pgWHO-TEQ PCDD/Fg(-1) of fat and from 0.050 to 3.000pgWHO-TEQ PCBg(-1) of fat, respectively. As expected, fish oils and shrimp present the highest WHO-TEQ PCDD/Fs and dl-PCBs values followed by butter and soybean oil sample, while the olive oil shows the lowest levels. In general, the vegetable oils show levels below the limits established by both the Colombian and European regulations. The levels from soybean oil found in this study were slightly higher than the threshold established both by the Commission Regulation European Union (EU) and the Colombian legislation, while fish oils showed concentrations above the European regulations. Furthermore, shrimp exhibited values below the maximum concentration levels established by the EU and Colombian regulation.

Diffusion in an expanding medium: Fokker-Planck equation, Green's function, and first-passage properties

We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time τ(t), which we define via the relation τ[over ̇]=1/a^{2}, where a(t) is the expansion scale factor. If the medium expansion is driven by a power law [a(t)∝t^{γ} with γ>0], then we find interesting crossover effects in the mixing effectiveness of the diffusion process when the characteristic exponent γ is varied. Crossover effects are also found at the level of the survival probability and of the moments of the first passage-time distribution with two different regimes separated by the critical value γ=1/2. The case of an exponential scale factor is analyzed separately both for expanding and contracting media. In the latter situation, a stationary probability distribution arises in the long-time limit.

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Dioxins, furans, biphenyls, arsenic, thorium and uranium in natural and anthropogenic sources of phosphorus and calcium used in agriculture

The aim of this study was to assess the presence of dioxins, furans and biphenyls, and the inorganic contaminants such as arsenic (As), thorium (Th) and uranium (U) in three main products used in Agriculture in Brazil: feed grade dicalcium phosphate, calcined bovine bone meal and calcitic limestone. The first two are anthropogenic sources of phosphorus and calcium, while calcitic limestone is a natural unprocessed mineral. Regarding to dioxin-like substances, all samples analyzed exhibited dioxins (PCDD) and furans (PCDF) and dioxin-like polychlorinated biphenyls (dl-PCBs) concentrations below limit of detection (LOD). In general, achieved is in accordance with regulation in Brazil where is established a maximum limit in limestone used in the citric pulp production (0.50pg WHO-TEQ g(-1)). In addition, reported data revealed very low levels for limestone in comparison with similar materials reported by European legislation. As result for toxic metals, achieved data were obtained using Instrumental Neutron Activation Analysis (INAA). On one hand, limestone sample exhibits the largest arsenic concentration. On another hand, dicalcium phosphate exhibited the largest uranium concentration, which represents a standard in animal nutrition. Therefore, it is phosphorus source in the animal feed industry can be a goal of concern in the feed field.

Theoretical study of carbon-based tips for scanning tunnelling microscopy

Motivated by recent experiments, we present here a detailed theoretical analysis of the use of carbon-based conductive tips in scanning tunnelling microscopy. In particular, we employ ab initio methods based on density functional theory to explore a graphitic, an amorphous carbon and two diamond-like tips for imaging with a scanning tunnelling microscope (STM), and we compare them with standard metallic tips made of gold and tungsten. We investigate the performance of these tips in terms of the corrugation of the STM images acquired when scanning a single graphene sheet. Moreover, we analyse the impact of the tip-sample distance and show that it plays a fundamental role in the resolution and symmetry of the STM images. We also explore in depth how the adsorption of single atoms and molecules in the tip apexes modifies the STM images and demonstrate that, in general, it leads to an improved image resolution. The ensemble of our results provides strong evidence that carbon-based tips can significantly improve the resolution of STM images, as compared to more standard metallic tips, which may open a new line of research in scanning tunnelling microscopy.

Photo-induced reactions from efficient molecular dynamics with electronic transitions using the FIREBALL local-orbital density functional theory formalism

The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.

Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers." A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ω(m). While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ω(m)-dependent optimal frequency ω=ω(opt) that maximizes the probability of eventual target detection. We work primarily in one-dimensional (d=1) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in d=2 domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the d=1 case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.

Competing reaction processes on a lattice as a paradigm for catalyst deactivation

We mobilize both a generating function approach and the theory of finite Markov processes to compute the probability of irreversible absorption of a randomly diffusing species on a lattice with competing reaction centers. We consider an N-site lattice populated by a single deep trap, and N-1 partially absorbing traps (absorption probability 0<s<1). The influence of competing reaction centers on the probability of reaction at a target site (the deep trap) and the mean walk length of the random walker before localization (a measure of the reaction efficiency) are computed for different geometries. Both analytic expressions and numerical results are given for reactive processes on two-dimensional surfaces of Euler characteristic Ω=0 and Ω=2. The results obtained allow a characterization of catalyst deactivation processes on planar surfaces and on catalyst pellets where only a single catalytic site remains fully active (deep trap), the other sites being only partially active as a result of surface poisoning. The central result of our study is that the predicted dependence of the reaction efficiency on system size N and on s is in qualitative accord with previously reported experimental results, notably catalysts exhibiting selective poisoning due to surface sites that have different affinities for chemisorption of the poisoning agent (e.g., acid zeolite catalysts). Deviations from the efficiency of a catalyst with identical sites are quantified, and we find that such deviations display a significant dependence on the topological details of the surface (for fixed values of N and s we find markedly different results for, say, a planar surface and for the polyhedral surface of a catalyst pellet). Our results highlight the importance of surface topology for the efficiency of catalytic conversion processes on inhomogeneous substrates, and in particular for those aimed at industrial applications. From our exact analysis we extract results for the two limiting cases s≈1 and s≈0, corresponding respectively to weak and strong catalyst poisoning (decreasing s leads to a monotonic decrease in the efficiency of catalytic conversion). The results for the s≈0 case are relevant for the dual problem of light-energy conversion via trapping of excitations in the chlorophyll antenna network. Here, decreasing the probability of excitation trapping s at sites other than the target molecule does not result in a decrease of the efficiency as in the catalyst case, but rather in enhanced efficiency of light-energy conversion, which we characterize in terms of N and s. The one-dimensional case and its connection with a modified version of the gambler's ruin problem are discussed. Finally, generalizations of our model are described briefly.

PCDD/PCDF and dl-PCB in the ambient air of a tropical Andean city: passive and active sampling measurements near industrial and vehicular pollution sources

Concentration gradients were observed in gas and particulate phases of PCDD/F originating from industrial and vehicular sources in the densely populated tropical Andean city of Manizales, using passive and active air samplers. Preliminary results suggest greater concentrations of dl-PCB in the mostly gaseous fraction (using quarterly passive samplers) and greater concentrations of PCDD/F in the mostly particle fraction (using daily active samplers). Dioxin-like PCB predominance was associated with the semi-volatility property, which depends on ambient temperature. Slight variations of ambient temperature in Manizales during the sampling period (15°C-27°C) may have triggered higher concentrations in all passive samples. This was the first passive air sampling monitoring of PCDD/F conducted in an urban area of Colombia. Passive sampling revealed that PCDD/F in combination with dioxin-like PCB ranged from 16 WHO-TEQ2005/m(3) near industrial sources to 7 WHO-TEQ2005/m(3) in an intermediate zone-a reduction of 56% over 2.8 km. Active sampling of particulate phase PCDD/F and dl-PCB were analyzed in PM10 samples. PCDD/F combined with dl-PCB ranged from 46 WHO-TEQ2005/m(3) near vehicular sources to 8 WHO-TEQ2005/m(3) in the same intermediate zone, a reduction of 83% over 2.6 km. Toxic equivalent quantities in both PCDD/F and dl-PCB decreased toward an intermediate zone of the city. Variations in congener profiles were consistent with variations expected from nearby sources, such as a secondary metallurgy plant, areas of concentrated vehicular emissions and a municipal solid waste incinerator (MSWI). These variations in congener profile measurements of dioxins and dl-PCBs in passive and active samples can be partly explained by congener variations expected from the various sources.

Long-term sampling of dioxin-like substances from a clinker kiln stack using alternative fuels

The aim of this work is to characterize atmospheric emissions of polychlorinated dibenzo-p-dioxins (PCDDs)/polychlorinated dibenzofurans (PCDFs) and dioxin-like polychlorinated biphenyls (dl-PCBs) from a cement production plant where the existing clinker production line was completely replaced by a new state-of-the-art installation. The project started in April 2008 with the installation of a long-term sampling system in the stack of the clinker kiln that used petroleum coke as fuel; PCDD/PCDF and dl-PCB emissions were then evaluated for a two year period. To carry out the second part of the study, in 2010 the sampling system was moved to the new installation in which, apart from conventional fuel, recovered derived fuel (RDF) and WWTP sludge were used as alternative fuels. For both the old and new clinker kilns, PCDD/PCDF emission values were well below the limit established by the European Waste Incineration Directive 2000/76/CE (EWID) of 100 pg I-TEQ/Nm(3); values ranged from 0.43 to 2.02 and from 0.07 to 3.31 pg I-TEQ/Nm(3), respectively. dl-PCBs accounted for approximately 25% of the WHO-TEQ toxicity. These results prove that the installation is capable of reducing PCDD/PCDF and dl-PCB emissions when alternative fuels are integrated into the process. In the case of PCDDs/PCDFs, the major contributions to total TEQ were usually from 2,3,7,8-TCDD (owing to its relative abundance) and 2,3,4,7,8-PeCDF (due to its high I-TEF of 0.5); while for dl-PCBs, the major contribution was from PCB-126. The slight shift in the congener profile between the old and new installations was characterized and a regression model was proposed for dl-PCB emissions depending on the RDF flow rate in the clinker.

Reaction mechanism of the bicopper enzyme peptidylglycine α-hydroxylating monooxygenase

Peptidylglycine α-hydroxylating monooxygenase is a noninteracting bicopper enzyme that stereospecifically hydroxylates the terminal glycine of small peptides for its later amidation. Neuroendocrine messengers, such as oxytocin, rely on the biological activity of this enzyme. Each catalytic turnover requires one oxygen molecule, two protons from the solvent, and two electrons. Despite this enzyme having been widely studied, a consensus on the reaction mechanism has not yet been found. Experiments and theoretical studies favor a pro-S abstraction of a hydrogen atom followed by the rebinding of an OH group. However, several hydrogen-abstracting species have been postulated; because two protons are consumed during the reaction, several protonation states are available. An electron transfer between the copper atoms could play a crucial role for the catalysis as well. This leads to six possible abstracting species. In this study, we compare them on equal footing. We perform quantum mechanics/molecular mechanics calculations, considering the glycine hydrogen abstraction. Our results suggest that the most likely mechanism is a protonation of the abstracting species before the hydrogen abstraction and another protonation as well as a reduction before OH rebinding.

Lattice statistical theory of random walks on a fractal-like geometry

We have designed a two-dimensional, fractal-like lattice and explored, both numerically and analytically, the differences between random walks on this lattice and a regular, square-planar Euclidean lattice. We study the efficiency of diffusion-controlled processes for flows from external sites to a centrosymmetric reaction center and, conversely, for flows from a centrosymmetric source to boundary sites. In both cases, we find that analytic expressions derived for the mean walk length on the fractal-like lattice have an algebraic dependence on system size, whereas for regular Euclidean lattices the dependence can be transcendental. These expressions are compared with those derived in the continuum limit using classical diffusion theory. Our analysis and the numerical results quantify the extent to which one paradigmatic class of spatial inhomogeneities can compromise the efficiency of adatom diffusion on solid supports and of surface-assisted self-assembly in metal-organic materials.

Metallicity enhancement in core–shell SiO2@RuO2nanowires

SiO₂@RuO₂composite nanowires exhibit an enhanced metallic nature of the external RuO₂shell, reflected in a significantly improved electronic conductance.

Quasi-resonant neutralization of He+ ions at a germanium surface

When low-energy He ions are scattered from a Ge surface, the fraction of positive ions exhibits characteristic oscillations as a function of ion energy. These oscillations are caused by quasi-resonant neutralization (qRN), a process which is active for materials with a narrow band nearly resonant with the unperturbed He 1s-level. In this paper we measure the fraction of He+ backscattered from Ge(100). In conjunction with recently developed theoretical methods, we extract quantitative information on the efficiency of qRN. Our evaluation reveals that qRN is a highly efficient process leading to ion fractions two orders of magnitude lower than in systems for which neutralization is only due to Auger processes.

Evanescent continuous-time random walks

We study how an evanescence process affects the number of distinct sites visited by a continuous-time random walker in one dimension. We distinguish two very different cases, namely, when evanescence can only occur concurrently with a jump, and when evanescence can occur at any time. The first is characteristic of trapping processes on a lattice, whereas the second is associated with spontaneous death processes such as radioactive decay. In both of these situations we consider three different forms of the waiting time distribution between jumps, namely, exponential, long tailed, and ultraslow.

Energetics of Multi-Ion Conduction Pathways in Potassium Ion Channels

Potassium ion channels form pores in cell membranes, allowing potassium ions through while preventing the passage of sodium ions. Despite numerous high-resolution structures, it is not yet possible to relate their structure to their single molecule function other than at a qualitative level. Over the past decade, there has been a concerted effort using molecular dynamics to capture the thermodynamics and kinetics of conduction by calculating potentials of mean force (PMF). These can be used, in conjunction with the electro-diffusion theory, to predict the conductance of a specific ion channel. Here, we calculate seven independent PMFs, thereby studying the differences between two potassium ion channels, the effect of the CHARMM CMAP forcefield correction, and the sensitivity and reproducibility of the method. Thermodynamically stable ion-water configurations of the selectivity filter can be identified from all the free energy landscapes, but the heights of the kinetic barriers for potassium ions to move through the selectivity filter are, in nearly all cases, too high to predict conductances in line with experiment. This implies it is not currently feasible to predict the conductance of potassium ion channels, but other simpler channels may be more tractable.

Tailoring structural and electronic properties of RuO2 nanotubes: a many-body approach and electronic transport

The electrical conduction properties of ruthenium oxide nanocables are of high interest. These cables can be built as thin shells of RuO2 surrounding an inner solid nanowire of a dielectric insulating silica material. With this motivation we have investigated the structural, electronic and transport properties of RuO2 nanotubes using the density functional formalism, and applying many-body corrections to the electronic band structure. The structures obtained for the thinnest nanotubes are of the rutile type. The structures of nanotubes with larger diameters deviate from the rutile structure and have in common the formation of dimerized Ru-Ru rows along the axial direction. The cohesive energy shows an oscillating behavior as a function of the tube diameter. With the exception of the thinnest nanotubes, there is a correlation such that the electronic band structures of tubes with high cohesive energies show small gaps at the Fermi energy, whereas the less stable nanotubes exhibit metallic behavior, with bands crossing the Fermi surface. The electronic conductance of nanotubes of finite length connected to gold electrodes has been calculated using a Green-function formalism, and correlations have been established between the electronic band structure and the conductance at zero bias.

Detailed Examination of a Single Conduction Event in a Potassium Channel

Although extensively studied, it has proved difficult to describe in detail how potassium ion channels conduct cations and water. We present a computational study that, by using stratified umbrella sampling, examines nearly an entire conduction event of the Kv1.2/2.1 paddle chimera and thereby identifies the expected stable configurations of ions and waters in the selectivity filter of the channel. We describe in detail the motions of the ions and waters during a conduction event, focusing on how waters and ions enter the filter, the rotation of water molecules inside the filter, and how potassium ions are coordinated as they move from a water to a protein environment. Finally, we analyze the small conformational changes undergone by the protein, showing that the stable configurations are most similar to the experimental crystal structure.

Polychlorinated dibenzo-p-dioxins, dibenzofurans, biphenyls, paraffins and polybrominated diphenyl ethers in marine fish species from Ebro River Delta (Spain)

The results of a surveillance programme on the determination of polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs), polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs) and short chain chlorinated paraffins (SCCPs) in marine fish and shellfish species which are fished, commercialised and consumed in the Ebro River Delta area (NE, Spain) are presented. The study included the analysis of five marine fish species (sardine, gilthead sea bream, conger, eel and flounder) and three shellfish species (murex, carpet shell and mussel) collected in 2012 in five fishing harbours near to this area. WHO-TEQ concentrations for PCDD/Fs and dioxin like PCBs (dl-PCBs) ranged from 0.03 to 0.31 pg WHO-TEQ2005PCDD/Fg(-1)wetweight (ww) and from 0.02 to 3.15 pg WHO-TEQ2005PCBg(-1)ww, respectively. All levels were below the maximum concentrations established by the EU Regulation. The PCBs and PCDD/Fs accumulation pattern found in the samples analysed showed a distribution typically reported for marine samples. For marker PCBs and PBDEs, concentration levels ranging from 929 to 57494 pg g(-1)ww and from 36.2 to 827 pg g(-1)ww were obtained, respectively, meanwhile for SCCPs levels were between 3.1 and 141 ng g(-1)ww. Finally, the trends in the levels of PCDD/F and dl-PCBs found from 2006 to 2012 in fish and shellfish species were studied. A slight decrease of PCDD/F and dl-PCB concentrations was found since 2006.

Exploration and trapping of mortal random walkers

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random walk properties may be profound. For instance, whereas the average number of distinct sites visited by an immortal walker grows with time without bound, that of a mortal walker may, depending on dimensionality and rate of evanescence, remain finite or keep growing with the passage of time. This number can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps. If the traps are immortal, the survival probability will vanish with increasing time. However, if the traps are evanescent, the target may be spared a certain death. We analytically calculate a number of basic and broadly used quantities for evanescent random walkers.

On the organic energy gap problem

In conjugated organic molecules, the difference between the HOMO and LUMO Kohn-Sham eigenvalues is significantly smaller than the transport gap measured experimentally. We discuss here, within a local-orbital formulation of DFT, how this problem can be corrected using appropriate hybrid potentials, that add a fraction of Hartree-Fock exchange interaction in the DFT calculation. We illustrate this approach presenting calculations for two simple systems: H(2) and C(6)H(6); then, we discuss how to implement this hybrid approach in a general local-orbital calculation, adjusting the hybrid contribution to yield the correct experimental HOMO/LUMO energy gap for the molecule. We also consider the case of an organic molecule on a metal and analyze the effect of the molecule-metal interaction on the organic energy gap. In particular, we discuss how to introduce in this hybrid-potential scheme the effect of the image potential, and present results for the organic molecules PTCDA, TTF, benzene and pentacene on the metal surfaces Au(111), Ag(111) and Cu(111).

Survival probability of an immobile target in a sea of evanescent diffusive or subdiffusive traps: a fractional equation approach

We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps (i.e., traps that disappear in the course of their motion). Our calculation is based on a fractional reaction-subdiffusion equation derived from a continuous time random walk model of the system. Contrary to an earlier method valid only in one dimension (d=1), the equation is applicable in any Euclidean dimension d and elucidates the interplay between anomalous subdiffusive transport, the irreversible evanescence reaction, and the dimension in which both the traps and the target are embedded. Explicit results for the survival probability of the target are obtained for a density ρ(t) of traps which decays (i) exponentially and (ii) as a power law. In the former case, the target has a finite asymptotic survival probability in all integer dimensions, whereas in the latter case there are several regimes where the values of the decay exponent for ρ(t) and the anomalous diffusion exponent of the traps determine whether or not the target has a chance of eternal survival in one, two, and three dimensions.