Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at the origin by a source which is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection and the probability density of such a particle. We show that asymptotically the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.Comment: 7 pages; version 2: section IV is re-written, references added, 8 pages (final version

On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion.Comment: 7 pages, 3 figure

Role of proton irradiation and relative air humidity on iron corrosion

This paper presents a study of the effects of proton irradiation on iron corrosion. Since it is known that in humid atmospheres, iron corrosion is enhanced by the double influence of air and humidity, we studied the iron corrosion under irradiation with a 45% relative humidity. Three proton beam intensities (5, 10 and 20 nA) were used. To characterise the corrosion layer, we used ion beam methods (Rutherford Backscattering Spectrometry (RBS), Elastic Recoil Detection Analysis (ERDA)) and X-ray Diffraction (XRD) analysis. The corrosion kinetics are plotted for each proton flux. A diffusion model of the oxidant species is proposed, taking into account the fact that the flux through the surface is dependent on the kinetic factor K. This model provides evidence for the dependence of the diffusion coefficient, D, and the kinetic factor, K, on the proton beam intensity. Comparison of the values for D with the diffusion coefficients for thermal oxygen diffusion in iron at 300 K suggests an enhancement due to irradiation of 6 orders of magnitude

From the solutions of diffusion equation to the solutions of subdiffusive one

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the system composed from two parts with normal diffusion and subdiffusion, respectively.Comment: 11 pages, 2 figure

2D pattern evolution constrained by complex network dynamics

Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome

Dissolution in a field

We study the dissolution of a solid by continuous injection of reactive ``acid'' particles at a single point, with the reactive particles undergoing biased diffusion in the dissolved region. When acid encounters the substrate material, both an acid particle and a unit of the material disappear. We find that the lengths of the dissolved cavity parallel and perpendicular to the bias grow as t^{2/(d+1)} and t^{1/(d+1)}, respectively, in d-dimensions, while the number of reactive particles within the cavity grows as t^{2/(d+1)}. We also obtain the exact density profile of the reactive particles and the relation between this profile and the motion of the dissolution boundary. The extension to variable acid strength is also discussed.Comment: 6 pages, 6 figures, 2-column format, for submission to PR

One dimensional drift-diffusion between two absorbing boundaries: application to granular segregation

Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit formulae, the splitting probability and the mean first passage time are also calculated. Applying the results we find optimal parameters for segregating binary granular mixtures.Comment: RevTeX, 5 pages, 6 figure

Realistic boundary conditions for stochastic simulations of reaction-diffusion processes

Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecules are reflected. The probability that the molecule is adsorbed rather than reflected depends on the reactivity of the boundary (e.g. on the rate constant of the adsorbing chemical reaction and on the number of available receptors), and on the stochastic model used. This dependence is derived for each model.Comment: 24 pages, submitted to Physical Biolog

An integrated model of exercise support for people affected by cancer: consensus through scoping

© 2020 Informa UK Limited, trading as Taylor & Francis Group. Introduction: Exercise support for people with cancer is a national priority. The purpose of this study was to identify the success factors necessary to create a model of exercise support for people affected by cancer in a large city in the north of England. Method: Two groups of participants were recruited; people affected by cancer (n = 26) and professional stakeholders (n = 14) contributing to either focus groups or semi-structured interviews. Data were analysed using framework analysis. Results: Results from this study suggest that the promotion of exercise is not a priority in routine cancer care. Patients identified a lack of support and difficulty attaining information as a barrier to becoming active, emphasising a gulf between the patients’ needs and the health professionals’ priorities. People affected by cancer and professionals agreed that exercise was beneficial to cancer patients both during and after treatment. For an exercise pathway to be successful, key factors were identified including accessibility; tailored support; social interaction; affordability; competence of exercise delivery staff. Conclusions: There was consensus on the importance of exercise and critical factors required to develop a sustainable, accessible and effective service. Evidence to inform the development of an exercise pathway for people affected by cancer is provided.Implications for rehabilitation Exercise should be an included component of a cancer treatment plan, discussed and initiated from diagnosis. Health professionals have a responsibility to provide clear, consistent evidence-based advice on exercise. Exercise professionals must be appropriately trained in cancer rehabilitation according to National Institute for Health and care Excellence (2014). Individual assessments of exercise needs, preferences and cancer limitations will result in a bespoke plan of recommendations and support. The option of group activities has the advantage of increased social interaction, peer support and shared experiences. Available exercise/physical activity services should be accessible and affordable but may involve a modest contribution

Effects of an exercise and hypocaloric healthy eating intervention on indices of psychological health status, hypothalamic-pituitary-adrenal axis regulation and immune function after early-stage breast cancer : a randomised controlled trial

INTRODUCTION: Many women experience emotional distress, depression and anxiety after a diagnosis of breast cancer. Psychological stress and depression have been associated with hypothalamic-pituitary-adrenal (HPA) axis dysregulation that may adversely affect immune system functioning and impact upon survival. This study investigated the effects of a lifestyle intervention on indices of psychological health status, HPA axis regulation and immune function in overweight women recovering from early-stage breast cancer treatment. METHODS: A total of 85 women treated for breast cancer 3 to 18 months previously were randomly allocated to a 6-month exercise and hypocaloric healthy eating program plus usual care or usual care alone (control group). Women in the intervention group received three supervised exercise sessions per week and individualized dietary advice, supplemented by weekly nutrition seminars. Depressive symptoms (Beck Depression Inventory version II: BDI-II), perceived stress (Perceived Stress Scale: PSS), salivary diurnal cortisol rhythms; inflammatory cytokines (IL-6 and Tumor necrosis factor-α), leukocyte phenotype counts, natural killer (NK) cell cytotoxicity and lymphocyte proliferation following mitogenic stimulation were assessed at baseline and 6-month follow up. RESULTS: Compared with the control group, the intervention group exhibited a reduction in depressive symptoms (adjusted mean difference, 95% confidence intervals (95% CI): -3.12, -1.03 to -5.26; P = 0.004) at the 6-month follow-up but no significant decrease in PSS scores (-2.07, -4.96 to 0.82; P = 0.16). The lifestyle intervention also had a significant impact on diurnal salivary cortisol rhythm compared with usual care alone, as evidenced by an increase in morning salivary cortisol at the 6-month follow-up (P <0.04), indicating a change in HPA axis regulation. Women in the control group had higher total leukocyte, neutrophil and lymphocyte counts in comparison to the intervention group at the 6-month follow-up (P ≤0.05), whereas there was no difference in NK cell counts (P = 0.46), NK cell cytotoxicity (P = 0.85) or lymphocyte proliferation responses (P = 0.11) between the two groups. CONCLUSION: Our results show that the lifestyle intervention resulted in a reduction in depressive symptoms and a normalisation of HPA axis regulation. Such changes could have important implications for long-term survival in women recovering from early-breast cancer treatment. TRIAL REGISTRATION: Current Controlled Trials: ISRCTN08045231