Continuous and discrete models of cooperation in complex bacterial colonies

We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the elements of the macroscopic pattern. We present two types of models. The first is the Communicating Walkers model, a hybrid model composed of both continuous fields and discrete entities - walkers, which are coarse-graining of the bacteria. Models of the second type are systems of reaction diffusion equations, where the branching of the pattern is due to non-constant diffusion coefficient of the bacterial field. The diffusion coefficient represents the effect of self-generated lubrication fluid on the bacterial movement. We implement the discreteness of the biological system by introducing a cutoff in the growth term at low bacterial densities. We demonstrate that the cutoff does not improve the models in any way. Its only effect is to decrease the effective surface tension of the front, making it more sensitive to anisotropy. We compare the models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the Communication Walkers model and the growth dynamics of the Non-Linear diffusion model are affected in the same manner. From such similarities and from the insensitivity of the Communication Walkers model to implicit anisotropy we conclude that the increased discreteness, introduced be the coarse-graining of the walkers, is small enough to be neglected.Comment: 16 pages, 10 figures in 13 gif files, to be published in proceeding of CMDS

Universality in escape from a modulated potential well

We show that the rate of activated escape $W$ from a periodically modulated potential displays scaling behavior versus modulation amplitude $A$. For adiabatic modulation of an optically trapped Brownian particle, measurements yield $\ln W\propto (A_{\rm c} - A)^{\mu}$ with $\mu = 1.5$. The theory gives $\mu=3/2$ in the adiabatic limit and predicts a crossover to $\mu=2$ scaling as $A$ approaches the bifurcation point where the metastable state disappears.Comment: 4 pages, 3 figure

Twelve month follow-up on a randomised controlled trial of relaxation training for post-stroke anxiety

© The Author(s) 2016. Objective: To follow up participants in a randomised controlled trial of relaxation training for anxiety after stroke at 12 months. Design: Twelve month follow-up to a randomised controlled trial, in which the control group also received treatment. Setting: Community. Participants: Fifteen of twenty one original participants with post-stroke anxiety participated in a one year follow-up study. Interventions: A self-help autogenic relaxation CD listened to five times a week for one month, immediately in the intervention group and after three months in the control group. Main measures: Hospital Anxiety and Depression Scale-Anxiety subscale and the Telephone Interview of Cognitive Status for inclusion. Hospital Anxiety and Depression Scale-Anxiety subscale for outcome. All measures were administered by phone. Results: Anxiety ratings reduced significantly between pre and post-intervention, and between pre-intervention and one year follow-up (‡2(2) = 22.29, p < 0.001). Conclusions: Reductions in anxiety in stroke survivors who received a self-help autogenic relaxation CD appear to be maintained after one year

Scaling and crossovers in activated escape near a bifurcation point

Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape $W$ scales with the driving field amplitude $A$ as $\ln W \propto (A_c-A)^{\xi}$, where $A_c$ is the bifurcational value of $A$. With increasing field frequency the critical exponent $\xi$ changes from $\xi = 3/2$ for stationary systems to a dynamical value $\xi=2$ and then again to $\xi=3/2$. The analytical results are in agreement with the results of asymptotic calculations in the scaling region. Numerical calculations and simulations for a model system support the theory.Comment: 18 page

Statistical properties of multistep enzyme-mediated reactions

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first () and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d/dt (or "dose-response" curve) and the Fano factor F=variance/ are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.Comment: 8 pages, 3 figure

Driving-Induced Symmetry Breaking in the Spin-Boson System

A symmetric dissipative two-state system is asymptotically completely delocalized independent of the initial state. We show that driving-induced localization at long times can take place when both the bias and tunneling coupling energy are harmonically modulated. Dynamical symmetry breaking on average occurs when the driving frequencies are odd multiples of some reference frequency. This effect is universal, as it is independent of the dissipative mechanism. Possible candidates for an experimental observation are flux tunneling in the variable barrier rf SQUID and magnetization tunneling in magnetic molecular clusters.Comment: 4 pages, 4 figures, to be published in PR

UK Large-scale Wind Power Programme from 1970 to 1990: the Carmarthen Bay experiments and the Musgrove Vertical-Axis Turbines

This article describes the development of the Musgrove Vertical Axis Wind Turbine (VAWT) concept, the UK ‘Carmarthen Bay’ wind turbine test programme, and UK government’s wind power programme to 1990. One of the most significant developments in the story of British wind power occurred during the 1970s, 1980s, and 1990s, with the development of the Musgrove vertical axis wind turbine and its inclusion within the UK Government’s wind turbine test programme. Evolving from a supervisor’s idea for an undergraduate project at Reading University, the Musgrove VAWT was once seen as an able competitor to the horizontal axis wind systems that were also being encouraged at the time by both the UK government and the Central Electricity Generating Board, the then nationalised electricity utility for England and Wales. During the 1980s and 1990s the most developed Musgrove VAWT system, along with three other commercial turbine designs was tested at Carmarthen Bay, South Wales as part of a national wind power test programme. From these developmental tests, operational data was collected and lessons learnt, which were incorporated into subsequent wind power operations.http://dx.doi.org/10.1260/03095240677860621

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.Comment: 11 pages, 8 figure

A reaction-diffusion model for the growth of avascular tumor

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determinant factor in generating papillary tumor morphology.Comment: 9 pages, 6 figures, to appear in PR