Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows.

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology

Reconstructing the gradient source position from steady-state fluxes to small receptors

Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape Time approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. {We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away}, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.This work was supported by EPSRC grant no EP/K032208/1. U.D. was supported by a Junior Interdisciplinary Fellowship via Wellcome Trust grant number 105602/Z/14/Z and a Herchel Smith Postdoctoral Fellowship. D.H. team is supported by a FRM grant

Stochastic models of intracellular transport

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures

Experimental and numerical heat transfer studies of nanofluids with an emphasis on nuclear fusion applications

A nanofluid is a mixture of a low concentration of solid particles (10-100nm in size at concentrations below 10%vol.) and a carrier fluid (usually conventional coolants). These novel fluids exhibit anomalous heat transfer phenomena which cannot be explained using classical thermodynamic models. The fluids can be designed to offer unsurpassed heat transfer rates for heat transfer related applications at low costs of manufacturing. This PhD thesis describes the efforts to test whether these fluids can be utilised for high heat flux applications (similar to those encountered in proposed future fusion reactors) and also to discover the mechanisms which give rise to the phenomenal heat transfer enhancements observed. A broad metadata statistical analysis was performed on published literature which provided qualitative results regarding the heat transfer enhancement to be expected from nanofluids, indicated trends connecting by part mixture properties and heat transfer enhancement values exhibited and provided probable explanations of the heat transfer mechanisms involved. This study was performed to tackle the novelty and scientific uncertainty issues encountered in the field. Optical laser diagnostics experiments were performed on a high heat flux device (HyperVapotron) in isothermal conditions. The study provided extensive information regarding the flow structures formed inside the device using conventional coolants and nanofluids. This helped to both, understand the conventional operation of the device as well as review probable suitable geometries for the utilisation of the device using nanofluids. Finally, a Molecular Dynamics Simulation code was composed to model heat conduction through a basic nanofluid. The code results suggested the formulation of a new type of complex heat transfer mechanism that might explain the augmentation of heat transfer encountered experimentally. A new low cost high throughput platform (HTCondor®) has been used to run the code in order to demonstrate the capabilities of the system for less financially able institutions.Open Acces

Flowing matter

This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena.Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents.Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter.This book is the legacy of the COST Action MP1305 “Flowing Matter”

Mixed active-passive systems in confinement

The dynamics of passive colloidal particles are explored when they interact with active Chlamydomonas reinhardtii, a green micro-algae. Through the implementation of different confining microfluidic geometries, we examine the resulting colloidal distributions and characterise the interactions which lead to them. Experiments are outlined in which we characterise the positional dependence of the `jumps' passive particles undergo, which result from interacting with the active particles. These jumps are then used to reconstruct the overall positional distributions. Additionally, we outline experiments performed in a circular microfluidic confinement. By exploiting the aforementioned positional distribution of colloids and a semi-permeable membrane, this microfluidic device can be used to segregate the passive particles out of the mixture. Finally, features of a model are outlined which allows for the modelling of active-passive mixtures. The active particle of which is easily tuneable, allowing both pusher or puller type swimmers, as well as a variety of boundary scattering behaviours. Results show that confinement results in inhomogeneous swimmer dynamics, which then feed into the behaviour of passive particle dynamics. Microswimmer confinement is a clear example in which spatial inhomogeneities lead to passive particle accumulation and, upon implementing a semi-permeable membrane, can be used to perform particle demixing. Such interactions present exciting new possibilities for controlling micro-scale particles using active particles whose dynamics have such spatially dependent characteristics

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding