710,681 research outputs found
Relativistic diffusive motion in random electromagnetic fields
We show that the relativistic dynamics in a Gaussian random electromagnetic
field can be approximated by the relativistic diffusion of Schay and Dudley.
Lorentz invariant dynamics in the proper time leads to the diffusion in the
proper time. The dynamics in the laboratory time gives the diffusive transport
equation corresponding to the Juettner equilibrium at the inverse temperature
\beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength
correlation function (Kubo's formula).Comment: the version published in JP
Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and A+A A and the
annihilation dynamics A+A -> 0 for particles moving subdiffusively in one
dimension. This scenario combines the "anomalous kinetics" and "anomalous
diffusion" problems, each of which leads to interesting dynamics separately and
to even more interesting dynamics in combination. Our analysis is based on the
fractional diffusion equation
Diffusion dynamics on multiplex networks
We study the time scales associated to diffusion processes that take place on
multiplex networks, i.e. on a set of networks linked through interconnected
layers. To this end, we propose the construction of a supra-Laplacian matrix,
which consists of a dimensional lifting of the Laplacian matrix of each layer
of the multiplex network. We use perturbative analysis to reveal analytically
the structure of eigenvectors and eigenvalues of the complete network in terms
of the spectral properties of the individual layers. The spectrum of the
supra-Laplacian allows us to understand the physics of diffusion-like processes
on top of multiplex networks.Comment: 6 Pages including supplemental material. To appear in Physical Review
Letter
Homogenization results for a linear dynamics in random Glauber type environment
We consider an energy conserving linear dynamics that we perturb by a Glauber
dynamics with random site dependent intensity. We prove hydrodynamic limits for
this non-reversible system in random media. The diffusion coefficient turns out
to depend on the random field only by its statistics. The diffusion coefficient
defined through the Green-Kubo formula is also studied and its convergence to
some homogenized diffusion coefficient is proved
Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems
In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics
Spatio-temporal dynamics in graphene
Temporally and spectrally resolved dynamics of optically excited carriers in
graphene has been intensively studied theoretically and experimentally, whereas
carrier diffusion in space has attracted much less attention. Understanding the
spatio-temporal carrier dynamics is of key importance for optoelectronic
applications, where carrier transport phenomena play an important role. In this
work, we provide a microscopic access to the time-, momentum-, and
space-resolved dynamics of carriers in graphene. We determine the diffusion
coefficient to be cm/s and reveal the impact of
carrier-phonon and carrier-carrier scattering on the diffusion process. In
particular, we show that phonon-induced scattering across the Dirac cone gives
rise to back-diffusion counteracting the spatial broadening of the carrier
distribution
Biscale Chaos in Propagating Fronts
The propagating chemical fronts found in cubic autocatalytic
reaction-diffusion processes are studied. Simulations of the reaction-diffusion
equation near to and far from the onset of the front instability are performed
and the structure and dynamics of chemical fronts are studied. Qualitatively
different front dynamics are observed in these two regimes. Close to onset the
front dynamics can be characterized by a single length scale and described by
the Kuramoto-Sivashinsky equation. Far from onset the front dynamics exhibits
two characteristic lengths and cannot be modeled by this amplitude equation. An
amplitude equation is proposed for this biscale chaos. The reduction of the
cubic autocatalysis reaction-diffusion equation to the Kuramoto-Sivashinsky
equation is explicitly carried out. The critical diffusion ratio delta, where
the planar front loses its stability to transverse perturbations, is determined
and found to be delta=2.300.Comment: Typeset using RevTeX, fig.1 and fig.4 are not available, mpeg
simulations are at
http://www.chem.utoronto.ca/staff/REK/Videos/front/front.htm
Quantitative image mean squared displacement (iMSD) analysis of the dynamics of profilin 1 at the membrane of live cells.
Image mean square displacement analysis (iMSD) is a method allowing the mapping of diffusion dynamics of molecules in living cells. However, it can also be used to obtain quantitative information on the diffusion processes of fluorescently labelled molecules and how their diffusion dynamics change when the cell environment is modified. In this paper, we describe the use of iMSD to obtain quantitative data of the diffusion dynamics of a small cytoskeletal protein, profilin 1 (pfn1), at the membrane of live cells and how its diffusion is perturbed when the cells are treated with Cytochalasin D and/or the interactions of pfn1 are modified when its actin and polyphosphoinositide binding sites are mutated (pfn1-R88A). Using total internal reflection fluorescence microscopy images, we obtained data on isotropic and confined diffusion coefficients, the proportion of cell areas where isotropic diffusion is the major diffusion mode compared to the confined diffusion mode, the size of the confinement zones and the size of the domains of dynamic partitioning of pfn1. Using these quantitative data, we could demonstrate a decreased isotropic diffusion coefficient for the cells treated with Cytochalasin D and for the pfn1-R88A mutant. We could also see changes in the modes of diffusion between the different conditions and changes in the size of the zones of pfn1 confinements for the pfn1 treated with Cytochalasin D. All of this information was acquired in only a few minutes of imaging per cell and without the need to record thousands of single molecule trajectories
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