1,721,096 research outputs found
An encounter-based approach to the escape problem
Get PDFWe revise the encounter-based approach to imperfect diffusion-controlled
reactions, which employs the statistics of encounters between a diffusing
particle and the reactive region to implement surface reactions. We extend this
approach to deal with a more general setting, in which the reactive region is
surrounded by a reflecting boundary with an escape region. We derive a spectral
expansion for the full propagator and investigate the behavior and
probabilistic interpretations of the associated probability flux density. In
particular, we obtain the joint probability density of the escape time and the
number of encounters with the reactive region before escape, and the
probability density of the first-crossing time of a prescribed number of
encounters. We briefly discuss generalizations of the conventional
Poissonian-type surface reaction mechanism described by Robin boundary
condition and potential applications of this formalism in chemistry and
biophysics
Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
No full textInternational audienceWe investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently proposed approach to express the joint probability density of the particle position and of its multiple boundary local times via a multi-dimensional Laplace transform of the conventional propagator satisfying the diffusion equation with mixed Robin boundary conditions. In the particular cases of an interval, a circular annulus and a spherical shell, this representation can be explicitly inverted to access the statistics of two boundary local times. We provide the exact solutions and their probabilistic interpretation for the case of an interval and sketch their derivation for two other cases. We also obtain the distributions of various associated first-passage times and discuss their applications
An encounter-based approach for restricted diffusion with a gradient drift
Get PDFWe develop an encounter-based approach for describing restricted diffusion
with a gradient drift towards a partially reactive boundary. For this purpose,
we introduce an extension of the Dirichlet-to-Neumann operator and use its
eigenbasis to derive a spectral decomposition for the full propagator, i.e.,
the joint probability density function for the particle position and its
boundary local time. This is the central quantity that determines various
characteristics of diffusion-influenced reactions such as conventional
propagators, survival probability, first-passage time distribution, boundary
local time distribution, and reaction rate. As an illustration, we investigate
the impact of a constant drift onto the boundary local time for restricted
diffusion on an interval. More generally, this approach accesses how external
forces may influence the statistics of encounters of a diffusing particle with
the reactive boundary
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Escape from textured adsorbing surfaces
Get PDFInternational audienceThe escape dynamics of sticky particles from textured surfaces is poorly understood despite importance to various scientific and technological domains. In this work, we address this challenge by investigating the escape time of adsorbates from prevalent surface topographies, including holes/pits, pillars, and grooves. Analytical expressions for the probability density function and the mean of the escape time are derived. A particularly interesting scenario is that of very deep and narrow confining spaces within the surface. In this case, the joint effect of the entrapment and stickiness prolongs the escape time, resulting in an effective desorption rate that is dramatically lower than that of the untextured surface. This rate is shown to abide a universal scaling law, which couples the equilibrium constants of adsorption with the relevant confining length scales. While our results are analytical and exact, we also present an approximation for deep and narrow cavities based on an effective description of one-dimensional diffusion that is punctuated by motionless adsorption events. This simple and physically motivated approximation provides high-accuracy predictions within its range of validity and works relatively well even for cavities of intermediate depth. All theoretical results are corroborated with extensive Monte Carlo simulations
First-passage times of multiple diffusing particles with reversible target-binding kinetics
Get PDFWe investigate a class of diffusion-controlled reactions that are initiated
at the time instance when a prescribed number among particles
independently diffusing in a solvent are simultaneously bound to a target
region. In the irreversible target-binding setting, the particles that bind to
the target stay there forever, and the reaction time is the -th fastest
first-passage time to the target, whose distribution is well-known. In turn,
reversible binding, which is common for most applications, renders theoretical
analysis much more challenging and drastically changes the distribution of
reaction times. We develop a renewal-based approach to derive an approximate
solution for the probability density of the reaction time. This approximation
turns out to be remarkably accurate for a broad range of parameters. We also
analyze the dependence of the mean reaction time or, equivalently, the inverse
reaction rate, on the main parameters such as , , and binding/unbinding
constants. Some biophysical applications and further perspectives are briefly
discussed
Statistics of diffusive encounters with a small target: Three complementary approaches
Get PDFInternational audienceDiffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between the diffusing particle and the target. While an exact solution of this problem was recently derived in the form of a spectral expansion over the eigenbasis of the Dirichlet-to-Neumann operator, the latter is generally difficult to access for an arbitrary target. In this paper, we present three complementary approaches to approximate the probability density of the rescaled number of encounters with a small target in a bounded confining domain. In particular, we derive a simple fully explicit approximation, which depends only on a few geometric characteristics such as the surface area and the harmonic capacity of the target, and the volume of the confining domain. We discuss the advantages and limitations of three approaches and check their accuracy. We also deduce an explicit approximation for the distribution of the first-crossing time, at which the number of encounters exceeds a prescribed threshold. Its relations to common firstpassage time problems are discussed
The localization regime in a nutshell
No full textInternational audienceHigh diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional Gaussian form, various models have been employed to interpret these deviations and to relate them with the microstructural properties of a sample. In this paper, we argue that the non-Gaussian behavior of the signal is a generic universal feature of the Bloch-Torrey equation. We provide a simple yet rigorous description of the localization regime emerging at high extended gradients and identify its origin as a symmetry breaking at the reflecting boundary. We compare the consequent non-Gaussian signal decay to other diffusion NMR regimes such as slow-diffusion, motional-narrowing and diffusion-diffraction regimes. We emphasize limitations of conventional perturbative techniques and advocate for non-perturbative approaches which may pave a way to new imaging modalities in this field
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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