7,604 research outputs found
Detection Limit for Optically Sensing Specific Protein Interactions in Free-solution
Optical molecular sensing techniques are often limited by the refractive
index change associated with the probed interactions. In this work, we present
a closed form analytical model to estimate the magnitude of optical refractive
index change arising from protein-protein interactions. The model, based on the
Maxwell Garnett effective medium theory and first order chemical kinetics
serves as a general framework for estimating the detection limits of optical
sensing of molecular interactions. The model is applicable to situations where
one interacting species is immobilized to a surface, as commonly done, or to
emerging techniques such as Back-Scattering Interferometry (BSI) where both
interacting species are un-tethered. Our findings from this model point to the
strong role of as yet unidentified factors in the origin of the BSI signal
resulting in significant deviation from linear optical response.Comment: 7 Page Manuscript + 14 Page Supplementary Informatio
The smooth cut-off Hierarchical Reference Theory of fluids
We provide a comprehensive presentation of the Hierarchical Reference Theory
(HRT) in the smooth cut-off formulation. A simple and self-consistent
derivation of the hierarchy of differential equations is supplemented by a
comparison with the known sharp cut-off HRT. Then, the theory is applied to a
hard core Yukawa fluid (HCYF): a closure, based on a mean spherical
approximation ansatz, is studied in detail and its intriguing relationship to
the self consistent Ornstein-Zernike approximation is discussed. The asymptotic
properties, close to the critical point are investigated and compared to the
renormalization group results both above and below the critical temperature.
The HRT free energy is always a convex function of the density, leading to flat
isotherms in the two-phase region with a finite compressibility at coexistence.
This makes HRT the sole liquid-state theory able to obtain directly fluid-fluid
phase equilibrium without resorting to the Maxwell construction. The way the
mean field free energy is modified due to the inclusion of density fluctuations
suggests how to identify the spinodal curve. Thermodynamic properties and
correlation functions of the HCYF are investigated for three values of the
inverse Yukawa range: z=1.8, z=4 and z=7 where Monte Carlo simulations are
available. The stability of the liquid-vapor critical point with respect to
freezing is also studied.Comment: 23 pages, 15 figures, 1 tabl
Partitioning a macroscopic system into independent subsystems
We discuss the problem of partitioning a macroscopic system into a collection
of independent subsystems. The partitioning of a system into replica-like
subsystems is nowadays a subject of major interest in several field of
theoretical and applied physics, and the thermodynamic approach currently
favoured by practitioners is based on a phenomenological definition of an
interface energy associated with the partition, due to a lack of easily
computable expressions for a microscopic (i.e.~particle-based) interface
energy. In this article, we outline a general approach to derive sharp and
computable bounds for the interface free energy in terms of microscopic
statistical quantities. We discuss potential applications in nanothermodynamics
and outline possible future directions.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in JSTA
Diffusion of multiple species with excluded-volume effects
Stochastic models of diffusion with excluded-volume effects are used to model
many biological and physical systems at a discrete level. The average
properties of the population may be described by a continuum model based on
partial differential equations. In this paper we consider multiple interacting
subpopulations/species and study how the inter-species competition emerges at
the population level. Each individual is described as a finite-size hard core
interacting particle undergoing Brownian motion. The link between the discrete
stochastic equations of motion and the continuum model is considered
systematically using the method of matched asymptotic expansions. The system
for two species leads to a nonlinear cross-diffusion system for each
subpopulation, which captures the enhancement of the effective diffusion rate
due to excluded-volume interactions between particles of the same species, and
the diminishment due to particles of the other species. This model can explain
two alternative notions of the diffusion coefficient that are often confounded,
namely collective diffusion and self-diffusion. Simulations of the discrete
system show good agreement with the analytic results
Fourier's Law in a Generalized Piston Model
A simplified, but non trivial, mechanical model -- gas of particles of
mass in a box partitioned by mobile adiabatic walls of mass --
interacting with two thermal baths at different temperatures, is discussed in
the framework of kinetic theory. Following an approach due to Smoluchowski,
from an analysis of the collisions particles/walls, we derive the values of the
main thermodynamic quantities for the stationary non-equilibrium states. The
results are compared with extensive numerical simulations; in the limit of
large , and , we find a good approximation of
Fourier's law.Comment: 14 pages, 5 figure
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