129 research outputs found
Continuous Model for Homopolymers
We consider the model for the distribution of a long homopolymer in a
potential field. The typical shape of the polymer depends on the temperature
parameter. We show that at a critical value of the temperature the transition
occurs from a globular to an extended phase. For various values of the
temperature, including those at or near the critical value, we consider the
limiting behavior of the polymer when its size tends to infinity
A fractional kinetic process describing the intermediate time behaviour of cellular flows
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging principle on shorter time scales. As a consequence of our main theorem, we obtain a homogenization result for the associated advection-diffusion equation. We show that on intermediate time scales the effective equation is a fractional time PDE that arises in modelling anomalous diffusion
Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
We extend the framework of forward and reverse processes commonly utilized in
the derivation and analysis of the nonequilibrium work relations to
thermodynamic processes with repeated discrete feedback. Within this framework,
we derive a generalization of the detailed fluctuation theorem, which is
modified by the addition of a term that quantifies the change in uncertainty
about the microscopic state of the system upon making measurements of physical
observables during feedback. As an application, we extend two nonequilibrium
work relations: the nonequilibrium work fluctuation theorem and the
relative-entropy work relation.Comment: 7 pages, 3 figure
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
B-1a cells acquire their unique characteristics by bypassing the pre-BCR selection stage
B-1a cells are long-lived, self-renewing innate-like B cells that predominantly inhabit the peritoneal and pleural cavities. In contrast to conventional B-2 cells, B-1a cells have a receptor repertoire that is biased towards bacterial and self-antigens, promoting a rapid response to infection and clearing of apoptotic cells. Although B-1a cells are known to primarily originate from fetal tissues, the mechanisms by which they arise has been a topic of debate for many years. Here we show that in the fetal liver versus bone marrow environment, reduced IL-7R/STAT5 levels promote immunoglobulin kappa gene recombination at the early pro-B cell stage. As a result, differentiating B cells can directly generate a mature B cell receptor (BCR) and bypass the requirement for a pre-BCR and pairing with surrogate light chain. This 'alternate pathway' of development enables the production of B cells with self-reactive, skewed specificity receptors that are peculiar to the B-1a compartment. Together our findings connect seemingly opposing lineage and selection models of B-1a cell development and explain how these cells acquire their unique properties
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