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R. Blossey

Publications and source records attributed to R. Blossey.

13 recordsLinked to original sources
arXiv2026

Generalized Geometric Brownian motion and the Infinite Ergodicity concept

We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate that the existence of such a measure depends sensitively on the structure of the drift and diffusion terms, as well as on the chosen discretization scheme of the underlying stochastic dynamics. To ground our discussion, we draw motivation from phenomenological models in statistical theories of turbulence, where geometric Brownian motion serves as a classical example. To address situations where the standard invariant measure fails to exist, we heuristically explore the concept of infinite ergodicity, a notion recently introduced in the context of statistical physics for drift-diffusion stochastic processes.

cond-mat.stat-mech↗
arXiv2021

Ion Solvation in Dipolar Poisson models in a dual view

We study the classic problem of ion solvation within the continuum theory of Dipolar-Poisson models. In this approach an ion is treated as a point charge within a sea of point dipoles. Both the standard Dipolar-Poisson model as well as the Dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential $ϕ$. Applying the Legendre transform approach introduced by A.C. Maggs [A.C. Maggs, Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement and the polarization field. We show that the Dipolar-Poisson-Langevin functional generalizes the harmonic polarization functional used in the theory of Marcus for electron transfer rate to nonlinear regimes and can be quantitatively parametrized by molecular dynamics simulations for SPC/E-water.

cond-mat.soft↗
arXiv2018

Dual free energies in Poisson-Boltzmann theory

Poisson-Boltzmann theory allows one to study soft matter and biophysical systems involving point-like charges of low valencies. The inclusion of fluctuation corrections beyond the mean-field approach typically requires the application of loop expansions around a mean-field solution for the electrostatic potential \(ϕ({\bf r})\), or sophisticated variational approaches. Recently, Poisson-Boltzmann theory has been recast, via a Legendre transform, as a mean-field theory involving the dielectric displacement field \({\bf D}({\bf r})\). In this paper we consider the path integral formulation of the dual theory. Exploiting the transformation between \(ϕ\) and \({\bf D}\), we formulate a dual Sine-Gordon field theory in terms of the displacement field and provide a strategy for precise numerical computations of free energies beyond the leading order.

cond-mat.soft↗
arXiv2017

Structural interactions in ionic liquids linked to higher order Poisson-Boltzmann equations

We present a derivation of generalized Poisson-Boltzmann equations starting {from} classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by (Bazant et al., 2011), whereby the structuring near the surface is determined by bulk coefficients.

cond-mat.stat-mech↗
arXiv2009

On the equilibria of the MAPK cascade: cooperativity, modularity and bistability

In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. (PNAS 101, 1822 (2004)). The model and its solution are extended in several respects: a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.

q-bio.MN↗
arXiv2008

Mean-field vs. stochastic models for transcriptional regulation

We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.

q-bio.MN↗
arXiv2007

Compositionality, stochasticity and cooperativity in dynamic models of gene regulation

We present an approach for constructing dynamic models for the simulation of gene regulatory networks from simple computational elements. Each element is called a ``gene gate'' and defines an input/output-relationship corresponding to the binding and production of transcription factors. The proposed reaction kinetics of the gene gates can be mapped onto stochastic processes and the standard ode-description. While the ode-approach requires fixing the system's topology before its correct implementation, expressing them in stochastic pi-calculus leads to a fully compositional scheme: network elements become autonomous and only the input/output relationships fix their wiring. The modularity of our approach allows to pass easily from a basic first-level description to refined models which capture more details of the biological system. As an illustrative application we present the stochastic repressilator, an artificial cellular clock, which oscillates readily without any cooperative effects.

q-bio.MN↗
arXiv2007

Stability domains of actin genes and genomic evolution

In eukaryotic genes the protein coding sequence is split into several fragments, the exons, separated by non-coding DNA stretches, the introns. Prokaryotes do not have introns in their genome. We report the calculations of stability domains of actin genes for various organisms in the animal, plant and fungi kingdoms. Actin genes have been chosen because they have been highly conserved during evolution. In these genes all introns were removed so as to mimic ancient genes at the time of the early eukaryotic development, i.e. before introns insertion. Common stability boundaries are found in evolutionary distant organisms, which implies that these boundaries date from the early origin of eukaryotes. In general boundaries correspond with introns positions of vertebrates and other animals actins, but not much for plants and fungi. The sharpest boundary is found in a locus where fungi, algae and animals have introns in positions separated by one nucleotide only, which identifies a hot-spot for insertion. These results suggest that some introns may have been incorporated into the genomes through a thermodynamic driven mechanism, in agreement with previous observations on human genes. They also suggest a different mechanism for introns insertion in plants and animals.

q-bio.BM↗
arXiv2004

A novel formulation of nonlocal electrostatics

The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel formulation allowing for numerical solutions for the nontrivial molecular geometries arising in the applications mentioned before. Our approach is based on the introduction of a secondary field, $ψ$, which acts as the potential for the rotation free part of the dielectric displacement field ${\bf D}$. For many relevant models, the dielectric function of the medium can be expressed as the Green's function of a local differential operator. In this case, the resulting coupled Poisson (-Boltzmann) equations for $ψ$ and the electrostatic potential $ϕ$ reduce to a system of coupled PDEs. The approach is illustrated by its application to simple geometries.

physics.class-ph↗
arXiv2003

Using nonlocal electrostatics for solvation free energy computations: ions and small molecules

Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii in a consistent way. We test our approach on simple ions and small molecules for which both experimental results and other theoretical descriptions are available for quantitative comparison. We conclude that our approach is both physically transparent and quantitatively reliable.

physics.bio-ph↗
arXiv2002

Dispersion of imbibition fronts

We have studied the dispersive behaviour of imbibition fronts in a porous medium by X-ray tomography. Injection velocities were varied and the porous medium was initially prewetted or not. At low velocity in the prewetted medium, the imbibition profiles are found to be distinctly hyperdispersive. The profiles are anomalously extended when compared to tracer fronts exhibiting conventional (Gaussian) dispersion. We observe a strong velocity dependence of the exponent characterizing the divergence of the dispersion coefficient for low wetting-fluid saturation. Hyperdispersion is absent at high imbibition velocities or when the medium is not prewetted.

cond-mat.stat-mech↗
arXiv1996

Critical holes in undercooled wetting layers

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be mapped onto an autonomous dynamical system in a three-dimensional phase space. The corresponding flux has a polynomial form and in general displays four fixed points, each with different stability properties. On the basis of this picture we derive the thermodynamic behaviour of critical holes in three different nucleation regimes of the phase diagram.

cond-mat.stat-mech↗