A model for effective interactions in binary colloidal systems of soft particles

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we propose a theory of binary systems which results in a relatively simple analytical expression combining arbitrary microscopic potentials into the effective interaction. The derivation is based on translating many particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language. Such transformation turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. In result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the effective attraction as a demixing factor in the binary systems of Gaussian particles, effective interactions in the binary mixtures of Yukawa particles and the system of particles consisting of both repulsive core and attractive/repulsive Yukawa interaction tail, for which we reproduce the 'attraction-through-repulsion' and 'repulsion-through-attraction' effects.Comment: Second version of article, after major revision due to the comments from reviewers. Includes overhauled introductory section, new, more compact derivation and more elaborate examples than previousl

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicts frictionless regime and transient attraction effect

While the origin of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of Spatially Correlated Noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, we derive the formal formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by SCN and the adequate Fluctuation-Dissipation Relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g. the singular behavior for certain interaction types. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a non-equilibrium mechanism facilitating the molecular binding of the like-charged particles.Comment: expanded and revised version resubmitted to Phys. Rev.

Non-Gaussian polymers described by alpha-stable chain statistics: model, applications and effective interactions in binary mixtures

The Gaussian chain model is the classical description of a polymeric chain, which provides the analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the alpha stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of alpha stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the alpha-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains with heavy-tailed distributions of persistence length, polymers adsorbed to the surface and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the alpha-stable chain and the coarse-grained interaction potential between two chains is constructed. These results are employed to discuss the model of binary mixture consisting of the alpha-stable chains. On what follows, we establish the spinodal decomposition condition generalized to the particles described by the shape of alpha-stable distributions. This condition is finally applied to analyze the on-surface phase separation of adsorbed polymers, which are known to be described with heavy tailed statistics.Comment: Complete version prepared for submission to Phys. Rev.

Selections and their Absolutely Continuous Invariant Measures

Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $I\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects onto $I_{i.}$ We define the lower and upper maps $\tau_{1},$ $\tau_{2}$ by the lower and upper boundaries of $G_{i},i=1,....,n,$ respectively. We assume $\tau_{1}$, $\tau_{2}$ to be piecewise monotonic and preserving continuous invariant measures $\mu_{1}$ and $\mu_{2}$, respectively. Let $$ and $F^{(2)}$ be the distribution functions of $\mu_{1}$ and $\mu_{2}.$ The main results shows that for any convex combination $F$ of $$ and $F^{(2)}$ we can find a map $\eta$ with values between the graphs of $\tau_{1}$ and $\tau_{2}$ (that is, a selection) such that $F$ is the $\eta$-invariant distribution function. Examples are presented. We also study the relationship of the dynamics of multi-valued maps to random maps

Optical Coherence Tomography for Examination of Parchment Degradation

A novel application of Optical Coherence Tomography utilizing infrared light of 830 nm central wavelength for non invasive examination of the structure of parchment, some covered with iron gall ink, is presented. It is shown that both the parchment and the ink applied are sufficiently transparent to light of this wavelength. In the study, Spectral OCT (SOCT) as well as Polarisation Sensitive OCT (PS-OCT) techniques were used to obtain cross-sectional images of samples of parchment based on scattering properties. The second technique was additionally employed to recover the birefringence properties and the optical axis orientations of the sample. It was shown that freshly produced parchment exhibits a degree of birefringence. However, this property declines with ageing, and samples of old parchment completely depolarise the incident light

Atmospheric multiple scattering of fluorescence and Cherenkov light emitted by extensive air showers

Atmospheric scattering of light emitted by an air shower not only attenuates direct fluorescence light from the shower, but also contributes to the observed shower light. So far only direct and singly-scattered Cherenkov photons have been taken into account in routine analyses of the observed optical image of air showers. In this paper a Monte Carlo method of evaluating the contribution of multiply scattered light to the optical air shower image is presented, as well as results of simulations and a parameterization of scattered light contribution to measured shower signal.Comment: 27 pages, 18 figures, accepted for publication in NIM

WW-like maps with various instabilities of acim's

This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an absolutely continuous invariant measure $\mu_a$. Depending on whether $\frac{1}{s_1}+\frac{1}{s_2}$ is larger, equal or smaller than 1, we show that the limit of $\mu_a$ is a singular measure, a combination of singular and absolutely continuous measure or an absolutely continuous measure, respectively. It is known that the invariant density of a single piecewise expanding map has a positive lower bound on its support. In Section 4 we give an example showing that in general, for a family of piecewise expanding maps with slopes larger than 2 in modulus and converging to a piecewise expanding map, their invariant densities do not necessarily have a positive lower bound on the support.Comment: 16 papges, 3 figure