Globule-coil transition in the dynamic HP model
We consider a dynamic version of the HP model of a linear polymer: a self-avoiding
walk on the square lattice, with monomers being either hydrophobic (H) or polar (P). We
simulate the model in two dimensions in the grand canonical assemble via the Berretti-Sokal
algorithm across the globule-coil transition and map out the phase diagram. Our results are
consistent with the universality class of the transition being the same as the universality class
of the theta-transition of an interacting self-avoiding walk.
We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute polymer solution is expressed as a function of the radius of gyration of the polymer and the average solvent number density within the gyration volume at the level of the mean-field approximation. Varying the strength of attraction between polymer and solvent we show that two qualitatively different regimes occur at the liquid-gas critical point. In case of weak polymer-solvent interactions the polymer chain is in a globular state. On the contrary, in case of strong polymer-solvent interactions the polymer chain attains an expanded conformation. We discuss the influence of the critical solvent density fluctuations on the polymer conformation. The reported effect could be used to excert control on the polymer conformation by changing the thermodynamic state of the solvent. It could also be helpful to estimate the solvent density within the gyration volume of the polymer for drug delivery and molecular imprinting applications.
We study the conformational behavior of polarizable polymer chain under an external homogeneous electric field within the Flory type self-consistent field theory. We consider the influence of electric field on the polymer coil as well as on the polymer globule. We show that when the polymer chain conformation is a coil, application of external electric field leads to its additional swelling. However, when the polymer conformation is a globule, a sufficiently strong field can induce a globule-coil transition.We show that such “field-induced” globule-coil transition at the sufficiently small monomer polarizabilities goes quite smoothly. On the contrary, when the monomer polarizability exceeds a certain threshold value, the globule-coil transition occurs as a dramatic expansion in the regime of first-order phase transition. The developed theoretical model can be applied to predicting polymer globule density change under external electric field in order to provide more efficient processes of polymer functionalization, such as sorption, dyeing, and chemical modification
We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.