A phase-field crystal model (PFC model) which takes into account exponential relaxation of the atomic flux and its fluctuations is developed. The model corresponds to a system undergoing phase transformation described with a partial differential equation of hyperbolic type. Such a model covers slow and rapid regimes of interface propagation at small and large driving forces during melting and solidification. The analysis is done for the evolution of atomic crystal lattices appearing from a metastable homogeneous liquid for the chemically pure system supercooled below its critical temperature. Numerical simulation of the system "Liquid -Body Centered Cubic (BCC) crystal lattice" allows us to formulate the hypothesis about the formation of metastable periodic solutions (atomic configurations which are not in the thermodynamic equilibrium) during the relaxation of atomic configurations to the stable equilibrium. These metastable states may be destroyed (or even avoided) due to the action of colored noise. Namely, considering spatiotemporal correlations of the atomic flux fluctuations, we have found that the temporal correlations promote selecting long-range atomic lattices, whereas the spatial correlations corresponding to the periodic structure scales decelerate such processes.

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Thermally induced shape memory poly­(ε-caprolactone) (PCL)-based polymers are one of the most extensively researched families of biocompatible materials. They are degradable under physiological conditions and have high applicability in general biomedical engineering, with cross-linked PCL networks being particularly useful for tissue engineering. In this study, we used the optimized potentials for liquid simulations (OPLS) force field, which is well suited for describing intermolecular interactions in biomolecules, and the class II polymer consistent force field (PCFF) to investigate the properties of telechelic PCL with diacrylates as reactive functionalities on its end groups. PCFF has been specifically parameterized for simulating synthetic polymeric materials. We compare the findings of all-atom molecular dynamics simulations with known experimental data and theoretical assumptions to verify the applicability of both these force fields. We estimated the melt density, volume, transition temperatures, and mechanical characteristics of two-branched PCL diacrylates with a molecular weight of 2481 Da. Our findings point to the utility of the aforementioned force fields in predicting the properties of PCL-based polymers. It also opens avenues for developing PCL cross-linked polymer models and employing OPLS to investigate the interactions of synthetic polymers with biomolecules.

Modeling of crystal micro-structures and their dynamics during fast phase transitions can be performed by the phase-field crystal (PFC) model in the hyperbolic formulation (Modified Phase Field Crystal [MPFC] model). This method is suitable for a continual modeling of the atomic density field at diffusion time intervals (slow diffusion dynamics) and short intervals of atomic flux relaxation (fast structural relaxation). Since the PFC model describes transitions of the first and second order, we present a description of both transitions in a unified manner. We show how phase transitions of each order can be treated using specific analytical transformations. To justify the unified approach to description of the first-and second-order transformations, we provide results of numerical simulation of phase changes between homogeneous structure and Body Centered Cubic (BCC) crystal lattice. The set of benchmarks for different domains shows coincidence of instantaneous atomic distributions and free energies in both forms.

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Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach. The main limitations and ways to minimize them are the subjects of discussion as well. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.