Consistent and transferrable coarse-grained model for semidilute polymer solutions in good solvent

We present a coarse-grained model for linear polymers with a tunable number of effective atoms (blobs) per chain interacting by intra- and inter-molecular potentials obtained at zero density. We show how this model is able to accurately reproduce the universal properties of the underlying solution of athermal linear chains at various levels of coarse-graining and in a range of chain densities which can be widened by increasing the spatial resolution of the multiblob representation, i.e., the number of blobs per chain. The present model is unique in its ability to quantitatively predict thermodynamic and large scale structural properties of polymer solutions deep in the semidilute regime with a very limited computational effort, overcoming most of the problems related to the simulations of semidilute polymer solutions in good solvent conditions.Comment: 19 pages, 15 figures, 3 table

Depletion effects in colloid-polymer solutions

The surface tension, the adsorption, and the depletion thickness of polymers close to a single nonadsorbing colloidal sphere are computed by means of Monte Carlo simulations. We consider polymers under good-solvent conditions and in the thermal crossover region between good-solvent and $\theta$ behavior. In the dilute regime we consider a wide range of values of $q$, from $q = 0$ (planar surface) up to $q\approx 30$-50, while in the semidilute regime, for $\rho_p/\rho_p^*\le 4$ ($\rho_p$ is the polymer concentration and $\rho_p^*$ is its value at overlap), we only consider $q = 0,0.5,1$ and 2. The results are compared with the available theoretical predictions, verifying the existing scaling arguments. Field-theoretical results, both in the dilute and in the semidilute regime, are in good agreement with the numerical estimates for polymers under good-solvent conditions.Comment: 26 pages, 12 figure

Integral-equation analysis of single-site coarse-grained models for polymer-colloid mixtures

We discuss the reliability of integral-equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterized by mutually interacting soft and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behavior when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we find that the hypernetted-chain approximation provides accurate estimates of thermodynamics and structure in the colloid-gas phase in which the density of colloids is small. On the other hand, all closures considered appear to be unable to describe the behavior of the mixture in the colloid-liquid phase, as they cease to converge at polymer densities significantly smaller than those at the binodal. As a consequence, integral equations appear to be unable to predict a quantitatively correct phase diagram.Comment: 16 pages, 11 figures, 3 table

Coarse-graining polymer solutions: a critical appraisal of single- and multi-site models

We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluid-fluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they presents a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.Comment: 23 pages, 9 figures, 4 table

Large-eddy simulation of cycle-resolved knock in a turbocharged SI engine

The paper presents a numerical study of cycle-to-cycle variability in a turbocharged GDI engine. The Large-Eddy Simulation technique is adopted in this study in conjunction with the recent ISSIM-LES model for spark-ignition, allowing a dedicated treatment of both the flame kernel formation and flame development phases. Numerical results are compared with an extended dataset of experimental test-bed acquisitions, where the engine is operated at knock-limited spark advance. The agreement of both ensemble averaged combustion pressure history and of its standard deviation confirm the validity of the adopted numerical framework able to correctly quantify the degree of CCV measured by the experiments. Knock tendency is evaluated by means of an in-house developed knock model, based on a tabulation technique for AI delays of the same RON98 gasoline as the one used in experiments. The results confirm the knock-free condition of the experimental KLSA, for which the cycle-resolved knock signature is extremely weak just for the cycles in the highest band of the CCV-affected combustion. The visualization of the pressure wave allows to identify the exhaust side as the most knock-prone region. Finally, spark-advance is increased by 3 CA with respect to the experimental edge-of knock limit, in order to simulate an experimentally prevented operating condition. Local pressure measurements mimicking flush-mounted transducers confirm the severe knock damage related to this condition. The predictive capability of the combustion CCV and of the adopted knock model confirm the heavy and recurrent cycle-resolved knock damage

Studio in silico dei meccanismi delle alternans cardiache nei modelli ORd e TNNP

Il cardiomiocita è un complesso sistema biologico in cui molti meccanismi interagiscono in maniera non lineare per regolare l'accoppiamento tra eccitazione elettrica e contrazione meccanica. Per questo motivo, lo sviluppo di modelli matematici è fondamentale nel campo dell'elettrofisiologia cardiaca, in cui l'uso di strumenti computazionali è diventato complementare alla sperimentazione classica. L'obiettivo di questo elaborato è stato quello di: 1) effettuare una revisione della letteratura sul tema delle alternans cardiache; 2) effettuare uno studio sperimentale in silico sulle alternans nei modelli di O'Hara-Rudy e di Ten Tusscher-Noble-Noble-Panfilov. Questo ha permesso di svelare le dinamiche molecolari e cellulari coinvolte nella genesi delle alternans, confermando come la modellazione matematica sia un ottimo strumento per lo studio dei meccanismi elettrofisiologici alla base delle aritmie cardiache

Analysis and Simulation of Non-Flamelet Turbulent Combustion in a Research Optical Engine

In recent years, the research community devoted many resources to define accurate methodologies to model the real physics behind turbulent combustion. Such effort aims at reducing the need for case-by-case calibration in internal combustion engine simulations. In the present work two of the most widespread combustion models in the engine modelling community are compared, namely ECFM-3Z and G-equation. The interaction of turbulent flows with combustion chemistry is investigated and understood. In particular, the heat release rate characterizing combustion, and therefore the identification of a flame front, is analysed based on flame surface density concept rather than algebraic correlations for turbulent burn rate. In the first part, spark-ignition (S.I.) combustion is simulated in an optically accessible GDI single-cylinder research engine in firing conditions. The turbulent combustion regime is mapped on the Borghi-Peters diagram for all the conditions experienced by the engine flame, and the consistency of the two combustion models is critically analysed. In the second part, a simple test case is defined to test the two combustion models in an ideally turbulence-controlled environment: this allows to fully understand the main differences between the two combustion models under well-monitored conditions. and results are compared against experimental databases of turbulent burn rate for wide ranges of Damkohler (Da) and Karlovitz (Ka) numbers. The joint experimental and numerical study presented in this paper evaluates different approaches within the unified flamelet/non-flamelet framework for modelling turbulent combustion in SI engines. It also indicates guidelines for reduced calibration effort in widespread combustion models

Predicting the thermodynamics by using state-dependent interactions

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We consider standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the low-density regime and polymer solutions under good-solvent conditions. Moreover, we show that the state-dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.Comment: 29 pages, 1 figure; To appear in J. Chem. Phy

Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part II: Les analysis

As discussed in the Part I of this paper, a numerical activity is carried out in order to analyse the effects of fuel composition modelling in a turbocharged GDI engine for sport car applications. While Part I analyses the "ensemble averaged" macroscopic effects on spray evolution, mixture stratification, combustion and knock tendency, in Part II of this paper cycle-to-cycle variations are analysed and discussed using a multi-cycle LES numerical framework, again comparing results from a more traditional single-component fuel surrogate model to those of a multi-component one. A purposely developed numerical approach is applied to properly account for the effects of the Discrete-Continuous-Multi-Component fuel formulation on the charge preparation: just before the spark timing, each vaporized fuel fraction is lumped back into a single-component surrogate fuel to allow the combustion model (ECFM-3Z, in its LES formulation) to take place. At the beginning of a new injection process, the numerical framework for the injected spray is switched back to Multi-Component, thus allowing each fuel fraction to independently spread, vaporize and diffuse in the combustion chamber according to the cycle-specific characteristics. A detailed comparison between the two fuel formulations is carried out on both average and rms values of the most influencing fields just before the spark discharge

Polymers as compressible soft spheres

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al., Soft Matter 6, 2282 (2010), and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radiiindependent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.Comment: 21 pages, 7 figure