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We numerically investigate the dynamic heterogeneity and its length scale found in the coarse-grained ionic liquid model systems. In our ionic liquid model systems, cations are modeled as dimers with positive charge, while anions are…
Building upon the classical chemo-mechanical theory of Larch{\'e} and Cahn for equilibrium, numerous studies have investigated the transport of species in solids, with or without trapping phenomena. In most applications -- such as the…
The temperature induced phase transition is investigated in the one-component scalar field \phi^4 model on a lattice by using Monte Carlo simulations. Using the GPGPU technology a huge amount of data is collected that gives a possibility to…
Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal.…
In view of recent intense experimental and theoretical interests in the biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), heteropolymer models with chain molecules configured as self-avoiding…
We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a…
We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is…
The problem of the helix-coil transition of biopolymers in explicit solvents, like water, with the ability for hydrogen bonding with solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide…
Thermoresponsive hydrogels exhibit reversible deswelling at the Volume Phase Transition (VPT), associated to a minimum of the Poisson's ratio $\nu$. Recent numerical investigations uncovered the occurrence of a Hyper-Auxetic Transition…
Effective pair interactions with a soft-repulsive component are a well-known feature of polymer solutions and colloidal suspensions, but they also provide a key to interpret the high-pressure behaviour of simple elements. We have computed…
The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard…
We present results for a lattice model of bio-polymers where the type of $\beta$-sheet formation can be controlled by different types of hydrogen bonds depending on the relative orientation of close segments of the polymer. Tuning these…
The basic models of helix-coil transitions in biomolecules are introduced. These include phenomenological, zipper (Bragg-Zimm) models of polypeptides, loop-entropy (Poland-Scheraga) and Hamiltonian (Peyrard-Bishop) models of homogeneous DNA…
Continuum Monte-Carlo simulations at constant pressure are performed on short chain molecules at surfaces. The rodlike chains, consisting of seven effective monomers, are attached at one end to a flat twodimensional substrate. It is found…
We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers…
The kinetic behavior of a three-dimensional off-lattice heteropolymer model is studied in terms of the time dependence of the average mean-square displacement between configurations. It is found that at short time-scales similar behavior is…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
We study geometrically frustrated antiferromagnets with magnetoelastic coupling. Frustration in these systems may be relieved by a structural transition to a low temperature phase with reduced lattice symmetry. We examine the statistical…