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In this thesis a new model for calculating the total energy of atomic and solid systems is presented. The model is used to study the properties of the Si(100) surface and dislocation dynamics in the diamond structure. For the Si(100)…
We focus on finding a coarse grained description able to reproduce the thermodynamic behavior of a molecular system by using mesoparticles representing several molecules. Interactions between mesoparticles are modelled by an interparticle…
In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very…
The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were…
The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk…
Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question…
The formal link between the linear combination of atomic orbitals approach to density functional theory and two-center Slater-Koster tight-binding models is used to derive an orthogonal $d$-band tight-binding model for iron with only two…
The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar…
A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…
An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
The time evolution of the formation probability of native bonds has been studied for designed sequences which fold fast into the native conformation. From this analysis a clear hierarchy of bonds emerge a) local, fast forming highly stable…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
We introduce an approach to exploit the existence of multiple levels of description of a physical system to radically accelerate the determination of thermodynamic quantities. We first give a proof of principle of the method using two…
Based on an analysis of the short range chemical environment of each atom in a system, standard machine learning based approaches to the construction of interatomic potentials aim at determining directly the central quantity which is the…
We present a tight-binding potential for transition metals, carbon, and transition metal carbides, which has been optimized through a systematic fitting procedure. A minimal basis, including the s, p electrons of carbon and the d electrons…
Simulations at the atomic scale provide a direct and effective way to understand the mechanical properties of materials. In the regime of classical mechanics, simulations for the thermodynamic properties of metals and alloys can be done by…
The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the…
Reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction…