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In this article we implemented simulations of the OFC model for earthquakes for two different topologies: regular and small-world, where in the latter the links are randomly rewired with probability $p$ . In both topologies, we have studied…
This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor…
The standard derivation of the Oldroyd-B model starts from a coupled system of the momentum equation for the macroscopic flow on the one hand, and Fokker-Planck dynamics for molecular dumbbells on the other. The constitutive equation is…
Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake…
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process.…
Using 9-sets of different laboratory earthquake tests, we examined the nature of cracking under true triaxial stress conditions in the lithosphere . We found that 3D stress state can induce oblique nucleation of many fractures, forming…
Classifier free guidance is a standard method for conditional sampling in diffusion models, but its sampling rule is not aligned with the objective used in training. This mismatch induces a structural sampling error through the interaction…
Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…
Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m^6) theory. In this model m = (N-Z)/A is the order parameter, a consequence of (one of) the…
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation…
The earthquake source after the main shock can theoretically be represented as a black box without an entrance. At the output, there is a signal in the form of aftershocks, the frequency of which decreases on average with time according to…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
Histogram-reweighting grand canonical Monte Carlo simulations are used to obtain the critical properties of lattice chains composed of solvophilic and solvophobic monomers. The model is a modification of one proposed by Larson \emph{et al.}…
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on…
Understanding the oscillating behaviors that govern organisms' internal biological processes requires interdisciplinary efforts combining both biological and computer experiments, as the latter can complement the former by simulating…
Regional dynamics of Bay of Bengal is studied using Open Boundary Condition (OBC) in Modular Ocean Model (MOM) to understand the effect of primary and secondary mesoscale features on various bulk ocean products and turbulent fluxes. A…
Classical empirical force fields have dominated biomolecular simulation for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability…