Related papers: Continuous-time multifarious systems -- Part II: n…
In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of…
Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects.…
Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling…
We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
We discuss recent observational data on the transverse and radial velocities, as well as on the masses of the main components of the Orion Trapezium. Based on the most reliable values of these quantities we study the dynamical evolution of…
We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system…
Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external…
The importance of unspanned macroeconomic variables for Dynamic Term Structure Models has been intensively discussed in the literature. To our best knowledge the earlier studies considered only linear interactions between the economy and…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
A distinguishing feature of a multicellular living system is that it operates at various scales, from the intracellular to organismal. Very little is known at present on how tissue level properties are related to cell and subcellular…
Understanding the influence of activity on dense amorphous assemblies is crucial for biological processes such as wound healing, embryogenesis, or cancer progression. Here, we study the effect of self-propulsion forces of amplitude $f_0$…
This paper is about partitioning in parallel and distributed simulation. That means decomposing the simulation model into a numberof components and to properly allocate them on the execution units. An adaptive solution based on…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…