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Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics…
Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…
We present an overview of phase field modeling of active matter systems as a tool for capturing various aspects of complex and active interfaces. We first describe how interfaces between different phases are characterized in phase field…
The theory of elastic rods can be used to describe certain geometric and topological properties of the DNA molecules. A similar effective field theory approach was previously suggested to describe the conformations and dynamics of proteins.…
Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles, and predict the…
Six major frameworks have emerged attempting to describe particle physics beyond the Standard Model. Despite their different theoretical genera, these frameworks have a number of common phenomenological features and problems. While it will…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Phase separation, crucial for spatially segregating biomolecules in cells, is well-understood in the simple case of a few components with pairwise interactions. Yet, biological cells challenge the simple picture in at least two ways: First,…
Modeling and simulation are recognized as important aspects of the scientific method for more than 70 years but its adoption in biology has been slow. Debates on its representativeness, usefulness, and whether the effort spent on such…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
The quantitative description of marine systems is constrained by a major issue of scale separation: most marine biochemical processes occur at sub-centimeter scales, while the contribution to the Earth's biogeochemical cycles is expressed…
We discuss the dynamics of a quintessence model involving two coupled scalar fields. The model presents two types of solutions, namely solutions that correspond to eternal and transient acceleration of the universe. In both cases, we obtain…
We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several…
Particle-in-Cell (PIC) methods employ particle representations of unknown fields, but also employ continuum fields for other parts of the problem. Thus projection between particle and continuum bases is required. Moreover, we often need to…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
A mathematical model of the Universe evolution, based on asymmetric doublet of classical and phantom dcalar Higgs fields with a kinetic connection between the components, has been constructed and studied. A detailed qualitative analysis was…
The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an…