Related papers: Statistical hydraulic model for the Leonardo's rul…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…
Efficient locomotion is important for the evolution of complex life, yet the physical principles selecting specific swimming strokes often remain entangled with biological constraints. In viscous fluids, the scallop theorem constrains the…
Monte Carlo optimizations of Number Partitioning and of Diophantine approximations are microscopic realizations of `Trap Model' dynamics. This offers a fresh look at the physics behind this model, and points at other situations in which it…
River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and…
This paper studies two classes of variational problems introduced in [7], related to the optimal shapes of tree roots and branches. Given a measure $\mu$ describing the distribution of leaves, a sunlight functional $\S(\mu)$ computes the…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize…
We propose a new Monte Carlo scheme to study the late-time dynamics of a 2-dim hard sphere fluid, modeled by a tethered network of hard spheres. Fluidity is simulated by breaking and reattaching the flexible tethers. We study the diffusion…
Taylor's Law (TL) relates the variance to the mean of a random variable via power law. In ecology it applies to populationsand it is a common empirical pattern shared among different ecosystems. Measurements give power law exponent to be…
Static and dynamic structure factors and various transport coefficients are computed for a Lennard-Jones model of a binary fluid (A,B) with a symmetrical miscibility gap, varying both temperature and relative concentration of the mixture.…
We introduce a multiscale Monte Carlo algorithm to simulate dense simple fluids. The probability of an update follows a power law distribution in its length scale. The collective motion of clusters of particles requires generalization of…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We describe the simulation method of modelling the population evolution using Monte Carlo based on the Penna model. Individuals in the populations are represented by their diploid genomes. Genes expressed after the minimum reproduction age…
What are the general principles that allow proper growth of a tissue or an organ? A growing leaf is an example of such a system: it increases its area by orders of magnitude, maintaining a proper (usually flat) shape. How can this be…
The drying rate profile of granular beds can be divided into the constant rate period (CRP), which is characterized by a nearly constant drying rate, and the falling rate period (FRP), in which the drying rate rapidly decays. In order to…
Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…