Related papers: Biological Growth in Bodies with Incoherent Interf…
The anomalous bulk-boundary correspondence in non-Hermitian systems featuring an intricate interplay between skin and boundary modes has attracted enormous theoretical and experimental attention. Still, in dimensions higher than one, this…
Unstoppable feedback loops and tipping points in socio-ecological systems are the main threats to sustainability. These behaviors have been extensively studied, notably to predict, and arguably deviate, dead-end trajectories. Behind the…
Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such…
Biological growth is often driven by mechanical cues, such as changes in external pressure or tensile loading. Moreover, it is well known that many living tissues actively maintain a preferred level of mechanical internal stress, called the…
A simple model for an interface moving in a disordered medium is presented. The model exhibits a transition between the two universality classes of interface growth phenomena. Using this model, it is shown that the application of…
Biofilm infections on medical implants are difficult to eradicate because insufficient nutrient availability promotes antibiotic-tolerant persister cells that survive treatment and reseed growth. Existing mathematical models usually omit…
Since laws of physics exist in nature, their possible relationship to terrestial growth is introduced. By considering the human body as a dynamic system of variable mass (and volume), growing under a gravity field, it is shown how natural…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient…
Understanding the spatial organisation of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical -- or epigenetic -- marks that are deposited along the genome are thought to play an…
Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. We propose a classification scheme of growth laws which includes human aging,…
Throughout biology, hierarchy is a recurrent theme in the geometry of structures where strength is achieved with minimal use of material. Acting over vast timescales, evolution has brought about beautiful solutions to problems of…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
A theory of aging based on the principles of the kinetics of chemical reactions and the rules of natural selection of organisms is proposed. The theory is based on a hypothesis that the biochemical processes in the organism can be described…
These are lecture notes of a course given at the 9th International Summer School on Fundamental Problems in Statistical Mechanics, held in Altenberg, Germany, in August 1997. In these notes, we discuss at an elementary level three themes…
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces…