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We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
The biological cell exhibits a fantastic range of behaviors, but ultimately these are governed by a handful of physical and chemical principles. Here we explore simple theory, known for decades and based on the simple thermodynamics of…
We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
The computational treatment of many-electron systems capable of exchanging {electrons and nuclei} with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of…
It is shown that a hot relativistic fluid could be viewed as a collection of self-interacting quantum objects. They obey a nonlinear equation which is a modification of the quantum equation obeyed by elementary constituents of the fluid. A…
Electrostatic correlations play an important role in physics, chemistry and biology. In plasmas they lead to thermodynamic instability similar to the liquid-gas phase transition of simple molecular fluids. For charged colloidal suspensions…
Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of…
We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional $\cal F$ for the coarse-grained solvent, cation, and anion densities, including the Debye-H\"uckel…
Experimental measurements of interactions in ionic liquids and concentrated electrolytes over the past decade or so have revealed simultaneous monotonic and oscillatory decay modes. These observations have been hard to interpret using…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology,…
Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called…