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We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of…
The inclusion of convection in stellar evolution models lacks realism, especially near convective-radiative interfaces. Furthermore, the interaction of convection with oscillations prevent us from accurately predicting seismic frequencies,…
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense…
By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of…
A four-dimensional differential Euler-Lagrange equation for continuously distributed materials is derived based on the principle of least action, and instead of Lagrangian, this equation contains the Lagrangian density. This makes it…
The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present…
We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the numerical integration approach based on the Langevin equation and is…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
A detailed program is proposed in the Lagrangian formalism to investigate the dynamical behavior of a theory with singular Lagrangian. This program goes on, at different levels, parallel to the Hamiltonian analysis. In particular, we…
We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is…
Run-and-tumble processes successfully model several living systems. While studies have typically focused on particles with isotropic tumbles, recent examples exhibit "tumble-turns", in which particles undergo 90{\deg} tumbles and so possess…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
This paper is interested in the description of the density of particles evolving according to some optimal policy of an impulse control problem. We first fix sets on which the particles jump and explain how we can characterize such a…
We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some…
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical…