Related papers: The physical leaky tank car problem, revisited
We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be…
Engines are open systems that can generate work cyclically, at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their…
We present a thermodynamics experiment suitable for first year undergraduate students employing Stirling Engines to create a demonstration of energy transformation and to measure the mechanical efficiency of such engines. Using an…
We report a detailed theoretical investigation on electrochemical capacitance of a nanoscale capacitor where there is a DC coupling between the two conductors. For this ``leaky'' quantum capacitor, we have derived general analytic…
We consider the planar Taylor-Couette system for the steady motion of a viscous incompressible fluid in the region between two concentric disks, the inner one being at rest and the outer one rotating with constant angular speed. We study…
Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a…
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr\"odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum…
In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the…
We consider the flow of a generalized Newtonian fluid through a thin porous medium of thickness $\epsilon$, perforated by periodically distributed solid cylinders of size $\epsilon$. We assume that the fluid is described by the 3D…
Motion of a cylinder dynamically interacting with n point vortices in a perfect fluid is considered. A nonliniear Poisson structure and two integrals of motion are found. The equations of motion a priori are not Hamiltonian. For n=1, the…
This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
The interaction of electrical fields and liquids can lead to phenomena that defies intuition. Some famous examples can be found in Electrohydrodynamics as Taylor cones, whipping jets or non-coalescing drops. A less famous example is the…
Leakages in drinking water distribution networks pose significant challenges to water utilities, leading to infrastructure failure, operational disruptions, environmental hazards, property damage, and economic losses. The timely…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
In this work we present some results from computer simulations of dynamical aspects of drop formation in a leaky faucet. Our results, which agree very well with the experiments, suggest that only a few elements, at the microscopic level,…
Fundamental aspects of inverse kinetic theories for the incompressible Navier-Stokes equations [Ellero and Tessarotto, 2004, 2005] include the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the…
Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore asked in [15] if hydrodynamics is capable…
Fluid flow past one or more solid bodies is a fundamental problem of much practical importance. Standard solutions of simplified problems involving incompressible inviscid irrotational flow past common geometries such as circular cylinders…
We study the mathematical evolution of a liquid fuel droplet inside a vessel. In particular, we analyze the evolution of the droplet radius on a finite time interval. The model problem involves an hyperbolic system coupled with the pressure…