Related papers: The physical leaky tank car problem, revisited
A fully non-dimensional correlation for the Nusselt number associated to cooling processes in vertical storage tanks under laminar natural convection is presented. The derived correlation depends on the average temperature and can be used…
A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
In this paper the analogy between a thermal engine and a waterwheel is developed in details, showing that the analogous of the flow of water in an hydraulic engine is the flow of entropy in a thermal one. This analogy mat serve to analyse…
The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…
The problem of a weak shock, reflected and diffracted by a wedge, is studied for the two-dimensional compressible Euler system. Some recent developments are overviewed and a perspective is presented within the context of a real gas, modeled…
These lecture notes have been prepared as a course in fluid mechanics up to the presentation of the millennium problem listed by the Clay Mathematical Institute. At the end, a very modern aspect of fluid mechanics is covered concerning the…
We show analytically that Newtonian iterations, when applied to a polynomial equation, have a positive topological entropy. In a specific example of an attempt to ``find'' the real solutions of the equation $x^2+1=0$, we show that the…
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…
The physics of walking is explored, using a toy as a concrete example and a 'toy' model applied to it. Besides the Newton's second law, the problem is also discussed from the thermodynamical perspective. Once the steady state (constant…
We want to understand whether and to which extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for…
It is shown that the Rayleigh's dissipation function can be successfully applied in the solution of mechanical problems involving friction non-linear in the velocities. Through the study of surfaces at contact we arrive at a simple integral…
We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient…
The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular moment. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle,…
Given a multilevel system coupled to a bath, we use a Feshbach P,Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace $\mathcal{S}_{i}$ of the system. The resultant equation properly treats the…
Flows involving liquid-coated grains are ubiquitous in nature (pollen capture, avalanches) and industry (air filtration, smoke-particle agglomeration, pharmaceutical mixing). In this work, three-body collisions between liquid-coated spheres…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We demonstrate that a Finite Bath Fluctuation Theorem of the Crooks type holds for systems that have been thermalized via weakly coupling it to a bath with energy independent finite specific heat. We show that this theorem reduces to the…
A recent first-principles approach to the non-linear rheology of dense colloidal suspensions is evaluated and compared to simulation results of sheared systems close to their glass transitions. The predicted scenario of a universal…
Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…