Elastic collision | EPFL Graph Search

In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy. During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute). Collisions of atoms are elastic, for example Rutherford backscattering. A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta. The molecules—as distinct from at

Propriétés hors-équilibre d'une paroi adiabatique

Séverine Pache

We study the evolution of a system composed of N non-interacting particles of mass m distributed in a cylinder of length L. The cylinder is separated into two parts by an adiabatic piston of a mass M ≫ m. The length of the cylinder is a fix parameter and can be finite or infinite (in this case N is infinite). For the infinite case we carry out a perturbative analysis using Boltzmann's equation based on a development of the velocity distribution of the piston in function of a small dimensionless parameter ε = √(m/M). The non-stationary case is solved up to the order ε ;; our analysis shows that the system tends exponentially fast towards a stationary state where the piston has an average velocity V. The characteristic time scale for this relaxation is proportional to the mass of the piston (τ0 = M/A where A is the cross-section of the piston). We show that for equal pressures the collisions of the particles induce asymmetric fluctuations of the velocity of the piston which leads to a macroscopic movement of the piston in the direction of the higher temperature. In the case of the finite model a perturbative approach based on Liouville's equation (using the parameter α = 2m/(M + m)) shows that the evolution towards thermal equilibrium happens on two well separated time scales. The first relaxation step is a fast, deterministic and adiabatic evolution towards a state of mechanical equilibrium with approximately equal pressures but different temperatures. The movement of the piston is more or less damped. This damping qualitatively depends on whether the ratio R = Mgas/M between the total mass of the gas and the mass of the piston is small (R < 2) or large (R > 4). The second part of the evolution is much slower ; the typical time scales are proportional to the mass of the piston. There is a stochastic evolution including heat transfer leading to thermal equilibrium. A microscopic analysis yields the relation XM(t) = L(1/2 - ξ(at)) where the function ξ is independent of M. Using the hypothesis of homogeneity (i.e. the values of the densities, pressures and temperatures at the surface of the piston can be replaced by their respective average values) introduced in the previous analysis the observed damping does not show up. This can be explained by shock waves propagating between the piston and the walls at the extremities of the cylinder. In order to study the behaviour of the system there is hence a need to adequately describe the non-equilibrium fluids around the piston. We carry out an analysis of the infinite case, based on the perturbative approach introduced earlier. In this case the initial conditions are chosen in such a manner that the piston on average stays at the origin. It is shown that it is possible to describe the evolution of the fluids in such a way that it is coherent with the two laws of thermodynamics and the phenomenological relationships. Finally we study the case of a constant velocity of the piston in a finite cylinder. Such a condition and elastic collisions allow us to derive an explicit expression for the distribution of the fluids and hence for the hydrodynamics fields. This expression reveals the presence of shock waves between the piston and the extremities of the cylinder.

EPFL2004

Luminosity control and beam orbit stability with beta star leveling at LHC and HL-LHC

Arkadiusz Andrzej Gorzawski

This thesis describes the wide subject of the luminosity leveling and its requirements for the LHC and the HL-LHC. We discuss the advantages and disadvantages of different leveling methods focusing the thesis on the beta star leveling technique. We review the beams offset build--up due to the environmental (i.e. natural ground motion) and mechanical (i.e. moving quadrupole) sources. We quantify the instrumentation requirements for the reliable and reproducible operation with small offsets at the interaction points. Last but not least, we propose a novel method for the beam offset stabilization at the collision point based on the feedback from the luminosity.

EPFL2016

Charge transfer dynamics in Ar+ + CO

Differential cross sections for the charge transfer reaction between Ar(+)and CO have been measured using three-dimensional velocity map imaging in a crossed beam setup at the two relative collision energies 0.55 and 0.74 eV. We find dominant forward scattering with CO(+)product ions predominantly in the vibrational levels=6,7 of the electronic ground state X. This is indicative of a direct resonant mechanism for the two argon spin-orbit states. At both collision energies also an isotropic distribution with product ions exhibiting high internal excitation is observed. This is more pronounced at the higher collision energy, where the first electronically excited state Abecomes accessible. We conclude that the A-state is partially populated by the product ions at 0.74 eV collision energy and suggest that the isotropic distribution stems from the formation of a charge-transfer complex, in concurrence with previously performed studies. [GRAPHICS] .

2020

Propriétés hors-équilibre d'une paroi adiabatique

Séverine Pache

EPFL2004