Collisional Langevin approach to bed load sediment velocity distributions

<p>Bed load experiments reveal a range of possibilities for the downstream velocity distributions of moving particles, including normal, exponential, and gamma distributions. Although bed load velocities are key for understanding fluctuations in transport rates, existing models have not accounted for the full range of observations. Here, we present a generalized Langevin model of particle transport that includes turbulent drag and episodic particle-bed collisions. By means of analytical calculations, we demonstrate that momentum dissipation by particle-bed collisions controls the form of the bed load velocity distribution. As collisions vary between elastic and inelastic, the velocity distribution interpolates between normal and exponential. These results add context to conflicting experiments on bed load velocities and suggest that granular interactions regulate sediment dynamics and transport rate fluctuations.</p>

Harmonic oscillator Brownian motion: Langevin approach revisited

The original strategy applied by Langevin to Brownian movement problem is used to solve the case of a free particle under a harmonic potential. Such straightforward strategy consists in separating the noise termin the Langevin equation in order to solve a deterministic equation associated with the Mean Square Displacement (MSD). In this work, to achieve our goal we first calculate the variance for the stochastic harmonic oscillator and then the MSD appears immediately. We study the problem in the damped and lightly damped cases and show that, for times greater than the relaxation time, Langevin's original strategy is quite consistent with the exact theoretical solutions reported by Chandrasekhar and Lemons, these latter obtained using the statistical properties of a Gaussian white noise. Our results for the MSDs are compared with the exact theoretical solutions as well as with the numerical simulation.

The description of the excitation energy sharing in nuclear fission within the Langevin approach

We apply the four-dimensional Langevin approach to the description of fission of 235U by neutrons and calculate the dependence of the excitation energy of fission fragments on their mass number. For this we run the Langevin equations until the compound nucleus splits into two separated fragments. This is possible since the we used in this work two-center shell model shape parametrization that describes well both compact and separated shapes. The excitation energies of each fragment are calculated assuming that the temperatures of both fragments are the same. The deformation energy of the fragment immediately after scission is added to its excitation energy. The saw-tooth structure of the dependence neutron multiplicity on the fragment’s mass number in reaction 235U + n at En = 5 Mev is qualitatively reproduced.