Curious behaviour of the diffusion coefficient and friction force for the strongly inhomogeneous HMF model
نویسنده
چکیده
We present first elements of kinetic theory appropriate to the inhomogeneous phase of the HMF model. In particular, we investigate the case of strongly inhomogeneous distributions for T → 0 and exhibit curious behaviour of the force auto-correlation function and friction coefficient. The temporal correlation function of the force has an oscillatory behaviour which averages to zero over a period. By contrast, the effects of friction accumulate with time and the friction coefficient does not satisfy the Einstein relation. On the contrary, it presents the peculiarity to increase linearly with time. Motivated by this result, we provide analytical solutions of a simplified kinetic equation with a time dependent friction. Analogies with self-gravitating systems and other systems with long-range interactions are also mentioned. PACS. 05.20.-y Classical statistical mechanics – 05.45.-a Nonlinear dynamics
منابع مشابه
Relaxation of the distribution function tails for systems described by Fokker-Planck equations.
We study the formation and the evolution of velocity distribution tails for systems with weak long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a Fokker-Planck equation where the diffusion coefficient depends on the velocity. We extend the theory of Potapenko et al [Phys. Rev. E 56, 7159 (1997)] developed for...
متن کاملInvestigation of the Forming Force in Torsion Extrusion Process of Aluminum Alloy 1050
In this paper, torsion extrusion (TE) process on 1050 aluminum alloy was investigated by simulation as a severe plastic deformation (SPD) method and the effects of friction coefficient, angular velocity of the rotating die and punch speed on maximum punch force were studied. A finite element (FE) model was developed to simulate the TE process via DEFORM software. The FE results were validated co...
متن کاملA New Temper Rolling Force Model for Dry Thick Strip Considering Fully Elastic Contact
Temper rolling or skin pass rolling is one of cold rolling processes composed of a horizontal pass cold rolling mill stand. In this process, the thick strip is subjected to very light reduction (0.5–4%) in thickness in the presence of high friction amplitudes. One of the basic parameters of strip rolling processes is temper rolling force. A new rolling force model has been proposed for temper r...
متن کاملA New Temper Rolling Force Model for Dry Thick Strip Considering Fully Elastic Contact
Temper rolling or skin pass rolling is one of cold rolling processes composed of a horizontal pass cold rolling mill stand. In this process, the thick strip is subjected to very light reduction (0.5–4%) in thickness in the presence of high friction amplitudes. One of the basic parameters of strip rolling processes is temper rolling force. A new rolling force model has been proposed for temper r...
متن کاملRelaxation of a test particle in systems with long-range interactions: diffusion coefficient and dynamical friction
Abstract. We study the relaxation of a test particle immersed in a bath of field particles interacting via weak long-range forces. To order 1/N in the N → +∞ limit, the velocity distribution of the test particle satisfies a Fokker-Planck equation whose form is related to the Landau and Lenard-Balescu equations in plasma physics. We provide explicit expressions for the diffusion coefficient and ...
متن کامل