Answer to comment on the paper of S. Dorbolo et al., Physica C 267 (1996) 24–30 entitled: Influence of Van Hove singularity on the electronic specific heat of high-Tc superconductors

Abstract

In their comment [1], J. Bok and J. Bouvier mentioned the lack of validity of work starting with the specific heat formula Eq. (1) in our paper [2]. They discussed two other points i.e. the variation of the physical parameters as well as the electronic band structure. Even though their points are well taken, we show that our conclusions are still valid from a qualitative point of view.In thermodynamics, the specific heat can be considered as the first derivative of the entropy, the first derivative of the internal energy or the second derivative of the free energy [3]. In Ref. [4], G. Rickayzen starts from the entropy S in order to compute the electronic specific heat co= ~)v=where fk is the Fermi-Dirac distribution function and E k is the quasiparticle spectrum:We computed the electronic specific heat C e from* E-mail: dorbolo@gw.unipc.ulg.ac.be.with U the internal energy. It is claimed in Eq.(1) that the last equality in Eq. (2) is invalid. In fact, the quasiparticle spectrum is defined bywhere u k and v k are the coefficients of the linear combination of creation and destruction operators of quasiparticles [5]. Therefore, after taking the temperature derivative of U in Eq. (3), Eq. (1) is found again. The difference between Eq. (2) and the r.h.s of Eq. (1) is Ek(OEk/OT)fk. This term becomes the most important one close to T~ when the gap varies strongly. Using Eq.(1), a few modifications to our previous results occur but the main qualitative conclusions are exactly obtained.In Fig. 1, we compare the electronic specific heat calculated with Eq. (2) and Eq. (1) for the same set of physical parameters A(0) = 20 meV and m* = 8 m 0. At low temperature, both results are quite similar. A linear contribution is observed. As expected, the deviation is more important when the temperature lies close to T~.The specific heat singularity at T¢ observed in many systems, though quantitatively different from each other, can still be explained with a quasiparticle spectrum containing a d-wave gap parameter for reasonable values of the physical parameters i.e.

Role of driving force on the clogging of inert particles in a bottleneck

“…Then, the average flow rate is calculated from all the avalanches obtained for the same value of . As expected [17][18][19][20], the flow rate increases with √ . Remarkably, the deviations from this behavior are found to be negligible over four orders of magnitude of the driving force.…”

“…This dependence was explained by assuming that the particles fall freely under the action of gravity from a height proportional to the size of the outlet [18]. Recent experimental results reported a dependence of the particle velocities on the outlet size, which is compatible with this idea [19], and a proof of the dependence of the flow rate on √ g by varying the force in a centrifuge [20]. Nevertheless, none of these experiments has studied systematically the effect of driving force on clogging.…”

“…4 and previously reported in Refs. [17,19,20]. Thus, the velocity increase could lead to a reduction of the probability of forming an arch, with the corresponding increase of the avalanche size.…”

Collision of Two Mass Baton With Massive External Surfaces

“…One of the simplest systems that includes multiple impacts is the collision of batons (also called dimers by others [6,7]) with extemal surfaces. Baton consists of two spherical balls connected by a light rod.…”

“…The contact phase, a unilaterally constrained motion, can be described as at least one end sliding on the ground. The solution for the ground impact of the baton during its flight phase has already been investigated in the literature (see [6][7][8][9]). …”