Entropy production in ac-calorimetry

In calorimetry and particularly in heat capacity measurements, different characteristic relaxation time constants may perturb the experiment which cannot be considered at thermodynamic equilibrium. In this case, thermodynamics of irreversible processes has to be taken into account and the calorimetric measurements must be considered as dynamic. In a temperature modulated experiment, such as ac-calorimetry, these non-equilibrium experiments give rise to the notion of frequency dependent complex heat capacity. In this paper, it is shown that for each irreversible process an experimental frequency dependent complex heat capacity can be inferred. Furthermore, we demonstrate rigorously that a same equality connects the imaginary part of these different complex heat capacities with the entropy produced during these irreversible processes. Finally, we claim that the presence of an imaginary part in the measured heat capacity always indicates that a certain amount of heat does not participate to the classical equilibrium heat capacity of the sample when measured over the observation time scale

Lagrangian Relations and Linear Point Billiards

Motivated by the high-energy limit of the $N$-body problem we construct non-deterministic billiard process. The billiard table is the complement of a finite collection of linear subspaces within a Euclidean vector space. A trajectory is a constant speed polygonal curve with vertices on the subspaces and change of direction upon hitting a subspace governed by `conservation of momentum' (mirror reflection). The itinerary of a trajectory is the list of subspaces it hits, in order. Two basic questions are: (A) Are itineraries finite? (B) What is the structure of the space of all trajectories having a fixed itinerary? In a beautiful series of papers Burago-Ferleger-Kononenko [BFK] answered (A) affirmatively by using non-smooth metric geometry ideas and the notion of a Hadamard space. We answer (B) by proving that this space of trajectories is diffeomorphic to a Lagrangian relation on the space of lines in the Euclidean space. Our methods combine those of BFK with the notion of a generating family for a Lagrangian relation.Comment: 29 pages, 4 figure

Implications of WMAP observations on Li abundance and stellar evolution models

The WMAP determination of the baryon-to-photon ratio implies, through Big Bang nucleosynthesis, a cosmological Li abundance larger, by a factor of 2 to 3, than the Li abundance plateau observed in the oldest Pop II stars. It is however inescapable that there be a reduction by a factor of at least 1.6 to 2.0 of the surface Li abundance during the evolution of Pop II field stars with [Fe/H] < -1.5. That the observed Li be lower than cosmologically produced Li is expected from stellar evolution models. Since at turnoff most of the Li abundance reduction is caused by gravitational settling, the presence of Lithium 6 in some turnoff stars is also understood. Given that the WMAP implications for Li cosmological abundance and the Li Spite plateau can be naturally explained by gravitational settling in the presence of weak turbulence, there appears little need for exotic physics as suggested by some authors. Instead, there is a need for a better understanding of turbulent transport in the radiative zones of stars. This requires simulations from first principles. Rather strict upper limits to turbulent transport are determined for the Sun and Pop II stars.Comment: The Astrophysical Journal, in pres

Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow

We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid

Supersonic propulsion simulation by incorporating component models in the large perturbation inlet (LAPIN) computer code

An approach to simulating the internal flows of supersonic propulsion systems is presented. The approach is based on a fairly simple modification of the Large Perturbation Inlet (LAPIN) computer code. LAPIN uses a quasi-one dimensional, inviscid, unsteady formulation of the continuity, momentum, and energy equations. The equations are solved using a shock capturing, finite difference algorithm. The original code, developed for simulating supersonic inlets, includes engineering models of unstart/restart, bleed, bypass, and variable duct geometry, by means of source terms in the equations. The source terms also provide a mechanism for incorporating, with the inlet, propulsion system components such as compressor stages, combustors, and turbine stages. This requires each component to be distributed axially over a number of grid points. Because of the distributed nature of such components, this representation should be more accurate than a lumped parameter model. Components can be modeled by performance map(s), which in turn are used to compute the source terms. The general approach is described. Then, simulation of a compressor/fan stage is discussed to show the approach in detail

Towards an understanding of the phases of goodwill accounting in four Western capitalist countries: From stakeholder model to shareholder model

The objective of this paper is to illustrate that the change in shareholders’ attitude towards firms (from stakeholder model to shareholder model) influences the accounting treatments of goodwill. This study is based on four countries (Great Britain, the United States, Germany, and France) and covers more than a century, starting in 1880. The authors explain that all these countries have gone through four identified phases of goodwill accounting, classified as (1) “static”(immediate or rapid expensing), (2) “weakened static” (write-off against equity), (3) “dynamic” (recognition with amortization over a long period) and (4) “actuarial” (recognition without amortization but with impairment if necessary).Goodwill – Accounting history – Social nature of accounting – Stakeholder/shareholder models – Corporate governance; France; Germany; Great Britain; United States

Non-equilibrium heat capacity of polytetrafluoroethylene at room temperature

Polytetrafluoroethylene can be considered as a model for calorimetric studies of complex systems with thermodynamics transitions at ambient temperature. This polymer exhibits two phase transitions of different nature at 292 K and 303 K. We show that sensitive ac-calorimetry measurements allow us to study the thermodynamic behaviour of polytetrafluoroethylene when it is brought out of thermodynamic equilibrium. Thanks to the thermal modelisation of our calorimetric device, the frequency dependent complex heat capacity of this polymer is extracted. The temperature and frequency variations of the real and imaginary parts of the complex heat capacity are obtained when polytetrafluoroethylene undergoes its first-order structural phase transition at 292 K

A symplectic analog of the Quot scheme

We construct a symplectic analog of the Quot scheme that parametrizes the torsion quotients of a trivial vector bundle over a compact Riemann surface. Some of its properties are investigated.Comment: Comptes Rendus Math. (to appear