arXiv subjects

Henni Ouerdane

Publications and source records attributed to Henni Ouerdane.

32 records · Page 2Linked to original sources

arXiv2020

Modeling flywheel energy storage system charge and discharge dynamics

Energy storage technologies are of great practical importance in electrical grids where renewable energy sources are becoming a significant component in the energy generation mix. Here, we focus on some of the basic properties of flywheel energy storage systems, a technology that becomes competitive due to recent progress in material and electrical design. While the description of the rotation of rigid bodies about a fixed axis is classical mechanics textbook material, all its basic aspects pertinent to flywheels, like, e.g., the evaluation of stress caused by centripetal forces at high rotation speeds, are either not covered or scattered over different sources of information; so it is worthwhile to look closer at the specific mechanical problems for flywheels, and to derive and clearly analyse the equations and their solutions. The connection of flywheels to electrical systems impose particular boundary conditions due to the coupling of mechanical and electrical characteristics of the system. Our report thus deal with the mechanical design in terms of stresses in flywheels, particularly during acceleration and deceleration, considering both solid and hollow disks geometries, in light of which we give a detailed electrical design of the flywheel system considering the discharge-stage dynamics of the flywheel. We include a discussion on the applicability of this mathematical model of the electrical properties of the flywheel for actual settings. Finally, we briefly discuss the relative advantages of flywheels in electrical grids over other energy storage technologies.

physics.class-ph↗

arXiv2017

True nature of the Curzon-Ahlborn efficiency

The Curzon-Ahlborn efficiency has long served as the definite upper bound for the thermal efficiency at maximum output power, and has thus shaped the development of finite-time thermodynamics. In this paper, we repeal the ruling consensus according to which it has a genuine universal character that can be derived from linear irreversible thermodynamics. We demonstrate that the Curzon-Ahlborn efficiency should instead properly be associated with a particular case of nonlinear heat engines, and we derive a generalized expression for the efficiency at maximum power beyond the restrictive case of linear models.

cond-mat.stat-mech↗

arXiv2016

Statistical analysis of the figure of merit of a two-level thermoelectric system: a random matrix approach

Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

cond-mat.mes-hall↗

arXiv2015

Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power

[...] By the beginning of the 20th century, the principles of thermodynamics were summarized into the so-called four laws, which were, as it turns out, definitive negative answers to the doomed quests for perpetual motion machines. As a matter of fact, one result of Sadi Carnot's work was precisely that the heat-to-work conversion process is fundamentally limited; as such, it is considered as a first version of the second law of thermodynamics. Although it was derived from Carnot's unrealistic model, the upper bound on the thermodynamic conversion efficiency, known as the Carnot efficiency, became a paradigm as the next target after the failure of the perpetual motion ideal. In the 1950's, Jacques Yvon published a conference paper containing the necessary ingredients for a new class of models, and even a formula, not so different from that of Carnot's efficiency, which later would become the new efficiency reference. Yvon's first analysis [...] went fairly unnoticed for twenty years, until Frank Curzon and Boye Ahlborn published their pedagogical paper about the effect of finite heat transfer on output power limitation and their derivation of the efficiency at maximum power, now known as the Curzon-Ahlborn (CA) efficiency. The notion of finite rate explicitly introduced time in thermodynamics, and its significance cannot be overlooked as shown by the wealth of works devoted to what is now known as finite-time thermodynamics since the end of the 1970's. [...] The object of the article is thus to cover some of the milestones of thermodynamics, and show through the illustrative case of thermoelectric generators, our model heat engine, that the shift from Carnot's efficiency to efficiencies at maximum power explains itself naturally as one considers continuity and boundary conditions carefully [...].

physics.hist-ph↗

arXiv2014

Enhanced thermoelectric coupling near electronic phase transition: the role of fluctuation Cooper pairs

Thermoelectric energy conversion is a direct but low-efficiency process, which precludes the development of long-awaited wide-scale applications. As a breakthrough permitting a drastic performance increase is seemingly out of reach, we fully reconsider the problem of thermoelectric coupling enhancement. The corner stone of our approach is the observation that heat engines are particularly efficient when their operation involves a phase transition of their working fluid. We derive and compute the thermoelastic coefficients of various systems, including Bose and Fermi gases, and fluctuation Cooper pairs. Combination of these coefficients yields the definition of the thermodynamic figure of merit, the divergence of which at $finite$ temperature indicates that conditions are fulfilled for the best possible use of the thermoelectric working fluid. Here, this situation occurs in the fluctuation regime only, as a consequence of the increased compressibility of the working fluid near its phase transition. Our results and analysis clearly show that efforts in the field of thermoelectricity can now be productively directed towards systems where electronic phase transitions are possible.

cond-mat.other↗

arXiv2013

On the efficiency at maximum cooling power

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency $η_{\rm CA}$ being considered as a universal upper bound. Yet, no valid counterpart to $η_{\rm CA}$ has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this Letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.

cond-mat.stat-mech↗

arXiv2013

From local force-flux relationships to internal dissipations and their impact on heat engine performance: The illustrative case of a thermoelectric generator

We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: the linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand, and of two classes of heat engines, autonomous and periodically-driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a "thermal" thermopower and an "electrical" thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.

cond-mat.stat-mech↗

arXiv2013

Mesoscopic thermoelectric transport near zero transmission energies

We study the thermoelectric transport coefficients of a one-dimensional (1D) electron waveguide connected to one and then two off-channel cavities, in the presence of dephasing phonons. The model system is that of a linear chain described as a 1D lattice. For simplicity we consider single-mode cavities, which may be tuned with external gates. While the presence of only one off-channel cavity yields a nearly symmetric transmission profile, which is canceled around the cavity mode, an additional cavity modifies this profile strongly and results in an asymmetric shape characterized by oscillations. In both cases, we consider electron-phonon interactions in our calculations and analyze their effects on the transmission function around the Fermi energy. Knowledge of the energy-dependent transmission function allows the numerical computation of thermoelectric transport coefficients, including the thermopower. In the presence of a second off-channel cavity, the sign of the thermopower depends on the relative position of this cavity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted, and becomes negative when the higher-energy electrons are not transmitted.

cond-mat.mes-hall↗

arXiv2011

Analytic model of effective screened Coulomb interactions in a multilayer system

The main objective of the present work is the development of an analytically tractable model of screened electron-electron and electron-exciton interactions in layered systems composed of two parallel semiconductor quantum wells separated by a dielectric layer. These systems are promising for superconductivity with excitons-polaritons, and spin manipulation. Polarization effects induced by the dielectric mismatch in the nanostructure are taken into account using the image charge method. The obtained analytic expressions are used to calculate screened electron-electron and electron-exciton interactions; these are compared to results computed using other recently published models.

cond-mat.mes-hall↗

arXiv2011

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that $Δl = 0, \pm 2$. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum $l$, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

cond-mat.mtrl-sci↗

arXiv2009

S-wave and p-wave scattering in a cold gas of Na and Rb atoms

Using improved experimentally based $X{}^1Σ^+$ and $a{}^3Σ^+$ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of $^{23}$Na atoms by $^{85}$Rb atoms and $^{87}$Rb atoms. These are the scattering lengths and volumes, numbers of bound states and effective ranges, which we use to obtain the low energy spin-change cross section as functions of the system temperature and the isotope masses. From an analysis of the contributions of s-wave and p-wave scatterings to the elastic cross section we estimate temperatures below which only s-wave scattering is dominant. We compare our quantal results to data obtained from the semiclassical approximation. We supply evidence for the existence of a near zero energy p-wave bound state supported by the singlet molecular potential.

physics.atom-ph↗

arXiv2008

Ultrafast pump-probe dynamics in ZnSe-based semiconductor quantum-wells

Pump-probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment-theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree-Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.

cond-mat.mtrl-sci↗

arXiv2008

Barnes slave boson approach to the two-site single impurity Anderson model with non-local interaction

The Barnes slave boson approach to the $U=\infty$ single impurity Anderson model extended by a non-local Coulomb interaction is revisited. We demonstrate first that the radial gauge representation facilitates the treatment of such a non-local interaction by performing the \emph{exact} evaluation of the path integrals representing the partition function, the impurity hole density and the impurity hole density autocorrelation function for a two-site cluster. The free energy is also obtained on the same footing. Next, the exact results are compared to their approximations at saddle-point level, and it is shown that the saddle point evaluation recovers the exact answer in the limit of strong non-local Coulomb interaction, while the agreement between both schemes remains satisfactory in a large parameter range.

cond-mat.str-el↗

arXiv2007

Slave bosons in radial gauge: a bridge between path integral and hamiltonian language

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green's function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.

cond-mat.str-el↗