Continuous Medium Approach Research Articles

Continuous medium approach to approximate the high concentrated aqueous electrolyte with different types of electrochemical structure.

Superconcentrated aqueous electrolytes have recently emerged as a new class of electrolytes, called water-in-salt electrolytes. They are distinguished, in both weight and volume, by a quantity of salt greater than water. Currently, these electrolytes are attracting major interest, particularly for application in aqueous rechargeable batteries. These electrolytes have only a small amount of free water due to an ultrahigh salt concentration. Consequently, the electrochemical stability window of water is wider than the predicted thermodynamic value of 1.23V. Hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) have been shown to be shifted to more negative and positive potentials, respectively. The decrease in free water population is recognized as being involved in the increase in the electrochemical stability window of water. Here, we study the quantitative contribution of the decrease in the free water molecule concentration to the permittivity of the solution and of the activity of water to the OER and HER overpotentials when the salt concentration increases. We compare our model with that of Kornyshev and get three types of electrolyte structures: diluted, gradient of water contents, and aggregation. The theoretical calculation of the redox potentials of the OER and HER is compared with the experimentally determined electrochemical properties of aqueous LiTFSI electrolytes.

Boltzmann-Poisson-like approach to simulating the galactic halo response to satellite accretion

Context. Recent studies have reported the detection of the galactic stellar halo wake and dipole triggered by the Large Magellanic Cloud (LMC), mirroring the corresponding response from dark matter (DM). These studies open up the possibility of adding constraints on the global mass distribution of the Milky Way (MW), and even on the nature of DM itself, with current and upcoming stellar surveys reigniting the discussion on response modes in dynamical friction. However, the simulation of such features remains computationally challenging. Aims. Using a continuous medium approach, we investigate the density and velocity response modes in simulations of Galactic-type DM halos accreting LMC-sized satellites, including the dependence on the halo density profile. Methods. We used, for the first time in the context of galactic dynamics, a collisionless Boltzmann equation (CBE)+Poisson solver based on an existing method from the literature. We studied the dynamical density and velocity response of halos to sinking perturbers. Results. We successfully captured both the local wake and the global over- and underdensity induced in the host halo. We also captured the velocity response. In line with previous studies, we find that the code can reproduce the core formation in the cuspy profile and the satellite core stalling. The angular power spectrum (APS) response is shown to be sensitive to each density profile. The cored Plummer density profile seems the most responsive, displaying a richness of modes. At the end of the simulation, the central halo acquires cylindrical rotation. When present, a stellar component is expected to behave in a similar fashion. Conclusions. The CBE description makes it tenable to capture the response modes with a better handling of noise in comparison to traditional N-body simulations. Hence, given a certain noise level, BPM has a lower computational cost than N-body simulations, making it feasible to explore large parameter sets. We anticipate that stellar spheroids in the MW or external galaxies could show central cylindrical rotation if they underwent a massive accretion event. The code can be adjusted to include a variety of DM physics.

The free path and generation rate of fast-moving electron interacting with dielectric media

In the framework of macroscopic continuous medium approach, we have studied interaction between a fast-moving charged particle and dielectric or semiconducting media with low energy electrically active excitations. The excitations contribute to frequency dispersion of the media dielectric permittivity. Two types of processes induced by a moving charged particle have been considered: electron-hole generation under interband transitions and excitation of polar optical phonons. For both processes, we calculated and analyzed the time- and space-dependent electric potential generated by the charged particle, polarization of the media, energy losses of the particle and other important constituents of the interaction patterns. Obtained results can contribute to deeper understanding of the charged particle beams interaction with a semiconducting medium, as well as may be useful for versatile applications of charged beams.

Mitigación de daños ocasionados por grietas en el suelo

The design of a trench of granular material is shown. This design can be used to mitigate the damages caused by cracks that have appeared in the soil in certain zones of Mexico City. The most destructive cracks are associated with differential settlements due to the regional subsidence of Mexico City and can show escarpments of considerable height. The proposal solution consists of constructing a trench of sand on the crack line, called “Dissipative box of unit deformations”. The trench behavior is assessed by means of numerical simulations with discontinuous media approach using the discrete element method. It is drawn that the unit deformations (differential settlements/horizontal distances) on the surface decrease when the depth of trench increases. The simulations allow to obtain an optimal design of the dissipative box distributing the vertical displacements in a sufficient horizontal length so that the escarpment disappears and is replaced by a surface with moderate inclination. In this way, a road affected by a crack can continue open to traffic. Analyzes with continuous media approach are presented, their results are compared with the discrete approach ones. Some conclusions and practical recommendations for the mitigation of damage caused by cracks are given.

Development of the Effective Reaction Model for Diamond Deposition Simulation within the Continuous Media Approach

Three models for diamond growth process by the chemical vapor deposition of methane are proposed. They differ in the degree of detail of the surface reaction description. The most complete model contains the reactions of deposition, etching and insertion. Gas-dynamic simulations have been performed for all those models. The species delivery to the substrate and the contribution from different species to the growth process is analysed. It is shown that different surface reaction models lead to different profiles of the species concentrations in the immediate vicinity of the substrate, thus, the experimental data on the growth rate may give information on the growth mechanism.

Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.

Strain evolution in GaN nanowires: From free-surface objects to coalesced templates

Top-down fabricated GaN nanowires, 250 nm in diameter and with various heights, have been used to experimentally determine the evolution of strain along the vertical direction of 1-dimensional objects. X-ray diffraction and photoluminescence techniques have been used to obtain the strain profile inside the nanowires from their base to their top facet for both initial compressive and tensile strains. The relaxation behaviors derived from optical and structural characterizations perfectly match the numerical results of calculations based on a continuous media approach. By monitoring the elastic relaxation enabled by the lateral free-surfaces, the height from which the nanowires can be considered strain-free has been estimated. Based on this result, NWs sufficiently high to be strain-free have been coalesced to form a continuous GaN layer. X-ray diffraction, photoluminescence, and cathodoluminescence clearly show that despite the initial strain-free nanowires template, the final GaN layer is strained.

Conservation laws of an electro-active polymer

Ionic electro-active polymers (E.A.P.) is an active material consisting in a polyelectrolyte (for example Nafion). Such material is usually used as thin film sandwiched between two platinum electrodes. The polymer undergoes large bending motions when an electric field is applied across the thickness. Conversely, a voltage can be detected between both electrodes when the polymer is suddenly bent. The solvent-saturated polymer is fully dissociated, releasing cations of small size. We used a continuous medium approach. The material is modelled by the coexistence of two phases; it can be considered as a porous medium where the deformable solid phase is the polymer backbone with fixed anions; the electrolyte phase is made of a solvent (usually water) with free cations. The microscale conservation laws of mass, linear momentum and energy and the Maxwell's equations are first written for each phase. The physical quantities linked to the interfaces are deduced. The use of an average technique applied to the two-phase medium finally leads to an Eulerian formulation of the conservation laws of the complete material. Macroscale equations relative to each phase provides exchanges through the interfaces. An analysis of the balance equations of kinetic, potential and internal energy highlights the 2 Mireille Tixier, Jo{\"e}l Pouget phenomena responsible of the conversion of one kind of energy into another, especially the dissipative ones : viscous frictions and Joule effect.

Accurate modeling of split ring metamaterial lenses for magnetic resonance imaging applications

The usefulness of thin split ring metamaterial slabs for imaging applications, including magnetic resonance imaging applications, has attracted some attention in the past years. However, the small number of unit cells across these thin slabs prevents the direct application of continuous medium models for its characterization. The main aim of this contribution is to provide a rigorous model for these structures, also clarifying the usefulness of continuous medium approach for their characterization. The proposed model is a generalization of the classical Lorentz procedure to two dimensions and is able to deal with electrically thin slabs made of small resonant closed current loops. The obtained results are validated by full-wave electromagnetic simulations and compared with the continuous model approximation of the slab.

A continuous media approach to modeling the stress saturation effect in granularsilos

A continuous media approach for the calculation of the stresses in an ensiled granularmedia which improves on the Janssen theory has been developed. This approach also allowsus to represent qualitatively as well as quantitatively the stress saturation phenomenon ingranular silos. It is based on three-dimensional equilibrium equations, coupled with a slipcondition and a Mohr–Coulomb criterion at the silo walls. Predictions obtained using theproposed model are in close agreement with the classical approaches for non-cohesivematerials. The effect of the cohesion and the friction walls on the stored materials was alsoinvestigated.

Modification of Spontaneous Emission of Quantum Dots: Purcell Effect in Semiconductor Microcavities

We study the spontaneous emission of a quantum dot embedded in a cavity. Purcell and local-field effects are investigated using the coupled dipole method and a comparison with a continuous medium approach is presented.

Effective thermal conductivity of clayey aerated concrete in the dry state: experimental results and modelling

The aim of this study was to determine the effective thermal conductivity of a new insulating building material, called clayey aerated concrete (CAC), when used in a dry state. A series of six mixtures having different porosities obtained by adding aluminium powder to the clay-cement matrix was used in the investigation. The measurements of thermal conductivity have been performed inside a closely controlled climatic cell at ambient temperature (20±1 °C) using a `line source' method. The experimental results reveal that enhanced thermal performances can thus be obtained by the development of local materials, and their use in building insulation reveals very interesting properties as compared to other building materials. The study has been extended to the research of theoretical models capable of predicting the effective thermal conductivity of dry CAC considered as a two-phase system. Three models based on a geometric mean approach (Asaad model, Veerendra and Chaudhary model) and a effective continuous medium approach (Pande and Chaudhary model) were used. In order to predict effective thermal conductivity of elaborated material using such models, a correction term has been empirically determined and introduced in these models, taking into account the effect of a higher ratio of the thermal conductivity (s/f). A very good agreement has been observed between the analytical and experimental results, thereby confirming the model's ability to predict the effective thermal conductivity of dry CAC.

Elastic Design Charts of Stiffened Coupled Structural Walls Structural Walls

Design charts are presented for the design of a stiffened coupled structural wall with a strong beam located somewhere along the building height. The analysis is based on a continuous medium approach with the deflection at the top. The couple due to the axial force in the walls and the shear force in the laminae are presented in the form of graphs. The variations of the couple due to the axial force in the walls and the laminar shear along the structural height are also presented to permit the curtailment of reinforcements where appropriate for achieving economy. The results are given in terms of two dimensionless structural parameters: one is the relative flexural rigidity of the strong beam, and the other is a measure of the effectiveness of the lintel beams. The application of the design charts is illustrated by determining the deflections and the internal forces of a typical 20‐story building.

Thermal conduction through porous and dispersed three-phase systems

A loose three-phase system made of metal, non-metal and air is considered resulting from small successive dispersions in effective continuous medium (ecm). The effective thermal conductivity of loose three-phase systems is estimated by extending theecm approach to multi-phase systems. The unsteady state line source (needle) method is employed to determine the effective thermal conductivity of some selected three-phase materials. The calculated and observed values show good agreement suggesting that the continuous medium approach can be applied to estimate effective thermal conductivity of multi-phase systems.

Stiffening of laterally loaded coupled shear walls on elastic foundations

An investigation is made of the relative effectiveness of using either a top or bottom connecting beam to stiffen a pair of laterally loaded coupled shear walls supported on independent elastic foundations. By basing the analysis on the continuous medium approach, a closed solution to the problem is achieved. A numerical example for a typical structure illustrates the influence of the stiffening beams on the forces and deformations in the structure for two different soil conditions.

A macroscopic theory of the response functions for a semi-infinite Heisenberg ferromagnet, and the application to light scattering

Linear response theory and the semiclassical torque equation for magnetisation are used to calculate the response functions (or Green functions) of a semi-infinite Heisenberg ferromagnet. These response functions provide a description of the bulk spin waves and surface spin waves in the ferromagnet, together with their spectral properties. A continuous medium approach is used, so the theory is appropriate to excitations with long wavelengths. The results are used to evaluate the lineshapes and integrated intensities for light scattering from bulk and surface spin waves.

Natural vibrations of shear wall buildings on flexible supports

AbstractA shear wall building is considered as an assembly of plane and curvilinear shear walls tied together by floor slabs to act as a composite unit. Based on this conception and the continuous medium approach, the governing dynamic equations and boundary conditions are derived from energy principles, using Vlasov's theory of thin‐walled beams. All primary and secondary inertia forces, as well as the influence of elastic foundation flexibility, have been taken into consideration. A numerical solution of the dynamic equations is achieved by employing the Ritz‐Galerkin technique, yielding both natural frequencies and mode shapes. The technique is applicable to buildings containing coupled and non‐coupled, open section shear walls oriented in plan in any arbitrary manner. The use of the method is illustrated by the example of a complex building with unsymmetric plan, and the analytical natural frequencies of two shear wall building models are compared with those obtained experimentally by other investigators.

Comparison of Karlson's model with the continuous medium model

The inaccuracy by Karlson (1962, 1963) in the derivation of the equation for the electric tield and due to equating the plasma density with the guiding centre's density is corrected in the framework of microscopic description. Moreover, the corrected equation of Karlson is derived in two different ways in the continuous medium approach: (1) with the use of the generalized Ohm law; (2) with the use of the two-liquid magnetohydrodynamic equations.