Continuous Medium Approximation Research Articles

Exotical solitons for an intrinsic fractional circuit using the sine-cosine method

This work focuses on seeking soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission network obtained through the simplest sine-cosine method. The studied model is governed by a fractional nonlinear partial differential-difference equation in (2 + 1) spatio-temporal dimensions, and the method used to get exact solutions is simple, concise and well-known. We achieve for the model studied here that, the sought solutions specifically by means of the sine-cosine method are functions of all the capacitor's nonlinearities (quadratic and cubic) if and only if, we use the fourth-order spatial dispersion (FOSD)during the continuous media approximation. In contrast, in the absence of the FOSD term, the solutions only exist if, either the quadratic or the cubic nonlinearity is considered separately. In addition, the obtained solutions shapes are exotical, unexpected and novel. These findings (singular bright solitary waves, pulse, U-shaped and M-shaped waves trains) get many applications; for instance, codifying data in the allowed or forbidden band for the signal's transmission in the waveguides.

Soliton Domain Wall Concept: Analytical and Numerical Investigation in Digital Magnetic Recording System

To introduce Soliton theory in magnetic recording systems, we begin with the profile of Domain Wall, which is key elements of recording systems, knowing that many different Domain Walls shape exist. For this, we consider the recording media as chain of atoms (spin) and, we use the Hamiltonian to describe the global state of the system; by taking into consideration interaction between the neighboring spin and anisotropic interaction. Spins are considered as classical vector; for that, we defined the cosine and sine of angles that specify the position of the spins. They are developed in Taylor’s series until second order then using the approximation of continuous medium we obtained the Lagragian relation. This Lagragian enables us to describe the dynamics of spin through the wave velocity. As we are fine just the profile of domain wall it is beneficial for us to consider the wall at rest (static) and by the aid of Euler equation we obtain two simple equations; using the equilibrium conditions, the differential equation is obtained and solved by the quadratic method and separation variables method. The profile of domain wall that we obtain is at a particular position, then analytical and numerical simulation give us the opportunity to see that profile of that domain wall is a Kink, anti-Kink Soliton and also Soliton Train. Using this magnetic Soliton wave (Domain Wall), we also evaluate the playback voltage V (x), the peak voltage and the half pulse width PW50 to confirm the uses of this DW profile in magnetic recording systems and insure validity of this work.

Magnetization wave dynamics within a diluted magnetic semiconductor

The paper presents a theoretical analysis of magnetization waves in a diluted magnetic semiconductor. Using the continuous medium approximation, we derived a dynamical equation system that describes the magnetization evolution of the paramagnetic matrix and magnetic admixture ions. Two possible solutions were considered. The first involved a travelling wave of finite amplitude, which was stable in the system with a ferromagnetic coupling with admixture ions. The second solution involved a solitary wave. Here, the soliton amplitude and velocity were determined by the interaction between the admixture ions themselves and between them and the base matrix. The dipolar coupling of the matrix and admixture had significant influence on the wave stability.

Electron g-factor in nanostructures: continuum media and atomistic approach

We report studies of {varvec{k}}-dependent Landé g-factor, performed by both continuous media approximation {varvec{k}}{varvec{cdot }}{varvec{p}} method, and atomistic tight-binding hbox {sp}^3hbox {d}^5hbox {s}^* approach. We propose an effective, mesoscopic model for InAs that we are able to successfully compare with atomistic calculations, for both very small and very large nanostructures, with a number of atoms reaching over 60 million. Finally, for nanostructure dimensions corresponding to near-zero g-factor we report electron spin states anti-crossing as a function of system size, despite no shape-anisotropy nor strain effects included, and merely due to breaking of atomistic symmetry of cation/anion planes constituting the system.

Observation of inhomogeneous plasmonic field distribution in a nanocavity.

The progress of plasmon-based technologies relies on an understanding of the properties of the enhanced electromagnetic fields generated by the coupling nanostrucutres1-6. Plasmon-enhanced applications include advanced spectroscopies7-10, optomechanics11, optomagnetics12 and biosensing13-17. However, precise determination of plasmon field intensity distribution within a nanogap remains challenging. Here, we demonstrate a molecular ruler made from a set of viologen-based, self-assembly monolayers with which we precisely measures field distribution within a plasmon nanocavity with ~2-Å spatial resolution. We observed an unusually large plasmon field intensity inhomogeneity that we attribute to the formation of a plasmonic comb in the nanocavity. As a consequence, we posit that the generally adopted continuous media approximation for molecular monolayers should be used carefully.

Numerical simulation of selective laser melting with local powder shrinkage using FEM with the refined mesh

A mathematical model of selective laser melting (SLM) of fine-grained metallic powders under the pulse laser annealing conditions has been developed. The processed powder bed is considered in the approximation of continuous medium where its effective thermophysical properties depend on local porosity. The model allows simulation of unsteady distributions of temperature, specific enthalpy, local porosity, morphology and thickness of the processed track. In the paper, all stages of problem analysis are described including its mathematical formulation and numerical implementation. To take into account shrinkage of the powder layer during sintering and remelting, the numerical model utilizes the arbitrary Lagrangian–Eulerian (ALE) method. Thus the finite element mesh provides robust control of quality and dynamic remeshing through adaptive mesh refinement. Using the proposed numerical model the unsteady thermal fields and local porosity of a Fe-based powder layer processed with a pulsed laser has been investigated.

Importance of second-order deformation potentials in modeling of InAs/GaAs nanostructures

Accurate modeling of electronic properties of nanostructures is a challenging theoretical problem. Methods making use of continuous media approximation, such as k.p, sometimes struggle to reproduce results obtained with more accurate atomistic approaches. On the contrary, atomistic schemes generally come with a substantially larger cost of computation. Here, we bridge between these two approaches by taking 8-band k.p method augmented with non-linear strain terms fit to reproduce sp3d5s* tight-binding results. We illustrate this method on the example of electron and hole states confined in quantum wells and quantum dots of photonics applications relevant InAs/GaAs material system, and demonstrate a good agreement of a non-linear k.p scheme with empirical tight-binding method. We discuss limits of our procedure as well as provide non-linear 8-band k.p parameter sets for InAs and GaAs. Finally, we propose a parameterization for effective term used to improve the accuracy of the standard effective mass method.

Relationship between Surface Self-Diffusion and Bubble Mobility in Solids: Theory and Atomistic Simulation

Diffusion processes in solids are characterized by complex mechanisms occurring at the atomistic level. The relevant theoretical concepts are sufficiently developed in the case of the diffusion of point defects. At the same time, the diffusion of objects such as clusters of vacancies or nanometer-size cavities in the crystal lattice is described only in terms of continuous-medium approximation. This paper attempts to link the existing theory of diffusion of bubbles in a crystalline matrix with the atomistic description of the process on the basis of the molecular dynamics method. For simplicity, the diffusion of cavities in a two-dimensional Lennard-Jones lattice is considered. A controlled molecular dynamics method is proposed to speed up the direct computation of the diffusion rate of bubbles. Based on the results of simulation, a practical interpretation is given to a parameter of the continuum theory such as the rate of surface self-diffusion. The applicability range of the continuum theory is demonstrated, and principles for the refinement of the theory in the case of minimum-size bubbles are formulated.

Propagation of Spin Waves Through an Interface Between Ferromagnetic and Antiferromagnetic Materials

Boundary conditions for order parameters at an interface between ferromagnetic (FM) and two-sublattice antiferromagnetic (AFM) materials were obtained in the continuous medium approximation similarly to the approach which allows one to take into account the finite thickness of the FM/FM interface, which is much less than spin wave length. Three order parameters are considered inside an interface of finite thickness with the magnetization $\mathbf{\text{M}}$ of FM, magnetizations of both sublattices $\mathbf{\text{M}}_{1}$ and $\mathbf{\text{M}}_{2}$ of AFM. The uniform and non-uniform exchange between all order parameters are taken into account to the interface energy. Using these boundary conditions, the excitation of a surface evanescent spin wave is considered in AFM when the spin wave in FM falls onto this interface. The coefficients and the phases of transmission and reflection of spin wave through the FM/AFM interface are derived.

Boundary conditions at the interface of finite thickness between ferromagnetic and antiferromagnetic materials

Systematic approach has been applied to obtain the boundary conditions for magnetization at an interface between ferromagnetic (FM) and antiferromagnetic (AFM) materials in the continuous medium approximation. Three order parameters are considered inside an interface of finite thickness magnetization M of FM, magnetizations of both sublattices M1 and M2 of AFM. The boundary conditions are defined in terms of some average properties of the FM/AFM interface. The interface has a finite thickness which is much less than spin wave length. This approach allowed to take into account the interface anisotropy, interface symmetric exchange coupling and interface coupling resulting from inversion symmetry breaking in the vicinity of the interface.

Surface sensitivity of secondary electrons emitted from amorphous solids: Calculation of mean escape depth by a Monte Carlo method

A Monte Carlo simulation method for study of electron-solid interaction based on modeling of cascade secondary electron (SE) production and transportation has been used to determine the escape depth of emitted SE signals from amorphous solid specimens. The excitation depth distribution function and emission depth distribution function for, respectively, excited and emitted SEs are obtained at first based on the continuous medium approximation, whose product yields the secondary electron depth distribution function from which the mean escape depth (MED) of SEs is calculated. In this work, we study systematically the dependence of the MED on the atomic number of the specimen, primary energy, and incident angle of the incident electron beam. The derived MEDs of SEs for C, Ni, Cu, Ag, Pt, and Au specimens are found surprisingly to fall into a shallow sub-nanometer region, i.e., 0.4–0.9 nm, while Al and Si present larger values, due to elastic scattering effects. Furthermore, SE energy-depth distributions indicate that lower-energy SEs are escaped mainly from the greater depth region under the surface whereas higher-energy SEs are from the near-surface region. The results hence show that the SE emission is dominated by very thin top-surface layers in most cases, leading to the surface sensitivity of SEs.

Magnetization boundary conditions at a ferromagnetic interface of finite thickness

We develop a systematic approach to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named ‘generalized Barnaś–Mills boundary conditions’. We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of non-uniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism.

Criteria of applicability of a gas-dynamic approximation of a continuous medium to describing the dispersion of combustion products of rocket propellants

Two criteria for the applicability of a gas-dynamic approximation of continuous medium to describing the dispersion of combustion products of rocket propellants at high altitudes are formulated. Related numerical estimates are given for different launch vehicles and one upper stage with fairly extended boost phases. The use of a continuous medium approximation is shown to have a clear altitude restriction.

Dissociative electron attachment to CH3I on surfaces and in bulk media: vibrational Feshbach resonance suppression

A previously developed theory (Fabrikant 2007 Phys. Rev. A 76 012902) is applied to the calculation of dissociative electron attachment to CH3I molecules condensed at the surface of a Kr film. The effect of vibrational Feshbach resonance that strongly dominates attachment in the gas phase is strongly suppressed in the condensed phase. This leads to an order of magnitude reduction of the condensed-phase cross section as compared to the gas phase cross section, in spite of the lower resonance width and higher negative-ion survival probability in the condensed phase. The result agrees with recent measurements (Jensen and Sanche 2008 J. Chem. Phys. 129 074703), although the peak in the cross section as a function of the electron energy is narrower than the experimental peak. When the adsorbed molecules are covered by an additional Kr film on top, the dissociative attachment cross section grows rather fast. This result does not agree with the experiment for physisorbed CH3I covered by a 2 ML of Kr film, perhaps due to inaccuracy of the continuous-medium approximation employed in the calculations.

Near infrared light emission quenching in organolanthanide complexes

We investigate the quenching of the near infrared light emission in Er3+ complexes induced by the resonant dipolar interaction between the rare-earth ion and high frequency vibrations of the organic ligand. The nonradiative decay rate of the lanthanide ion is discussed in terms of a continuous medium approximation, which depends only on a few, easily accessible spectroscopic and structural data. The model accounts well for the available experimental results in Er3+ complexes, and predicts an ∼100% light emission quantum yield in fully halogenated systems.

Effect of protein binding on charge transfer in DNA: A simple model based on the superexchange mechanism

The effect of protein binding on the electronic coupling between distant redox centers in DNA is investigated in DNA–protein complex systems using the superexchange formalism. The systems (bridges) studied are described by a tight-binding electronic Hamiltonian in which site orbitals interact with one another through an exponentially decaying function of distance. Based on the "continuous-medium approximation," previously developed for large homogeneous three-dimensional systems (J.-M. Lopez-Castillo et al. J. Phys. Chem. 99, 6864 (1995)), the intervening bridge is defined by a unique dimensionless parameter Γ /E that controls the distance dependence of the electronic coupling. Here, E is the energy separation between the orbitals of the bridging medium and the redox sites (tunneling energy), and Γ is the electronic bandwidth of the bridge taken as a continuous medium. It was found that, for a given value of (Γ/E)DNAfar from the DNA's resonance conditions and for (Γ/E)proteinvalues near the protein's resonance conditions, the electronic coupling is independent of the donor–acceptor distance when the acceptor lies within the "recognition region" of DNA. Moreover, when the redox centers are located on both sides of this region, the electronic coupling is many orders of magnitude larger than it should be, far from the protein's resonance conditions.Key words: DNA, DNA–protein complexes, long-range electron and hole transfers, electronic coupling, superexchange mechanism, energetic control, continuous-medium approximation.

Couplage électronique et transferts de charges dans l'ADN : étude du contrôle énergétique

The influence of the energetic gap on the effective distance-decay rate of electronic coupling (beta(eff)) in DNA is investigated in the context of the superexchange mechanism. The DNA double helix is described by a tight-binding electronic Hamiltonian model, in which all orbitals have the same energy and interact with one another through an exponentially decaying function of distance. Our numerical results concerning the beta(eff) values obtained for two different DNA molecules are analyzed within the theoretical framework of the "continuous-medium approximation," previously developed by Lopez-Castillo et al. (J.-M. Lopez-Castillo, A. Filali-Mouhim, I.L. Plante, and J.-P. Jay-Gerin. J. Phys. Chem. 99 : 6864-6875, 1995). We find that the intervening DNA bridge between the donor and acceptor sites is defined by a unique dimensionless control parameter gamma/E, where E is the energy of the orbitals of this medium with respect to those of the redox site orbitals (energetic gap) and gamma is the electronic band width of the bridge considered as a continuous medium. In the narrow-band regime, our "through-space" coupling model predicts beta(eff) values that are in good order of magnitude agreement with those calculated by other theoretical approaches as well as with those obtained from experiment. Moreover, under equivalent energetic conditions, the DNA-mediated transfers of holes and electrons differ considerably. This difference depends upon the sign of the parameter gamma/E.

Molecular static model of CuInSe2 crystal: Energy properties of some structural defects

A molecular static model of a CuInSe2 crystal is constructed, and the energies of formation of isolated defects are calculated. An analysis of the interaction between defects shows that, for a high defect concentration (exceeding 1%), the energies of interaction between defects can considerably exceed the values obtained in the continuous medium approximation. It is found that the role of interaction between defects in quantum-chemistry calculations using the model of supercells (periodic defect) is considerably underestimated.

X-ray diffuse scattering from extended microdefects of orthorhombic symmetry for Si single crystals

The displacement field of a crystal lattice, in the continuous media approximation, caused by extended microdefects of rectangular parallelepiped shape, is considered. X-ray diffuse scattering from the defect core as well as the long-range displacement field is analyzed. A theoretical expression for the intensity of X-ray diffuse scattering resulting from randomly distributed microdefects of orthorhombic symmetry is presented using the kinematical approximation of X-ray statistical diffraction theory. The computer simulations of the isointensity contours for two sets of defect parameters are performed. A way of obtaining the defect parameters by fitting the computer simulations to the experimental data is proposed.

Prediction of effective thermal conductivity of moist wood concrete

From the set of existing models available for predicting the thermal conductivity of porous materials such as soils, building materials, etc. two models based on two different approaches have been selected in order to estimate the thermal conductivity of moist wood concrete. The first model is based on the strictly mathematical solution to the heat conduction equation using a continuous medium approximation. The second employs the Ohm's law approach. Besides the characteristics of the various phases, such as each phase's thermal conductivity and its volume fraction, both the Pande and Gori and the Jackson and Black models take into account the geometrical arrangement of the particles by introducing a morphological parameter such as the coefficient of effective continuous medium, P and the stereological concept of contiguity, respectively. A new parameter named the liquid-liquid contiguity has been introduced to preserve the validity of the model as proposed by Jackson and Black for saturation greater than 0.9. Based on the same electrical analogy as Jackson and Black, an expression for calculating the effective thermal conductivity of unsaturated material has been proposed. A new coaxial thermal probe, developed at the LTHE (France), has been used for measuring thermal conductivity at various moisture contents. One original feature of the corresponding probe is its very low mass by unit length - less than 10 g m-1. It allows for taking measurements even if the thermal contact is very poor. Calculated values of the effective thermal conductivity of these materials have been compared with experimental measurements. These models are found to yield predictions which agree quite closely with experimental data for wood concrete for different amounts of wood aggregates and saturation degrees.