Self-consistent Formulation Research Articles

Macroscopic descriptions of non-linear electromagnetic interactions in many-electron systems

Reduced-density-matrix descriptions are developed for linear and non-linear (possibly coherent) electromagnetic interactions of many-electron systems. Applications of interest include pump-probe optical phenomena in warm atomic vapors, partially-ionized plasmas, and condensed matter. Collision processes are treated within the framework of environmental perturbations, giving rise to decoherence and relaxation phenomena, and externally applied magnetic fields are taken into account on an equal footing with the electromagnetic fields. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semi-classical perturbation-theory treatment of the electromagnetic interaction is adopted. However, it is emphasized that a quantized-electromagnetic-field approach will be necessary for a fully self-consistent quantum-mechanical formulation. The primary quantities of interest are the linear and the non-linear macroscopic electromagnetic-response tensors. Coherent initial electronic excitations and the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation can incorporated in the expressions for these macroscopic electromagnetic-response tensors. Collisional interactions can be treated in various approximations for the Liouville-space self-energy operator, and the influence of Zeeman coherences on the macroscopic electromagnetic response can be investigated.

Turing instabilities in reaction-diffusion systems with cross diffusion

The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.

Biaxial Deformation of the Magnesium Alloy AZ80

The multiaxial deformation of magnesium alloys is important for developing reliable, robust models for both the forming of components and also analysis of in-service performance of structures, for example, in the case of crash worthiness. The current study presents a combination of unique biaxial experimental tests and biaxial crystal plasticity simulations using a visco-plastic self-consistent (VPSC) formulation conducted on a relatively weak AZ80 cast texture. The experiments were conducted on tubular samples which are loaded in axial tension or compression along the tube and with internal pressure to generate hoop stresses orthogonal to the axial direction. The results were analyzed in stress and strain space and also in terms of the evolution of crystallographic texture. In general, it was found that the VPSC simulations matched well with the experiments. However, some differences were observed for cases where basal 〈a〉 slip and \( \left\{ {10\bar{1}2} \right\} \) extension twinning were in close competition such as in the biaxial tension quadrant of the plastic potential. The evolution of texture measured experimentally and predicted from the VPSC simulations was qualitatively in good agreement. Finally, experiments and VPSC simulations were conducted on a second AZ80 material which had a stronger initial texture and a higher level of mechanical anisotropy. In the previous case, the agreement between experiments and simulations was good, but a larger difference was observed in the biaxial tension quadrant of the plastic potential.

Improved Efficiency of Backward-Wave Oscillator With an Inclined Electron Beam

The possibility of the efficient operation of a backward-wave oscillator (BWO) with an electron beam inclined with respect to the surface of a periodic structure-a clinotron-is analyzed here. The beam inclination provides the possibility of effective interaction by all particles of a thick electron beam with the slow evanescent harmonic of the cavity modes. The problem of electron-beam-wave interaction is treated in a self-consistent formulation. A theoretical analysis shows that the inclination of the electron beam to the grating surface decreases the demand of the clinotron for magnetic field magnitude and beam velocity spread compared to a conventional BWO. It is demonstrated that, for an optimal inclination angle and an optimal beam thickness, the clinotron efficiency exceeds the efficiency of a conventional BWO considerably given the same electron beam parameters. The developed multimode theory results are in satisfactory agreement with the theory of a BWO in terms of reflections and particle-in-cell simulations.

ELECTROMAGNETIC WAVES RADIATION INTO THE SPACE OVER A SPHERE BY A SLOT IN THE END-WALL OF A SEMI-INFINITE RECTANGULAR WAVEGUIDE

The problem of electromagnetic waves radiation into a space outside a perfectly conducting sphere through a narrow slot, cut in an end-wall of a semi-inflnite rectangular waveguide, excited by a fundamental wave of H10 type is solved using a rigorous self-consistent formulation. The starting point for the analysis is the one-dimensional integral equation for the equivalent magnetic current in the slot, obtained by using the efiective thickness of the slot. The asymptotic solution of the equation was found by the generalized method of induced magnetomotive forces (MMF). The physical adequacy of the constructed mathematical model to the real physical process is conflrmed by experimental data. In∞uence of the sphere radius upon energy characteristics of the slot radiator was investigated numerically. It was shown that at any frequency of waveguide single-mode range, the radiation coe-cient of a spherical antenna can be made close to one by choosing the slot length, the sphere radius and the waveguide height. Conditions for correct application of inflnite screen approximation for spherical scatterers with su-ciently large radii are formulated.

Recent developments of the hierarchical reference theory of fluids and its relation to the renormalization group

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behaviour of the theory at first-order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non-perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.

Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence

Abstract. A generalized mass-flux formulation is presented, which no longer takes a limit of vanishing fractional areas for subgrid-scale components. The presented formulation is applicable to a~situation in which the scale separation is still satisfied, but fractional areas occupied by individual subgrid-scale components are no longer small. A self-consistent formulation is presented by generalizing the mass-flux formulation under the segmentally-constant approximation (SCA) to the grid–scale variabilities. The present formulation is expected to alleviate problems arising from increasing resolutions of operational forecast models without invoking more extensive overhaul of parameterizations. The present formulation leads to an analogy of the large-scale atmospheric flow with multi-component flows. This analogy allows a generality of including any subgrid-scale variability into the mass-flux parameterization under SCA. Those include stratiform clouds as well as cold pools in the boundary layer. An important finding under the present formulation is that the subgrid-scale quantities are advected by the large-scale velocities characteristic of given subgrid-scale components (large-scale subcomponent flows), rather than by the total large-scale flows as simply defined by grid-box average. In this manner, each subgrid-scale component behaves as if like a component of multi-component flows. This formulation, as a result, ensures the lateral interaction of subgrid-scale variability crossing the grid boxes, which are missing in the current parameterizations based on vertical one-dimensional models, and leading to a reduction of the grid-size dependencies in its performance. It is shown that the large-scale subcomponent flows are driven by large-scale subcomponent pressure gradients. The formulation, as a result, furthermore includes a self-contained description of subgrid-scale momentum transport. The main purpose of the present paper is to appeal the importance of this new possibility suggested herein to the numerical weather forecast community with implications for the other parameterizations (cloud fraction, mesoscale organization) as well as resolution-dependence of parameterizations.

Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium

SUMMARY The effective bulk and shear viscosity of the matrix of a partially molten rock are important properties for the process of melt migration and matrix compaction. A set of porosity-dependent effective bulk and shear viscosity models is presented based on a self-consistent poroelastic formulation for partially molten rock where the melt occurs in spherical, ellipsoidal, film-like or tubular inclusions. For these melt geometries a graphical user interface operated MATLAB program is provided which allows the calculation of effective bulk and shear viscosities as a function of porosity, as well as effective elastic moduli and seismic velocities. For all melt geometries an inverse porosity—dependence of the effective bulk viscosity is found. Depending on the assumed melt geometry, this formulation predicts both the effective bulk and shear viscosity to drop to zero at and above finite melt fractions of 20–50 per cent. Fitting equations are derived allowing direct implementation into two-phase flow melt–matrix formulations.

Design and production of gentamicin/dextrans microparticles by supercritical assisted atomisation for the treatment of wound bacterial infections

In this work, the supercritical assisted atomisation (SAA) is proposed, for the first time, for the production of topical carrier microsystems based on alginate-pectin blend. Gentamicin sulphate (GS) was loaded as high soluble and hygroscopic antibiotic model with poor flowability. Particularly, different water solutions of GS/alginate/pectin were processed by SAA to produce spherical microparticles (GAP) of narrow size (about 2 μm). GS loading was varied between 20% and 33% (w/w) with an encapsulation efficiency reaching about 100%. The micronised powders also showed high flow properties, good stability and constant water content after 90 days in accelerated storage conditions. The release profiles of the encapsulated drug were monitored using vertical diffusion Franz cells to evaluate the application of GAP microsystems as self-consistent powder formulation or in specific fibres or gels for wound dressing. All formulations showed an initial burst effect in the first 6h of application (40-65% of GS loaded), and in particular GAP4 produced with a GS/alginate/pectin ratio of 1:3:1, exhibited the ability to release GS continuously over 6 days. Antimicrobial tests against Staphylococcus aureus indicated that GS antibiotic activity was preserved at 6 days and higher than pure GS at 12 and 24 days for all SAA formulations, especially for GAP1.

Local modulations of the spin-fluctuation-mediated pairing interaction by impurities ind-wave superconductors

We present a self-consistent real space formulation of spin-fluctuation mediated d-wave pairing. By calculating all relevant inhomogeneous spin and charge susceptibilities in real space within the random phase approximation (RPA), we obtain the effective pairing interaction and study its spatial dependence near both local potential and hopping impurities. A remarkably large enhancement of the pairing interaction may be obtained near the impurity site. We discuss the relevance of our result to inhomogeneities observed by scanning tunneling spectroscopy on the surface of cuprate superconductors.

The implementation of a self-consistent constricted variational density functional theory for the description of excited states

We present here the implementation of a self-consistent approach to the calculation of excitation energies within regular Kohn-Sham density functional theory. The method is based on the n-order constricted variational density functional theory (CV(n)-DFT) [T. Ziegler, M. Seth, M. Krykunov, J. Autschbach, and F. Wang, J. Chem. Phys. 130, 154102 (2009)] and its self-consistent formulation (SCF-CV(∞)-DFT) [J. Cullen, M. Krykunov, and T. Ziegler, Chem. Phys. 391, 11 (2011)]. A full account is given of the way in which SCF-CV(∞)-DFT is implemented. The SCF-CV(∞)-DFT scheme is further applied to transitions from occupied π orbitals to virtual π(∗) orbitals. The same series of transitions has been studied previously by high-level ab initio methods. We compare here the performance of SCF-CV(∞)-DFT to that of time dependent density functional theory (TD-DFT), CV(n)-DFT and ΔSCF-DFT, with the ab initio results as a benchmark standard. It is finally demonstrated how adiabatic TD-DFT and ΔSCF-DFT are related through different approximations to SCF-CV(∞)-DFT.

Application of Visco-Plastic Self Consistent Approach to Model Deformation Characteristics of Magnesium with Different Textures

The viscoplastic self-consistent (VPSC) formulation is by now a well established approach for simulating texture development and constitutive response during plastic forming of high and low-symmetry polycrystals. In this work we have used the VPSC approach to model the uniaxial tensile and compressive deformation characteristics of pure magnesium with random and extruded texture. We compare our results with experimental data and find that they are in good agreement with the available experimental evidence.

Dynamic Structure Factor for Large Aggregate Clusters with Internal Motions: A Self-Consistent Light-Scattering Study on Conjugated Polymer Solutions

The aggregation properties of a standard conjugated polymer, poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV), in two distinct solvents (chloroform and toluene) and a range of polymer concentrations (c = 0.1-3 mg/mL) have been unequivocally resolved using combined dynamic and static light scatterings (DLS/SLS). The prime challenges for analyzing this peculiar, practically important, solution system arise from the wide size distribution and unknown aggregate morphology, as well as pronounced interferences between translational and internal motions of aggregate clusters of considerably varying size. To cope with these central difficulties, we propose a self-consistent formulation for analyzing the dynamic structure factor in DLS experiment by extending an existing theory on free-draining bead-spring chains that explicitly accounts for internal fluctuations, along with two candidate form factors on Gaussian coil and rigid sphere, respectively, serving as two limiting cases to be discriminated in combined DLS and SLS measurements. Given that no accessibility to ultrasmall angular resolutions is a prerequisite, the suggested protocol can readily be carried out in conventional light-scattering apparatus. The present analyses unanimously support the rigid-sphere form factor in describing the entire set of light-scattering data on MEH-PPV solutions, differing from early small-angle neutron/X-ray scattering interpretations suggesting certain 2D fractal structures for the aggregation network. Scrutiny into the interior dynamics of aggregate clusters further disclosed that the segmental motions are noticeably more suppressed than for usual, nonaggregated polymer solutions, and no existing theories based on the bead-spring picture can yet capture the observed scaling behavior as manifested by the present data. Accordingly, we report several first-revealed properties of MEH-PPV solutions on the aggregate morphology, the size distribution (and mean size), mean aggregation number, and interior segmental dynamics, which serve as valuable information for linking solution properties with those for dried thin films in contemporary applications with conducting conjugated polymers.

Self-consistent formulation for the evolution of ionospheric conductances at the ionosphericEregion within the M-I coupling scheme

[1] We formulate the evolution of ionospheric conductivity in the framework of 3-D M-I coupling. Two important physical processes are taken into account. One is the ionization process by precipitating mono-energetic particles, which are accelerated by parallel-potential drops in the auroral acceleration region. The other process reflects the fact that part of field-aligned current (FAC) carried by electrons is closed with a perpendicular ionic current. Here, whereas the electric current is divergence-free, the divergence of electron current is finite. Therefore, the ionospheric electron density changes, and so does the conductivity. If the energy of electron precipitation is below ∼10 eV, this second process plays an important role in plasma transportation, production, and evacuation processes. In this case the density variation does not extend in space at the perpendicular electron velocity, but it rather moves at the ion perpendicular velocity. If the energy of electron precipitation is above ∼1 keV, in contrast, the precipitation has a nonlinear effect on plasma evolution. That is, the propagation speed of the density variation increases with increasing upward-FAC density, and the propagation takes place in the direction of the converging current into the upward FAC region. The Cowling effect on the plasma evolution process is crucially important. Our formulation is more general than the previous studies and is not limited to certain geometries, current component or interaction modes between the ionosphere and magnetosphere. It is therefore better-suited for describing the self-organized M-I coupling system, which evolves with current systems, conductivity, and magnetospheric processes interacting with each other.

Twinning effects in a rod-textured AM30 Magnesium alloy

We experimentally and numerically investigated the effect of twinning on plasticity using an extruded rod-textured magnesium alloy. The rod-texture is a 〈 1 0 1 ¯ 0 〉 -axis fiber texture that presents a fundamentally different anisotropy correlated to twinning with respect to the widely discussed c-axis fiber texture generated by clock rolling. We quantified a profuse { 1 0 1 ¯ 2 } 〈 1 0 1 ¯ 1 〉 extension twinning along the extrusion direction (ED) that consumed the entire parent before the inflection point in the stress–strain behavior. However, under compression along the extrusion radial direction (ERD), the twinning model in the viscoplastic self-consistent formulation still predicts substantial extension twinning. However, in this case the stress–strain curve did not inflect, and Regime II hardening was absent. We demonstrate via EBSD analyses that the absence of Regime II hardening along the ERD was due to a non-Schmid effect by multivariant “stopped” twinning. The intersecting variants of stopped twins incurred twin–twin interactions that limited the twin growth. Profuse { 1 0 1 ¯ 1 } 〈 1 0 1 ¯ 2 〉 double twinning occurs both under ED and ERD but peculiarly triggered earlier under ERD than under ED, so the Voce model under VPSC could not capture their effect. The complex networks of stopped twins in the ERD clearly negate a possible Hall–Petch effect on Regime II by twin segmentation, since otherwise Regime II would be more marked in the ERD. Rather, the stopped twins suggest preferential latent hardening within the twinned regions by parent dislocation transmutation upon their incorporation in the twins. In fact, since twin–twin interactions mitigate the growth rates of sweeping extension twin boundaries, dislocation transmutation could be limited to the extent that Regime II hardening will be eliminated.

Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements

This paper is concerned with the multiscale simulation of plastic deformation of metallic specimens using physically-based models that take into account their polycrystalline microstructure and the directionality of deformation mechanisms acting at single-crystal level. A polycrystal model based on self-consistent homogenization of single-crystal viscoplastic behavior is used to provide a texture-sensitive constitutive response of each material point, within a boundary problem solved with finite elements (FE) at the macroscale. The resulting constitutive behavior is that of an elasto-viscoplastic material, implemented in the implicit FE code ABAQUS. The widely-used viscoplastic selfconsistent (VPSC) formulation for polycrystal deformation has been implemented inside a user-defined material (UMAT) subroutine, providing the relationship between stress and plastic strain-rate response. Each integration point of the FE model is considered as a polycrystal with a given initial texture that evolves with deformation. The viscoplastic compliance tensor computed internally in the polycrystal model is in turn used for the minimization of a suitable-designed residual, as well as in the construction of the elasto-viscoplastic tangent stiffness matrix required by the implicit FE scheme. Uniaxial tension and simple shear of an FCC polycrystal have been used to benchmark the accuracy of the proposed implicit scheme and the correct treatment of rotations for prediction of texture evolution. In addition, two applications are presented to illustrate the potential of the multiscale strategy: a simulation of rolling of an FCC plate, in which the model predicts the development of different textures through the thickness of the plate; and the deformation under 4-point bending of textured HCP bars, in which the model captures the dimensional changes associated with different orientations of the dominant texture component with respect to the bending plane.

Concomitant modulated superfluidity in polarized Fermi gases

Recent ground-breaking experiments studying the effects of spin polarization on pairing in unitary Fermi gases encountered mutual qualitative and quantitative discrepancies which seem to be a function of the confining geometry. Using numerical algorithms we study the solution space for a three-dimensional fully self-consistent formulation of realistic systems with up to ${10}^{5}$ atoms. A study of the three types of solutions obtained demonstrates a tendency toward metastability as the confining geometry is elongated. One of these solutions, which is consistent with Rice experiments at high trap aspect ratio, supports a state strikingly similar to the long sought Fulde-Ferrel-Larkin-Ovchinnikov state. Our study helps to resolve the long-standing controversy concerning the discrepancies between the findings from two different experimental groups and highlights the versatility of actual-size numerical calculations for investigating inhomogeneous fermionic superfluids.

Self-consistent input-output formulation of quantum feedback

A simple method of analyzing quantum feedback circuits is presented. The classical analysis of feedback circuits can be generalized to apply to quantum systems by mapping the field operators of various outputs to other inputs via the standard input-output formalism. Unfortunately, this has led to unphysical results such as the violation of the Heisenberg uncertainty principle for in-loop fields. This paper shows that this general approach can be redeemed by ensuring a self-consistently Hermitian Hamiltonian. The calculations are based on a noncommutative calculus of operator derivatives. A full description of several examples of quantum linear and nonlinear feedback for optical systems is presented.

Recent advances in high pressure and temperature rheological studies

Rheological studies at high pressure and temperature using in-situ X-ray diffraction and imaging have made significant progresses in recent years, thanks to a combination of recent developments in several areas: (1) advances in synchrotron X-ray techniques, (2) advances in deformation devices and the abilities to control pressure, temperature, stress, strain and strain rates, (3) theoretical and computational advances in stress determination based on powder and single crystal diffraction, (4) theoretical and computational advances in modeling of grain-level micromechanics based on elasto-plastic and visco-plastic self-consistent formulations. In this article, we briefly introduce the experimental techniques and theoretical background for in-situ high pressure, high temperature rheological studies, and then review recent studies of rheological properties of major mantle materials. Some currently encountered issues have prompted developments in single-crystal quasi-Laue diffraction for complete stress tensor determination and textural evolution of poly-phased composites based on X-ray microtomography. Future prospects are discussed.

The role of disc-type crystal shape for micromechanical predictions of elasticity and strength of hydroxyapatite biomaterials

The successful design of ceramic bone biomaterials is challenged by two competing requirements: on the one hand, such materials need to be stiff and strong, which would suggest a low porosity (of pore sizes in the 10-100 microm range) to be targeted; on the other hand, bone biomaterials need to be bioactive (in particular vascularized), which suggests a high porosity of such materials. Conclusively, reliable information on how porosity drives the stiffness and strength properties of ceramic bone biomaterials (tissue engineering scaffolds) is of great interest. In this context, mathematical models are increasingly being introduced into the field. Recently, self-consistent continuum micromechanics formulations have turned out as expressedly efficient and reliable tools to predict hydroxyapatite biomaterials' stiffness and strength, as a function of the biomaterial-specific porosity, and of the 'universal' properties of the individual hydroxyapatite crystals: their stiffness, strength and shape. However, the precise crystal shape can be suitably approximated by specific ellipsoidal shapes: while it was shown earlier that spherical shapes do not lead to satisfactory results, and that acicular shapes are an appropriate choice, we here concentrate on disc-type crystal shape as, besides needles, plates are often reported in micrographs of hydroxyapatite biomaterials. Disc-based model predictions of a substantial set of experimental data on stiffness and strength of hydroxyapatite biomaterials almost attain the quality of the very satisfactory needle-based models. This suggests that, as long as the crystal shape is clearly non-spherical, its precise shape is of secondary importance if stiffness and strength of hydroxyapatite biomaterials are predicted on the basis of continuum micromechanics, from their micromorphology and porosity.