Two classes of multisecant methods for nonlinear acceleration

Many applications in science and engineering lead to models that require solving large‐scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasi‐Newton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition. We present two classes of multisecant methods which allow to take into account a variable number of secant equations at each iteration. The first is the Broyden‐like class, of which Broyden's family is a subclass, and Anderson mixing is a particular member. The second class is that of the nonlinear Eirola–Nevanlinna‐type methods. This work was motivated by a problem in electronic structure calculations, whereby a fixed point iteration, known as the self‐consistent field (SCF) iteration, is accelerated by various strategies termed ‘mixing’. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of strain-induced crystallization in natural rubbers

Strain-Induced Crystallization (SIC) is a phenomenon characterized by a considerable increase in stiffness of natural rubbers. In this contribution, this phenomenon is studied in filled natural rubbers and a constitutive model of SIC is proposed. The influence of SIC on the mechanical behavior is described by means of the entropic strain energy subjected to a change due the crystallization. The distribution of crystallines is formulated on the basis of a statistical approach. Their contribution to the partial immobilization of polymer chains is accounted for by assuming the crystalline phase and the amorphous phase to be two separate networks. Finally, the model is compared with available experimental results of uniaxial tension tests. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Steric communication of chiral information observed in dendronized polyacetylenes

Structural and retrostructural analysis of helical dendronized polyacetylenes (i.e., self-organizable polyacetylenes containing first generation dendrons or minidendrons as side groups) synthesized by the polymerization of minidendritic acetylenes with [Rh(nbd)Cl]2 (nbd = 2,5-norbornadiene) reveals an approximately 10% change in the average column stratum thickness (l) of the cylindrical macromolecules with a chiral periphery, through which a strong preference for a single-handed screw-sense is communicated. The cylindrical macromolecules reversibly interconvert between a three-dimensional (3D) centered rectangular lattice (Phi r-c,k) exhibiting long-range intracolumnar helical order at lower temperatures and a two-dimensional (2D) hexagonal columnar lattice (Phi h) with short-range helical order at higher temperatures. A polymer containing chiral, nonracemic peripheral alkyl tails is found to have a larger l as compared to the achiral polymers. In methyl cyclohexane solution, the same polymer exhibits an intense signal in circular dichroism (CD) spectra, whose intensity decreases upon heating. The observed change in l indicates that the chiral tails alter the polymer conformation from that of the corresponding polymer with achiral side chains. This change in conformation results in a relatively large free energy difference (DeltaGh) favoring one helix-sense over the other (per monomer residue). The capacity to distort the polymer conformation and corresponding free energy is related to the population of branches in the chiral tails and their distance from the polymer backbone by comparison to recently reported first and second generation dendronized polyphenylacetylenes.     

Regioselective bond cleavage in the dissociative electron transfer to benzyl thiocyanates: the role of radical/ion pair formation

Important aspects of the electrochemical reduction of a series of substituted benzyl thiocyanates were investigated. A striking change in the reductive cleavage mechanism as a function of the substituent on the aryl ring of the benzyl thiocyanate was observed, and more importantly, a regioselective bond cleavage was encountered. A reductive alpha-cleavage (CH(2)-S bond) was seen for cyano and nitro-substituted benzyl thiocyanates leading to the formation of the corresponding nitro-substituted dibenzyls. With other substituents (CH(3)O, CH(3), H, Cl, and F), both the alpha (CH(2)-S) and the beta (S-CN) bonds could be cleaved as a result of an electrochemical reduction leading to the formation of the corresponding substituted monosulfides, disulfides, and toluenes. These final products are generated through either a protonation or a nucleophilic reaction of the two-electron reduction-produced anion on the parent molecule. The dissociative electron transfer theory and its extension to the formation/dissociation of radical anions, as well as its extension to the case of strong in-cage interactions between the produced fragments ("sticky" dissociative electron transfer (ET)), along with the theoretical calculation results helped rationalize (i) the observed change in the ET mechanism, (ii) the dissociation of the radical anion intermediates formed during the electrochemical reduction of the nitro-substituted benzyl thiocyanates, and more importantly (iii) the regioselective reductive bond cleavage.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Computational study of plasma-assisted photoacoustic response from gold nanoparticles irradiated by off-resonance ultrafast laser

The gold nanoparticles (AuNPs) are capable of enhancing the incident laser field in the form of scattered near field for even an off-resonance irradiation where the incident laser wavelength is far away from the localized surface plasmon resonance (LSPR). If the intensity of the pulse laser is large enough, this capability can be employed to generate a highly localized free electron (plasma) in the vicinity of the particles. The generated plasma can absorb more energy during the pulse, and this energy deposition can be considered as an energy source for structural mechanics calculations in the surrounding media to generate a photoacoustic (PA) signal. To show this, in this paper, we model plasma-mediated PA pressure wave propagation from a 100-nm AuNPs and the surrounding media irradiated by an ultrashort pulse laser. In this model, the AuNP is immersed in water and the laser pulse width is ranging from 70 fs to 2 ps at the wavelength of 800 nm (off-resonance). Our results qualitatively show the substantial impact of the energy deposition in plasma on the PA signal through boosting the pressure amplitudes up to ～1000 times compared to the conventional approach.     

Predicting a major role of surface spins in the magnetic properties of ferrite nanoparticles

Room‐temperature magnetization hysterisis measurements were conducted on Mn_0.5Zn_0.5Gd_xFe_(2‐x)O₄ ferrite nanoparticles, with x = 0, 0.5, 1.0, 1.5. The structure of this ferrite is normal spinel where the added of Gd³⁺ ions occupied the octahedral sites and replaces Fe³⁺ ions. The saturation magnetization was found to increase with the initial addition of the Gd³⁺ ions followed by a sharp decrease with further addition of Gd³⁺ ions. The Curie temperature was found to increase up to Gd³⁺ concentration of x = 1.0, and then decreases at x = 1.5. These results were attributed to the surface spins. Because the size of Gd³⁺ ions is larger than that of Fe³⁺ ions, the substitution of Fe³⁺ ions with the Gd³⁺ ions results in surface disorder which results in surface spins. A core‐shell magnetization model was introduced where several factors were combined to explain our results. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modulating opto-electronic and magnetic responses of Mo- and Zn-adsorbed LiNbO3 (1 1 1) surface for advanced energy harvesting applications: A comprehensive study

This study aimed to comprehensively investigate the optoelectronic and magnetic properties of Mo, Zn/LiNbO₃ (1 1 1) material. The primary objectives were to understand the potential for manipulating the material's magnetism and to elucidate the origin of spin-polarized states and magnetic moments, particularly with respect to the unpaired d orbitals of Nb, Mo, and Zn atoms. To achieve these objectives, we employed the Pardew–Burke–Ernzerhof (PBE) method within the Generalized Gradient Approximation (GGA + U) framework. This computational approach allowed us to examine the optoelectronic and magnetic characteristics of the material in detail. Our research yielded several key findings that enhance our understanding of Mo, Zn/LiNbO₃ (1 1 1) material. We observed a modest improvement in the material's absorption capacity within the visible spectrum, accompanied by a discernible red-shift. Notably, our study involved the calculation of the dielectric function and refractive constant of the material, revealing a strong correlation between absorption trends and the dielectric constant. Furthermore, our investigation uncovered that Mo, Zn/LiNbO₃ (1 1 1) exhibits distinct conduction and valence bands, with p and d orbitals predominantly contributing to each, respectively. The energy gap of the material falls within a range of 0.30–1.04 eV. A particularly significant finding was the narrower band gap of Mo, Zn/LiNbO₃ (1 1 1) material, which can be attributed to the superposition of Mo-d and Zn-p orbit energy levels with O-p orbit energy levels, ultimately forming a covalent bond. Importantly, our research demonstrated the material's heightened optical absorption within the visible spectrum, suggesting its suitability for various photonic and optoelectronic applications. Additionally, we calculated a wide range of optical characteristics, including the dielectric function, absorption coefficient, energy loss, reflectivity, refractive index, extinction coefficient, and optical conductivity, providing a comprehensive assessment of the material's optical properties.     

Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV–Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold(hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space–time fractional KdV–Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.     

The collisions of two ion acoustic solitary waves in a magnetized nonextensive plasma

Using the extended Poincaré-Lighthill-Kuo (EPLK) method, the interaction between two ion acoustic solitary waves (IASWs) in a multicomponent magnetized plasma (including Tsallis nonextensive electrons) has been theoretically investigated. The analytical phase shifts of the two solitary waves after interaction are estimated. The proposed model leads to rarefactive solitons only. The effects of colliding angle, ratio of number densities of (positive/negative) ions species to the density of nonextensive electrons, ion-to-electron temperature ratio, mass ratio of the negative-to-positive ions and the electron nonextensive parameter on the phase shifts are investigated numerically. The present results show that these parameters have strong effects on the phase shifts and trajectories of the two IASWs after collision. Evidently, this model is helpful for interpreting the propagation and the oblique collision of IASWs in magnetized multicomponent plasma experiments and space observations.