Allometry and growth: A unified view

Allometry is crucial in biology; scaling relations are implied in laws of growth of living systems. The self similarity of Gompertzian growths of biological organisms plays a key role, in this regard, in biological similitude. The origin of allometric relationships and values of the scaling exponents is a source of debate, as well as the origin of the range of biological scales. But, besides biology, scaling and growth characterize many different complex systems. Encompassing these aspects in a unified view is an interesting target. In this paper we propose a coarse but significant model that is applied to astrophysical structures and biological organisms. The inclusion of such different systems suggests applications to fields where allometry is emerging, such as economics, urban planning and the social sciences.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

A unified semiclassical description of elastic scattering by a central field

The diffraction-integral formulation of the semiclassical limit of the quantal wavefunction, as proposed in an earlier paper, is applied to the treatment of elastic scattering by a general central-field potential. Angular-momentum quantisation is shown to be a natural consequence of the theory and partial-wave series representations of the s-matrix and asymptotic wavefunction are derived. In addition, the method and results establish a connection between refractive, diffractive, dynamical and uniform-approximation theories of semiclassical scattering.     

Towards a unified view of the solvatochromism of phenolate betaine dyes

An attempt has been made in order to unify the three types of solvatochromisms (negative, positive and inverted) of phenolate betaine dyes by a working model which describes them as particular cases of a general behavior. The model, based on the calculation (gas phase) of the chemical hardness of donor and acceptor fragments, was applied to 56 examples from the literature. As a result, the investigated compounds were grouped according to the sum of the hardnesses of their (non‐interacting) fragments, this sum being larger for a negative, intermediate for an inverted, and smaller for a positive solvatochromic behavior. Copyright © 2009 John Wiley & Sons, Ltd.     

A comparison of laser ultrasound measurements and finite element simulations for evaluating the elastic properties of tissue mimicking phantoms

Advances in the field of laser ultrasonics have opened up new possibilities in medical applications. This paper presents a finite element modelling technique, which studies laser generated surface acoustic waves in different concentration of soft tissue mimicking agar-agar phantoms. In addition, we propose a novel approach that utilises a low coherence interferometer to detect the laser-induced surface acoustic waves from the tissue mimicking phantoms. A Nd:YAG focused laser line-source is applied to the agar-agar phantoms, which as the same with the FE simulation. The generated SAW signals are detected by a time domain low coherence interferometry system. SAW phase velocity dispersion curves from both of the FE simulation and experiment are calculated. By comparison, we show that the experimental results agree well with those of the FE simulation and theoretical expectations. This study is the first report that a laser-generated SAW phase velocity dispersion technique is applied to soft materials. This technique may open a way for laser ultrasonics to detect the mechanical properties of soft tissues, such as skin.     

A unified view of particles and fields in a simple model of a physical system

We start from the primitive concepts of preparticle and membership relation of set theory to obtain the derivative concepts of particle (already introduced in a previous work), field, and the interaction between systems of particles. We have explicitly stated, in addition, what the relationship between a system of particles and the field it produces is in the present model of physical systems. In order to discuss the motion of particles we have analyzed one of the possible definitions of a reference frame.On leave of absence from Instituto Venezolane de Investigaciones Científicas (I.V.I.C.).     

Energy spectra of quantum turbulence in He II and 3He-B: A unified view

Quantum turbulence in superfluid He II and in ³He-B that can be regarded as nearly isothermal, isotropic, and homogeneous is discussed within the two-fluid model. A general form of the 3D energy spectrum is proposed: at large length scales, where normal and superfluid eddies are locked together by the mutual friction force, the energy spectrum is essentially classical and includes an inertial range of a Kolmogorov K62 form. With increasing wavenumber k, the normal fluid part of the spectrum terminates due to finite viscosity, while the superfluid part of the spectral energy density changes towards k ⁻³ and then back into Kolmogorov-like k ^−5/3 again. Agreement with computer simulations and experiments is claimed if account is taken of the turbulent box size and of the energy decay rate. The text was submitted by the author in English.     

Anisotropic elastic properties of microtubules

The present study aims at providing insight into the acceleration mechanism of a bubble chain rising in shear-thinning viscoelastic fluids. The experimental investigation by the Particle Image Velocimetry (PIV), birefringence visualisation and rheological simulation shows that two aspects are central to bubble interactions in such media: the stress creation by the passage of bubbles, and their relaxation due to the fluids memory forming an evanescent corridor of reduced viscosity. Interactions between bubbles were taken into account mainly through a linear superposition of the stress evolution behind each bubble. An analytical approach together with the rheological consideration was developed to compute the rise velocity of a bubble chain in function of the injection period and bubble volume. The model predictions compare satisfactorily with the experimental investigation.     

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.     

Magneto-optical imaging of elastic strain-controlled magnetization reorientation

We study strain-controlled magnetization-reorientation processes in nickel thin film/piezoelectric actuator hybrid structures. To obtain a consistent picture of the connection between magnetic microstructure and magnetoresistance, we correlate simultaneously measured spatially resolved magneto-optical Kerr effect imaging and integral magnetotransport measurements at room temperature. Our results show that the magnetization predominantly reorients by coherent rotation as a function of the voltage applied to the hybrid, except for a narrow region around the coercive field for which the magnetization reorientation evolves via domain effects. This demonstrates that both magnetic-field and strain-driven magnetization reversal can be modeled in terms of a macrospin model.     

A unified dynamic scaling property for the unified hybrid network theory framework

In this article, we present a new type of unified dynamic scaling property for synchronizability, which can describe the scaling relationship between dynamic synehronizability and four hybrid ratios under the unified hybrid network theory framework （UHNTF）. Our theory results can not only be applied to judge and analyze dynamic synehronizability for most of complex networks associated with the UHNTF, but also we can flexibly adjust and design different hybrid ratios and sealing exponent to meet actual requirement for the dynanfic characteristics of the UHNTF.     

Local elastic properties of nano-confined fluids: A density functional study

The understanding of mechanical properties of confined fluids is essential for modeling and manipulating of nano-scaled systems. Unlike the uniform phase, the confined fluids usually display different features in structure and related properties. Due to the presence of the confining geometry, the density profile and many physical and chemical properties may be position-dependent. The aim of our research is to derive an expression for the local elastic property by using the classical elastic theory. Both the bulk and shear moduli are expressed as functional of density of particle. The theoretical result derived is applied to the Lennard-Jones fluids confined in nano-cavity. Comparison of our numerical result and the simulation result is made and qualitative agreement is observed. Further, influence of bulk density, temperature and external potential on moduli is calculated and the physical mechanism is analyzed. Relationship between contact modulus and the interfacial tension is also calculated. Their opposite trend with temperature is observed.     

Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.     

Some elastic properties of solid nematics

The general approach to study the properties of the mechanical deformations of solid nematics, which are the macroscopic homogeneous elastic media having the rotational symmetry of the nematic liquid crystals is proposed. The stress tensor, the Young modulus and the Poisson ratios for the parallel and perpendicular homogeneous orientations of nematic molecules relative to the axis of external forces influence are obtained by the varying of the free energy of mechanical deformation. It is shown that these constants have the anisotropic character and the experiments for the direct measurement of five elasticity coefficients entering the free energy expression are proposed.     

A study of the size-dependent elastic properties of silicon carbide nanotubes: First-principles calculations

The size dependence of elastic properties in single-walled silicon carbide nanotubes are investigated by first-principles calculations. We found the Young?s modulus of the nanotubes increases with increasing diameter and is inversely proportional to Si–C bond length, whereas the Poisson ratio shows an opposite trend. For small tubes the elastic properties change dramatically with the tube size. While for the tubes with the diameter larger than 8 Å, the difference of these properties is small and almost independent of the size and symmetry. The strength of bonding between Si and C atoms is elucidated by the amount of the charge transfer calculated by the Bader analysis.     

Magnetic and elastic properties of CeAg

Magnetic and elastic measurements in single crystals of CeAg and Ce_0.09La_0.91 Ag are presented. The magnetic susceptibility of Ce_0.09La_0.91 Ag can be quantitatively interpreted with taking Γ₈ as the ground state of the crystal field split $\text{J =}\text{5}\text{2}$ state of the Ce³⁺-ion. In CeAg we confirm a ferromagnetic phase transition at T_c = 5.3 K and a structural transition at 15 K. This latter one is clearly observed with the elastic constant measurements where c₁₁ - c₁₂ exhibits appreciable softening. This structural transition is probably due to a phonon softening at the zone boundary. The magnetic properties of CeAg, especially the small magnetic moment in the ordered region, are discussed.