Search

A high-accuracy polarimetric technique has been used for the characterization of a lead germanate ferroelectric single crystal. The measurement results of the linear and circular birefringence in the [010] direction at a wavelength of 633 nm under the influence of an electric field are presented. Gyration–electric field hysteresis loops at alternative crystal positions in the polarization system have been used to determine the ellipticity of the eigenwaves. A temperature dependence of the gyration tensor component g 11 in the temperature range of 300–450 K was found.

The structure formation of particles with induced dipoles dispersed in a viscous fluid, under a spatially and temporarily uniform external electric or magnetic field, is investigated by means of Brownian Dynamics simulations. Dipole–dipole interactions forces, excluded volume forces and thermal fluctuations are accounted for. The resulting structures are characterized in terms of average orientation of their inter-particle vectors (second Legendre polynomial), network structure, size of particle clusters, anisotropy of the gyration tensor of every cluster and existence of (cluster) percolation. The magnitude of the strength of the external field and the volume fraction of particles are varied and the structural evolution of the system is followed in time. The results show that the characteristic timescale calculated from the interaction of only two dipoles is also valid for the collective dynamics of many-particle simulations. In addition, the magnitude of the strength of the external field in the range of values we investigate influences only the magnitude of the deviations around the average behavior. The main characteristics (number density of branch-points and thickness of branches) of the structure are mainly affected by the volume fraction. The possibility of 3D printing these systems is explored. While the paper provides the details about the case of an electric field, all results presented here can be translated directly into the case of a magnetic field and paramagnetic particles.

Conoscopic interference patterns, channelled spectra and polarimetric techniques have been used for the characterization of pure and doped (with L-arginine amino acid) potassium dihydrogen phosphate (KDP) single crystals. Experimental polarimetric data have been obtained for the frequently used wavelength of 633 nm and for two close wavelengths of 532 and 543 nm in a high-accuracy dual-wavelength polarimeter. The measurement of eigenwave ellipticity in the [100] and [010] directions and between 295 and 340 K shows small differences in the absolute values of the specific optical rotations of KDP crystals doped with L-arginine in the range of 0.7–3.8 wt%. It is found that the gyration tensor component g 11, specific optical rotation and eigenwave ellipticity show different dispersion in the visible spectral region.

This paper presents a theoretical study of the excitonic spectra of a hexagonal 2D lattice of trimers (the structure of bacteriorhodopsin – BR). Formalism of dielectric permittivity and of gyration tensor allows to calculate the components of both tensors near the frequency of electronic excitation of retinal with λ≈ 570 nm. The two cases of oblique and normal incidence of left- and right-circularly polarized electromagnetic waves have been considered. In accordance with the experimental data at oblique incidence a negative circular dichroism (CD) couplet appears connected with the chiral excitonic coupling. At perpendicular incidence a single CD band of Lorentz type is caused by the internal gyrotropy of the molecules.

Multicanonical simulations of hydrophobic-polar heteropolymers were performed with a simple and effective coarse-grained off-lattice model to identify the folding pathways and the topology of the energy landscape with gyration tensor-based parameters. We examined six exemplified sequences of heteropolymers and illustrated three of them which present definitely different folding types such as two-state folding, folding through intermediates, as well as metastability. The major advantage of this study is our chosen ”order” parameter, namely gyration tensor-based analysis, does not require any reference state before the simulation as that is the need for the other order parameters which are chosen in other studies in the same context. Our paper presents the use of very useful parameters to detect conformational phase transitions in polymer chains. Another order parameter that requires a reference conformation is presented in earlier works related to this aspect. This extends the simulation into two steps. With our analysis, there is no need for a global minimum conformation so-called reference state and our simulation will be completed in one step. Furthermore, there is no relative evaluation according to the reference state.

Theoretical calculations have been proposing to determine the gyration tensor components of Hg3Te2Br2, based on the phenomenological theory of optical activity for the homogeneous medium. This study provides the better understanding of gyrotropy mechanism and its origin in acentric crystals. The results are interpreted with the assumption that the optical rotation excludes the distortion. The correlation between the existence of optical activity phenomenon and realization of direct optical transitions in crystal under investigation was established. This is the first theoretical report on the optical properties of Hg3Te2Br2.

In situ, synchrotron-based micro computerized tomography is used to investigate three-dimensional (3D) deformation dynamics of open-cell porous titanium under uniaxial compression. The 3D pore structures are captured, segmented, and transformed into separated pores (spheres) connected by throats (bars) according to the pore network model (PNM). Pore and throat size distributions are quantified via the PNM, while pore shape and orientation distributions, via gyration tensor analysis. After yield, the mean values of equivalent diameter, sphericity and aspect ratios of the pores decrease as deformation progresses, indicating increased pore anisotropy. However, the number and equivalent diameter of the throats decrease even at the elastic stage, and the average diameter decreases approximately linearly with increasing bulk strain. The collapse of individual pores is tracked, and the pores with their longest axes aligned perpendicular to the loading direction are prone to compaction compared to those aligned parallel to the loading direction, because of different stress concentrations. Microstructure-based finite element (FE) analysis reproduces the overall deformation characteristics observed in the experiments. The deformation mechanisms and FE model may be useful for guiding material assessment and design related to porous Ti.

A molecular field theory of the cholesteric ordering in nematic nanocomposites doped with chiral nanoparticles was developed taking into consideration chiral dispersion interaction between rod-like nanoparticles. It was shown that the inverse pitch of the cholesteric helical structure is proportional to the anisotropy of the effective polarizability and the anisotropy of the effective gyration tensor of a nanoparticle in the nematic host. The theory enables one to predict the helical sense inversion induced by a change of the low-frequency dielectric susceptibility of the nematic host phase. The components of the high-frequency effective polarizability and the effective optical activity of a gold rod-like nanoparticle in a particular nematic solvent were calculated numerically.

Molecular dynamics simulations are carried out to investigate the structure of a single poly(oxyethylene) (POE) chain in aqueous and methanolic solutions in a strong external electric field. The conformational changes of the polymer chain induced by the strong external electric field are monitored by measuring the radius of gyration, the components of the gyration tensor, the end-to-end distance, dihedral angle distribution, and the helical content. The isotropic coil size measures, i. e., the radius of gyration and the end-to-end distance mostly decrease with growing intensity of the electric field except a small increase occurring between 0 and 1 V/nm in water. Therefore, in most cases the field compresses the polymer coil. Nevertheless, the deformation is anisotropic, leading to an average spheroid which is prolate in water (again with the exception of fields less or equal to 1 V/nm) and oblate in methanol. Analysis of dihedrals suggests that POE chain’s partially helical structure is promoted at electric fields above 1 V/nm. Changes caused by the strong external electric field in the solvent–solvent and solvent–polymer hydrogen-bonding structure are monitored by measuring the number of hydrogen bonds, their strength, and the volume of the bonding region. Results show non-trivial, solvent-specific effects, which are yet to be fully understood.

A method is presented for quantitatively evaluating the shape and size of deformed particles in dispersion from their two-dimensional anisotropic spectra by small-angle scattering. By means of real spherical harmonic expansion, we derive analytical expressions of the gyration tensor R in terms of experimentally measured anisotropic scattering functions, yielding a tensorial extension of the Guinier law. We demonstrate the usefulness of this approach by a model study of an affinely deformed Gaussian chain. We further show that radius of gyration Rg is the source term of intraparticle structure factor at the mean-field limit, and from this perspective, we address the connection between R and conformation asphericity. The developed method not only facilitates quantitative scattering studies of deforming materials, but also provides insightful information regarding their deformation behavior at the molecular level based on the symmetric properties of real spherical harmonics.

For the description of the optical response of optically active media, different constitutive equations have been proposed and are still used in literature. Here, we demonstrate on potassium titanyl phosphate (KTiOPO4) by means of ellipsometry that only the symmetric constitutive equation describes the observed spectra properly and allows the unique determination of the gyration tensor.

Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.

Coarse-grained molecular dynamics simulations of Kremer–Grest-type bead-spring models were performed on mixtures of ring and linear polymers to investigate the effects of chain-penetration on polymer ring shape. We found that the number of linear chains penetrating through a ring increased with ring size, while penetration was inhibited for smaller rings composed of less than 80 beads. From the eigenvalue analyses of the gyration tensor of each ring, the ring shape was characterized by asphericity and prolateness. The number of chains penetrating through a ring (nP) was determined from the Gauss linking numbers of all ring and linear chain pairs. The radius of gyration of the rings were dependent on the nP value, suggesting that the linear chains expanded the ring upon penetration. The obtained results provide important insights in ring-linear blends for theoretical research as well as simulations and experiments especially for rheological measurements.

This paper focuses on optical activity investigations of Hg 3 X 2 Cl 2 (X = Se, Te) crystals. To understand better the nature of gyrotropy occurrence, relation to the crystal structure of Hg 3 X 2 Cl 2 (X = Se, Te) crystals and contribution of interband transitions to optical rotation the detailed theoretical analysis is conducted. The gyration tensor of Hg 3 Se 2 Cl 2 crystals is calculated. The theoretical results are confirmed by experimental observation of optical activity. Nanomaterials based on Hg 3 X 2 Y 2 (X = S, Se, Te; Y = F, Cl, Br, I) gyrotropic crystals have tremendous potential in addressing the two major issues faced by our society: the searching for new energy sources and improving healthcare. Obtained data suggest that the phenomenon of optical activity should be taken into account in the studies concerning optical diagnostic methods in medicine.

We investigate the typical sizes and shapes of sets of points obtained by irregularly tracking two-dimensional Brownian bridges. The tracking process consists of observing the path location at the arrival times of a non-homogeneous Poisson process on a finite time interval. The time varying intensity of this observation process is the tracking strategy. By analysing the gyration tensor of tracked points we prove two theorems which relate the tracking strategy to the average gyration radius, and to the asphericity -- a measure of how non-spherical the point set is. The act of tracking may be interpreted either as a process of observation, or as process of depositing time decaying "evidence" such as scent, environmental disturbance, or disease particles. We present examples of different strategies, and explore by simulation the effects of varying the total number of tracking points., Comment: 12 pages of the main article followed by the supplementary material

Crystals and crystal symmetry - structure of solids close-packing structures two-dimensional lattices three-dimensional lattices crystallographic indices for planes - Miller indices crystallographic direction indices introducing tensors - introduction to the notation reducing the numbers of components transformations of axes transformation of a vector transformation of the co-ordinates of a point transformation and the definition of a tensor second-rank symmetrical tensors - the representation quadric Neumann's principle second-rank tensors - conductivity: thermal conductivity and thermal resistivity heat flow in crystal samples the radius-normal property of the representation quadric electrical conductivity and electrical resistivity diffusion fourth-rank tensors - elasticity strain symmetrical and antisymmetrical tensors the strain tensor stress elasticity the matrix notation effect of crystal symmetry - equating components in cubic crystals and polycrystalline samples elasticity components in other crystal systems crystal optics the indicatrix the wave-surface biaxial crystals double refraction (birefringence) at a boundary definition of an axial tensor transformation of axial vectors transformation of axial tensors optical activity optical activity in the presence of birefringence the gyration tensor - second-rank axial tensor the Hall effect - third rank axial tensor Hall effect - relationship to symmetry magnetresistance and other effects further tensor applications thermal expansion pyroelectric effect piezoelectricity photoelasticity the linear electro-optic effect (the Pockels effect) the quadratic electro-optic effect (the Kerr effect).

En annexe:Corrigendum to «Statistics about collisions of ellipsoids under shear flow» [Colloids Surf. A: Physicochem. Eng. Aspects 558 (2018) 250–262], Colloids and Surfaces A: Physicochemical and Engineering Aspects, Elsevier, 562, p.431, 2019,DOI: 10.1016/j.colsurfa.2018.10.083; International audience; Shear aggregation is an important phenomenon occurring during particle precipitation in a stirred chemical reactor. It concerns micro-particles that are often non-spherical or aggregated. Modelling of precipitation involves the selection of internal parameters describing the particle. Among them, morphological or geometrical descriptors are required. In this paper, the inertia or gyration tensor of primary particles and of their cluster is considered and evaluated for the modelling of aggregation. An equivalent ellipsoid is defined from the inertia tensor. In this framework, the collision event becomes the collision between two equivalent ellipsoids and leads to a larger ellipsoid. The inertia tensor and the semi-axis lengths of the equivalent ellipsoid are explicitly calculated in the case of shear aggregation in a three-dimensional space. Two ways for performing these calculations are presented. The statistics of the equivalent ellipsoids associated with the set of collision events undergone by two given ellipsoids have been computed. Statistics includes the probability density for geometrical parameters and the average value. Collision rate constant, i.e. aggregation kernel, is also calculated. Corresponding approximate expressions are presented and checked. Finally, equivalence between the sphere cluster and the equivalent ellipsoid with respect to the aggregation act is checked and ascertained.

The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for non-grafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work dicussed here could have experimental implications from protein-ligand interactions to designing nano smart materials.

Optical activity in the X-ray range stems from the electric-dipole–electric-quadrupole interference terms mixing multipoles of opposite parity, and can be observed exclusively in systems with broken inversion symmetry. The gyration tensor formalism is used to describe the X-ray optical activity in langasite La3Ga5SiO14 crystal with the P321 space group. An experimental study of the X-ray natural circular dichroism (XNCD) near the Ga K-edge in La3Ga5SiO14 single crystal was performed at ESRF beamline ID12, both along and perpendicular to the crystal optical axis. The combination of the quantum mechanical calculations and high-quality experimental results has allowed us to separate the contributions into X-ray absorption and XNCD spectra of Ga atoms occupying three distinct Wyckoff positions.

The planar elongational melt rheology and structural properties of dendrimers and hyperbranched polymers of different molecular weights (generations 1–4) and their linear counterparts have been studied using nonequilibrium molecular dynamics simulation techniques in the isothermal-isobaric ensemble. The extensional viscosity showed three distinctive regions against strain-rate, including an initial Newtonian region at low strain-rates, followed by a thickening behavior at medium strain-rates and terminated with a thinning region at very high strain-rates, in agreement with the Sarkar and Gupta model [J. Rein. Plast. Comp. 20, 1473–1484 (2001)]. In addition, a structural analysis was performed to study the size, shape, and spatial distributions within globular dendrimers and hyperbranched polymer molecules under planar elongational flow (PEF). Ratios of the eigenvalues of the gyration tensor showed that contrary to shear flow, under PEF even at low strain rates, dendrimers and hyperbranched molecules have ellipsoidal conformations and change to a much more flattened prolate shape at higher strain rates. In combination with the eigenvalue ratios, the distribution of monomers from the central core of the molecules showed that the thickening region occurs due to branches being stretched, and terminal thinning behavior stems primarily from flow-induced alignment and finite extensibility effects.

Selective adsorption of homopolymers is exploited as a model for pattern recognition. To this end the strong adsorption regime of Gaussian polymers adsorbed on a regularly structured surface is investigated for square and triangular lattices within a discrete Edwards model. The equilibrium behaviour of the specific heat, the gyration tensor and the (nematic) bond order tensor are analysed and compared to the properties for adsorbed freely jointed polymer chains.

It was shown in the course of developing the high-accuracy universal polarimeter (HAUP) that any polarimetric optical analyses cannot be free from a systematic error γ originating in the parasitic ellipticities of the constituent Nicol prisms. A method by which one can remove γ in the HAUP method is presented. This has been successfully applied to measurements of the gyration tensors and birefringence of two enantiomorphic crystals of α-quartz. It was found that the order of magnitude of this error for a polarizer is about 10−4 and consequently γ lies between 10−4 and 10−3 in typical optical systems. Our results, g11 = 5.7 ± 0.52 × 10−5 and g33 = −13.6 ± 0.52 × 10−5 with a wavelength of 6328 A for laevorotatory quartz at 300 K are in good agreement with some of the previous reports.

Depletion forces and macromolecular crowding govern the structure and function of biopolymers in biological cells and the properties of polymer nanocomposite materials. To isolate and analyze the influence of polymer shape fluctuations and penetrability on depletion-induced interactions and crowding by nanoparticles, we model polymers as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor of an ideal random walk. Within this model, we apply Monte Carlo simulation methods to compute the depletion-induced potential of mean force between hard nanospheres and crowding-induced shape distributions of polymers in the protein limit, in which polymer coils can be easily penetrated by smaller nanospheres. By comparing depletion potentials from simulations of ellipsoidal and spherical polymer models with predictions of polymer field theory and free-volume theory, we show that polymer depletion-induced interactions and crowding depend sensitively on polymer shapes and penetrability, with important implications for bulk thermodynamic phase behavior., 12 pages, 6 figures

Through the analysis of individual chain dynamics alongside the corresponding molecular structures under shear via nonequilibrium molecular dynamics simulations of C178H358 linear and short-chain branched polyethylene melts under shear flow, we observed that the conventional method based on the chain end-to-end vector (and/or the gyration tensor of chain) is susceptible to quantitatively inaccurate measurements and often misleading information in describing the rotational dynamics of polymers. Identifying the flaw as attributed to strong irregular Brownian fluctuations inherent to the chain ends associated with their large free volume and strong molecular collisions, we propose a simple, robust way based on the chain center-to-center vector connecting the two centers of mass of the bisected chain, which is shown to adequately describe polymer rotational dynamics without such shortcomings. We present further consideration that the proposed method can be useful in accurately measuring the overall chain structure and dynamics of polymeric materials with various molecular architectures, including branched and ring polymers.

We developed a new program, MSpin-RDC for the analysis of residual dipolar coupling data. This software, specially designed for small molecule analysis, can directly read many molecular-modeling and popular chemistry file formats and accept RDC values as a simple free-format table. Alignment tensor can then be computed by singular value decomposition, as well as predicted using inertia and gyration tensor-based methodologies. Trial structures are then ranked according to their Cornilescu's quality factor (Q) values. Analysis of multiconformational problems and fitting of RDC data to relative populations can be accomplished using the single-tensor approximation.

Following a recent effort [J. Am. Soc. Mass Spectrom. 23, 386-396 (2012)], we continue to explore computational methodologies for generating molecular conformations to support collisional cross sections suggested by ion mobility measurements. Here, adaptively biased molecular dynamics (ABMD) simulations are used to sample the configuration space and to achieve flat-histogram sampling along the reaction coordinates of the first two moments of the gyration tensor. The method is tested and compared with replica-exchange simulations on triply-protonated bradykinin and on a larger 25-residue peptide. It is found to have a much higher efficiency for producing large sets of conformations in a broad range of diffusion cross-sections, whereas it does not compete with conventional replica-exchange molecular dynamics in locating the lowest-energy structure. Nevertheless, the broad sampling obtained from the ABMD method allows to quantitatively correlate the diffusion cross-section Ω with other geometric order parameters that have simpler interpretation. The strong correlations found between the diffusion cross-section and the radius of gyration, the surface area and the volume of the convex hull suggest an optimal template for accurately mimicking the variations of Ω in a broad range of conformations, using only geometrical information and doing so at a very moderate computational cost. The existence of such a correlation is confirmed on the much larger protein α-lactalbumin.

Due to the relatively long time scales inherent to ionic surfactant self-assembly (>μs), an aggressive computational approach is needed to obtain converged data on micellar solutions. This work presents a study of micellization using a coarse-grained (CG) model of aqueous ionic surfactants in replicated molecular dynamics (MD) simulations run on graphics processing unit hardware. The performance of our implementation of the CG model with electrostatics into the HOOMD-Blue GPU-accelerated MD software package is comparable to that of a modest sized cluster running a highly optimized parallel CPU code. From 0.36 ms of cumulative trajectory data, we are able to predict equilibrium thermodynamic and morphological properties of ionic surfactant micellar solutions. Estimating the critical micelle concentrations (CMC) from the free monomer (ρ1) and premicellar concentrations obtained from simulations of sodium hexyl sulfate (S6S, CMC of 460 ± 6 mM) at high (1 M) concentration, a value in good agreement with experimental results is obtained; however, the same method applied to simulations of sodium nonyl sulfate (S9S, ρ1 of 2.4 ± 0.01 mM) and sodium dodecyl sulfate (SDS, ρ1 of 0.02 ± 0.01 mM) at the same total concentration systematically underestimates the CMCs. An alternative method for calculating the CMC is presented, where the free monomer concentration computed from high concentration CG-MD data is used as the input to a simple theoretical model which can be used to extrapolate to a more accurate prediction of the CMC. Better agreement between the empirical and predicted CMC is obtained from this theory for S9S (28.7 ± 0.3 mM) and SDS (3.32 ± 0.04 mM), though the CMC for S6S is slightly underestimated (304 ± 3 mM). We also present statistically converged morphological data, including aggregation number distributions and the principal components of the gyration tensor. This data suggest a transition from spherical micelles to rod-like at a specific aggregation number, which increases with increasing hydrocarbon length.

We present a Monte Carlo study of the structure of an entangled polymer melt confined between parallel plates separated by a distance smaller than the radius of gyration R g of the chains. Within that regime, we find a dramatic increase in the molecular weight between entanglements and in the eigenvalues of the gyration tensor of the chains in the plane of the plates. The chains however appear to retain their Gaussian behavior throughout confinement. Interestingly, we also observe that individual chains at short length scales form “globules” whose density and size increase with the extent of confinement.

In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation for large elastic deformation of micropolar hypo-elastic media based on the simplified constitutive equations in conjunction with Jaumann and gyration rates is presented. As an example, buckling of a shallow arc is examined, and it is shown that an increase in the micropolar material parameters results in an increase in the buckling load of the arc. Also, it is shown that micropolar effects become important for deformations taking place at small scales.

The detection of optical activity (OA) with X-rays became possible with third generation synchrotron radiation sources. X-ray detected OA stems mainly from electric dipole–electric quadrupole interference terms, which mix multipoles of opposite parity: this implies that these effects can be observed only in systems with broken inversion symmetry. Natural OA refers to effects that are even with respect to time-reversal symmetry, while nonreciprocal OA is concerned with time-reversal odd contributions. Various types of X-ray dichroisms related to either natural or nonreciprocal OA were measured at the ESRF and are briefly reviewed in this chapter.

We study the evolution of turbulent puffs by means of high-resolution numerical simulations. Puffs are bunches of passive particles released from an initially spherical distribution at regular time intervals of the order of the Kolmogorov time. The instantaneous shapes of particle puffs, in particular their asphericity and prolateness, are characterized by measuring the gyration tensor. Analysis has been performed by following, up to one large scale eddy-turn-over time, more than $10^4$ different puffs, each made of 2000 particle tracers, emitted from different places in a homogeneous and isotropic turbulent fluid with Taylor-scale Reynolds number $Re_\lambda \sim 300$. We also analyze the probability of hitting a given target placed downstream with respect to the local wind at the time of emission, presenting data for three different cases: (i) without any reconstruction of the shape, i.e. considering the bunch of point tracers, and approximating the particle-puff as a (ii) sphere or as an (iii) ellipsoid. The results show a strong dependence on the fluctuations of the instantaneous wind at the moment of the emission and appear to be robust with respect to the approximations (i)-(iii)., Comment: postprint version, Published online 28 August 2015 European Journal of Mechanics -B/Fluids

International audience; Multidimensional population balance modelling is a powerful tool to study the dynamics of the precipitation and particularly the aggregation of particles. This approach involves the selection of internal parameters describing the particle. Among them, morphological or geometrical descriptors are required. In this paper, the inertia or gyration tensor is considered and evaluated for the modelling of aggregation. An equivalent ellipsoid to the aggregate is defined from the tensor. Firstly, a general expression for the inertia tensor of the aggregate resulting from the collision of two aggregates is presented. In this framework, the collision event becomes the collision between two equivalent ellipsoids and leads to a larger ellipsoid. Secondly, the inertia tensor and the characteristics of the equivalent ellipsoid are explicitly calculated in the case of shear aggregation in a two-dimensional space. An approximate calculation is also presented and checked. Finally, the shear aggregation of a set of disks in a two-dimensional space is simulated using simultaneously this modelling of the collision event and Monte-Carlo simulations for all the collisions. This is compared with classical Monte Carlo simulations where the colliding particles are clusters of disks. Physical properties of the cluster population as, for instance, the distribution of elongation or anisotropy factor at different times are presented.

The complete optical gyration tensor of monoclinic pure L-arginine phosphate monohydrate (LAP) and deuterated LAP (d-LAP) crystals has been determined. Variation of the optical activity in the presence of birefringence of d-LAP crystal with pure LAP is found from the high-accuracy universal polarimeter (HAUP) method at a wavelength of 632.8 nm. The gyration tensor components in terms of rotatory power were found to be r11 = -6.6(3) º/mm, r22 = 19(2) º/mm; r33 = 49.7(7) º/mm; and r13 = -43.7(8) º/mm for the LAP, and r11 = -1.2(1) º/mm, r22 = 5.0(4) º/mm; r33 = 41.4(3) º/mm; and r13 = -38.0(4) º/mm for d-LAP at room temperature.

The stress and conformational relaxation of an initially straight flexible polymer is studied through Brownian dynamics simulations covering a broad range of time scales and polymer lengths. At short times $t\,{\ll}\, N^{-2}$ , the strong stress component scales as $\sigma_{11}\,{\sim}\, N^3$ (‘1’ is the direction of the original alignment), while the weak component is $\sigma_{22} \,{\sim}\, N$ (where $N$ is the polymer length). At intermediate times $N^{-2}\,{\ll}\, t\,{\ll}\, N^{2}$ , the stress decay is shown to be anisotropic: $\sigma_{11} \,{\sim}\, N^2 t^{-1/2}$ while $\sigma_{22} \,{\sim}\, N^{1/2} t^{-1/4}$ . At long times $t\,{\gg}\, N^2$ , both stress components show the same exponential decay associated with the reduction of the chain's length, while their magnitudes are still different; $\sigma_{11}\,{=}\, \mbox{\it O}(N)$ while $\sigma_{22} \,{=}\, \mbox{\it O}(1)$ . The configuration relaxation is studied over the same extended time periods by employing scaling laws for the evolution of the eigenvalues of the gyration tensor. After the short-time free diffusion, the configuration relaxation is anisotropic at intermediate times: the chain's width grows as $R_{\perp} \,{\sim}\, N^{-1/4} t^{3/8}$ while its length is reduced as $R_{\parallel}(0)\,{-}\,R_{\parallel} \,{\sim}\, t^{1/2}$ . During long times, the polymer length shows an exponential decay towards the equilibrium coil-like shape. The polymer chain remains aligned along the original direction until late in long times where the chain rotation is shown to be significant. The chain is shown to be far from equilibrium during the entire transient relaxation. By focusing on the chain's longitudinal relaxation, a quasi-steady equilibrium of the link tensions in shown to exist along the chain's length; the mechanism is identical to that found in Grassia & Hinch (1996) based on a sideways motion model. This mechanism also explains the ability of the FENE model to describe the longitudinal relaxation of the flexible bead-rod chain. A comparison with experimental findings from initially straight single tethered DNA molecules is also included.

In the case of propagation of plane elastic waves in anisotropic gyrotropic media, Christoffel tensor is complex; its real part contains stiffnesses and an imaginary part includes components of the fifth-rank gyration tensor. Inequalities relating stiffnesses and gyration constants are derived from the conditions for potential energy to be positive. The necessary and sufficient conditions for the positive definiteness of the complex matrix of stiffnesses and gyration constants are used. Sets of inequalities are obtained for two types of rocks belonging to acentric limit groups ∞∞ and ∞. These inequalities provide a possibility to carry out modelling of elastic wave propagation in the media considered, setting the values of gyration constants not arbitrarily but in accordance with physical laws.

In this paper, we study the steady-state birefringence, deformation, and scattering of wormlike macromolecules under the influence of an electric field. We use a model of N + 1 pointlike elements whose connectors define N axially symmetric subunits. The model is able to describe some properties of segmentally flexible and wormlike macromolecules depending on the choice of N. We use the Monte Carlo computer simulation technique to characterize the effect of the electric field on the orientation and deformation of molecules with permanent and induced dipoles. Using this technique, we study the effect of the field in different models with the same flexibility (defined as 〈s 2 〉0/〈s 2 〉0,str). Orientation is studied through changes in birefringence and deformation through changes in the gyration tensor of the molecule. When the behavior of a broken rod (typical case of segmental flexibility) and a wormlike chain is compared, the differences are generally quantitative although significant enough to be used to obtain information about the internal structure of a macromolecule.

The optical anisotropy at different temperatures (birefringence, complete optical gyration tensor, and optical indicatrix rotation) for a monoclinic crystal of L-arginine phosphate has been determined by using the high-accuracy universal polarimeter (HAUP) method at a wavelength of 632.8 nm. The thermal variation coefficients of the birefringence along the (010), (101), (100), and (-201) planes were found to be -25.9×10-6 K-1, 11.1×10-6 K-1, 6.4×10-6 K-1, and -10.7×10-6 K-1, respectively. The tensor components in terms of rotatory power were found to be ϱ11=-6.6°/mm, ϱ22=19°/mm-1, ϱ33=49.7°/mm, and ϱ13=-43.7°/mm at room temperature.

Knowledge of the conformational evolution of a polymer chain provides invaluable information for all polymer properties. However, the chain evolution is usually determined by monitoring single beads for short times only. In this paper, we numerically determine the configuration evolution over extended time periods by monitoring the eigenvalues of the gyration tensor and applying the scaling law methodology. Results of Brownian dynamics simulations of initially straight chains reveal that after the early free transverse diffusion, flexible polymers exhibit a transverse intermediate-time behavior of t3/4, while stiff polymers reveal two intermediate-time behaviors: an early t5/6 power law accompanied by a late t3/4 evolution. These results are associated with the inherent nonlinearity of the problem. The scaling law methodology we develop in this paper for monitoring the chain configuration should have wide applications in the study of polymer rheology.

The optical activity of uniaxial γ1-(GaxIn1−x )2Se3 crystals (x=0.1, 0.2, 0.3, 0.4) is studied at T=295 and 77 K in the spectral range 0.5–0.8 πm. It is found that the cationic substitution In → Ga leads to a nonlinear increase in the specific rotation of the plane of polarization ρ and the component g 33 of the gyration tensor. It is shown that the gyrotropy of the crystals studied is determined by high-energy transitions whose energy exceeds the energy of the edge transitions and that the gyrotropy observed has a molecular origin.

Low order interference curves in optic-axis light figures of the optically active AgGaS2 and TeO2 are investigated in the visible spectral range at room temperature. Light figure patterns of AgGaS2 are found not to be affected by optical activity within the incidence angles of 10° for which, according to our symmetry considerations, the normal component of gyration tensor is small and evolution of light figures with wavelength is overwhelmingly determined by optical anisotropy. The absolute value of this anisotropy is falling down to null when passing through the isotropic point, with the result of a remarkable change of the parameters of light figure patterns. Unlike the case of AgGaS2 and consistently with our symmetry considerations, light figures of TeO2 are influenced by optical activity especially strongly in low orders of interference. The obtained results are compared with similar results for optically inactive CaCO3 and discussed in the frameworks of our recent analyses.

In this article, we establish the validity of a relation between the true angular velocity and gyration tensor for a dilute polymer solution in the case of a steady shear flow by means of nonequili...