The Sharkskin Onset and Stability Diagram

The onset of sharkskin extrudate was investigated in terms of molecular structure, molecular weight, temperature, and die geometry. The recoverable shear S_R or the ratio of wall shear stress over the storage modulus was determined and found to be independent of molecular weight, temperature, and die geometry for linear low-density polyethylenes (LLDPEs), but it depended critically on these factors and the molecular weight distribution for high-density polyethylenes (HDPEs). The plot of S_R versus λ _s /? _s , or the sharkskin wavelength roughness amplitude ratio, constituted a sharkskin marginal stability curve common for all molecular weights, temperatures, and die geometry investigated; it is unique for each polymer type or molecular structure. Sharkskin instability occurred without hysteresis effect.     

Light scattering from mesoscopic objects in diffusive media

No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean free path .The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on the intensity field is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object are its capacitance Q or its effective radius ,and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is provided by radiative transfer theory. This formalism is worked out in detail, in the case of spherical and cylindrical objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance, effective radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which only depends on the ratio .The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained for objects of intermediate size .For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with ,while for case (iii) it is larger than one and decreasing with . Received: 7 August 1998 / Accepted: 3 September 1998     

A percolation context evidenced by thermostimulated currents in oil-resin art media

Degradation over time of home-made thixotropic oil/resin mixtures, similar to those used as natural media by the art painter J.M. William Turner (1775–1851) is investigated by using a combination of dielectric methods, i.e., low-frequency dielectric spectroscopy (LFDS) and the technique of thermostimulated currents (TSC). These address the direct conductivity (d.c.), i.e., the circulation of free charges, and the anelastic orientation of permanent dipoles, respectively. The oil/resin mixtures can be regarded as conducting/insulating-like composite systems with respect to the two conductivities. This provides the opportunity to follow selectively the behavior of the oil, at any composition. In fresh mixtures, LFDS measurements give evidence for three d.c. regimes, delimited by the critical resin-contents (R) R₁30% and R₂60%. This parallels observation with the naked eye of phase separation at R<40% and color change at R>R₂ in four-year-old naturally-aged samples. Such a stable composition-dependent context with two marked thresholds encourages a discussion of the time-behavior in terms of percolation, i.e., relative spatial organization of the parent substances, rather than by using a microscopic approach at the molecular scale. At R>R₁ the surveillance of the TSC signal indicates that the oil clusters tend to coalesce so as to form bigger clusters with aging. The coalescence process appears to be more efficient when the resin forms a continuum (R>R₂) than a dispersion (R<R₂). PACS 82B43     

Flow Rate and Concentration‐dependent Effects of Molecular Dynamics on Elution Behaviors of Flexible Polymers in Gel Permeation Chromatography: A Multi‐angle Laser Light Scattering Study

Gel permeation chromatography (GPC) coupled with multi‐angle laser light scattering (MALLS) provides a tool to simultaneously measure the elution behavior and molecular shape of flexible polymers in their dependence on column flow rate and solute concentration. As flow rate was increased, the radius of gyration (R _g) of flexible polymers first decreased a little and then increased gradually. In all cases, the values of R _g, the hydrodynamic radius (R _h), and ρ (R _g/R _h) decreased as the concentration increased. As a result, flow‐induced molecular stretch and concentration‐induced molecular shrinking for flexible polymers in the gel pores were deduced from the size‐related elution behaviors and tested by light scattering. In addition, the flow rate and concentration‐dependent effect of elution behavior parameters such as the elution volume (V _e), the weight‐averaged molecular weight (M _w), and polydispersity index (PI) were interpreted in terms of molecular deformation and orientations of flexible polymers.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Non-equilibrium critical behavior of O(n)-symmetric systems

Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures and in - and -dimensional subspaces, respectively. In the case of the Sasvári-Schwabl-Szépfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the -dimensional sector in wavevector space with lower noise temperature . The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for .We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and , i.e., about the equilibrium theory.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Synthesis and Kinetic Study of Thermal Cycloimidization of Novel Poly(Amide Amic Acid) to Poly(Amide Imide) by Thermogravimetric Analysis

A new series of fluorinated poly(amide imide)s (PAIs) were prepared by polycondensation of diamine amic acid (DAA) with isophthaloyl, terephthaloyl, or trimellitic anhydride chloride in dimethylformamide, and their subsequent thermal cycloimidization. DAAs were obtained by reacting 4, 4′ (hexafluoroisopropylidene) diphthalic anhydride (6FDA) with diamines in dimethylformamide at 0–5°C. The kinetics of thermal cycloimidization of poly(amide amic acid) (PAA) to PAIs was investigated by thermogravimetric analysis under isothermal conditions at four different temperatures, i.e. 175, 200, 225, and 260°C, for 75 min. A generalized equation to calculate the theoretical amount of weight loss upon complete imidization, i.e. T_w % = 18Nw/R _Mw, was developed. In the above equation numeral 18 corresponds to the molecular weight of water, N is the number of water molecules, which are eliminated per repeat unit of PAA upon cycloimidization, w is the weight of PAA taken for TGA, and R _Mw is the molecular weight of the repeat unit of PAA. The polymers were characterized by FT-IR spectra. Complete cycloimidization process is discussed in terms of monomer structure (diamines and acid chlorides), effect of imidization temperature and time, types of linkages (meta or para) present, and influence of electron withdrawing groups, such as sulfone, in the monomer structure. It was observed that cycloimidization occurred at a faster rate at the beginning, up to about 30 min, and then proceeded at a slower rate till the end of curing. The thermal and thermooxidative stabilities of PAIs were also investigated in nitrogen and oxygen atmosphere.     

Studies of molecular motions and interactions in acetonitrile

Microwave and far-infrared absorption coefficients are reported for acetonitrile over the whole concentration range in carbon tetrachloride solution. The data have been used to compute dipole reorientational correlation functions and relaxation times as a function of concentration. These show that τ_1R ^T increases non-linearly as the acetonitrile concentration increases (in contrast to the values of τ_2R ^T obtained from light scattering measurements) and as the viscosity decreases. This behaviour is examined in terms of intermolecular correlations between rotating dipoles. Intensity data are used to provide a check on the importance of induced dipole absorption in the far-infrared spectra and to calculate ‘static’ correlation factors g ⁽¹⁾. Both g ⁽¹⁾ and the dynamic correlation factor f ⁽¹⁾ reflect the effects of strong molecular interactions in these solutions.     

Studies on the spin Hamiltonian parameters for Mn2+ in the ZnS nanocrystals and bulks

The spin Hamiltonian parameters (zero-field splitting D, g factors and hyperfine structure constants) are theoretically studied for Mn²⁺ in the ZnS nanocrystals and bulks from the perturbation formulae of these quantities for trigonal and cubic tetrahedral 3d⁵ clusters, respectively. The trigonal Mn²⁺ centre in the ZnS nanocrystals is attributed to the impurity–ligand bond angle related to the C₃ axis about 0.39° larger than that (≈109.47°) of an ideal tetrahedron. Almost the same g factors and hyperfine structure constants for the nanocrystals and bulks can be ascribed to similar crystal-field environments (i.e. comparable cubic field parameters Dq), nearly the same covalency (i.e. the equal covalency factors N) and the Mn²⁺ 3d–3s orbital admixture (i.e. the identical core polarisation constants κ) in both systems. The ligand orbital and spin–orbit coupling contributions are found to be important and should be included in the electron paramagnetic resonance analysis in view of significant covalency.     

Quasi-elastic and elastic charge-exchange differential cross sections (critical review)

More than 50 years ago the charge-exchange of one nucleon in the quasi-elastic nucleon deuteron scattering was proposed to determine the spin independent, or the spin dependent parts of the elastic backward neutron proton differential cross section. For this purpose two measurements are to be performed using unpolarized particles only. Such a suggestion was very attractive for experimentalists, since at that time polarized beams were rare and polarized targets were nonexistent. One experiment consists in the inclusive measurement of the charge-exchange quasi-elastic nucleon deuteron differential cross section. The energy of the fast outgoing nucleon is to be approximately the same as that of the incident nucleon. The intrinsic momenta of the remaining two identical nucleons should be small. The impulse approximation has been assumed, i.e. in the final state of the two nucleons their interaction can be neglected. The quasi-elastic result is to be compared with the elastic np differential cross section in the backward direction at the same energy. The theory related the ratio R _QE (π) of the quasi-elastic to the elastic np charge-exchange differential cross sections to the spin dependent part of the np backward elastic scattering amplitude. Several experiments in the nucleon kinetic energy interval below 1 GeV were carried out, where the R _QE (π) values were determined. Recently the energy interval was extended up to 2 GeV by successful experiments at the JINR VBLHE Nuclotron. The quasi-elastic results can be compared with the values of the analogous quantity R _np (π) for the np elastic scattering, calculated from the phase shift analyses below 1.3 GeV. The present paper is a critical review checking expressions for R _np (π) in different amplitude representations, listing numerical values of elastic np quantities and results of existing quasi-elastic experiments. Conclusions and statements of some authors and the validity of the relevant theory is discussed.     

Topological aspect of vortex lines in two-dimensional Gross—Pitaevskii theory

Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.     

Three-sphere low-Reynolds-number swimmer with a cargo container

A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the swimming strokes and net motion of this system can be studied analytically using the Stokes Green's function of a point force in front of a sphere of arbitrary radius R provided by Oseen. The swimming velocity is calculated, and shown to scale as 1/R ³ with the radius of the sphere.     

Measurement of the Relaxation Rates ofH Longitudinal Modes

Accurate decay rate measurements for longitudinal modes are essential for many of the methods proposed for investigating molecular dynamics by NMR. However, the effects of cross relaxation often make it impossible to determine accurate values for these quantities. A method is presented that enables the effects of cross relaxation to be largely eliminated from such measurements. Its reliability is assessed by comparing the values for internuclear distances that can be determined from the resulting relaxation rates with values obtained using other methods. Other consequences of using this technique include an increased robustness of experiments to short (i.e., <5T₁) relaxation times and the ability to make multiple “selective” relaxation measurements simultaneously.     

Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field <Emphasis Type="Italic">F</Emphasis> with an Explanation of the Trouton-Noble Experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four-dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer-independent expressions for the stress-energy vector T(n) (1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K ((1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.     

Variational principle in canonical variables,Weber transformation,and complete set of the local integrals of motion for dissipation-free magnetohydrodynamics

The intriguing problem of the “missing” MHD integrals of motion is solved in this paper; i.e., analogues of the Ertel, helicity, and vorticity invariants are obtained. The two latter have been discussed earlier in the literature only for specific cases, and the Ertel invariant is presented for the first time. The set of ideal MHD invariants obtained appears to be complete: to each hydrodynamic invariant corresponds its MHD generalization. These additional invariants are found by means of the fluid velocity decomposition based on its representation in terms of generalized potentials. This representation follows from the discussed variational principle in Hamiltonian (canonical) variables, and it naturally decomposes the velocity field into the sum of “hydrodynamic” and “ magnetic” parts. The “missing” local invariants are expressed in terms of the “ hydrodynamic” part of the velocity and therefore depend on the (nonunique) velocity decomposition; i.e., they are gauge-dependent. Nevertheless, the corresponding conserved integral quantities can be made decomposition-independent by the appropriate choice of the initial conditions for the generalized potentials. It is also shown that the Weber transformation of MHD equations (partial integration of the MHD equations) leads to the velocity representation coinciding with that following from the variational principle with constraints. The necessity of exploiting the complete form of the velocity representation in order to deal with general-type MHD flows (nonbarotropic, rotational, and with all possible types of breaks as well) in terms of single-valued potentials is also under discussion. The new basic invariants found allow one to widen the set of the local invariants on the basis of the well-known recursion procedure.     

A Monte-Carlo study of meanders

We study the statistics of meanders, i.e. configurations of a road crossing a river through n bridges, and possibly winding around the source, as a toy model for compact folding of polymers. We introduce a Monte-Carlo method which allows us to simulate large meanders up to n=400. By performing large n extrapolations, we give asymptotic estimates of the connectivity per bridge R=3.5018(3), the configuration exponent , the winding exponent and other quantities describing the shape of meanders. Received 21 June 1999