Amorphous and crystalline states of ultrasoft colloids: a molecular dynamics study

In this work, we study the temperature-induced development of “dynamically arrested” states in dense suspensions of “soft colloids” (multi-arm star polymers and/or block-copolymers micelles) by means of molecular dynamics (MD) simulations. Temperature increase in marginal solvents results in “soft sphere” swelling, dynamical arrest, and eventually crystallization. However, two distinct “dynamically arrested” states were found, one almost amorphous (“glassy”) and one with a considerable degree of crystallinity, yet lower than that of the fully equilibrated crystal. It is remarkable that even that latter state permitted self-diffusion in the timescale of the simulations, an effect that underlies the importance of the “ultra-soft” nature of inter-particle potential. The “number of connections” criterion for crystallinity proved to be very successful in identifying the ultimate thermodynamic trend from the very early stages of the α-relaxation. This paper was presented at the Third Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Forced nonlinear oscillator with nonsymmetric dry friction

In this paper we discuss an approximately steady motion of an oscillator as a single whole with a constant “on the average” velocity. For that purpose we analyze the position and stability of some special points of the phase portrait. In the presence of internal excitation and nonsymmetric Coulomb dry friction, a motion of the oscillator with a constant “on the average” velocity is possible. The algebraic equation for this constant velocity is found. For different parameters of the model there exist at most three regimes of motion with a constant velocity, but only one or two of them are stable. The theoretical results obtained can be used for the design of worm-like moving robots.     

A rheological approach to drill-in fluids optimization

The aim of this work is to propose design criteria, based on rheological characterisation for improving drill-in fluids performance. In particular, it reports an example in which rheological approaches helped improve drill-in fluids resistance to temperature. As a starting system a commercial drill-in fluid containing xanthan gum and calcium carbonate was chosen and evaluated. Different samples were then prepared by changing the initial formulation in order to increase the system's stability to temperature. Drill-in fluids' performance have been compared by considering their “damaging potential”, filtration properties and, “cakes”. All drill-in fluids have been tested before and after aging at a given temperature with “hot rolling tests”. The systems' gel structure was characterized by measuring dynamic moduli (G′ and G′′) in the linear viscoelastic range and all samples were compared by evaluating their “melting” temperature and gel network strength during time cure tests. The results obtained from this work suggest that the rheological tests carried out on the whole drill-in fluid can provide insights into fluids' damaging potential and “cake” structure. In particular, rheology proved to be able to provide quantitative information about gel strength and temperature stability that permitted one to improve drill-in fluids' formulation in order to preclude formation damage and to meet industrial requirements. Received: 6 February 2000 Accepted: 15 November 2000     

Stability of Thermosolutal Natural Convection in Superposed Fluid and Porous Layers

This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers.     

Laminar–turbulent transition in oscillating boundary layer: experimental and numerical analysis using continuous wavelet transform

The laminar–turbulent transition of a forced oscillating boundary layer with a varying pressure gradient is experimentally and numerically investigated for two Strouhal numbers. Time-dependent characterization of the natural instability modes is carried out using continuous wavelet analysis of velocity signals. The periodic evolution of the total growth rates of the most unstable disturbances are measured and compared to the results of the linear stability theory. The “Tollmien–Schlichting” (TS) and “convective” transition modes are identified. It is shown that they correspond to the extrema of opposite signs of the skewness factor of unstable wavelet transform of the most unstable frequencies.     

Measurements of mean and fluctuating wall shear stress beneath spanwise-invariant separation bubbles

 Pulsed-wire measurements of wall shear stress have been made beneath two separation bubbles. In one a cross flow was generated by means of a (25°) swept separation line. Fluctuating stresses in orthogonal “streamwise” and cross-flow directions are very nearly equal and independent of at least moderate cross flow velocity. These fluctuations are largely determined by large-scale motions in the outer flow, whereas the mean shear stresses are not. The pdf of the “streamwise” fluctuations is unchanged by the cross flow. When a cross flow is present the pdf of the cross-flow stresses is similar to the “streamwise” pdf. Dependence on Reynolds number is the same in both flows. Received: 10 April 1998/Accepted: 17 July 1998     

Evolution of perturbations of a charged interface between immiscible inviscid fluids in the interelectrode gap

Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the “shallow” and “deep” upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation. In the cases of the “shallow” and “deep” upper fluid examples of the development of an initial perturbation of the “step” type are given. The development of an initial perturbation of the “step” type are also considered in the near-critical electric fields and in the case of degeneration of cubic dispersion.     

Imaging spectroscopy of the nonequilibrium shock front radiation in air

The nonequilibrium radiation of shock fronts in air is experimentally investigated by means of the imaging spectroscopy technique. Shock velocity ranges from 9.7 to 11.6 km/s and initial pressure from 13.3 to 41.6 Pa. The spectral diagnostic system consists of an imaging spectrograph, a streak camera, a gated image-intensified CCD camera and a personal computer for data acquisition/processing. This spectral diagnostic system is capable of simultaneous wavelength-, intensity- and time-resolved spectroscopic measurements in the nanosecond order. The image processing of the streak images includes a combined smoothing/deconvolution process in the time direction to diminish experimental noise effects and the temporal broadening due to the streak camera entrance slit. Wavelength range is chosen to investigate the first negative band of . “Large” and “slim” streak image types are observed. In the “large” streak images greater contribution from (1-)(1,0) behind the radiation peak is observed. Experimental data are compared with a streak image numerically simulated. The numerical simulation agrees better with the “slim” streak image. Received 7 July 1995 / Accepted 10 January 1996     

Measure-theoretic foundations of statistical mechanics

The basic formulas of classical equilibrium statistical mechanics are derived from well-known theorems in measure theory and ergodic theory. The method used is a generalization of the methods of Khinchin and Grad and deals with several, in fact a “complete set”, of “invariants” or “integrals of the motion”. Most of the results are simple corollaries of Birkhoff's ergodic theorem, and since time-averages are used, the whole approach is characterized by an absence of statistical “ensembles” and probability notions. In the course of the development a “generalized temperature” is introduced, and a generalization of the second law of thermodynamics is derived. Formulas for the “microcanonical”, “canonical”, and “grand canonical” distributions appear as special cases of the general theory.     

The “rebel travelling” of general nonlinear evolutional equation and discussion on related problems

This paper is a part of series works for discussing the “auto-destruction effects” of general nonlinear evolutional equations. The blown-up of Navier-Stockes equation is discussed in references [1,2]. Some expansion is made in this paper, and the blown-up of order-1 or 2 models and the “rebel travelling” of complex model of poly-order are discussed. The results indicate that “semi-rupture” appears for some models on specific condition: the blown-up appears during the whole evolution. For fluid, however, the weakly-nonlinear model is of more artificiality and there is much room for arguing about the smoothing scheme of the numerical integral on the basis of continuous thinking and so on.     

Dynamic flight stability of hovering insects

The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the “rigid body” assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects (hoverfly, cranefly, dronefly and hawkmoth) in hovering flight is studied (the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157 Hz). The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the “rigid body” assumption is tested and how differences in size and wing kinematics influence the applicability of the “rigid body” assumption is investigated. The primary findings are: (1) For insects considered in the present study and those with relatively high wingbeat frequency (hoverfly, drone fly and bumblebee), the “rigid body” assumption is reasonable, and for those with relatively low wingbeat frequency (cranefly and howkmoth), the applicability of the “rigid body” assumption is questionable. (2) The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. (3) Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative M _u (pitching moment produced by unit horizontal speed) as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Z _w (vertical force produced by unit vertical speed) as the primary source of the stable slow subsidence mode. The project supported by the National Natural Science Foundation of China (10232010 and 10472008).     

Effects of the weak/micro-discontinuity of interface on the fracture behavior of a functionally graded coating with an inclined crack

The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed, the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed. It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous combination than “stiffer coating and softer substrate”.     

Some properties of three-dimensional Biltrami flows

The investigation of Beltrami flows is important for the research on the mechanism of turbulent structure. In this paper the general solutions of the Beltrami flows are given, which depend explicitly on the solutions of three independent Helmholtz equations with scalar unknowns. Velocity fields of Beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equations. On the basis of the exact solutions of Euler equations given above, we obtain one kind of exact solutions of non-steady Navier-Stokes equations which are also the Beltrami flows. Some interesting examples of Beltrami flows other than “ABC flows”, “Kolmogolov flows”, “Rayleigh-Bernard flows”, “Q-flows” are given. The detailed analytic results of these examples will be published in the near future.     

Constructal Design of Vascular Porous Materials and Electrokinetic Mass Transfer

According to constructal theory, the “generation of flow configuration” is a universal phenomenon in physics. This phenomenon is covered by the constructal law: “For a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it.” This paper shows how the constructal law can be used to (1) predict and explain features of “design” in nature, and (2) design effective strategies and configurations for engineering. Many natural flow designs rely on two flow mechanisms: channels with relatively low resistivity, interwoven with diffusion across the interstices. The “design” is the balance between the two mechanisms. The flow from line to line (or plane to plane) through a sufficiently fine porous medium encounters less resistance than the flow through parallel channels when it is configured as trees that alternate with upside down trees: from this follows the prediction that natural porous media (e.g., hill slope) should be multiscale (bidisperse) and non-uniformly distributed. A porous medium contaminated with ionic species is decontaminated the fastest when the ionic flow is configured as two flow mechanisms in balance: “channeling” driven by potential differences between optimally positioned electrodes, and diffusion driven by concentration differences across the interstices between the channels.     

Minimal essential sets and essential components of the equilibria of production economies

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ [1 ] ,Ｄｉｅｒｋｅｒｉｎｔｒｏｄｕｃｅｄｔｈｅｃｏｎｃｅｐｔｏｆｅｓｓｅｎｔｉａｌｅｑｕｉｌｉｂｒｉａｆｏｒｐｕｒｅｅｘｃｈａｎｇｅｅｃｏｎｏｍｉｅｓａｎｄｐｒｏｖｅｄｔｈａｔｉｎ‘ｍｏｓｔ’ｐｕｒｅｅｘｃｈａｎｇｅｅｃｏｎｏｍｉｅｓ (ｉｎｔｈｅｓｅｎｓｅｏｆＢａｉｒｅｃａｔｅｇｏｒｙ)ａｌｌｅｑｕｉｌｉｂｒｉａａｒｅｅｓｓｅｎｔｉａｌ.Ｉｎ [2 ] ,ｔｈｅｃｏｎｃｅｐｔｏｆｅｓｓｅｎｔｉａｌｅｑｕｉｌｉｂｒｉａｆｏｒｐｒｏｄｕｃｔｉｏｎｅｃｏｎｏｍｉｅｓｗａｓｆｉｒｓｔ…     

Two-group kinetic theory of vehicular traffic

Summary We study a two-group model of vebicular traffic oli a highway which generalizes the Prigogine-Herman model. According to the two-group theory, drivers are divided into “slow” and “fast”. Correspondingly, we introduce a slow and a fast desired distribution representing the program that drivers of each of the two groups wish to follow. We first prove the existence and the uniqueness of a solution belonging to a suitable Banach space by using the theory of semigroups. Then, we indicate some sufficient conditions for the stability of an x and t independent solution.

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Sommario Si generalizza il modello di Prigogine-Herman del traffico automobilistico su un'autostrada, introducendo due gruppi di guidatori: i “lenti” ed i “veloci”. Ognuno dei due gruppi riene caratterizzato da un'opportuna funzione “desiderio”, che traduce i programmi che i guidatori intendono seguire nel corso del loro viaggio. Facendo poi uso della teoria dei semigruppi, si prova l'esistenza e l'unicità di una soluzione appartenente ad un opportuno spazio di Banach e si danno condizioni sufficienti per la stabilità.

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Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).As the choice of the appropriate model for these problems is still a controversial matter, the Editorial Board welcomes any comment or discussion from the readers.     

Statement of the two-body problem in the parameters of the extended Galilei group

The classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the 13-parameter extended Galilean group (translations, rotations, boosts, and gravitational transformations) without using such traditional notions as “point” and “force.”     

The unstable modes of natural convection boundary layer

The instability of natural convection boundary layer around a vertical heated flat plate is analyzed theoretically in this paper. The results illustrate that the “loop” in the neutral curve is not a real loop but a twist of the curve in the frequency-wave number-Grashof number space, and there is only one unstable mode at small Prandtl numbers. Specially, when the Prandtl number is large enough two unstable modes will be found in the “loop” region. Along the amplyfying surface intersection the two unstable modes have the same Grashof number, wave number and frequency but different amplifying rates. Their instability characteristics are analyzed and the criterion for determining the existence of the multi-unstable modes is also discussed.     

Studies of quality of geometrically nonlinear elasticity theory for small strains and arbitrary displacements

Earlier it was shown in [1, 2] that the equations of classical nonlinear elasticity constructed for the case of small strains and arbitrary displacements are ill posed, because their use in specific problems may result in the appearance of “spurious” bifurcation points. A detailed analysis of these equations and the construction, in their stead, of consistent equations of geometrically nonlinear theory of elasticity can be found in [3]. Certain steps in this direction were also made in [4, 5]. In [3], it was also stated that the methods and applied program packages (APPs) based on the use of the classical relations of nonlinear elasticity require some revision and correction. In the present paper, this conclusion is justified and confirmed by numerical finite-element solutions of several three-dimensional geometrically nonlinear deformation problems and linearized problems on the stability of equilibrium of a rectilinear beam. These solutions were obtained by using two APPs developed by the authors and the well-known APP “ANSYS.” It is shown that the classical equations of the geometrically nonlinear theory of elasticity, which underly the first of the developed APP and the well-known APP “ANSYS,” often lead to overestimated buckling loads for structural members as compared with the consistent equations proposed in [1–3].     

On the stability of liquid droplets with line tension

Prompted by recent works on line tension effects upon the stability of liquid droplets laid on a rigid substrate, we prove existence and stability of equilibrium configurations when the substrate is either planar or spherical. For positive line tension our argument involves only set symmetrization, while for negative line tension a stability criterion is proposed which makes variational problems well-posed in the framework of sets with finite perimeter. Several applications illustrate the role of the criterion in providing a natural cutoff length that selects destabilizing modes. The work of M. Negri has been partially supported by INdAM through the grant “Mathematical challenges in nanomechanics at the interface between atomistic and continuum models”.