On the six-field model of fluids based on extended thermodynamics

We study the six-field model of fluids (ET6) derived from extended thermodynamics. The six fields are the mass density, the velocity, the temperature, and the dynamic pressure (nonequilibrium pressure). We present the basic system of field equations of ET6. And we elucidate its characteristic features through the studies of the singular limit from polyatomic to monatomic rarefied gases, of hydrodynamic fluctuation, and of a hard-sphere system. Open problems remained in ET6 at present are also pointed out.     

Entropy principle for the moment systems of degree $\alpha$ associated to the Boltzmann equation. Critical derivatives and non controllable boundary data

m moments and of degree . For such theories the entropy principle is still valid only, if the non equilibrium field variables and their derivatives are sufficiently small with respect to the required approximation order. In this paper we prove through simple examples of stationary problems that the entropy principle fails in general, if all the non-equilibrium variables are of the same order of magnitude. This is due to the fact that there exist some derivatives of non equilibrium variables (critical derivatives) that are not small along all the solutions. This property can be used to fix the non controllable boundary data in such a manner that the critical derivatives are kept small for the solution that we may choose. Thus, for the stationary unidimensional case we propose the requirement that the critical derivatives vanish on the boundary, eventually with some successive derivatives. This is a sufficient condition for the validity of the entropy principle at least in a neighborhood of the boundary and makes it possible to assign the non controllable data in a simple manner when the number of moments is greater than 13. We have tested this procedure in several cases of theories, showing that the criterion implies continuity with respect to the change of the moment number and to the truncation order. In particular for the planar unidimensional heat conduction problem we have obtained a behavior for the temperature that is always the same as the one predicted by the classical Fourier law. This result is in evident contrast with the minimax principle expectation. However we have qualitative differences between the temperature behavior described by Extended Thermodynamics and the one by Fourier-Navier-Stokes theory for heat conduction in radial symmetry. Received June 25, 2001 / Published online February 28, 2002     

Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2 ^N −2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases. (Accepted October 6, 1995)     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

Supersonic cluster beam fabrication of metal–ionogel nanocomposites for soft robotics

Soft robotics is an emerging field targeting at the development of robotic bodies and architectures characterized by flexibility, adaptability, and motility typical of that of biological systems. The use of electroactive ionic polymer–metal nanocomposites able to reversibly deform in response to low-intensity electric fields constitutes a promising solution for the implementation of actuators into soft robots. Currently, the use of this class of nanocomposites is hampered by several drawbacks, mainly related to the mismatch between the mechanical properties of the polymer and the metallic electrodes compromising their stability and resilience upon cyclic deformation.Here, we report and discuss on the use of supersonic cluster beam implantation (SCBI) as an effective strategy for the fabrication of soft electroactive ionic polymeric nanocomposite actuators. SCBI relies on the use of supersonically accelerated beams of neutral metal nanoparticles that can be aerodynamically collimated and directed onto a polymeric target to generate thin nanostructured metal layers physically interpenetrating with the polymer.Soft electroactive actuators based on engineered ionogel and ionogel-based hybrid nanocomposites provided with monolithically integrated cluster-assembled gold electrodes will be discussed. These systems can undergo long-term bending deformation in a low-voltage regime, due to the nanostructured electrode resilience. The use of cluster-assembled nanostructured electrodes opens new opportunities for the high-throughput manufacturing of soft ionic actuators with excellent mechanical resiliency, high-performance actuation, and high durability.     

Birationally rigid hypersurfaces

We prove that for N≥4, all smooth hypersurfaces of degree N in ? ^N are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.     

Isopropenyl acetate: A cheap and general acylating agent of alcohols under metal-free conditions

Functionalized primary, secondary and tertiary alcohols are efficiently acetylated by isopropenyl acetate and catalytic p-TsOH.