Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e., continua) is usually related to the so-called ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution.The goal of this paper is to show that the tracer-particle dynamics can be exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) [M. Tessarotto, M. Ellero, Bull. Am. Phys. Soc. 45 (9) (2000) 40; M. Tessarotto, M. Ellero, AIP Conf. Proc. 762 (2005) 108. RGD24, Italy, July 10-16, 2004; M. Ellero, M. Tessarotto, Physica A 355 (2005) 233; M. Tessarotto, M. Ellero, Physica A 373 (2007) 142, arXiv: physics/0602140; M. Tessarotto, M. Ellero, in: M.S. Ivanov, A.K. Rebrov (Eds.), Proc. 25th RGD, International Symposium on Rarefied gas Dynamics, St. Petersburg, Russia, July 21-28, 2006, Novosibirsk Publ. House of the Siberian Branch of the Russian Academy of Sciences, 2007, p. 1001, arXiv:physics/0611113; M. Tessarotto, C. Cremaschini, Strong solutions of the incompressible Navier-Stokes equations in external domains: Local existence and uniqueness, arXiv:0809.5164v1 [math-ph], 2008]. As an example, the case of an incompressible Newtonian thermofluid is considered here.     

Bis{1‐n‐hex­yl‐3‐meth­yl‐4‐[1‐(phenyl­imino)prop­yl]‐1H‐pyrazol‐5‐olato}­copper(II): a new copper(II) complex with a chelating alkyl­pyrazolone‐based enamine

The title compound, [Cu(C₁₉H₂₆N₃O)₂], is the first reported complex of the alkyl­pyrazolone‐derived ligand 1‐n‐hexyl‐3‐methyl‐4‐[1‐(phenylimino)propyl]‐1H‐pyrazol‐5(4H)‐one. The most notable feature is the imine–enol character presented by the ligand due to coordination, in spite of its enamine–ketone structure in the free state. The ligand chelates through N and O atoms, resulting in a square‐planar coordination around the Cu^II atom, which lies on an inversion centre.     

Total synthesis of (±)-dihydroactinidiolide using selenium-stabilized carbenium ion

A new, short total synthesis of dihydroactinidiolide 1 is described using selenium carbenium ion-promoted carbon–carbon bond formation as the key step. Our synthetic strategy starts with a lactonization reaction between 1,3,3-trimethylcyclohexene 13 and α-chloro-α-phenylseleno ethyl acetate 14, affording the key intermediate, α-phenylseleno-γ-butyro lactone 15, which reacted via a selenoxide elimination to the target compound 1.     

Detection of picramic acid and picramate in henné products by NMR Spectroscopy

Painting and body art are increasing their utilisation as well as their cultural impact, since piercing and tattoos are expanding social phenomena, involving many young people. However, the utilised materials often enter the market with insufficient control and several cases of skin damages are reported. Safety of the utilised products must be ensured by adequate quality controls which must be easily made, rapid, low cost, clear and persuasive. The method here reported, regards the analysis on the possible presence of picramic acid in the ethyl acetate extracts of commercial henné powders by NMR Spectroscopy. In the proton spectrum, three sets of peaks could be detected, corresponding to the three classes of makers resonances: hennosides, typical markers of Lawsonia inermis, the henné plant; picramic acid or picramate; fatty acids. In particular, the set of signals corresponding to hennosides can be used as markers of the utilisation of the correct raw material of henné.     

Steady states and nonlinear buckling of cable-suspended beam systems

This paper deals with the equilibria of an elastically-coupled cable-suspended beam system, where the beam is assumed to be extensible and subject to a compressive axial load. When no vertical load is applied, necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the stationary solutions are shown to exhibit at most two non-vanishing Fourier modes and the critical values of the axial-load parameter which produce their pitchfork bifurcation (buckling) are established. Depending on two dimensionless parameters, the complete set of resonant modes is devised. As expected, breakdown of the pitchfork bifurcations under perturbation is observed when a distributed transversal load is applied to the beam. In this case, both unimodal and bimodal stationary solutions are studied in detail. Finally, the more complex behavior occurring when trimodal solutions are involved is briefly sketched.     

Interpreting Quantum Logic as a Pragmatic Structure

Many scholars maintain that the language of quantum mechanics introduces a quantum notion of truth which is formalized by (standard, sharp) quantum logic and is incompatible with the classical (Tarskian) notion of truth. We show that quantum logic can be identified (up to an equivalence relation) with a fragment of a pragmatic language \(\mathcal {L}_{G}^{P}\) of assertive formulas, that are justified or unjustified rather than trueor false. Quantum logic can then be interpreted as an algebraic structure that formalizes properties of the notion of empirical justification according to quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic.     

Tunneling mediated by 2D+1 conical waves in a 1D lattice

The propagation of 2D+1 wave packets in 1D band gap systems shows that the interplay of periodicity and nonlinearity leads to the spontaneous formation of fast and slow conical localized waves. Such nonlinear tunneling has features that differ on the two edges of the band gap and it is characterized by the competition of bullets and nonlinear X waves.     

Irrational versus rational charge and statistics in two-dimensional quantum systems

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-binding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge rerationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).