Scale anomaly as the origin of time

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schrödinger equation. As with the Wheeler–DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schrödinger equation with a repulsive cosmological force in the ‘late-time’ physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts.     

Optimal design of the cooling plunger cavity

An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity. The cost functional is the second power of the norm in the weighted space L _r ² of difference of trace of temperature from given constant, which is evaluated on the outward boundary of the plunger. Existence and uniqueness of the state problem solution and existence of a solution of the optimization problem are proved.     

Photoelectrochemical platform for sensing propyl gallate in edible oil samples based on CdTe quantum dots and poly(D-glucosamine)

Journal of Solid State Electrochemistry - This paper reports the development of a photoelectrochemical platform based on indium tin oxide (ITO) electrode modified with carboxyl-functionalized...     

Molecularly Imprinted Polymers Combined with Electrochemical Sensors for Food Contaminants Analysis

Detection of relevant contaminants using screening approaches is a key issue to ensure food safety and respect for the regulatory limits established. Electrochemical sensors present several advantages such as rapidity; ease of use; possibility of on-site analysis and low cost. The lack of selectivity for electrochemical sensors working in complex samples as food may be overcome by coupling them with molecularly imprinted polymers (MIPs). MIPs are synthetic materials that mimic biological receptors and are produced by the polymerization of functional monomers in presence of a target analyte. This paper critically reviews and discusses the recent progress in MIP-based electrochemical sensors for food safety. A brief introduction on MIPs and electrochemical sensors is given; followed by a discussion of the recent achievements for various MIPs-based electrochemical sensors for food contaminants analysis. Both electropolymerization and chemical synthesis of MIP-based electrochemical sensing are discussed as well as the relevant applications of MIPs used in sample preparation and then coupled to electrochemical analysis. Future perspectives and challenges have been eventually given.     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.