A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure

Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys. Rev.

A Synthetic Single-Site Fe Nitrogenase: High Turnover, Freeze-Quench ^(57)Fe Mössbauer Data, and a Hydride Resting State

The mechanisms of the few known molecular nitrogen-fixing systems, including nitrogenase enzymes, are of much interest but are not fully understood. We recently reported that Fe–N_2 complexes of tetradentate P_3^E ligands (E = B, C) generate catalytic yields of NH_3 under an atmosphere of N_2 with acid and reductant at low temperatures. Here we show that these Fe catalysts are unexpectedly robust and retain activity after multiple reloadings. Nearly an order of magnitude improvement in yield of NH_3 for each Fe catalyst has been realized (up to 64 equiv of NH_3 produced per Fe for P_3^B and up to 47 equiv for P_3^C) by increasing acid/reductant loading with highly purified acid. Cyclic voltammetry shows the apparent onset of catalysis at the P_3^BFe–N_2/P_3^BFe–N_2– couple and controlled-potential electrolysis of P_3^BFe^+ at −45 °C demonstrates that electrolytic N_2 reduction to NH_3 is feasible. Kinetic studies reveal first-order rate dependence on Fe catalyst concentration (P_3^B), consistent with a single-site catalyst model. An isostructural system (P_3^(Si)) is shown to be appreciably more selective for hydrogen evolution. In situ freeze-quench Mössbauer spectroscopy during turnover reveals an iron–borohydrido–hydride complex as a likely resting state of the P_3^BFe catalyst system. We postulate that hydrogen-evolving reaction activity may prevent iron hydride formation from poisoning the P_3^BFe system. This idea may be important to consider in the design of synthetic nitrogenases and may also have broader significance given that intermediate metal hydrides and hydrogen evolution may play a key role in biological nitrogen fixation

Fe-Mediated Nitrogen Fixation with a Metallocene Mediator: Exploring pK_a Effects and Demonstrating Electrocatalysis

Substrate selectivity in reductive multi-electron/proton catalysis with small molecules such as N_2, CO_2, and O_2 is a major challenge for catalyst design, especially where the competing hydrogen evolution reaction (HER) is thermodynamically and kinetically competent. In this study, we investigate how the selectivity of a tris(phosphine)borane iron(I) catalyst, P_3^BFe^+, for catalyzing the nitrogen reduction reaction (N_2RR, N_2-to-NH_3 conversion) versus HER changes as a function of acid pK_a. We find that there is a strong correlation between pKa and N_2RR efficiency. Stoichiometric studies indicate that the anilinium triflate acids employed are only compatible with the formation of early stage intermediates of N_2 reduction (e.g., Fe(NNH) or Fe(NNH_2)) in the presence of the metallocene reductant Cp*_2Co. This suggests that the interaction of acid and reductant is playing a critical role in N–H bond forming reactions. DFT studies identify a protonated metallocene species as a strong PCET donor and suggest that it should be capable of forming the early stage N–H bonds critical for N_2RR. Furthermore, DFT studies also suggest that the observed pK_a effect on N_2RR efficiency is attributable to the rate and thermodynamics, of Cp*_2Co protonation by the different anilinium acids. Inclusion of Cp*_2Co^+ as a co-catalyst in controlled potential electrolysis experiments leads to improved yields of NH_3. The data presented provide what is to our knowledge the first unambiguous demonstration of electrocatalytic nitrogen fixation by a molecular catalyst (up to 6.7 equiv NH_3 per Fe at −2.1 V vs Fc^(+/0))

Long-term multidisciplinary follow-up programs in pediatric cardiac arrest survivors

Long-term outcome studies after pediatric cardiac arrest (CA) are few. They require a CA registry and dedicated outcome teams. Learning about the long-term outcomes is very important for developing prognostication guidelines, improving post-cardiac care, counseling caregivers about the future of their child, and creating opportunities for therapeutic intervention studies to improve outcomes. Few PICUs worldwide provide a multidisciplinary follow-up program as routine practice at an outpatient clinic with standardized measurements, using validated instruments including neuropsychological assessments by psychologists. The primary goal of such a follow-up program should be to provide excellent care to children and their caregivers, thereby resulting in a high attendance. Pediatric psychologists, neurologists and pediatricians/pediatric intensivists should ideally be involved to screen for delayed development and psychosocial problems and offer appropriate care at the same time. Preferably, outcomes should consist of evaluation of morbidity (physical and neuropsychological), functional health and Health Related Quality Of Life (QoL) of the patient and their caregivers.</p

Long-term multidisciplinary follow-up programs in pediatric cardiac arrest survivors

Long-term outcome studies after pediatric cardiac arrest (CA) are few. They require a CA registry and dedicated outcome teams. Learning about the long-term outcomes is very important for developing prognostication guidelines, improving post-cardiac care, counseling caregivers about the future of their child, and creating opportunities for therapeutic intervention studies to improve outcomes. Few PICUs worldwide provide a multidisciplinary follow-up program as routine practice at an outpatient clinic with standardized measurements, using validated instruments including neuropsychological assessments by psychologists. The primary goal of such a follow-up program should be to provide excellent care to children and their caregivers, thereby resulting in a high attendance. Pediatric psychologists, neurologists and pediatricians/pediatric intensivists should ideally be involved to screen for delayed development and psychosocial problems and offer appropriate care at the same time. Preferably, outcomes should consist of evaluation of morbidity (physical and neuropsychological), functional health and Health Related Quality Of Life (QoL) of the patient and their caregivers.</p

Monitoring of the arterial pressure in effort. dominant, not dominant arm or both?

Objetivo: evaluar la diferencia de los valores de Presión arterial (PA) entre ambos brazos, medida simultáneamente, durante una prueba de esfuerzo. Diseño del estudio: estudio transversal. Series de casos. Nivel de evidencia: 3 Material y Métodos: La población se compone de 225 deportistas sanos que realizaron una prueba de esfuerzo en nuestro centro. 128 hombres y 97 mujeres. Edad: 17± 5,5 años. Resultados: La PA tanto sistólica como diastólica no difiere significativamente entre ambos miembros superiores. No obstante, hemos encontrado casos de variabilidad individual donde la PA predomina en un brazo durante el reposo y en el otro brazo durante el máximo esfuerzo. Los valores de TA son independientes del brazo dominante. Conclusiones: La posibilidad que el brazo donde predomina la PA de Reposo no coincida durante el máximo esfuerzo, hace necesario, en nuestra opinión, que se mida la PA en ambos miembros superiores durante la prueba de esfuerzoObjective: To evaluate different blood pressure readings between both arms. Study design: cross-sectional study. Case series. Level of evidence: 3. Methods: a population of 225 healthy athletes underwent stress tests in our center: 128 males and 97 females. Age range: 17 +/- 5.5 years. Results: no significant differences in systolic or diastolic blood pressure readings were found between the right or left arm. We did, however, find cases where blood pressure is higher in one arm while resting and in the other arm during maximal exercise. Blood pressure readings were not associated with the dominant arm. Conclusions: The possibility that the arm in which there is a predominant rest blood pressure does not coincide during maximum stress, makes it necessary, according to our judgment, to measure blood pressure in both upper limbs during stress test

Catalytic N_2-to-NH_3 Conversion by Fe at Lower Driving Force: A Proposed Role for Metallocene-Mediated PCET

We have recently reported on several Fe catalysts for N_2-to-NH_3 conversion that operate at low temperature (−78 °C) and atmospheric pressure while relying on a very strong reductant (KC_8) and acid ([H(OEt_2)_2][BArF_4]). Here we show that our original catalyst system, P_3^BFe, achieves both significantly improved efficiency for NH_3 formation (up to 72% for e^– delivery) and a comparatively high turnover number for a synthetic molecular Fe catalyst (84 equiv of NH_3 per Fe site), when employing a significantly weaker combination of reductant (Cp*_2Co) and acid ([Ph_2NH_2][OTf] or [PhNH_3][OTf]). Relative to the previously reported catalysis, freeze-quench Mössbauer spectroscopy under turnover conditions suggests a change in the rate of key elementary steps; formation of a previously characterized off-path borohydrido–hydrido resting state is also suppressed. Theoretical and experimental studies are presented that highlight the possibility of protonated metallocenes as discrete PCET reagents under the present (and related) catalytic conditions, offering a plausible rationale for the increased efficiency at reduced driving force of this Fe catalyst system