Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

Avaliação da influência da interação polímero-solvente sobre a porosidade de copolímeros de acrilonitrila e divinilbenzeno obtidos por polimerização em suspensão

Neste trabalho, copolímeros à base de acrilonitrila e divinilbenzeno foram sintetizados, utilizando a técnica de polimerização em suspensão, na presença de três agentes porogênicos diferentes (álcool isoamílico, metil-etil-cetona e tolueno). Esses copolímeros foram caracterizados por meio da determinação da densidade aparente, do volume e diâmetro de poros, por microscopia ótica e microscopia eletrônica de varredura e foram avaliados quanto à capacidade de inchamento em heptano e tolueno. O principal intuito dessa pesquisa foi correlacionar a formação da estrutura porosa desses materiais com os principais parâmetros de síntese (grau de diluição dos monômeros, poder solvatante do diluente e teor do agente de reticulação). Desses parâmetros, o que mais influenciou na formação da estrutura porosa desses materiais foi o poder solvatante do diluente. A teoria dos parâmetros de solubilidade de Hansen e Hildebrand foi utilizada com o intuito de fazer uma previsão das características porosas dos copolímeros à base de acrilonitrila e divinilbenzeno sintetizados na presença de três diluentes diferentes. Dentre esses diluentes, o álcool isoamílico foi o pior solvente para os copolímeros de AN-DVB, em todos os teores de agente de reticulação e em todas as diluições utilizadas. O tolueno foi o melhor solvente para os copolímeros que contêm altos teores de agente de reticulação. Estas observações estão de acordo com as previsões dos parâmetros de solubilidade de Hansen e Hildebrand. A metil-etil-cetona foi o melhor solvente para os copolímeros que contêm teores intermediários de agente de reticulação. Esta observação só está condizente com o parâmetro de solubilidade de Hansen.

On the formation of ephippia in some Cladocera (Crustacea) [Translation from: Zoologicheskie Zhurnal 61, 1425-1427, 1982]

The determination of relative connections between families and genera of Cladocera, necessary for the construction of their natural systems, must be based on various criteria, among them on the structure of the ephippia. Of particular interest is the study of the process of formation and structure of the ephippium in Macrothricidae, different representatives of which differ significantly among themselves according to this criterion. In this article are presented the results of an investigation of the features of formation of the ephippium in seven species of Macrothricidae and in the moinid Moina weismanni Ishikawa (Moinidae).

Studies on the complex formation of iron with humic substances [Translation from: Vom Wasser 53, 243-247, 1979]

Most of the humic substances which occur in natural waters have an iron content of a few percent, indicated by the mg/1 content of organically-bonded carbon. This iron is apparently bound in a complex with the humic substances, for it quite plainly differs in its chemical and physico-chemical properties from what one would expect from the purely inorganic iron-water system. The deviations range from the solubility to the redox behaviour, and thus are frequently the basis of analytical and technical difficulties. The key to the solution of most of this problem lies in a better understanding of the aforementioned bonds between the iron and the humic substances. This paper studies the iron content of the humic substance concentration from a bog lake sample and the complexing of iron by humic substances from the surface of the bog lake.

Mechanism of mass transfer in the formation of hydrothermal deposits of sulphides [Translation from: Trudy Inst.Geol.rudn.Mesterozh. 16, 80 [pages 44-46 ”Solubility of sulphides of iron” only], 1958]

This partial translation of the original paper provides the summary of this study of the mechanism of mass transfer in the formation of hydrothermal deposits of sulphides. For determining the solubility of sulphides of iron, the radioactive isotope Fe59 was used. The solubility of two sulphides was determined.

Criação de mesoporos em zeólitas ZSM-5, mordenita e ferrierita e análise de seu efeito na reação de hidroisomerização do n-heptano

As zeólitas têm recebido grande atenção acadêmica e industrial devido às suas características ácidas e estruturais. A estrutura da zeólita pode ser utilizada para conduzir uma reação catalítica na direção do produto desejado, evitando assim reações paralelas. Porém, essa mesma estrutura cria restrições difusivas com relação ao acesso aos sítios ativos no interior dos microporos. Neste trabalho foram estudados dois métodos de criação de mesoporos (térmico e básico) com o intuito de modificar a acessibilidade aos sítios catalíticos das zeólitas. A reação de hidroisomerização do n-heptano foi selecionada para avaliar as zeólitas após a criação de mesoporosidade. O tratamento térmico (via calcinação em temperaturas elevadas) foi utilizado para as zeólitas do tipo ZSM-5, Mordenita e Ferrierita, tendo sido observado um aumento pouco significativo na mesoporosidade. Este tratamento promoveu, porém, uma significativa desaluminização das amostras, acompanhada da formação de quantidades importantes de espécies de Al extra-rede (ALER), o que se refletiu num bloqueio parcial dos mesoporos gerados e dos microporos preexistentes, e na redução na densidade de sítios ácidos das amostras. A ampliação da escala do tratamento térmico (aumento da quantidade tratada de 2 g para 30 g) não se mostrou reprodutível, gerando menos mesoporos do que o observado no preparo em pequena escala. O tratamento básico (via dessilicação por meio de NaOH), ao contrário do anterior, promoveu a formação de mesoporos gerando menos quantidade de ALER e se mostrou mais reprodutível quando da ampliação da escala. O desempenho dos catalisadores Pt/Al2O3+zeólita na reação de hidroisomerização do n-heptano foi influenciado pela densidade de sítios ácidos fortes e pela estrutura porosa da zeólita. Com relação ao efeito dos tratamentos térmico e básico sobre o desempenho dos catalisadores à base de ZSM-5, os resultados mostraram que o comportamento do catalisador submetido ao tratamento básico (Pt/Al2O3+BZSM-5/85-2) foi similar ao do tratado termicamente (Pt/Al2O3+TZSM-5/1000-2) com relação à distribuição de produtos na reação de hidroisomerização do n-heptano, particularmente com relação aos produtos leves e aos isômeros monorramificados. No entanto, a presença mais significativa de mesoporos na zeólita após tratamento básico (BZSM-5/85-2), se refletiu num leve favorecimento à formação dos isômeros birramificados

A Unifying model of strategic network formation

Documento de trabajo

Formation of jets by implusive acceleration of a curved free surface

The sudden axial acceleration of a column of liquid bounded at one end by a concave free surface has been found, experimentally, to produce a jet which issues from the free surface with a speed several times that imparted to the column.

Theoretical approximations to such flows, valid for small time, are formulated subject to the assumption that the fluid is inviscid and incompressible. In a special two-dimensional case, it is found that, for vanishingly small time, the velocity at the point on the free surface from which the jet emanates is π/2 times the velocity imparted to the column. The solutions to several problems in two and three dimensions assuming that the initial curvature of the free surface is small, lead to values for this ratio dependent upon the curvature—the initial velocity in the case of axial symmetry exceeding that of the analogous two-dimensional problem by approximately 25%.

Experiments conducted upon the phenomenon give values systematically in excess of those predicted by the theory, although theory and experiment are in qualitative agreement with respect to the displacement of the free surface. It is suggested that the discrepancy is attributable to effects of finite curvature having been imperfectly accounted for in the axially-symmetric analysis.

Photographic materials on pp. 115, 120, and 121 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Efficiency vs. Stability in a Mixed Network Formation Model

Documentos de Trabajo

Design, Synthesis, and Study of Novel Platforms for Iron-N2 Chemistry and Photoinduced, Copper-mediated C-N Bond Formation

Several new ligand platforms designed to support iron dinitrogen chemistry have been developed. First, we report Fe complexes of a tris(phosphino)alkyl (CP^iPr₃) ligand featuring an axial carbon donor intended to conceptually model the interstitial carbide atom of the nitrogenase iron-molybdenum cofactor (FeMoco). It is established that in this scaffold, the iron center binds dinitrogen trans to the C_alkyl anchor in three structurally characterized oxidation states. Fe-C_alkyl lengthening is observed upon reduction, reflective of significant ionic character in the Fe-C_alkyl interaction. The anionic (CP^iPr₃)FeN₂^- species can be functionalized by a silyl electrophile to generate (CP^iPr₃)Fe-N₂SiR₃. This species also functions as a modest catalyst for the reduction of N₂ to NH₃. Next, we introduce a new binucleating ligand scaffold that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N₂-Fe(μ-SAr)Fe-N₂) across at least three oxidation states (Fe^IIFe^II, Fe^IIFe^I, and Fe^IFe^I). Despite the sulfur-rich coordination environment of iron in FeMoco, synthetic examples of transition metal model complexes that bind N₂ and also feature sulfur donor ligands remain scarce; these complexes thus represent an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. The (N₂-Fe(μ-SAr)Fe-N₂) system undergoes reduction of the bound N₂ to produce NH₃ (~50% yield) and can efficiently catalyze the disproportionation of N₂H₄ to NH₃ and N₂. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Next, inspired by the importance of secondary-sphere interactions in many metalloenzymes, we present complexes of iron in two new ligand scaffolds ([SiP^NMe₃] and [SiP^iPr₂P^NMe]) that incorporate hydrogen-bond acceptors (tertiary amines) which engage in interactions with nitrogenous substrates bound to the iron center (NH₃ and N₂H₄). Cation binding is also facilitated in anionic Fe(0)-N₂ complexes. While Fe-N₂ complexes of a related ligand ([SiP^iPr₃]) lacking hydrogen-bond acceptors produce a substantial amount of ammonia when treated with acid and reductant, the presence of the pendant amines instead facilitates the formation of metal hydride species.

Additionally, we present the development and mechanistic study of copper-mediated and copper-catalyzed photoinduced C-N bond forming reactions. Irradiation of a copper-amido complex, ((m-tol)₃P)₂Cu(carbazolide), in the presence of aryl halides furnishes N-phenylcarbazole under mild conditions. The mechanism likely proceeds via single-electron transfer from an excited state of the copper complex to the aryl halide, generating an aryl radical. An array of experimental data are consistent with a radical intermediate, including a cyclization/stereochemical investigation and a reactivity study, providing the first substantial experimental support for the viability of a radical pathway for Ullmann C-N bond formation. The copper complex can also be used as a precatalyst for Ullmann C-N couplings. We also disclose further study of catalytic C_alkyl-N couplings using a CuI precatalyst, and discuss the likely role of [Cu(carbazolide)₂]^- and [Cu(carbazolide)₃]^- species as intermediates in these reactions.

Finally, we report a series of four-coordinate, pseudotetrahedral P₃Fe^II-X complexes supported by tris(phosphine)borate ([PhBP₃Fe^R]^-) and phosphiniminato X-type ligands (-N=PR'₃) that in combination tune the spin-crossover behavior of the system. Low-coordinate transition metal complexes such as these that undergo reversible spin-crossover remain rare, and the spin equilibria of these systems have been studied in detail by a suite of spectroscopic techniques.

Bicyclo[3.2.0]hepta-1,4,6-triene: synthesis, thermal rearrangement, and anion formation

In order to determine the properties of the bicycloheptatrienyl anion (Ia) (predicted to be conjugatively stabilized by Hückel Molecular Orbital Theory) the neutral precursor, bicyclo[3. 2. 0] hepta-1, 4, 6-triene (I) was prepared by the following route.

Reaction of I with potassium-t-butoxide, potassium, or lithium dicyclohexylamide gave anion Ia in very low yield. Reprotonation of I was found to occur solely at the 1 or 5 position to give triene II, isolated as to its dimers.

A study of the acidity of I and of other conjugated hydrocarbons by means of ion cyclotron resonance spectroscopy resulted in determination of the following order of relative acidities:

H₂S ˃ C₅H₆ ˃ CH₃NO₂ ˃ 1, 4- C₅H₈ ˃ I ˃ C₂H₅OH ˃ H₂O; cyclo-C₇H₈ ˃ C₂ H₅OH; фCH₃ ˃ CH₃OH

In addition, limits for the proton affinities of the conjugate bases were determined:

350 kcal/mole ˂ PA(C₅ H₅^-) ˂ 360 kcal/mole

362 kcal/mole ˂ PA(C₅H₇^-, Ia, cyclo-C₇H₇^-) ˂ 377 kcal/mole PA(фCH₂^-) ˂ 385 kcal/mole

Gas phase kinetics of the trans-XVIII to I transformation gave the following activation parameters: E_a = 43.0 kcal/mole, log A = 15.53 and ∆S^ǂ (220°) = 9.6 cu. The results were interpreted as indicating initial 1,2 bond cleavage to give the 1,3-diradical which closed to I. Similar studies on cis-XVIII gave results consistent with a surface component to the reaction (E_a = 22.7 kcal/mole; log A = 9.23, ∆S^ǂ (119°) = -18.9 eu).

The low pressure (0.01 to 1 torr) pyrolysis of trans-XVIII gave in addition to I, fulvenallene (LV), ethynylcyclopentadiene (LVI) and heptafulvalene (LVII). The relative ratios of the C₇H₆ isomers were found to be dependent upon temperature and pressure, higher relative pressure and lower temperatures favoring formation of I. The results were found to be consistent with the intermediacy of vibrationally excited I and subsequent reaction to give LV and LVI.

Effects of magnetostriction and superlattice formation in ferromagnetic thin films

The contribution to the magnetic uniaxial perpendicular anisotropy which arises from substrate constraint through magnetostrictive effects has been measured in Ni-Fe and Ni-Co thin films evaporated on substrates at room temperature. This was accomplished by measuring the perpendicular anisotropy before and after removal of the film from the substrate. Data are given for the fcc crystal structure regions of both alloy systems, but data for Ni-Co include compositions with less than 60% Ni which have a small percentage of the hcp phase mixed with the fcc phase. The constraint contribution to the perpendicular anisotropy correlates well with the value of the bulk magnetostriction constant using the equation ∆K_˔=3/2λ_sσ. Measured values of isotropic stress for films thicker than 600 Å were 1.6 x 10¹⁰ dyn/cm². In films less than 600 Å thick the isotropic stress decreased with decreasing thickness. After removal of the films from the substrates, the measured perpendicular anisotropy deviated from the expected geometrical shape anisotropy near pure Ni in both alloys. This indicates that additional significant sources of anisotropy exist at these compositions.

The effect of substrate constraint on the crystalline anisotropy K₁ of Ni-Fe epitaxial films has been studied by use of a film removal technique, which involves the evaporation of an epitaxial layer of LiF on MgO, the epitaxial growth of the metallic film on the LiF, and the stripping of the film with water soluble tape. Films ranging in composition from 50% to 100% Ni have been studied. For compositions below 90% Ni the experimental values agree reasonably well with the first order theoretical prediction, ∆K₁=[-9/4(C₁₁-C₁₂)λ² 100+9/2C₄₄λ²111].

In order to compare the magnetic properties of epitaxial thin films more completely with the properties of bulk single crystals, Ni-Fe films ranging in composition from 60% to 90% Ni, which were evaporated epitaxially on (100) MgO substrates, have been subsequently annealed at 400°C in a vacuum of less than 10^-7 Torr to form the ordered Ni₃Fe structure near the 75% composition. This ordered structure has been confirmed by electron diffraction.

The saturation magnetization at Ni₃Fe increased about 6% with ordering which is in good agreement with previous bulk data. Measurements of the magnetocrystalline anisotropy energy K₁ for the epitaxial films show the same large changes with ordering as observed in bulk single crystal samples. In the (001) plane the magnetostriction constants ^λ100, ^λ111 are directly related to the induced anisotropy due to a uniform uniaxial strain in the [100] and [110] directions respectively. Assuming that the elastic constants of a film are the same as in bulk material and are unchanged by ordering, the changes in strain sensitivity with ordering for the epitaxial films are found to be in good agreement with values predicted from bulk data. The exchange constant A as measured by ferromagnetic resonance has been measured at the Ni₃Fe composition and found to increase 25% with ordering. This seems to indicate a significant increase in the Curie temperature which has only been inferred indirectly for bulk material.

Conditioned responses in the reticular formation

Unit activity was recorded from the midbrain and pons of 40 freely moving rats in an appetitive classical conditioning situation. Responses to auditory stimuli were observed from 100 units before and during a conditioning procedure in which presentation of food occurred 1 sec after the onset of the auditory stimulus. Conditioned unit responses (i.e., spike rate accelerations or decelerations) were considered to be positive when 1) no similar responses appeared prior to conditioning, and 2) latencies were equal to or less than those of sensory responses derived from the inferior colliculus. Such short latency conditioned unit responses were recorded from 11 probes located in the mid-lateral pert of the ventral region of the brain stem. This region was differentiated from paramedian, far lateral and dorsal parts of the brain stem reticular formation. Conditioned unit responses of considerably longer latencies were recorded from 76 probe located in these other regions. Among the longer latency responses interesting differences appeared in experiments conducted after the first conditioning series was completed. With additional training, units in the "reticular activating system" of midbrain and pons tended to yield stabilized responses in the early portion of the CS-US interval closely related in time to the orientation responses evoked by the CS. In contrast, the responses of units in the limbic midbrain tended to stabilize in the later part of the CS-US interval closely related in time to preparatory responses tied to the US. During extinction when the auditory stimulus was no longer followed by presentation of food, many of the responses were reduced to their pre-conditioning levels. However, there was a tendency for units which had displayed short latency responses on the first conditioning day to be more resistant to extinction than units which had displayed longer latency conditioned responses. The data were interpreted as indicating a local correlate of learning in the reticular formation of midbrain end pons and a separation of the midbrain system into at least two areas: 1) the classical "reticular activating system" related to orienting reactions, and 2) the limbic midbrain areas related to drives and rewards. Because the ventral and mid-lateral area with very short latency conditioned responses was not clearly tied to either of these; it was considered as possibly representing a third division.