Scale Relativity and Fractal Space-Time: Theory and Applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology.     

Informational Branching Universe

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information.     

Preparation of Al<Subscript>72</Subscript>Ni<Subscript>8</Subscript>Ti<Subscript>8</Subscript>Zr<Subscript>6</Subscript>Nb<Subscript>3</Subscript>Y<Subscript>3</Subscript> amorphous powders and bulk materials

Amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were successfully fabricated by mechanical alloying. The microstructure, glass-forming ability, and crystallization behavior of amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM), and differential scanning calorimetry (DSC). The isothermal crystallization kinetics was analyzed by the Johnson–Mehl–Avrami equation. In the results, the supercooled liquid region of the amorphous alloy is as high as 81 K, as determined by non-isothermal DSC curves. The activation energy for crystallization is as high as 312.6 kJ·mol?1 obtained by Kissinger and Ozawa analyses. The values of Avrami exponent (n) imply that the crystallization is dominated by interface-controlled three-dimensional growth in the early stage and the end stage and by diffusion-controlled two- or three-dimensional growth in the middle stage. In addition, the amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were sintered under 2 GPa at temperatures of 673 K and 723 K. The results show that the Vickers hardness of the compacted powders is as high as Hv 1215.     

Synthesis, Characterization and Calorimetry of Ni（C4H8N2O3）2Cl2

A coordination complex was synthesized from NiCl2 and dipeptide glycylglycine（GG）. It was characterized by element analysis, NMR and TG methods, and then was determined to be Ni（C4HsN2O3）2Cl2. Using an isoperibolic reaction calorimeter, the standard molar enthalpy of formation of Ni（GG）2Cl2（solid） has been determined to be -（1 674.66±2.02） kJ · mol^-1 at 298.15 K.     

Synthesis of CaCO3 crystals using hydroxypropylmethyl cellulose hydrogel as template

Calcium carbonate crystallization was performed in hydrogel of hydroxypropylmethyl cellulose (HPMC). Results showed that the polyhydroxy functionalities in HPMC gel network facilitated the nucleation of aragonite which was not found in experiment without HPMC hydrogel and in experiment using methylcellulose (MC) hydrogel as template. On the other hand, due to the unique assembly of the macromolecules in HPMC hydrogel network, which was different from other hydrogels used in some previous reports, particular crystal morphology, corncob-like CaCO_3, was obtained for the first time.     

Microwave sintering of Ca<Subscript>0.6</Subscript>La<Subscript>0.2667</Subscript>TiO<Subscript>3</Subscript> microwave dielectric ceramics

Ca_0.6La_0.2667TiO₃ ceramics were prepared by conventional and microwave sintering techniques and their sinterability, microstructure, and microwave dielectric properties were investigated in detail for comparison. Densified Ca_0.6La_0.2667TiO₃ ceramics were obtained by microwave sintering at 1350°C for 30 min and by conventional sintering at 1450°C for 4 h. An unusual phenomenon was found that some larger grains (grain size range: 8–10 μm) inclined to assemble in one area but some smaller ones (grain size range: 2–4 μm) inclined to gather in another area in the microwave sintered ceramics. The microwave dielectric properties of Ca_0.6La_0.2667TiO₃ ceramics prepared by microwave sintering at 1350°C were as follows: dielectric constant (ɛ _r) = 119.6, quality factor (Qf) = 17858.5 GHz, and temperature coefficient of resonant frequency (τ _f) = 155.5 ppm/°C. In contrast, the microwave dielectric properties of the ceramics prepared by conventional sintering at 1450°C were ɛ _r = 117.4, Qf = 13375 GHz, and τ _f = 217.2 ppm/°C.     

Ferroelectricity of nanocrystalline BaTiO<Subscript>3</Subscript> ceramics by first principle calculation

The vibrational modes of BaTiO₃ in different crystalline phases have been investigated by means of density functional theory pseudo potential method. The evidence of tetragonal to orthorhombic and orthorhombic to rhombohedral phase transitions present for 8 nm BaTiO₃ ceramics further demonstrates that the similar successive transitions in 8 nm BaTiO₃ ceramics from rhombohedral to orthorhombic, tetragonal and cubic transitions are as those in coarse BaTiO₃ ceramics.     

Mapping of genetic modifiers of <Emphasis Type="Italic">Plcd1</Emphasis> in scant hair mice (<Emphasis Type="Italic">snthr</Emphasis><Superscript><Emphasis Type="Italic">1Bao</Emphasis></Superscript>)

The scant hair mutant mouse (locus symbol: snthr ^1Bao ) is a recessive mutation that originated in an ethylnitrosourea chemical carcinogenesis study using the DBA/2J inbred strain. The gene responsible for the mutation was previously determined to be phospholipase C, delta 1 (Plcd1; mutant allele symbol Plcd1 ^snthr1Bao ). To map the modifiers of Plcd1, an intercross (DBA/2J-snthr ^1Bao /snthr ^1Bao × C57BL/6J+/+) was conducted. The F2 mutant progeny exhibited a variety of alopecia phenotypes; all F2 mutants (n=507) were classified into 3 groups (mild, moderate, and severe alopecia) and genotyped based on 96 microsatellites. A major QTL was identified on mouse chromosome (mChr) 15 at 12 cM with an LOD score greater than 7 (P < 0.0001). Three minor QTLs were detected on mChr 2, 5, and 7 at 40, 84 and 48 cM, respectively. The QTLs on mChr 7 and 15 were associated with minor alopecia while the QTLs on mChr 2 and 5 were associated with moderate to severe alopecia. No antagonistic or synergistic effects among or between the 4 QTLs were found. Integrating the functions of the 4 potential regulatory QTLs and mutant Plcd1 ^snthr1Bao , we found that these QTLs might contribute to variations of scant hair severity by altering the Ca²⁺ signal pathways in mouse skin.     

New testing methodology for the quantification of rock crushability: Compressive crushing value (CCV)

Crushing is a size reduction process that plays a key role in both mineral processing and crushing-screening plant design. Investigations on rock crushability have become an important issue in mining operations and the manufacture of industrial crusher equipment. The main objective of this research is to quantify the crushability of hard rocks based on their mineralogical and mechanical properties. For this purpose, the mineralogical, physical, and mechanical properties of various hard rocks were determined. A new compressive crushing value (CCV) testing methodology was proposed. The results obtained from CCV tests were compared with those from mineralogical inspections, rock strength as well as mechanical aggregate tests. Strong correlations were found between CCV and several rock and aggregate properties such as uniaxial compressive strength (UCS), the brittleness index (S₂₀), and aggregate impact value (AIV). Furthermore, the relationship between the mineralogical properties of the rocks and their CCVs were established. It is concluded that the proposed testing methodology is simple and highly repeatable and could be utilized as a pre-design tool in the design stage of the crushing process for rock quarries.