From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100?km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed “hydrolytic weakening”. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.     

Real-time tomographic reconstructor based on convolutional neural networks for solar observation

Solar observation is the branch of astronomy devoted to the study of the Sun. When the light wavefront that comes from the Sun penetrates the atmosphere, it suffers some distortions caused by optically turbulent layers that change the wavefront's shape and morphology. Therefore, in order to obtain a good-quality image, it is necessary to correct the induced error. This is done by applying adaptive optics (AO) techniques. In the case of the present research, it is performed with the help of a Single Conjugate Adaptive Optics System (SCAO). The reconstruction technique proposed in this research is a SCAO based on convolutional neural networks (CNNs). This research develops and assesses a real-time tomographic reconstructor based on CNN, able to correct the error introduced by the atmosphere in the light wavefront received from the Sun. The CNN was trained and validated using data from the Durham AO Simulation Platform as input information. This platform incorporates certain solar functionalities that have been employed in the present research, allowing us to simulate a solar telescope. The normalized errors obtained for both ReLu and Leaky ReLu kernels were promising, without showing statistically significant differences among kernels in the value of RMSE volts of the deformable mirror commands. When different kernel dimensions are compared, statistically significant differences are found, showing that RMSE volts of the deformable mirror commands are lower for 3 × 3 kernels when compared with those of dimensions 5 × 5 and 7 × 7. As far as the authors know, this is the first time that an AO system based on CNN has been developed for solar telescopes.     

Effects of Medium Permeability Anisotropy on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is considered to derive the analytical solution for the critical condition, which is used to judge whether or not the chemical dissolution front can become unstable during its propagation. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved-mineral equilibrium concentration in the pore-fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid-saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when medium permeability anisotropic effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two-dimensional fluid-saturated porous media including medium anisotropic effects. The related theoretical and numerical results demonstrated that: (1) a decrease in the medium anisotropic permeability factor (or ratio), which is defined as the ratio of the principal permeability in the transversal direction to that in the longitudinal direction parallel to the pore-fluid inflow direction, can stabilize the chemical dissolution front so that it becomes more difficult for a planar chemical-dissolution front to evolve into different morphologies in the chemical dissolution system; (2) the medium anisotropic permeability ratio can have significant effects on the morphological evolution of the chemical dissolution front. When the Zhao number of the chemical dissolution system is greater than its critical value, the greater the medium anisotropic permeability ratio, the faster the irregular chemical-dissolution front grows.     

Superposition as a Relativistic Filter

By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz filtering process, removing paths that are relativistically inequivalent. In a model that includes a stochastic component, the free-particle Schrödinger equation emerges from a completely relativistic context in which its origin and function is known. The result establishes the fact that the phase of wavefunctions in Schrödinger’s equation and the attendant superposition principle may both be considered remnants of time dilation. This strongly argues that quantum mechanics has its origins in special relativity.     

A quantitative densitometric method for the rapid separation and quantitation of the major lipids of tissues and lipoproteins by high-performance thin-layer chromatography. II. Reduction of the densitometric data

A BASIC program is described for acquisition of data and data reduction for an automated densitometric system for quantitation of lipids separated by high-performance thin-layer chromatography. The program allows calculation of mass of samples from log/log calibration curves computed from standards. The calculated masses are reported as nmol/volume or nmol/mg protein. The program contains a flexible dialog system which permits its use for a variety of applications in addition to the system described for quantitation of lipids.     

An optical study of the deposition and conversion of nickel hydroxide films

The deposition and conversion of nickel hydroxide films on platinum in nickel nitrate solution is studied using a self-nulling ellipsometer. The cathodically deposited hydroxide film, α-Ni(OH)₂, has a refractive index of 1.502 — 0.0i. When anodically oxidized, the α-Ni(OH)₂ converts to a film of γ-NiOOH of index 1.502 — 0.27i Alternate oxidation and reduction causes the hydroxide film to convert to β-Ni(OH)₂ with refractive index 1.43 — 0.0i. Oxidation of the β-Ni(OH)₂ produces a film of β-NiOOH with refractive index 1.43 — 0.165i. The conversion processes take place uniformly throughout the film with the film thickness increasing by a factor of 1.43 on oxidation. When further deposition of α-Ni(OH)₂ is attempted on a layer of α-Ni(OH)₂, the layer of β-Ni(OH)₂ converts to α-Ni(OH)₂ before deposition begins.     

Highly diastereoselective synthesis of anti-gamma-N-benzylamino-beta-hydroxyphosphonates

The reduction of gamma-N-benzylamino-beta-ketophosphonates derived from readily available amino acids can be carried out stereoselectively with Zn(BH(4))(2) at -78 degrees C to produce the anti-gamma-amino-beta-hydroxyphosphonates.     

Graviton dominance in quantum Kaluza-Klein theory

We compute, at the one-loop level, the effective potential for pure gravity in a Kaluza-Klein background geometry which is the direct product of four-dimensional Minkowski spacetime M⁴ with the N-sphere S^N, N odd. The computation is performed in the physical Lorentz-signature spacetime, avoiding the difficulties of “euclideanization”. We find that the contribution of each gravitational degree of freedom to the O(?) part of the effective potential is significantly greater than that of a scalar or spinor in the same background geometry. No stable minima of the effective potential exist for 3 ≤ N ≤ 13. Geometries which may be interpreted as “unstable solutions” are found for all N from 3 through 13. These results, obtained in Lorentz-signature spacetimes, differ from those obtained by “euclideanization”; our “euclideanized” results agree with those obtained by Chodos and Myers using a different regularization scheme.     

Forecasting time series with multiple seasonal patterns

A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the innovations approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods from exponential smoothing. The proposed model is used to examine hourly and daily patterns in hourly data for both utility loads and traffic flows. Our formulation provides a model for several existing seasonal methods and also provides new options, which result in superior forecasting performance over a range of prediction horizons. In particular, seasonal components can be updated more frequently than once during a seasonal cycle. The approach is likely to be useful in a wide range of applications involving both high and low frequency data, and it handles missing values in a straightforward manner.