Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance

Low-frequency variability (LFV) of the atmosphere refers to its behavior on time scales of 10–100 days, longer than the life cycle of a mid-latitude cyclone but shorter than a season. This behavior is still poorly understood and hard to predict. The present study compares various model reduction strategies that help in deriving simplified models of LFV.Three distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation.Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV.     

Phase-field model for multiphase systems with different thermodynamic factors

A modified phase-field model for quantitative simulations of low-speed phase transitions in multiphase systems is proposed, which takes into account the difference between thermodynamic factors in all the phases. The presented model is based on the quantitative phase-field concept developed by Steinbach et al. [I. Steinbach, F. Pezolla, B. Nestler, M. Seeelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135] for multiphase systems allowing to consider the multiphase transition as a superposition of pairwise interactions between two phases. We complete this approach and develop a model, which uses parameters derived from chemical free energy functions of individual phases evaluated from experimental data by the CALPHAD method Lukas et al. (2007) [17]. Because the thermodynamic factors are different in various phases we need to evaluate a special form of total chemical free energy function of a multiphase mixture and use it in the phase-field model. It is shown, that for the developed model the thin-interface asymptotic and the anti-trapping term developed previously for the solidification of pure substances can be applied. The model is verified by an example of the Al-Ni system whose peritectic structural morphology during the directional solidification is investigated. The suggested model can be also extended to multicomponent systems.     

Electromagnetic Field Theory Without Divergence Problems 2. A Least Invasively Quantized Theory

Classical electrodynamics based on the Maxwell–Born–Infeld field equations coupled with a Hamilton–Jacobi law of point charge motion is partially quantized. The Hamilton–Jacobi phase function is supplemented by a dynamical amplitude field on configuration space. Both together combine into a single complex wave function satisfying a relativistic Klein–Gordon equation that is self-consistently coupled to the evolution equations for the point charges and the electromagnetic fields. Radiation-free stationary states exist. The hydrogen spectrum is discussed in some detail. Upper bounds for Born's “aether constant” are obtained. In the limit of small velocities of and negligible radiation from the point charges, the model reduces to Schrödinger's equation with Coulomb Hamiltonian, coupled with the de Broglie–Bohm guiding equation.     

Predictions of mechanical and thermodynamic properties of Mg17Al12 and Mg2Sn from first-principles calculations

Using first-principles calculations, we predict mechanical and thermodynamic properties of both Mg₁₇Al₁₂ and Mg₂Sn precipitates in Mg–Al–Sn alloys. The elastic properties including the polycrystalline bulk modulus, shear modulus, Young’s modulus, Lame’s coefficients and Poisson’s ratio of both Mg₁₇Al₁₂ and Mg₂Sn phases are determined with the Voigt–Reuss–Hill approximation. Our results of equilibrium lattice constants agree closely with previous experimental and other theoretical results. The ductility and brittleness of the two phases are characterized with the estimation from Cauchy pressure and the value of B/G. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Young’s modulus. The higher Debye temperature of Mg₁₇Al₁₂ phase means that it has a higher thermal conductivity and strength of chemical bonding relative to Mg₂Sn. The anisotropic sound velocities also indicate the elastic anisotropies of both phase structures. Additionally, density of states and Mulliken population analysis are performed to reveal the bonding nature of both phases. The calculations associated with phonon properties indicate the dynamical stability of both phase structures. The temperature dependences of thermodynamic properties of the two phases are predicted via the quasi-harmonic approximation.     

Surface topography,nano-mechanics and secondary structure of wheat gluten pretreated by alternate dual-frequency ultrasound and the correlation to enzymolysis

The effects of alternate dual-frequency ultrasound (ADFU) pretreatment on the degree of hydrolysis (DH) of wheat gluten (WG) and angiotensin I-converting enzyme (ACE) inhibitory activity were investigated in this research. The surface topography, nano-mechanics and secondary structure of WG were also determined using atomic force microscope (AFM) and circular dichroism (CD). The correlations of ACE inhibitory activity and DH with surface topography, nano-mechanics and secondary structure of WG were determined using Pearson’s correlation analysis. The results showed that with an increase in either pretreatment duration or power, the ACE inhibitory activity of the hydrolysate also increases, reaching maximum at 10 min and 150 W/L, respectively, and then decreases thereafter. Similarly, AFM analysis showed that as the pretreatment duration or power increases, the surface roughness also increase and again a decrease occurs thereafter. As the pretreatment duration or power increased, the Young’s modulus and adhesion of WG also increased and then declined. Young’s modulus and adhesions average values were compared with ACE inhibitory activity reversely. The result of the CD spectra analysis exhibited losses in the relative percentage of α-helix of WG. Pearson’s correlation analysis showed that the average values of Young’s modulus and the relative percentage of α-helix correlated with ACE inhibitory activity of the hydrolysates linearly and significantly (P < 0.05); the relative percentage of β-sheet correlated linearly with DH of WG significantly (P < 0.05). In conclusion, ADFU pretreatment is an efficient method in proteolysis due to its physical and chemical effect on the Young’s modulus, α-helix and β-sheet of WG.     

Punctuated equilibrium and power law in economic dynamics

This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called ‘feedback’ was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of ‘fitness’ and ‘selection’ in the present model of economic evolution.     

Interface reaction of Ta/NiO and its effect on exchange coupling

Ta/NiO/NiFe/Ta multilayers, utilizing Ta as the buffer layer, were prepared by RF reactive and DC magnetron sputtering. The exchange coupling field between NiO and NiFe reached a maximum value of 120 Oe at a NiO film thickness of 50 nm. The composition and chemical state at the interface region of Ta/NiO/Ta were studied using the X-ray photoelectron spectroscopy (XPS) and peak decomposition technique. The results show that there is an `intermixing layer’ at the Ta/NiO (and NiO/Ta) interface due to a thermodynamically favorable reaction: 2Ta+5NiO=5Ni+Ta<sub>2</sub>O<sub>5</sub>. This interface reaction has an effect on the exchange coupling. The thickness of the `intermixing layer’ as estimated by XPS depth-profiles was about 8–10 nm.     

Carrier transport mechanism of strained AlGaN/GaN Schottky contacts

Using polarization field effect-based thermionic field emission (PFE-TFE) model based on current–voltage–temperature data, possible carrier transport mechanisms for Pt/Au and Cr/Pd Schottky contacts to Al_0.25Ga_0.75N/GaN layers were investigated. Thermionic emission (TE) model was also investigated to compare to the PFE-TFE. It was shown that Schottky barrier heights (SBHs) are significantly affected by a polarization field-induced carrier density of the AlGaN layer. In addition, relatively little temperature dependence on the leakage current density of both contacts was found, which is in good agreement with the PFE-TFE model. The results indicate that the TFE is responsible for the current flow across the metal/AlGaN–GaN interface at T ≥ 293 K.     

Analysis of the effect of impact of near-wall acoustic bubble collapse micro-jet on Al 1060

The bubble collapse near a wall will generate strong micro-jet in a liquid environment under ultrasonic field. To explore the effect of the impact of near-wall acoustic bubble collapse micro-jet on an aluminum 1060 sheet, the cavitation threshold formula and micro-jet velocity formula were first proposed. Then the Johnson-Cook rate correlation material constitutive model was considered, and a three-dimensional fluid-solid coupling model of micro-jet impact on a wall was established and analyzed. Finally, to validate the model, ultrasonic cavitation test and inversion analysis based on the theory of spherical indentation test were conducted. The results show that cavitation occurs significantly in the liquid under ultrasonic field, as the applied ultrasonic pressure amplitude is much larger than liquid cavitation threshold. Micro pits appear on the material surface under the impact of micro-jet. Pit depth is determined by both micro-jet velocity and micro-jet diameter, and increases with their increase. Pit diameter is mainly related to the micro-jet diameter and d_p/d_j ≈ 0.95–1.2, while pit’s diameter-to-depth ratio is mainly negatively correlated with the micro-jet velocity. Wall pressure distribution is mostly symmetric and its maximum appears on the edge of micro-jet impingement. Obviously, the greater the micro-jet velocity is, the greater the wall pressure is. Micro pits formed after the impact of micro-jet on aluminum 1060 surface were assessed by ultrasonic cavitation test. Inversion analysis results indicate that equivalent stress, equivalent strain of the pit and impact strength, and velocity of the micro-jet are closely related with pit’s diameter-to-depth ratio. For the pit’s diameter-to-depth ratio of 16–68, the corresponding micro-jet velocity calculated is 310–370 m/s.     

AlGaN barrier thickness dependent surface and interface trapping characteristics of AlGaN/GaN heterostructure

The aluminium gallium nitride (AlGaN) barrier thickness dependent trapping characteristic of AlGaN/GaN heterostructure is investigated in detail by frequency dependent conductance measurements. The conductance measurementsin the depletion region biases (−4.8 V to −3.2 V) shows that the Al_0.3Ga_0.7N(18 nm)/GaN structure suffers from both the surface (the metal/AlGaN interface of the gate region) and interface (the AlGaN/GaN interface of the channel region) trapping states, whereas the AlGaN/GaN structure with a thicker AlGaN barrier (25 nm) layer suffers from only interface (the channel region of AlGaN/GaN) trap energy states in the bias region (−6 V to −4.2). The two extracted time constants of the trap levels are (2.6–4.59) μs (surface) and (113.4–33.8) μs (interface) for the Al_0.3Ga_0.7N(18 nm)/GaN structure in the depletion region of biases (−4.8 V to −3.2 V), whereas the Al_0.3Ga_0.7N (25 nm)/GaN structure yields only interface trap states with time constants of (86.8–33.3) μs in the voltage bias range of −6.0 V to −4.2 V. The extracted surface trapping time constants are found to be very muchless in the Al_0.3Ga_0.7N(18 nm)/GaN heterostructure compared to that of the interface trap states. The higher electric field formation across the AlGaN barrier causes de-trapping of the surface trapped electron through a tunnelling process for the Al_0.3Ga_0.7N(18 nm)/GaN structure, and hence the time constants of the surface trap are less.     

Nanoindentation of a hard ceramic coating formed on a soft substrate

The hardness and Young’s modulus of the thin hydroxyapatite-based coatings deposited by RF magnetron sputtering onto magnesium alloy, titanium, and steel substrates are studied. As the penetration depth increases, the hardness and Young’s modulus of these coatings are found to tend toward the values that are characteristic of the substrates. It is shown that the difference between the values of hardness and Young’s modulus at small penetration depths (h < 80–100 nm) can be caused by the difference between the physicomechanical properties inside the coatings and that this difference at large penetration depths (h > 100 nm) can be induced by an additional effect of the strength properties of the substrate material.     

Nontrivial tensile behavior of rutile TiO<Subscript>2</Subscript> nanowires: a molecular dynamics study

In this paper, we study the tensile behavior of cylindrical rutile TiO₂ nanowires, employing molecular dynamics (MD) simulation technique. The third-generation charge optimized many-body (COMB3) has been used for interatomic potential modeling. The influence of temperature and nanowire diameter on Young’s modulus is investigated. Our simulations exhibit the anisotropic behavior of Young’s modulus as a function of diameter for different crystallographic orientations. Although our results are in good accord with the existing results in [1 0 0] direction, Young’s modulus adds up monotonically with increasing the cross-sectional diameter of nanowire in [0 0 1] direction. It is found that Young’s modulus of the nanowires are lower (higher) than the bulk value for [0 0 1] ([1 0 0]) direction. Furthermore, simulation results also indicate that Young’s modulus of rutile TiO₂ nanowire increases as a function of temperature for a given diameter, unexpectedly. The obtained results may be useful in the field of nanotechnology for optimizing mechanical performance to gain specific applications.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Interaction phenomena among lump,periodic and kink wave solutions to a (3 + 1)-dimensional Sharma-Tasso-Olver-like equation

In this article, we consider a (3 + 1)-dimensional Sharma–Tasso–Olver-like (STOL) model describing dynamical propagation of nonlinear dispersive waves in inhomogeneous media. Applying Hirota's bilinear technique and a trial function, we explore nonlinear dynamical properties of basic solutions to the STOL model. We find that the fission fusion pattern occurs in the collision between the lump and kink waves, the collision between the lump and periodic waves, and the collision among the lump, kink and periodic waves, which is a novel fascinating collision pattern. We also observe that a large value of the coefficient in the periodic function produces a hybrid lump wave by fission in the collision solution. To better understand the dynamic properties of the obtained collision solutions, we plot a number of 3D and contour diagrams by choosing suitable parametric values with the aid of the computational software Maple 18.     

Non-acoustical and acoustical properties of reticulated and partially reticulated polyurethane foams

A series of measurements on four polyurethane foam samples with pore membranes and a polyurethane foam sample without pore membranes have been made. Tortuosity has been deduced using the ultrasonic slope method. It has been found that the deduced value of tortuosity depends on the measurement temperature and for two of the polyurethane foam samples with many pore membranes physically meaningful values of tortuosity cannot be obtained at a temperature of around 25 °C. However more realistic values of tortuosity have been obtained by from measurements at or around the glass transition temperature of polyurethane foam (i.e. at ?20 °C) when using the ultrasonic slope method.Flow resistivity, Young’s moduli and loss factors have been measured also.Vibration of the pore membranes has been observed to influence the effective density and characteristic impedance derived from the surface impedance measured in an impedance tube. This paper discusses relationships between membrane vibration and the slow and fast compressional waves. The relative merits of predictions based on rigid-porous models and the Biot–Johnson–Champoux–Allard model are discussed also.     

A first-principles study on structural stability and mechanical properties of polar intermetallic phases CaZn2 and SrZn2

Structural stability and electronic properties of polar intermetallic CaZn₂ and SrZn₂ in both CeCu₂-type and MgZn₂-type structures have been investigated using first-principles method. The calculated equilibrium lattice parameters agree closely with the available experimental and other theoretical results. In terms of formation enthalpy, it is discovered that the present compounds with CeCu₂-type structure are energetically more stable than that with MgZn₂-type. They are all mechanically stable according to the criteria of elastic stability. In particular, we have investigated the pressure effect on the compressive behaviour and structural stability of each compound. Subsequently, the bulk modulus, shear modulus, Young’s modulus, theoretical hardness, Poisson’s ratio and Debye temperature in the ground state can be estimated using Voigt–Reuss–Hill homogenization method. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Young’s modulus. Finally, the electronic structures are determined to reveal the bonding characteristics of considered phases.     

An examination of the shrinking-core model of sub-micron aluminum combustion

We revisit the shrinking-core model of sub-micron aluminum combustion with particular attention to the mass flux balance at the reaction front which necessarily leads to a displacement velocity of the alumina shell surrounding the liquid aluminum. For the planar problem this displacement simply leads to an equal displacement of the entire alumina layer, and therefore a straightforward mathematical framework can be constructed. In this way we are able to construct a single curve which defines the burn time for arbitrary values of the diffusion coefficient of O atoms, the reaction rate, the characteristic length of the combustion field, and the O atom mass concentration within the alumina provided that it is much smaller than the aluminum density. This demonstrates a transition between a ‘d  ²–t’ law for fast chemistry and a ‘d–t’ law for slow chemistry. For the spherical geometry, the one of physical interest, the outward displacement velocity creates not a simple displacement, but a stress field which, when examined within the framework of linear elasticity, strongly suggests the creation of internal cracking. We note that if the molten aluminum is pushed into these cracks by the high internal pressure characteristic of the stress field, its surface, where reaction occurs, could be fractal in nature and affect the fundamental nature of the burning law. Indeed, if this ingredient is added to the planar model, a single curve for the burn time can again be derived, and this describes a transition from a ‘d  ²–t’ law to a ‘d  ^ν–t’ law, where 0<ν<1.     

Analysis and applications of the Voronoi Implicit Interface Method

We analyze a new mathematical and numerical framework, the “Voronoi Implicit Interface Method” (“VIIM”), first introduced in Saye and Sethian (2011) [R.I. Saye, J.A. Sethian, The Voronoi Implicit Interface Method for computing multiphase physics, PNAS 108 (49) (2011) 19498–19503] for tracking multiple interacting and evolving regions (“phases”) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.). From a mathematical point of view, the method provides a theoretical framework for moving interface problems that involve multiple junctions, defining the motion as the formal limit of a sequence of related problems. Discretizing this theoretical framework provides a numerical methodolology which automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions. Topological changes in the system occur naturally, with no surgery required. In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a per-phase basis, as well as multiphase fluid flow in which density, viscosity and surface tension can be defined on a per-phase basis.We test this method in a variety of ways. We perform rigorous analysis and demonstrate convergence in both two and three dimensions for a variety of evolving interface problems, including verification of von Neumann–Mullins’ law in two dimensions (and its analog in three dimensions), as well as normal driven flow and curvature flow with and without constraints, demonstrating topological change and the effects of different boundary conditions. We couple the method to a second order projection method solver for incompressible fluid flow, and study the effects of membrane permeability and impermeability, large shearing torsional forces, and the effects of varying density, viscosity and surface tension on a per-phase basis. Finally, we demonstrate convergence in both space and time of a topological change in a multiphase foam.     

Magnetization reorientation in Ni (1 1 1) ultrathin films studied by low-temperature hysteresis measurements

Surface magneto-optical Kerr effect (SMOKE) magnetometry in the temperature range 10–300 K was exploited to investigate the magnetic properties of high-quality Cu/Ni/Cu/Si(1 1 1) epitaxial heterostructures with thickness of the Ni layer, d_Ni, between 10 and 60 Å. For a fixed temperature, the equilibrium direction of the magnetization is parallel or perpendicular to the film surface, depending on the Ni thickness, because of the competition among shape anisotropy, magnetoelastic anisotropy and interface anisotropy. No reorientation of the magnetization could be observed as a function of temperature, for any of the specimens analyzed, while a large variation of the loop squareness and coercivity was found. This last variation has been qualitatively explained using a theoretical model based on a Green's function technique, valid for a monodomain film with a coherent rotation of the magnetization.