Logarithmic Rate Research Articles

An Extended Three-Dimensional Finite Strain Constitutive Model for Shape Memory Alloys

AbstractA 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for smooth thermomechanical response; temperature dependence of the critical force required for (re)orientation, temperature, and load dependence of the hysteresis width; and asymmetry between forward and reverse phase transformation, and it is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated, and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, and nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, which further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments, and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

Ultrafast photoinduced electron transfer in o-aminobenzoate – d-Amino acid oxidase complex

Absorption spectrum of ortho-amino benzoate (oAB) – D-amino acid oxidase complex (ODC) displays a charge transfer (CT) band around 570 nm. The fluorescence decays of the second lowest electronic state of ODC were measured using a fluorescence up-conversion technique. The lifetimes were 100 fs and 130 fs at 500 nm and 514 nm fluorescence emission wavelengths, respectively. These ultrafast lifetimes are ascribed to the photoinduced electron transfer (PET) from the oAB to the excited isoalloxazine (Iso*) in the ODC. The PET mechanism in ODC was studied with Marcus-Kakitani-Mataga (MKM) theory. The protein structures were obtained by molecular dynamics simulation (MDS). Mean distances between Iso and oAB over 12,500 MDS snapshots were 0.60 in subunit A (Sub A) and 0.58 nm in Sub B. The calculated lifetimes at 514 nm-emission were 97 and 179 fs in Sub A and Sub B, while at 500 nm there were 97 and 101 fs, respectively. Solvent reorganization energy was quite different between Sub A and Sub B, which is main reason for difference in the calculated lifetimes. Electrostatic (ES) energies between the photoproducts of donor -acceptor, and net ES energies between the photoproducts and ionic groups in the protein were calculated with MDS structures. These ES energies were evaluated with charge densities of neutral radical of oAB produced after PET and anion radical of Iso obtained by semi-empirical molecular orbital (MO) method. The logarithmic PET rate did not display any clear dependence on Rc, despite the ultrafast scale of the PET rates. Most of the logarithmic PET rates in Sub A displayed in the inverted region of the standard free energy gap in the energy gap law. The transition dynamics among local excited states of Iso, CT state and the ion-pair state were discussed.

Does the slope of the yield curve of the interbank market influence prices on the Warsaw Stock Exchange? A sectoral perspective

The interest rate curve is often viewed as the leading indicator of economic prosperity in a broad sense. This paper studies the ability of the slope of the yield curve in the term structure of interest rates to impact the sectoral indices on the Warsaw Stock Exchange, using daily data covering the period from 1 January 2001 to 30 September 2020. The results of the research indicate an ambiguous dependence of the logarithmic rates of return of sub-indices on the change of the interbank interest rate curve. The only sectors showing a clear relationship of this type is energy and pharmaceuticals.

Experimental and modeling investigation on the viscoelastic-viscoplastic deformation of polyamide 12 printed by Multi Jet Fusion

The viscoelastic-viscoplastic deformation of Multi Jet Fusion-printed polyamide 12 (MJF PA12) was investigated with experimental and numerical approaches. Multi-loading–unloading–recovery tests were conducted to distinguish between the viscoelastic and viscoplastic deformations. The influence of the void defects on deformation of PA12 was investigated through the micro-computed tomography (μCT) and field emission scanning electron microscope. A finite-strain viscoelastic-viscoplastic constitutive model based on the logarithmic stress rate for the matrix of MJF PA12 was developed within the thermodynamic framework as well as an introduction of the accumulated plastic deformation–induced damage into the proposed model. A representative volume element was modeled based on the μCT results of MJF PA12. The simulated results, such as stress–strain and strain–time curves, agreed with the experimental results. Moreover, the model revealed the mechanism that the low tensile ductility of MJF PA12 is caused by the increase in strain localization and narrowing of the shear band.

Development of dynamic constitutive model of epoxy resin considering temperature and strain rate effects using experimental methods

Epoxy resin composite materials are increasingly used in the aerospace field. The dynamic mechanical behavior of the resin matrix is of great significance in studying the impact response of composites. In the current study, the quasi-static and dynamic compression properties of TDE86 epoxy are studied at different temperatures, and the influence of the temperature and strain rate on the mechanical properties of epoxy are analyzed. The quasi-static and dynamic compression stress–strain curves are used to fit the parameters of the Zhu–Wang–Tang (ZWT) constitutive equation at different temperatures. A subroutine for the ZWT constitutive model is developed in ABAQUS, and numerical simulations of split Hopkinson pressure bar tests are performed. The results show that, at low strain rates, the elastic modulus, yield stress, and yield strain of the epoxy increase as the strain rate increases and decrease as the temperature increases. The dynamic stress–strain curve of the epoxy can be divided into four stages, namely the initial elastic, yield, strain softening, and unloading stages. There is no distinct relationship between the yield strain and the logarithmic strain rate under high strain rates, although the yield strain is generally smaller than that under low strain rates. The yield stress increases linearly with the logarithmic strain rate. Under the same strain rate, the yield stress decreases as the temperature increases, whereas the yield strain does not change monotonically. By comparing the stress–strain curves obtained by simulations with the test results, the developed subroutine is validated and the applicability of the ZWT constitutive model at different temperatures is verified.

Antioxidant Ascorbic Acid Modulates NLRP3 Inflammasome in LPS-G Treated Oral Stem Cells through NFκB/Caspase-1/IL-1β Pathway.

Human gingival mesenchymal stem cells (hGMSCs) and endothelial committed hGMSCs (e-hGMSCs) have considerable potential to serve as an in vitro model to replicate the inflammation sustained by Porphyromonas gingivalis in periodontal and cardiovascular diseases. The present study aimed to investigate the effect of ascorbic acid (AA) on the inflammatory reverting action of lipopolysaccharide (LPS-G) on the cell metabolic activity, inflammation pathway and reactive oxygen species (ROS) generation in hGMSCs and e-hGMSCs. Cells were treated with LPS-G (5 μg mL−1) or AA (50 μg mL−1) and analyzed by 3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide (MTT) assay, immunofluorescence and Western blot methods. The rate of cell metabolic activity was decreased significantly in LPS-G-treated groups, while groups co-treated with LPS-G and AA showed a logarithmic cell metabolic activity rate similar to untreated cells. AA treatment attenuated the inflammatory effect of LPS-G by reducing the expression of TLR4/MyD88/NFκB/NLRP3/Caspase-1/IL-1β, as demonstrated by Western blot analysis and immunofluorescence acquisition. LPS-G-induced cells displayed an increase in ROS production, while AA co-treated cells showed a protective effect. In summary, our work suggests that AA attenuated LPS-G-mediated inflammation and ROS generation in hGMSCs and e-hGMSCs via suppressing the NFκB/Caspase-1/IL-1β pathway. These findings indicate that AA may be considered as a potential factor involved in the modulation of the inflammatory pathway triggered by LPS-G in an vitro cellular model.

Optimal-order convergence of Nesterov acceleration for linear ill-posed problems* *Dedicated to A Neubauer on the occasion of his 60th birthday.

We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a priori stopping rule and for the discrepancy principle under Hölder source conditions. Furthermore, some converse results and logarithmic rates are verified. The essential tool to obtain these results is a representation of the residual polynomials via Gegenbauer polynomials.

Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition

We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The iterative regularization is terminated by the a posteriori discrepancy principle.

Improving phase stability, hardness, and oxidation resistance of reactively magnetron sputtered (Al,Cr,Nb,Ta,Ti)N thin films by Si-alloying

Reactively magnetron sputtered high-entropy metal-sublattice (Al,Cr,Nb,Ta,Ti)N coatings have been alloyed with Si concentrations between x Si = 6.4 and 15.0 at.%. All coatings are single-phase fcc structured and their hardness initially increases from ~32 to 35 GPa with Si-alloying up to x Si = 9.8 at.%, and then decreases to ~24 GPa for higher Si contents. Contrary, the indentation modulus E continuously decreases from ~470 to 350 GPa by Si-alloying. Also, the decomposition of the fcc structure during vacuum annealing is shifted from 1000 to 1200 °C with the addition of Si. The hardness initially increases during vacuum annealing and reaches a maximum of 37 GPa with T a = 1000 °C at x Si = 12.0 at.%. During oxidation experiments in ambient air at 850 °C for up to 100 h, a 2700 nm single-phase rutile-structured oxide scale forms at the Si-free (Al,Cr,Nb,Ta,Ti)N with a parabolic growth rate. The rate changes to a logarithmic-like behavior with the addition of Si, resulting in only ~280 nm oxide scale after 100 h. Also, for the Si-containing coatings, the oxide scale shows only one crystalline rutile structure. The pore size in the oxide scale of the Si-free coating is considerably reduced by Si-addition. The oxides growing at the Si-containing coatings show an opposing Si- and Cr-gradient - with much smaller pores in the Si-rich inner region - which shows a gradual transition to the remaining nitride. Ab initio based calculations confirm that the formation of a single-phase rutile-structured solid solution oxide, (Al,Cr,Nb,Ta,Ti)O 2 , is energetically preferred over separate phases above 509 K, due to the higher configurational entropy. Below this temperature the decomposition towards (Al,Ta,Ti)O 2 + (Cr,Nb)O 2 would be favored (when considering just chemical contributions), but kinetically restricted. • Reactively sputtered fcc-(Al,Cr,Nb,Ta,Ti)N alloyed with Si • Improved phase stability in vacuum, hardness, and lower E -modulus • Logarithmic oxide growth rate in ambient air at 850 °C • Single phase rutile structured oxide forms during oxidation. • Ab-initio calculations confirm thermodynamically stable (Al,Cr,Nb,Ta,Ti)O 2 phase.

Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin–Voigt damping

In this paper, we consider the stabilization for the Kirchhoff plate and equations connected by transmission conditions. We show that the energy of the transmission system is stable with logarithmic decay rate when feedback control acts on the small part of the plate as a viscoelastic material with Kelvin–Voigt constitutive relation. The proof is based on a new resolvent estimate by using some careful analysis for Kirchhoff plate-wave transmission system.

Spatial Distribution of Crusts in Antarctic and Greenland Snowpacks and Implications for Snow and Firn Studies

The occurrence of snowpack features has been used in the past to classify environmental regimes on the polar ice sheets. Among these features are thin crusts with high density, which contribute to firn stratigraphy and can have significant impact on firn ventilation as well as on remotely inferred properties like accumulation rate or surface mass balance. The importance of crusts in polar snowpack has been acknowledged, but nonetheless little is known about their large-scale distribution. From snow profiles measured by means of microfocus X-ray computer tomography we created a unique dataset showing the spatial distribution of crusts in snow on the East Antarctic Plateau as well as in northern Greenland including a measure for their local variability. With this method, we are able to find also weak and oblique crusts, to count their frequency of occurrence and to measure the high-resolution density. Crusts are local features with a small spatial extent in the range of tens of meters. From several profiles per sampling site we are able to show a decreasing number of crusts in surface snow along a traverse on the East Antarctic Plateau. Combining samples from Antarctica and Greenland with a wide range of annual accumulation rate, we find a positive correlation (R2 = 0.89) between the logarithmic accumulation rate and crusts per annual layer in surface snow. By counting crusts in two Antarctic firn cores, we can show the preservation of crusts with depth and discuss their temporal variability as well as the sensitivity to accumulation rate. In local applications we test the robustness of crusts as a seasonal proxy in comparison to chemical records like impurities or stable water isotopes. While in regions with high accumulation rates the occurrence of crusts shows signs of seasonality, in low accumulation areas dating of the snowpack should be done using a combination of volumetric and stratigraphic elements. Our data can bring new insights for the study of firn permeability, improving of remote sensing signals or the development of new proxies in snow and firn core research.

Sequential Leaching of Strategic Metals from Exhausted LNCM-Cathode Batteries Using Oxalic and Sulfuric Acid Lixiviants

Hydrometallurgical extraction of strategic metals from exhausted Li-ion batteries has been explored using sequential application of biodegradable oxalic acid and sulfuric acid solutions. Following L25 orthogonal design of experiment (DoE), optimized extraction of > 99% Li and Cu with organic acid was achieved using a H2C2O4 concentration of 0.25 mol L−1, solid–liquid ratio of 10%, H2O2 at 0.5%, temperature of 80°C, and duration of 90 min. Subsequently, leaching of the residual mass in mineral acid yielded 99% efficiency of Ni, Co, and Mn at the optimal condition of H2SO4 concentration of 3.0 mol L−1, solid–liquid ratio of 6%, H2O2 at 2%, temperature of 60°C, and duration of 120 min. Fitting of the kinetic data using a logarithmic rate law revealed that, except for Cu that followed an intermediate-controlled mechanism with Ea = 27.6 kJ mol–1, all the other metals exhibited a diffusion-controlled mechanism with Ea < 12 kJ mol–1. Not only does this study demonstrate selectivity that will be beneficial to downstream processing, but the use of DoE also makes it applicable industrially.

Galaxy skew-spectra in redshift-space

Modern galaxy surveys focus on the galaxy power spectrum or 2-point correlation function to test and constrain cosmological models.Additional information comes from higher-order N-point functions, but their analysis is challenging. A simple solution is to compute the cross-power spectrum between the squared galaxy density and the galaxy density. Being simple to measure and to plot, this skew-spectrum shares many of the familiar useful properties of the standard galaxy power spectrum. We show that by computing multiple quadratic fields and correlating them with the density, all contributions to the tree-level redshift-space galaxy bispectrum can be captured with skew-spectra. Using synthetic datasets, we show that our measurement pipeline matches analytical predictions, and that their dependence on galaxy bias parameters and the logarithmic growth rate is as expected theoretically.

Two-step leaching process and kinetics for an eco-friendly recycling of critical metals from spent Li-ion batteries

With growing awareness to protect the urban environment and fulfill the soaring demand for critical metals, recycling of postconsumer Li-ion batteries has become imperative to deal in a sustainable manner. In this context, a two-step leaching of the exhausted LiNixCoyMnzO2 cathode material was studied by sequential application of both organic and mineral acids. To optimize the experimental parameters of both steps, leaching was conducted using the L25 orthogonal array design. In the first-step leaching, lithium and copper was selectively leached into oxalic acid at the optimal condition of C2H2O4 (OA), 0.25 M; pulp density (PD1), 10%; H2O2 dosage (HPD1), 0.5%; temperature (T1), 80 °C; and time (t1), 90 min. The parametric influences for achieving more than 99% efficiency of lithium and copper followed the order: t1 > HPD1 > OA > PD1 > T1 and t1 > T1 > OA > HPD1 > PD1, respectively. Residual metal-oxalates of cobalt, nickel, and manganese were subsequently dissolved into sulfuric acid solutions. Approximately 99% of all remaining metals could be leached at the optimal condition of H2SO4 (SA), 3.0 M; pulp density (PD2 -), 6%; H2O2 dosage (HPD2), 2%; temperature (T2), 60 °C; and time (t2), 120 min. The parametric influences on sulfuric acid leaching of metals followed the order as: SA > HPD2 > t2 > PD2 > T2. Leaching followed logarithmic rate law and exhibition of the diffusion-controlled mechanism was revealed through the values of apparent activation energy determined to be Ea(Li), 9.7 kJ/mol; Ea(Cu), 22.3 kJ/mol; Ea(Co), 9.5 kJ/mol; Ea(Ni), 11.2 kJ/mol; and Ea(Mn), 6.2 kJ/mol. This study successfully demonstrated the applicability of OA in the selective leaching of LiNixCoyMnz-type cathode materials, eliminating the need for copper and lithium separation from leach liquor of SA-medium. The present process offers two-fold advantages that securing the secondary supply for critical metals, and providing an environmentally sustainable route for waste valorization in a circular economy.

Towards efficient near-infrared fluorescent organic light-emitting diodes

The energy gap law (EG-law) and aggregation quenching are the main limitations to overcome in the design of near-infrared (NIR) organic emitters. Here, we achieve unprecedented results by synergistically addressing both of these limitations. First, we propose porphyrin oligomers with increasing length to attenuate the effects of the EG -law by suppressing the non-radiative rate growth, and to increase the radiative rate via enhancement of the oscillator strength. Second, we design side chains to suppress aggregation quenching. We find that the logarithmic rate of variation in the non-radiative rate vs. EG is suppressed by an order of magnitude with respect to previous studies, and we complement this breakthrough by demonstrating organic light-emitting diodes with an average external quantum efficiency of ~1.1%, which is very promising for a heavy-metal-free 850 nm emitter. We also present a novel quantitative model of the internal quantum efficiency for active layers supporting triplet-to-singlet conversion. These results provide a general strategy for designing high-luminance NIR emitters.

Athermal sediment creep triggered by porous flow

Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.

Measurement and Analysis of Deformation Behavior of Polyethylene Tube Subjected to Biaxial Tensile Stress with Large Strain

A material testing apparatus for measuring the biaxial deformation behavior of a polymer tube is developed to quantitatively evaluate the deformation behavior of polymeric materials. The testing apparatus can apply axial force and internal pressure to a tubular specimen. A noncontact strain measurement system is also developed, and the biaxial strain components and the radius of curvature in the axial direction of the specimen are continuously measured to control the stress path applied to the specimen. Polyethylene tubes with an outer diameter of 17 mm and a thickness of 2 mm are used as test specimens, that are subjected to linear stress paths with stress ratios of σφ :σθ =1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1, where σφ and σθ are the axial and circumferential stress components applied to the center of the bulging specimen, respectively. Biaxial stress-strain curves are successfully measured for every linear stress path at a nearly constant logarithmic strain rate of 1×10-3 s-1. A maximum equivalent strain of up to 0.71 is achieved for a specimen with a stress path of σφ :σθ =2:1. The contours of equal work plotted in the principal stress space show a significant anisotropy of the test material.

Research on Financial Market Risk Based on GARCH-M Model

Since 1970, with the gradual acceleration of economic globalization and the rapid development of information technology, the financial market has become increasingly unstable. Therefore, we must enhance our competitiveness in the financial market, enhance our ability to resist risks, and master effective measures such as measuring risks. In this paper, GARCH-M model and VAR method are used to study the value at risk of financial market and make an empirical analysis. Firstly, the VAR value calculation method based on GARCH-M model under generalized error distribution is given. Secondly, the closing price of Shanghai Stock Exchange Index is selected as sample data, and Eviews software is used to analyze its characteristics. The results show that the logarithmic yield series of the closing price of Shanghai Stock Exchange Index is not normally distributed, and the series has fluctuation aggregation effect, autocorrelation effect and heteroscedasticity effect. Finally, GARCH-M model is established, and VAR estimates at 95% and 99% confidence levels are calculated and tested. The results show that GARCH-M(1,1) model is more suitable for estimating the risk of logarithmic return rate of closing price of Shanghai Composite Index.

Gas sorption phenomena on solid surfaces

A model explaining the logarithmic rate law used in adsorption/desorption of gas-solid processes is presented. The association of free surface sites in greater ones can be produced in adsorption processes. The dissociation of these new sites into the initial free sites can be obtained in desorption processes.

Zmiana poziomu efektywności amerykańskiego rynku akcji – od kryzysu finansowego 2007-2009 do pandemii COVID-19

Purpose – Verification of the change in the efficiency of the US stock market from the 2007-2009 financial crisis to the COVID-19 pandemic. Research method – The BDS test (occurrence of non-linear relationships between daily logarithmic rates of return) and the Quenouille autocorrelation test up to the fifth order (occurrence of linear relationships between daily logarithmic rates of return) for the S&amp;P500 and DJIA indices were used. Results – The occurrence of unusual phenomena changes the level of US stock market effectiveness. An increase in inefficiency was observed both during the 2007-2009 financial crisis and now, during the COVID-19 pandemic. Higher-level relationships between rates of return were found during the COVID-19 pandemic. Originality / value / implications / recommendations – A comparison of the impact of two recent global events on the level of efficiency of the US stock market. Additionally, the article indicates which of the two key US stock indices provided more frequent investment opportunities.