Number Of Constants Research Articles

Analytical solutions for the injection of wettability modifiers in carbonate reservoirs based on a reduced surface complexation model

The potential of tuned-composition waterflooding to enhance oil recovery from carbonate reservoirs has been widely investigated, where wettability alteration is the dominant mechanism. It is hypothesized that the sulfate in seawater adsorbs on the rock surface, removing acidic hydrocarbon species adsorbed thereon. Glycine, the simplest amino acid, has also been investigated as a wettability modifier for carbonates that acts similarly to sulfate.Wettability alteration by the adsorption of sulfate ion and glycine anion has been satisfactorily modeled by extending calcite's surface complexation model (SCM) based on zeta potential measurements. However, determining the relevance of the individual geochemical reactions is obscured by the complexity of the SCM. Moreover, the large number of equilibrium constants and their associated uncertainty result in many degrees of freedom when matching corefloods and spontaneous imbibition experiments.This research determines the chemical reactions in the calcite's SCM that govern wettability alteration and the incremental oil recovery by glycine-enhanced waterflooding in carbonate reservoirs. We found that the wettability alteration by SCM can be approximated by two anion exchange reactions between the wettability modifiers, sulfate and glycine anions, and the carboxylic acids adsorbed on the rock surface. Moreover, the wettability of the system described by the adsorption of carboxylic acids and the incremental oil recovery by waterflooding are linearly correlated with the K value of the reaction of carboxylic acids with the carbonate surface and the concentration of carboxylic acids in the system, which is a function of the total acid number.We present analytical solutions for the two-phase, multicomponent reactive-transport model coupled with anion exchange reactions. To the best of our knowledge, this is the first time the presented analytical solutions are applied to describe enhanced waterflooding in carbonate reservoirs where more than one wettability modifier is injected. The analytical solutions showed that glycine injection enhances oil recovery over waterflooding by the formation of two wettability alteration waves. The number of waves and their types (rarefaction or shock) depend on glycine's and sulfate's concentration at the injection. The improvement in oil recovery by wettability alteration mainly occurs because the more favorable mobility ratio increases the displacement efficiency with no reduction in residual oil saturation. A synergy was found between glycine and sulfate, where the presence of glycine promotes the formation of a wettability-alteration shock by sulfate that improves the displacement efficiency.

A unified ductile fracture criterion suitable for sheet and bulk metals considering multiple void deformation modes

In engineering practice, it is critical to accurately forecast the fracture initiation of ductile metals. Currently, various uncoupled ductile fracture criteria (DFCs) have been constructed to forecast the ductile fracture initiation of sheet metals, and several uncoupled DFCs have been presented to predict the fracture incipience of bulk metals from high to negative stress triaxiality (HNST). However, there is still lack a unified uncoupled DFC that is capable of predicting the fracture initiation of both sheet and bulk metals, efficiently. To deal with the problem and fill the gap above, a simple general uncoupled DFC is proposed in this paper via taking into account multiple void deformation modes and the effects of accelerated void growth and coalescence under high stress triaxiality based on the theoretical analyses of void nucleation, growth and coalescence. Then, the effects of material parameters on the asymmetry of fracture loci, the predictive ability of the new model for the coupling effect of the Lode parameter and stress triaxiality on the ductility of different materials, the number of material constants, and the flexibility of the new model are investigated to fully comprehend the new DFC. In addition, the experimental results of four different metal materials are utilized to verify the effectiveness of the new DFC, and comparative studies with two representative uncoupled DFCs are conducted using the four different metal materials to demonstrate the advantage of the new DFC. Research findings show that the new DFC can accurately forecast both the fracture initiation of sheet metals from equi-biaxial tension (EBT) to shear and bulk metals from HNST, superior to the other uncoupled DFCs. Due to the high prediction accuracy and flexibility of the proposed new DFC, its use in engineering applications and integration with finite element analysis software is recommended.

Quantifier elimination for o-minimal structures expanded by a valuational cut

Let R be an o-minimal expansion of a group in a language in which Th(R) eliminates quantifiers, and let C be a predicate for a valuational cut in R. We identify a condition that implies quantifier elimination for Th(R,C) in the language of R expanded by C and a small number of constants, and which, in turn, is implied by Th(R,C) having quantifier elimination and being universally axiomatizable. The condition applies for example in the case when C is a convex subring of an o-minimal field R and its residue field is o-minimal.

Laser Ultrasound Investigations of AlScN(0001) and AlScN(11-20) Thin Films Prepared by Magnetron Sputter Epitaxy on Sapphire Substrates.

The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.

Multivariate Conway-Maxwell-Poisson Distribution: Sarmanov Method and Doubly Intractable Bayesian Inference

ABSTRACT In this article, a multivariate count distribution with Conway-Maxwell (COM)-Poisson marginals is proposed. To do this, we develop a modification of the Sarmanov method for constructing multivariate distributions. Our multivariate COM-Poisson (MultCOMP) model has desirable features such as (i) it admits a flexible covariance matrix allowing for both negative and positive nondiagonal entries; (ii) it overcomes the limitation of the existing bivariate COM-Poisson distributions in the literature that do not have COM-Poisson marginals; (iii) it allows for the analysis of multivariate counts and is not just limited to bivariate counts. Inferential challenges are presented by the likelihood specification as it depends on a number of intractable normalizing constants involving the model parameters. These obstacles motivate us to propose Bayesian inferential approaches where the resulting doubly intractable posterior is handled with via the noisy exchange algorithm or the Grouped Independence Metropolis–Hastings algorithm. Numerical experiments based on simulations are presented to illustrate the proposed Bayesian approach. We demonstrate the potential of the MultCOMP model through a real data application on the numbers of goals scored by the home and away teams in the English Premier League from 2018 to 2021. Here, our interest is to assess the effect of a lack of crowds during the COVID-19 pandemic on the well-known home team advantage. A MultCOMP model fit shows that there is evidence of a decreased number of goals scored by the home team, not accompanied by a reduced score from the opponent. Hence, our analysis suggests a smaller home team advantage in the absence of crowds, which agrees with the opinion of several football experts. Supplementary materials for this article are available online.

Classical group matrix models and universal criticality

We study generalizations of the Gross-Witten-Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment — employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant — that in the large N limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure.

Swelling of Thermo-Responsive Gels in Aqueous Solutions of Salts: A Predictive Model.

The equilibrium degree of swelling of thermo-responsive (TR) gels is strongly affected by the presence of ions in an aqueous solution. This phenomenon plays an important role in (i) the synthesis of multi-stimuli-responsive gels for soft robotics, where extraordinary strength and toughness are reached by soaking of a gel in solutions of multivalent ions, and (ii) the preparation of hybrid gels with interpenetrating networks formed by covalently cross-linked synthetic chains and ionically cross-linked biopolymer chains. A model is developed for equilibrium swelling of a TR gel in aqueous solutions of salts at various temperatures T below and above the critical temperature at which collapse of the gel occurs. An advantage of the model is that it involves a a small (compared with conventional relations) number of material constants and allows the critical temperature to be determined explicitly. Its ability (i) to describe equilibrium swelling diagrams on poly(N-isopropylacrylamide) gels in aqueous solutions of mono- and multivalent salts and (ii) to predict the influence of volume fraction of salt on the critical temperature is confirmed by comparison of observations with results of numerical simulation.

Equilibrium Swelling of Thermo-Responsive Gels in Mixtures of Solvents

Thermo-responsive (TR) gels of the LCST (lower critical solution temperature) type swell in water at temperatures below their volume phase transition temperature Tc and collapse above the critical temperature. When water is partially replaced with an organic liquid, these materials demonstrate three different types of equilibrium solvent uptake diagrams at temperatures below, above, in the close vicinity of Tc. A model is developed for equilibrium swelling of TR gels in binary mixtures of solvents. It takes into account three types of phase transitions in TR gels driven by (i) aggregation of hydrophobic side groups into clusters from which solvent molecules are expelled, (ii) replacement of water with cosolvent molecules in cage-like structures surrounding these groups, and (iii) replacement of water with cosolvent as the main element of hydration shells around backbone chains. The model involves a relatively small number of material constants that are found by matching observations on covalently cross-linked poly(N-isopropylacrylamide) macroscopic gels and microgels. Good agreement is demonstrated between the experimental data and results of numerical analysis. Classification is provided of the phase transition points on equilibrium swelling diagrams.

Understanding biofilm impact on electrochemical impedance spectroscopy analyses in microbial corrosion and microbial corrosion inhibition phenomena

Electrochemical impedance spectroscopy (EIS) is a non-disruptive technique that can be used to assess the corrosion behavior of materials. In this work, case studies on microbial corrosion (MIC) and microbial corrosion inhibition (MICI), drawn from the recent literature, were re-elaborated and discussed to determine which underlying information EIS analysis could or could not provide, concerning the roles of biofilms and bacteria on the corrosive and inhibitive processes. The data were suitably integrated and elaborated upon using Differential impedance analysis (DIA) to estimate the maximum number of time constants (T) that constituted the electric equivalent circuit (EEC) of each considered corrosion process. Additional analyses on the corrosion products performed by XPS and EIS showed that the bacterial biofilm had a significant influence on the faradaic charge transfer and film resistance of the corrosive process, as well as on its inhibition, at the metal-biofilm interface; however, it did not constitute an additional time constant.

Modification optical properties of TiO2 nanostructure as solar cell

In the process of this work, the Pulsed Laser Deposition (PLD) technique was used to deposit nanoparticles of pure titanium oxide (TiO2) onto a glass substrate at temperatures ranging from 100 to 400 degrees Celsius. This experiment made use of a Nd: YAG laser that had its frequency-doubled. The laser had a wavelength of 532 nanometers and an average laser strength of 800 millijoules. To explore the optical properties, transmittance spectrometry measurements were carried out for both visible and ultraviolet wavelengths. These measurements were carried out. The results of the optical transmittance test showed that it was more than 80 percent, which indicates that it is suitable for use in applications involving solar cells. The research was conducted on a number of optical constants, including the refractive index, the absorption coefficient, and the attenuation coefficient, and the values of these optical constants were determined. The value of the refractive index was found to be 2.49 when measured at a temperature of 400 degrees Celsius and a wavelength of 550 nanometers. Additionally, it was feasible to calculate the density of the titanium dioxide coating, which came out to be 3.6881 grams per cubic centimeter after the calculation was complete. The use of a numerical equation was utilized to ascertain the connection that exists between density and base temperature. It is an empirical equation that may be employed in the process of calculating the density of the components that are being used, and it has the potential to do so successfully. This equation is one of a kind since it was produced via the use of a theoretical computer program, and it is specific to the results that were obtained from the research.

One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes

In this study, we analytically solved the thermal stress problem of a bimodular functionally graded bending beam under arbitrary temperature rise modes. First, based on the strain suppression method in a one-dimensional case, we obtained the thermal stress of a bimodular functionally graded beam subjected to bending moment under arbitrary temperature rise modes. Using the stress function method based on compatibility conditions, we also derived two-dimensional thermoelasticity solutions for the same problem under pure bending and lateral-force bending, respectively. During the solving, the number of unknown integration constants is doubled due to the introduction of bimodular effect; thus, the determination for these constants depends not only on the boundary conditions, but also on the continuity conditions at the neutral layer. The comparisons indicate that the one- and two-dimensional thermal stress solutions are consistent in essence, with a slight difference in the axial stress, which exactly reflects the distinctions of one- and two-dimensional problems. In addition, the temperature rise modes in this study are not explicitly indicated, which further expands the applicability of the solutions obtained. The originality of this work is that the one- and two-dimensional thermal stress solutions for bimodular functionally graded beams are derived for the first time. The results obtained in this study may serve as a theoretical reference for the analysis and design of beam-like structures with obvious bimodular functionally graded properties in a thermal environment.

FUNCTION-ON-FUNCTION LINEAR QUANTILE REGRESSION

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finitedimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models.

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

Strongly Nonlinear Diffusion in Turbulent Environment: A Problem with Infinitely Many Couplings

The field theoretic renormalization group is applied to the strongly nonlinear stochastic advection-diffusion equation. The turbulent advection is modelled by the Kazantsev–Kraichnan “rapid-change” ensemble. As a requirement of the renormalizability, the model necessarily involves infinite number of coupling constants (“charges”). The one-loop counterterm is calculated explicitly. The corresponding renormalization group equation demonstrates existence of a pair of two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant), the critical dimensions of the scalar field Δθ, the response field Δθ′ and the frequency Δω are nonuniversal (through the dependence on the effective couplings) but satisfy certain exact identities. For the second surface (advection is relevant), the dimensions are universal and they are found exactly.

Bayesian parameter estimation in chiral effective field theory using the Hamiltonian Monte Carlo method

The number of low-energy constants (LECs) in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) grows rapidly with increasing chiral order, necessitating the use of Markov chain Monte Carlo techniques for sampling their posterior probability density function. For this we introduce a Hamiltonian Monte Carlo (HMC) algorithm and sample the LEC posterior up to next-to-next-to-leading order (NNLO) in the two-nucleon sector of $\ensuremath{\chi}\mathrm{EFT}$. We find that the sampling efficiency of HMC is three to six times higher compared to an affine-invariant sampling algorithm. We analyze the empirical coverage probability and validate that the NNLO model yields predictions for two-nucleon scattering data with largely reliable credible intervals, provided that one ignores the leading-order EFT expansion parameter when inferring the variance of the truncation error. We also find that the NNLO truncation error dominates the error budget.

Predicting ductile fracture during biaxial sheet stretching using an ellipsoidal void model

Ductile fracture during biaxial sheet stretching for two types of ferrous alloys and one type of nonferrous pure metal was predicted using the ellipsoidal void model proposed by one of the authors. First, fracture forming limit obtained experimentally by the Nakajima test scarcely differed from that obtained experimentally by the Marciniak test. Next, fracture forming limit obtained by the experiment scarcely depended on the magnitude of prestrain, which was applied to the sheet by rolling, and scarcely depended on the type of prestrain. Since the number of material constants on ductile fracture is only one, the material constant was determined so that the material thickness at fracture calculated from the simulation agreed with that obtained by the experiment. Fracture forming limit calculated using the ellipsoidal void model agreed closely with that obtained by the experiment, whereas fracture forming limit calculated using conventional ductile fracture criteria differed from that obtained by the experiment. Furthermore, fracture forming limit calculated using the ellipsoidal void model and that calculated using the conventional ductile fracture criteria changed drastically when the strain ratio changed across one for simulating biaxial stretching using a prestrained sheet.

An Analysis of the Forgeability of Ti-10V-2Fe-3Al β Titanium alloy using a combined Estrin Mecking and Avrami Material Constitutive Model

A constitutive model was developed to predict the high temperature sub-transus flow behavior of a metastable β Ti-10V-2Fe-3Al alloy, and its applicability for industrial scale forging process has been evaluated using a finite element simulation. Cylindrical samples extracted from a cogged billet of the alloy after β recrystallisation treatment were subjected to hot compression tests at sub-transus temperatures ranging from 720 °C to 780 °C with an increment of 15 °C under varying strain rates from 0.025 to 0.2 s−1. The sub-transus flow curves of the alloy exhibited work hardening followed by dynamic recovery and flow softening beyond the strain equivalent to peak stress. Formation of low angle grain boundaries within the prior β grains and dynamic recrystallisation of β phase were observed to contribute to the flow softening. A constitutive model based on Estrin Mecking and Avrami methods was developed with minimised number of material constants, using the data derived from the hot compression tests. The model was successfully verified using the deformation behaviour measured for the alloy in the region of interest. The constitutive model was implemented into a finite element package as a user subroutine to predict the flow behaviour of industrial scale billets during open die hot forging processes and validated using experimental trials. A fairly good predictive capability with more than 95% convergence for open die forging was achieved, confirming the suitability of the material model developed for predicting sub-transus forgeability of the Ti-10V-2Fe-3Al alloy during industrial scale forging.

Monitoring the interactions between bovine serum albumin and ZnO/Ag nanoparticles by spectroscopic techniques

Inducing the bio-functionalization in noble metal nanoparticles like gold, silver, zinc is very important to accomplish their biocompatibility in biological activities. These metal nanoparticles are being rigorously used in bio-sensing tools keeping their remarkable properties in mind. Amongst the serum albumins, the most ample proteins in plasma are bovine serum albumin and human serum albumin. A broad variety of physiological functions of bovine serum albumin has made it a model protein for bio-functionalization. In the present study, ZnO/Ag nanoparticles were synthesized and characterized by SEM and XRD techniques and the interaction between bovine serum albumin and ZnO/Ag nanoparticles was evaluated by employing ultra-violet, steady state fluorescence, circular dichroism and FTIR spectroscopic techniques. Upon the excitation of bovine serum albumin, ZnO/Ag nanoparticles appreciably reduced the intrinsic fluorescence intensity of bovine serum albumin. The number of binding locations and apparent binding constants at different temperatures were calculated by the fluorescence quenching method. Static mechanism of quenching and conformational modifications in bovine serum albumin were also found. Communicated by Ramaswamy H. Sarma

Rank 2 Bäcklund transformations of hyperbolic Monge-Ampère systems

This article studies rank 2 Bäcklund transformations of hyperbolic Monge-Ampère systems using Cartan's method of equivalence. Such Bäcklund transformations have two main types, which we call Type A and Type B. For Type A, we completely determine a subclass whose local invariants satisfy a specific but simple algebraic constraint. We show that such Bäcklund transformations are parametrized by a finite number of constants; in a subcase of maximal symmetry, we determine the coordinate form of the underlying PDEs, which turn out to be Darboux integrable. For Type B, we present an invariantly formulated condition that determines whether a Bäcklund transformation is one that, under suitable choices of local coordinates, relates solutions of two PDEs of the form zxy=F(x,y,z,zx,zy) and preserves the x,y variables on solutions.

FORMULATION OF TOOL WEAR LAW WHEN CUTTING POLYMER COMPOSITES

Numerous experimental studies in the field of mechanical processing of composite materials for individual materials and tools made it possible to formulate particular models for describing tool wear, changing its microgeometry during operation and predicting durability. There are significant difficulties in measuring current wear and recalculation in mathematical models, since they include a large number of parameters. This does not allow for simple technical control of cutting edge wear and predicting tool life. The formulation of the wear-contact problem of the tool tip and the material interaction during turning of reinforced composite plastics is presented. Based on known studies, it is assumed that wear occurs along the flank of the tool, and is accompanied by an asymmetric change in the geometry of its tip. A model of abrasive wear during sliding of a tool tip rear surface with a polymer composite reinforcement material and fracture products is considered. It is assumed that the wear law is hereditary and there is a linear dependence of the wear rate on the rate of contact interaction and pressure. Shear stresses through the contact pressure and the coefficient of friction nonlinearly depend on the operating time of the tool due to the change due to wear in the geometric shape of the tool and the processing parameters of the product over time. The volumetric wear factor is a tool run time function. It reflects the fact that the interaction of the “tool-workpiece” pair with time should, as it were, forget about the running-in stage, which has a high wear rate, and the fact that the dependence of wear on the load (contact pressure) is characterized by the presence of aftereffect. A simplified relationship is obtained for the wear law under the assumption that there is no change in the coefficient of friction, temperature and contact pressure over time. Ultimately, to describe the wear law and predict the tool life, it is necessary to know a number of empirical constants, the values of which are determined by the change in the microgeometry of the tool tip during interaction during cutting.