Alternative Equation Research Articles

Optimization of environmental variable functions of GPP quantitative model based on SCE-UA and minimum loss screening method

Environmental variable functions are of key importance for gross primary productivity (GPP) modeling. This study proposes a method about the optimization of environmental variable function to obtain a more robust and accurate GPP quantitative model. The key idea is to explore the impact of environmental factors on the accuracy of the GPP quantitative model from the following three aspects: the first is using tensor as the alternative environmental factor equation to construct the basis-function set of photosynthetically active radiation (PAR), atmospheric temperature and atmospheric carbon dioxide concentration for the given environmental conditions, and soil moisture functions of new environmental conditions. The second is building 144 candidate model based on a tensor product. The third is finding the best model from the candidates according to the Shuffled Complex Evolution (SCE-UA) algorithm and the Minimum Loss Screening Method. Through the above experiments, we have the following conclusions: First, this paper obtains two new best models from 144 candidate models, and their accuracy is higher than that of the initial model, indicating that this paper proposes a more robust and accurate GPP quantitative model. Then, the model proposed in this paper has common characteristics, that is, PAR and atmospheric temperature can be replaced by more appropriate quantitative functions, named Sigmoid-like function and Q10 equation, and the carbon dioxide equation can use half-saturated equation or Sigmoid function. Finally, the method in this paper can provide new ideas for simulating the fluxes of other ecosystems, including soil carbon decomposition and plant respiration.

Constrained Reversible System for Navier-Stokes Turbulence.

Following a Gallavotti's conjecture, stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the Navier-Stokes equation itself. We discuss a model system symmetric under time reversal based on the Navier-Stokes equations constrained to keep the enstrophy constant. It is demonstrated through highly resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations (DNS) at different Reynolds numbers. The possibility of using reversible models to mimic turbulence dynamics is of practical importance for the coarse-grained version of Navier-Stokes equations, as used in large-eddy simulations. Furthermore, the reversible model appears mathematically simpler, since enstrophy is bounded to be constant for every Reynolds number. Finally, the theoretical interest in the context of statistical mechanics is briefly discussed.

Experimental study on group effect of perfobond strip connectors encased in UHPC

The group effect on the shear capacity of perfobond strip (PBL) connector group embedded in ultrahigh performance concrete (UHPC) in the steel–concrete joints of hybrid structures was studied experimentally. Push-out tests were performed on 26 encased PBL specimens parameterized by the concrete type, row (or hole) number, and row spacing of connectors. The test results revealed that the failures of all the connections were characterized by the shear fracture of the reinforced concrete dowels. The average ultimate capacities per row of shear connectors in UHPC without steel fibers and with 2% volume fraction of steel fibers were approximately 19% and 42% higher, respectively, than those in C55 normal concrete, owing to the high shear strength of the matrix in UHPC and further enhancement by steel fibers. The effect of increasing the row number from 1 to 3 was a decrease of approximately 17% in the average ultimate load per row of connectors. Similarly, a decrease in row spacing from 3.85 to 2.0 times the hole diameter caused an approximately 14% decrease in the average ultimate load per row. With a reduction coefficient accounting for the group effect introduced, an alternative equation for the ultimate capacity of multirow PBLs was proposed, verified, and adopted in the simplified shear safety evaluation.

Enhancing the concentric tube properties by optimizing operational parameters

Concentric tube warmth interchanger are used for multitude employment ranging from heat transfer for low cease packages to coolants in space cars. Typical heat alternate equations are sufficient to resolve problems related to finite temperature difference. However, scientific solutions require complicated calculations that considers losses and minute hast dissipations to offer accurate outcomes. Mathematical and analytical methods of counter go with the flow heat exchanger is carried out in this look at. Enumeration of heat change throughout counter float is facilitated by way of incorporating Runge-Kutta Method. Comparison among the two evaluation techniques is executed for 2 situations making use of NTU approach. During one of the conditions the input values had been maintained as same, all through the second one conditions, the input values were various. The Runge-Kutta Method gave correct results for both the situations.

Ultra Low-Cycle Fatigue Behavior Comparison between Additively Manufactured and Rolled 17-4 PH (AISI 630) Stainless Steels

This study investigates the mechanical behavior of additively manufactured (AM) 17-4 PH (AISI 630) stainless steels and compares their behavior to traditionally produced wrought counterparts. The goal of this study is to understand the key parameters influencing AM 17-4 PH steel fatigue life under ULCF conditions and to develop simple predictive models for fatigue-life estimation in AM 17-4 steel components. In this study, both AM and traditionally produced (wrought) material samples are fatigue tested under fully reversed (R = −1) strain controlled (2–4% strain) loading and characterized using micro-hardness, x-ray diffraction, and fractography methods. Results indicate decreased fatigue life for AM specimens as compared to wrought 17-4 PH specimens due to fabrication porosity and un-melted particle defect regions which provide a mechanism for internal fracture initiation. Heat treatment processes performed in this work, to both the AM and wrought specimens, had no observable effect on ULCF behavior. Result comparisons with an existing fatigue prediction model (the Coffin–Manson universal slopes equation) demonstrated consistent over-prediction of fatigue life at applied strain amplitudes greater than 3%, likely due to inherent AM fabrication defects. An alternative empirical ULCF capacity equation is proposed herein to aid future fatigue estimations in AM 17-4 PH stainless steel components.

Distinguishing within- from between-individual effects: Howto use the within-individual centring method for quadraticpatterns.

Any average pattern observed at the population level (cross‐sectional analysis) may confound two different types of processes: some processes that occur among individuals and others that occur within individuals. Separating within‐ from among‐individual processes is critical for our understanding of ecological and evolutionary dynamics.The within‐individual centring method allows distinguishing within‐ from among‐individual processes and this method has been widely used in ecology to investigate both linear and quadratic patterns. Here we show that two alternative equations could be used for the investigation of quadratic within‐individual patterns. We explain the different assumptions and constraints of both equations. Reviewing the literature, we found that mainly one of these two equations has been used in studies investigating quadratic patterns. Yet this equation might not be the most appropriate in all circumstances leading to bias and imprecision.We show that these two alternative equations make different assumptions about the shape of the within‐individual pattern. One equation assumes that the within‐individual effect is related to an absolute process whereas the other assumes the effect arises from an individual relative process. The choice of using one equation instead of the other should depend upon the biological process investigated.Using simulations, we showed that a mismatch between the assumptions made by the equation used to analyse the data and the biological process investigated might led to flawed inference affecting output of model selection and accuracy of estimates. We stress that the equation used should be chosen carefully. We provide step by step guidelines for choosing an equation when studying quadratic pattern with the within‐individual centring approach. We encourage the use of the within‐individual centring method, promoting its relevant application for nonlinear relationships.

A Study of Efficiency Corrections for Centrifugal Pumps Handling Viscous Liquids in ISO/TR 17766:2005

Pump efficiency correction equations for converting from water to viscous liquids have been established for the turbulent-flow and laminar-flow regions. However, the two equations are discontinuous in the transient-flow region. This paper proposes a new equation for the transient-flow region that is based on fluid-dynamical considerations. Moreover, an alternative equation is examined for the turbulent-flow region that avoids an underestimate caused by the current efficiency correction equation that was adopted in ISO/TR 17766.

Erratum: Alternative flow equation for the functional renormalization group [Phys. Rev. D 100 , 101702(R) (2019)

Erratum: Alternative flow equation for the functional renormalization group [Phys. Rev. D <b>100</b> , 101702(R) (2019)

Nonlinear thermodynamic phase field theory with application to fracture and dynamic inelastic phenomena in ceramic polycrystals

A geometrically nonlinear phase field theory accounting for dissipation, rate effects, nonlinear thermoelasticity, fracture, and other structural changes is constructed in the context of continuum thermodynamics. First, a general framework accommodating arbitrary strain energy potentials, inelastic deformation kinematics, and unlimited order parameters is formulated. Next, the framework is specialized to account for deformation physics pertinent to crystalline ceramics and minerals deformed at high rates and high pressures. Notably, a logarithmic elastic strain tensor referred to an intermediate material configuration enters the nonlinear thermoelastic potential. Order parameters represent fractures, solid–solid phase transformations, deformation twinning, or slip of partial dislocations. Thermodynamically consistent kinetics manifest in equations reminiscent of Ginzburg–Landau dynamics, wherein viscosity coefficients are most generally state- and rate-dependent. Pressure-dependent strength commensurate with frictional resistance is enabled in alternative kinetic equations for dynamic fracture with irreversibility constraints. Linearization of the model suitable for moderate volume changes but small deviatoric elastic strain and rotation is undertaken. The theory is applied to study deformation and failure of polycrystalline forms of boron carbide (B4C), titanium diboride (TiB2), and a B4C-TiB2 ceramic composite. Solutions are derived and evaluated numerically for uniaxial stress tension and compression, uniaxial strain compression, and planar shock compression. The latter analysis yields relationships among viscosity coefficients, gradient regularization lengths, and characteristics of steady plastic waveforms. Results give new insight into high-rate deformation mechanisms previously speculated in these materials.

Basic properties of an alternative flow equation in gravity theories

Basic properties of alternative flow equation in Quantum Gravity are studied. It is shown that the alternative flow equation for effective two-particle irreducible effective action is gauge independent and does not depend on IR parameter $k$ on shell.

COMMENT ON GERMAN DZIEBEL

This comment is directed critically at certain arguments made by German Dziebel concerning the derivation of Crow-Omaha terminologies. Dziebel asks why such features cannot be derived from alternate generation equations. It is shown that this would have to happen indirectly, if at all. Dziebel's difficulties with the mixing of cross and parallel and the place of bifurcate merging and collateral terminological features in this context are also commented on, it being argued that they are all perfectly compatible with Crow-Omaha and indeed regularly found with such terminologies.

Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

We consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space {{mathcal {H}}^{1}}. The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

Application of an Artificial Neural Network and Multiple Nonlinear Regression to Estimate Container Ship Length Between Perpendiculars

Abstract Container ship length was estimated using artificial neural networks (ANN), as well as a random search based on Multiple Nonlinear Regression (MNLR). Two alternative equations were developed to estimate the length between perpendiculars based on container number and ship velocity using the aforementioned methods and an up-to-date container ship database. These equations could have practical applications during the preliminary design stage of a container ship. The application of heuristic techniques for the development of a MNLR model by variable and function randomisation leads to the automatic discovery of equation sets. It has been shown that an equation elaborated using this method, based on a random search, is more accurate and has a simpler mathematical form than an equation derived using ANN.

Recursive finite-difference Lattice Boltzmann schemes

The motivation of this study is twofold. First, a recursive mathematical formulation of the discrete-velocity Boltzmann equation (DVBE) under the Bhatnagar-Gross-Krook (BGK) approximation is introduced. This formulation allows us to formally express the solution of the DVBE as an infinite sum over successive particle derivatives of the distributions associated with local equilibrium. A Chapman-Enskog multiple-scales expansion shows that this sum can be safely truncated beyond the second order if the Navier-Stokes level of description is requested. Therefore, the distribution functions depend only on the first and second-order derivatives of the related equilibrium distributions. This alternative equation to the DVBE defines a basis to design kinetic schemes for the evolution of the distribution functions based solely on flow variables that are sufficient to define local equilibrium. Second, a family of mass-conserving numerical schemes is introduced from this kinetic equation by discretizing the particle derivatives by backward finite differences. Interestingly, a so-called “simplified Lattice Boltzmann method” introduced by Chen et al. in 2017 can be recast in this family. Numerical simulations highlight a level of numerical dissipation that is generally higher than the level obtained with a standard Lattice Boltzmann scheme, as expected by approximating derivatives by finite differences. Nevertheless, we show by using a von Neumann analysis that it is possible to parametrize our scheme, according to the relaxation coefficient of the DVBE, to reduce significantly its numerical dissipation and improve its spectral properties.We believe that this modeling can also be of interest to connect macroscopic and kinetic representations, e.g. when dealing with initial and boundary conditions or in hybrid simulations matching Navier-Stokes and Lattice Boltzmann schemes.

Alternative formulation of the induced surface and curvature tensions approach

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace–Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals (VdW) approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not the exponential, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.

Computation of Acoustic Velocity of Natural Gases With an Alternative Heat Capacity Ratio Equation and Application to Seismic Modeling

Abstract We investigate three formulations for computing acoustic velocity of natural gas and derive an equation for the heat capacity ratio, which plays a central role in these formulations. The first formulation is a compilation of fundamental equations available in the engineering literature, referred to as the DASH formulation. The second formulation is a development from the first, in which we use the derived equation for the heat capacity ratio (modified DASH). The third formulation is a mainstream method implemented in Geoscience (BW formulation). All three formulations stem from virial Equations of State that take preponderance in the exploration stage, when the detailed fluid composition is unknown and compositional methods are frequently inapplicable. We test the formulations on an extensive experimental data set of acoustic velocity of natural gases and compare the resulting accuracies. Both DASH and modified DASH formulations provide significantly higher accuracy when compared to the BW formulation. Additionally, the modified DASH, as we derive in this work, has the highest accuracy at pressures above 7000 psi, a condition typically encountered in the Brazilian pre-salt reservoirs. In a final step, we investigate how these different formulations and corresponding accuracies in velocity computation may affect seismic modeling, using a single interface model between a dense gas reservoir and a sealing rock. A direct comparison of amplitude versus offset modeling using our modified DASH formulation and the BW formulation shows up to 50% difference in amplitude calculation in a sensitivity exercise, especially at the longer offsets and higher pressures.

In-Plane Shear-Axial Strain Coupling Formulation for Shear-Deformable Composite Thin-Walled Beams

This paper presents an improved description of the in-plane strain coupling in Librescu-type shear-deformable composite thin-walled beams (CTWB). Based on existing descriptions for Euler-type CTWB, an analogous formulation for shear-deformable CTWB is here developed by building, via the Mindlin–Reissner theory and an orthotropic constitutive law of the shell wall, an alternate equation for the in-plane shear force which effectively couples the axial and shear in-plane strains. It is observed that this strain coupling formulation includes some of the transversal (out-of-plane) shear strain terms, thus also functioning as a path for transferring transversal shear energy to the in-plane strain field and therefore improving shear-deformability. The performance of the new CTWB model is compared against that of previously available CWTB (i.e. Euler-type with strain coupling and Timoshenko-type without strain coupling) for several aspect ratios, fibre-orientations and laminate types. Error measures are calculated by comparing several relevant stiffness coefficients and displacement shapes to reference results provided by corresponding 3D shell-based ANSYS finite-element models. Results indicate that for cases involving significant shear energy (i.e. short aspect ratios) and/or in-plane shear-axial strain coupling (i.e. off-axis or asymmetric/unbalanced laminates), the new CTWB model proposed in this work can attain an accuracy level comparable to that associated to more sophisticated models, two to three orders of magnitude larger, at a fraction of the computational cost.

The Rank Upgrading Technique for a Harmonic Restoring Force of Nonlinear Oscillators

An enhanced analytical technique for nonlinear oscillators having a harmonic restoring force is proposed. The approach is passed on the change of the auxiliary operator by another suitable one leads to obtain a periodic solution. The fundamental idea of the new approach is based on obtaining an alternative equation free of the harmonic restoring forces. This method is a modification of the homotopy perturbation method. The approach allows not only an actual periodic solution but also the frequency of the problem as a function of the amplitude of oscillation. Three nonlinear oscillators including restoring force, the simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon equation are offered to clarify the effectiveness and usefulness of the proposed technique. This approach allows an effective mathematical approach to noise and uncertain properties of nonlinear vibrations arising in physics and engineering.

Effects of shear deformation and orthotropy on the buckling behaviour of oriented strand boards

ABSTRACT The literature is replete with studies conducted on wood-based boards. However, studies involving the influence of orthotropy and shear deformation on the one-dimensional buckling behaviour of oriented strand boards are lacking. This study is a step-by-step approach towards investigating and discussing the influence of orthotropy and shear deformation on the bending and one-dimensional buckling behaviour of oriented strand boards using specimens which are 12, 18, and 25 mm in thickness, measuring 400 and 780 mm in length for the bending analyses and 400, 425, 450, 475, and 500 mm for the buckling analyses. FE-models were developed which considered the boards as orthotropic and were able to determine their load-displacement behaviour considering the effects of geometric non-linearities. Results of the analyses showed that orthotropy have significant effects on the bending while shear deformation influences both the bending and buckling behaviour of oriented strand boards. In bending, the effects are generally higher in the main strength than in the secondary strength direction. In buckling, it is a reduction in the buckling loads in a range of between 4% and 26%, compared to what would have been obtained using the Euler equation. An alternative Equation with a better ability to predict the one-dimensional buckling load of wood-based boards was presented and discussed.

Alternative Cauchy equation in three unknown functions

In this paper we deal with the product of two or three Cauchy differences equaled to zero. We show that in the case of two Cauchy differences, the condition of absolute continuity and differentiability of the two functions involved implies that one of them must be linear, i.e., we have a trivial solution. In the case of the product of three Cauchy differences the situation changes drastically: there exists non trivial {mathcal {C}}^{infty } solutions, while in the case of real analytic functions we obtain that at least one of the functions involved must be linear. Some open problems are then presented.