New Set Of Equations Research Articles

P- and S-wave energy flux density vectors

The conventional energy flux density vector indicates the propagation direction of mixed P- and S-wave wavefields, which means when a wavefront of P-wave encounters a wavefront of S-wave with different propagation directions, the vectors cannot indicate both directions accurately. To avoid inaccuracies caused by superposition of P- and S-waves in a conventional energy flux density vector, P- and S-wave energy flux density vectors should be calculated separately. Because the conventional energy flux density vector is obtained by multiplying the stress tensor by the particle-velocity vector, the common way to calculate P- and S-wave energy flux density vectors is to decompose the stress tensor and particle-velocity vector into the P- and S-wave parts before multiplication. However, we have found that the P-wave still interfere with the S-wave energy flux density vector calculated by this method. Therefore, we have developed a new method to calculate P- and S-wave energy flux density vectors based on a set of new equations but not velocity-stress equations. First, we decompose elastic wavefield by the set of equations to obtain the P- and S-wave particle-velocity vectors, dilatation scalar, and rotation vector. Then, we calculate the P-wave energy flux density vector by multiplying the P-wave particle-velocity vector by dilatation scalar, and we calculate the S-wave energy flux density vector as a cross product of the S-wave particle-velocity vector and rotation vector. The vectors can indicate accurate propagation directions of P- and S-waves, respectively, without being interfered by the superposition of the two wave modes.

Modification of the Grood and Suntay Joint Coordinate System equations for knee joint flexion

Since its introduction, the Grood and Suntay Joint Coordinate System (JCS) has been embraced by the International Society of Biomechanics (ISB) and been widely used for biomechanical reporting. There is, however, a limitation in its ability to provide correct flexion values over a wide range of clinically relevant flexion angles. This technical note addresses the limitation of the JCS equations and introduces a new set of equations to overcome this problem.

Advantages of isochoric freezing for food preservation: A preliminary analysis

Motivated by an interest in developing more efficient and economical methods for long-term preservation of food in a frozen state, we have explored the concept of isochoric (constant volume) freezing. In this theoretical study, we have developed a new set of equations that describe the process of freezing in the isochoric system. Unlike isobaric systems, in isochoric systems, the pressure is not constant and affects the phase transition temperature in a way prescribed by equilibrium thermodynamics. Fundamental thermodynamic principles, were used to derive an equation that facilitates the calculation of the temperature of the change of phase interface during the freezing process as a function of the quality of the system (the extent of freezing). A simple one-dimensional case study demonstrates the advantages of isochoric freezing of food. These advantages include the ability to freeze only part of the system at recommended food storage temperature, which results in substantial energy savings and conditions that will likely lead to stored food of better quality.

Improving lidar turbulence estimates for wind energy

Remote sensing devices (e.g., lidars) are quickly becoming a cost-effective and reliable alternative to meteorological towers for wind energy applications. Although lidars can measure mean wind speeds accurately, these devices measure different values of turbulence intensity (TI) than an instrument on a tower. In response to these issues, a lidar TI error reduction model was recently developed for commercially available lidars. The TI error model first applies physics-based corrections to the lidar measurements, then uses machine-learning techniques to further reduce errors in lidar TI estimates. The model was tested at two sites in the Southern Plains where vertically profiling lidars were collocated with meteorological towers. Results indicate that the model works well under stable conditions but cannot fully mitigate the effects of variance contamination under unstable conditions. To understand how variance contamination affects lidar TI estimates, a new set of equations was derived in previous work to characterize the actual variance measured by a lidar. Terms in these equations were quantified using a lidar simulator and modeled wind field, and the new equations were then implemented into the TI error model.

Improved Bond Equations for Fiber-Reinforced Polymer Bars in Concrete.

This paper explores a set of new equations to predict the bond strength between fiber reinforced polymer (FRP) rebar and concrete. The proposed equations are based on a comprehensive statistical analysis and existing experimental results in the literature. Namely, the most effective parameters on bond behavior of FRP concrete were first identified by applying a factorial analysis on a part of the available database. Then the database that contains 250 pullout tests were divided into four groups based on the concrete compressive strength and the rebar surface. Afterward, nonlinear regression analysis was performed for each study group in order to determine the bond equations. The results show that the proposed equations can predict bond strengths more accurately compared to the other previously reported models.

Optimal sizing and sitting of DG with load models using soft computing techniques in practical distribution system

In the deregulated power market environment, distributed generation (DG) is an effective approach to manage performance, operation and control of the distribution system. Methods available in the literature for DG planning are often not able to simultaneously provide technical and economical benefits. Therefore an effective methodology is developed to improve the technical as well as economical benefits as compared with the existing approaches. This study reports the optimal installation of multi-DG in the standard 33-bus, 69-bus radial distribution systems and 54-bus practical radial distribution system. Several performance evaluation indices such as active and reactive power loss indices, voltage deviation index, reliability index and shift factor indices are used to develop a novel multi-objective function (MOF). A new set of equations is developed for representing different practical load models. A novel MOF has been solved to find optimal sizing and placement of DGs using genetic algorithm and particle swarm optimisation technique. The comparative result analysis is also discussed for both techniques. The result analysis reveals that system losses, energy not supplied, system MVA intakes are reduced, whereas available transfer capability, voltage profile, reliability and cost benefits are improved for the case with-DGs in the distribution system.

Poincaré’s Equations for Cosserat Media: Application to Shells

In 1901 Henri Poincare discovered a new set of equations for mechanics. These equations are a generalization of Lagrange's equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we extend these equations from classical mechanical systems to continuous Cosserat media, i.e. media in which the usual point particles are replaced by small rigid bodies, called micro-structures. In particular, we will see how the Shell balance equations used in nonlinear structural dynamics, can be easily derived from this extension of the Poincare's result.

Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective

The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112–118 (1956)]. Many attempts have been made ever since. Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD. However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium. Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients. The present work is an outgrowth of the paper on “Alfven Waves in Gyrokinetic Plasmas” by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].

Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach.

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.

Curvilinear smoothed particle hydrodynamics

SummaryWe suggest a new set of equations to employ smoothed particle hydrodynamics (SPH) in a curvilinear space, and we refer to it as curvSPH. In classical SPH, the horizontal and vertical resolution of discretization is supposed to be equal for fluid particles. However, curvSPH makes the horizontal and vertical resolutions independent from each other. This is performed by transformation of physical space into an appropriate computational space with a different scale in horizontal and vertical directions. Solving a problem using SPH in a curvilinear space also provides capability to model curved boundaries as straight lines. In classical SPH, special care is needed to reach a uniform mass distribution along curved boundaries; however, producing uniform mass distribution along a line using curvSPH is straight forward. Different simulations, including simulation of a flip bucket are performed to demonstrate the applicability of the proposed method. Good agreement of results with experimental data and classical SPH confirms the capabilities of curvSPH. Copyright © 2016 John Wiley & Sons, Ltd.

Structural parameters identification of uncertain multi-storey shear buildings using fuzzy neural network modelling

Present paper proposes a fuzzy neural network (FNN)-based modelling for the identification of structural parameters of uncertain multi-storey shear buildings. Here, the method is developed to identify uncertain structural mass, stiffness and damping matrices from the dynamic responses of the structure without any optimization processes that are generally used to solve inverse vibration problems. Uncertainty has been taken in term of fuzzy numbers. The governing equations of motion are first solved by the classical method to get responses of the consecutive stories. Further the governing equations of motion are modified based on relative responses of consecutive stories in such a way that the new set of equations can be implemented in a cluster of FNNs. As such the model starts solving the nth floor by FNN modelling to estimate the structural parameters. Subsequently, series of FNN models are used to estimate the parameters for (n − 1)th storey to the first storey. One may note that single layer FNNs have been used for training for each cluster of the FNN such that the converged weights give the uncertain structural parameters. The initial weights in the FNN architecture are taken as the design parameters in uncertain (fuzzy) form. In order to validate the present model, various example problems of different multi-storey shear structures have been considered. Related results are incorporated in term of tables and graphs. Comparisons between theoretical and identified results are carried out and are found to be in good agreement.

Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure

We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate i) the cosmological expansion, ii) linear cosmological perturbations theory and iii) stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.

Extensors and the Hilbert scheme

The Hilbert scheme $Hilb_{p(t)}^n$ parametrizes closed subschemes and families of closed subschemes in the projective space $P^n$ with a fixed Hilbert polynomial $p(t)$. It is classically realized as a closed subscheme of a Grassmannian or a product of Grassmannians. In this paper we present a method that allows to derive scheme theoretical global equations for $Hilb_{p(t)}^n$ in the Plucker coordinates of a Grassmannian $Grass_p^N$, where $p$ and $N$ depend on the dimension $n$ of the projective space and on the Hilbert polynomial $p(t)$. Using this method we obtain the already known set of equations given by Iarrobino and Kleiman in 1999, the one conjectured by Bayer in 1982 and proved by Haiman and Sturmfels in 2004, and also a new set of equations of degree lower than the previous ones. The novelties of our approach are essentially two. The first one is a local study of the Hilbert functor through special sets of open subfunctors obtained exploiting the symmetries of the Hilbert scheme and the combinatorial properties of monomial ideals, mainly the Borel-fixed ones. The second one is a generalization of the theory of extensors to the setting of free modules over any ring $A$ and the description of any exterior product of elements of a free submodule in terms of Plucker coordinates.

A practical workflow for characterizing stress-dependent behaviour of coal from changes in well productivity

Stress (or pressure) dependence of coal permeability is a commonly observed and generally accepted dynamic behaviour that is often ignored from production performance forecasting. Reasons for this omission typically include (a) the difficulties in reliably characterizing stress dependent effects from a limited number of pressure buildup (PBU) tests, and (b) large uncertainties in our understanding of both the porosity and compressibility of coals. This paper demonstrates a new analytical workflow, and proposes a new set of equations that overcomes some of those limitations. Engineers can use this paper to analytically translate expected permeability changes with pressure, to productivity changes with pressure differences.This paper utilizes a slightly modified form of Palmer-Mansoori (P&M) model in a workflow that includes. 1Estimation of coal cleat volume compressibility using permeability-depth trends. 2Characterization of mechanical skins from interpreted apparent skins. 3Calculation of stress dependent pseudo pressure (SDPP) – converting permeability changes with pressure to productivity changes with pressure differences – enabling the use of well productivities over time as part of a SDP characterization process. 4The matching through regression of relative changes in well productivity indices in groups of wells - utilizing the SDPP approach – with a single stress dependent controlling parameter, in a way that is suited to extrapolating away from well control.Theoretical support for this approach is provided via derivations from published models. A methodology is outlined – sharing the results of a field example – to demonstrate the relative ease with which the analytical process can be applied. Further, pitfalls are highlighted of using well productivities as a direct proxy for permeability changes, or even utilizing coarse grid numerical simulation in the matching process. Finally, further applications and limitations of its application are also discussed.This paper addresses existing knowledge gaps in the coal bed methane (CBM) industry by providing a simple, yet efficient, workflow for characterizing and incorporating stress-dependence of permeability in CBM Reservoir Engineering. This is achieved through the application of new analytical equations to characterize stress dependent pseudo pressure, enabling the direct use of well productivity changes, and can be used standalone, or as a means to accelerate a numerical history matching workflow.

Phase space dynamics of triaxial collapse: joint density–velocity evolution

We investigate the dynamics of triaxial collapse in terms of eigenvalues of the deformation tensor, the velocity derivative tensor and the gravity Hessian. Using the Bond-Myers model of ellipsoidal collapse, we derive a new set of equations for the nine eigenvalues and examine their dynamics in phase space. The main advantage of this form is that it eliminates the complicated elliptic integrals that appear in the axes evolution equations and is more natural way to understand the interplay between the perturbations. This paper focuses on the density-velocity dynamics. The Zeldovich approximation implies that the three tensors are proportional; the proportionality constant is set by demanding `no decaying modes'. We extend this condition into the non-linear regime and find that the eigenvalues of the gravity Hessian and the velocity derivative tensor are related as ${\tilde q}_d + {\tilde q}_v=1$, where the triaxiality parameter ${\tilde q} = (\lambda_{\mathrm{max}} - \lambda_{\mathrm{inter}})/(\lambda_{\mathrm{max}} - \lambda_{\mathrm{min}})$. This is a {\it new universal relation} holding true over all redshifts and a range of mass scales to within a few percent accuracy. The mean density-velocity divergence relation at late times is close to linear, indicating that the dynamics is dictated by collapse along the largest eigendirection. This relation has a scatter, which we show, is intimately connected to the velocity shear. Finally, as an application, we compute the PDFs of the two variables and compare with other forms in the literature.

Prediction of seaward slope recession in berm breakwaters using M5' machine learning approach

In the design process of berm breakwaters, their front slope recession has an inevitable rule in large number of model tests, and this parameter being studied. This research draws its data from Moghim’s and Shekari’s experiment results. These experiments consist of two different 2D model tests in two wave flumes, in which the berm recession to different sea state and structural parameters have been studied. Irregular waves with a JONSWAP spectrum were used in both test series. A total of 412 test results were used to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession parameters. In this paper, a new set of equations for berm recession is derived using the M5' model tree as a machine learning approach. A comparison is made between the estimations by the new formula and the formulae recently given by other researchers to show the preference of new M5' approach.

Propeller Jet–Induced Suspended-Sediment Concentration

AbstractWhen subjected to a strong swirling jet flow induced by a rotating ship’s propeller, the bed of a waterway may undergo significant changes. These changes will not only cause instability to quay structures and damage the protection work of the beds/banks of rivers and canals, but also resuspend the bed sediment. The latter likely will pollute the water column and affect the aquatic life. In this study, the propeller-jet velocity and sediment-concentration profiles downstream of a propeller are measured using an acoustic Doppler velocity profiler and a suction device, respectively. The estimates obtained by using formulas for the axial velocity and four published methods for calculating the reference near-bed concentration of suspended sediment are compared with the experimental data. Moreover, the behavior underlying the temporal and spatial variations in seabed scour and sediment suspension is also investigated. A new set of equations for estimating the sediment concentration profiles is developed...

Power density improvement of bi-conductive polymer membrane fuel cells by optimization of its internal resistances

This paper reports the development of a new set of equations that defines the internal resistances in bi-conductive membrane (BCM) fuel cells and allows optimization of its critical dimensions and power density. Based on these equations, a design approach is proposed and fabrication steps that limit the power density of the final device are identified. The equations developed in this study can be used for any configuration and shape of holes and current collectors. It demonstrates that by improving fabrication techniques used in a previous study, total internal resistance of the BCM fuel cell could be reduced by 80%, showing that this type of fuel cell could potentially deliver very high power density compared to standard PEMFCs.

Experimental study on post-fire mechanical properties of high strength Q460 steel

In order to evaluate the residual strength of high strength Q460 steel structures after fire, an experimental study was undertaken to investigate the post-fire mechanical properties of high strength Q460 steel. Tensile coupons taken from high strength Q460 steel sheets were exposed to different temperatures up to 900°C, and were then allowed to cool down to ambient temperature before they were tested to failure. Two cooling methods were considered, namely; natural air cooling and cooling by water. Tensile coupon tests were conducted to obtain their post-fire stress–strain curves and associated mechanical properties (yield strength, elastic modulus, ultimate strength and elongation). It was found that the post-fire mechanical properties of high strength Q460 steel are significantly reduced below the original ambient temperature mechanical properties if they had been exposed to temperatures exceeding 600°C. Hence a new set of equations is proposed to predict the post-fire mechanical properties of high strength Q460 steel. Such post-fire mechanical property assessments allows structural and fire engineers to make an accurate prediction of the safety of fire exposed high strength Q460 steel buildings.

Equivalence of two different approaches to global δf gyrokinetic simulations

A set of flux tube gyrokinetic equations that includes the effect of the spatial variation of the density, temperature and rotation gradients on the turbulence is derived. This new set of equations uses periodic boundary conditions. In the limit l⊥/L ≪ 1, where l⊥ is the characteristic perpendicular length of turbulent structures and L is the characteristic size of the device, this new set of flux tube gyrokinetic equations is shown to be equivalent to the traditional global δf gyrokinetic equations to an order higher in l⊥/L than the usual flux tube formulations.