Exact Field Research Articles

A new look at the Schrödinger equation in exact scalar field cosmology

We propose a new representation of the Schrödinger-like equation for scalar field Friedmann cosmology where the scalar field is the argument, and the Hubble parameter is the analogue to the wave function. Such an approach gives us the possibility to use the Schrödinger potential as a generating function which leads to generalization of known exact solutions. Further, we find a simple transformation of the Hubble parameter which generates new solutions from the Schrödinger-like equation. Several examples are identified where exact forms for the scale factor, Hubble parameter and scalar potential can be written in closed form. Earlier results are regained in our approach.

Transient thermal boundary value problems in the half-space with mixed convective boundary conditions

Numerous problems in thermal engineering give rise to problems with abrupt changes in boundary conditions particularly as regards structural and construction applications. There is a continual need for improved analytical and numerical techniques for the study and analysis of such canonical problems. The present work considers transient heat propagation in a two-dimensional half-space with mixed boundary conditions of the Dirichlet and the Robin (convective) type. The exact temperature field is obtained in double integral form by applying the Wiener–Hopf technique, and this integral is then efficiently evaluated numerically with the help of numerical algorithms developed for the present problem and by exploiting the properties of the integrand. The results are then compared to the numerical solutions using finite element methods, and excellent agreement is shown. Some potential application areas of the theory are also discussed, specifically in the regime where edge effects can influence thermal convection processes.

Free and circular jets cooled by single phase nanofluids

Abstract Nanofluids are widely known to enhance the heat transfer rate resulting in a cooled system. In the present paper, we show mathematically that the nanofluids indeed cool the system as the nanoparticles volume fraction is increased. The key role is explained for a two-dimensional laminar free nanofluid jet and for a circular axisymmetric free nanofluid jet issuing into the same nanofluid medium. Exact nanofluid flow results are obtained and, integral flux relations of momentum and thermal layers concerning five most studied nanofluids, respectively Ag, Cu, CuO, Al2O3 and TiO2, are derived. A shape factor is defined controlling the momentum layer thickness. By means of another shape factor representing the thermal layer thickness, the relevant energy equation enables one to identify the regimes of nanoparticle size leading to a coolant jet, without a need to solve the energy equation fully. Two recently popular nanofluid models, resulting in the same conclusion, are examined on the considered free nanofluid jets. Additionally, an exact temperature field associated with the laminar two-dimensional free jet of nanoparticles is obtained offering explicit support to the current approach.

Prediction of many-electron wavefunctions using atomic potentials: Refinements and extensions to transition metals and large systems.

For a given many-electron molecule, it is possible to define a corresponding one-electron Schrödinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-determinant and multideterminant wavefunctions for the molecule. The energy is not predicted and must be evaluated by calculating Coulomb and exchange interactions over the predicted orbitals. Transferable potentials for first-row atoms and transition metal oxides that can be used without modification in different molecules are reported. For improved accuracy, molecular wavefunctions can be refined by slightly scaling nuclear charges and by introducing potentials optimized for functional groups. The accuracy is further improved by a single diagonalization of the Fock matrix constructed from the predicted orbitals. For a test set of 20 molecules representing different bonding environments, the transferable potentials with scaling give wavefunctions with energies that deviate from exact self-consistent field or configuration interaction energies by less than 0.05 eV and 0.02 eV per bond or valence electron pair, respectively. On diagonalization of the Fock matrix, the corresponding errors are reduced by a factor of three to less than 0.016 eV and 0.006 eV, respectively. Applications to the ground and excited states of a Ti18O36 nanoparticle and chlorophyll-a are reported.

Exact conformal field theories from mutually T-dualizable σ -models

Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual $\sigma$-models (here as the PL T-duality on a semi-Abelian double) on $2+2$-dimensional target manifolds $M \approx O \times \bf G$ and ${\tilde M} \approx O \times {\bf {\tilde G}}$, where $\bf G$ and ${\bf {\tilde G}}$ as two-dimensional real non-Abelian and Abelian Lie groups act freely on $M$ and $\tilde M$, respectively, while $O$ is the orbit of $\bf G$ in $M$. The findings of our study show that the original models are equivalent to Wess-Zumino-Witten (WZW) models based on the Heisenberg $(H_4)$ and $GL(2,\mathbb{R})$ Lie groups. In this way, some new T-dual backgrounds for these WZW models are obtained. For one of the duals of the $H_4$ WZW model, we show that the model is self-dual. In the case of the $GL(2,\mathbb{R})$ WZW model it is observed that the duality transformation changes the asymptotic behavior of solutions from $AdS_{3} \times \mathbb{R}$ to flat space. Then, the structure and asymptotic nature of the dual spacetime of this model including the horizon and singularity are determined. We furthermore get the non-critical Bianchi type III string cosmological model with a non-vanishing field strength from T-dualizable $\sigma$-models and show that this model describes an exact CFT (equivalent to the $GL(2,\mathbb{R})$ WZW model). After that, the conformal invariance of T-dual models up to two-loop order (first order in $\alpha'$) is discussed.

Održaj kao način sticanja prava svojine na nepokretnosti

The aim of the paper is to determine the exact field of application of the institute of acquisitive prescription, that is, to find the answer in which situations in practice it is possible to fulfill all the conditions required by the legislator and acquire the ownership by usucapio. The main question raised in the paper is whether there is an actual need for the existence of acquisitive prescription in contemporary Serbian law, bearing in mind that the data in the real estate cadastre has been duly kept. The institute of usucapio has also been analyzed from a perspective of application of the reliance principle on land registry. Certainly one of the most problematic question is the justification (and also the legal basis) of this institute having in mind the idea of the inviolability of ownership.

Nonlocal dynamic response of double-nanotube-systems for delivery of lagged-inertial-nanoparticles

This paper deals with transverse vibrations of doubly parallel nanotubes acted upon by doubly lagged-moving nanoparticles accounting for nonlocality. By exploiting the nonlocal Rayleigh and higher-order beam models, equations of motion of the nanosystem are obtained by considering the nonlocal inertial force as well as the lag of moving nanoparticles. For the case of ignorance of lateral inertia of moving nanoparticles, an analytical solution based on the Laplace transform method is suggested and the exact deformation fields of the nanosystem are presented for two patterns. In the case of consideration of the lateral inertia of moving nanoparticles, a numerical approach based on the Galerkin approach and admissible modes is suggested and the elasto-dynamic fields of the nanosystem are appropriately determined at each time. By comparing the predicted results by the proposed nonlocal numerical models with those of another work and the analytical approach, a reasonably good agreement is achieved. Subsequently, the roles of shear deformation, nonlocality, lag effect, geometry of the nanosystem, and kinematic properties of the moving nanoparticles on the dynamic deflections of the constitutive tubes are displayed. This scrutiny is aimed to be a solid base for examining vibrations of a membrane of nanotubes for delivery of multiple nanoparticles through their pores.

Efficient Sensitivity Based Reconstruction Technique to Accomplish Breast Hyperelastic Elastography.

Hyperelastic models have been acknowledged as constitutive equations which reliably model the nonlinear behaviors observed from soft tissues under various loading conditions. Among them, the Mooney-Rivlin, Yeoh, and polynomial models have been proved capable of accurately modeling responses of breast tissues to applied compressions. Hyperelastic elastography technique takes advantage of the disparities between hyperelastic parameters of varied tissues and the change in hyperelastic parameters in pathological processes. The precise reconstruction of hyperelastic parameters of a completely unknown pathology in the breast in a noninvasive and nondestructive way using the ultrasound elastography has been scrutinized in this paper. In the ultrasound elastography, tissue displacement field is extracted from radio frequency signals or images recorded using the ultrasound medical imaging system; hence the exact displacement field might not be obtained. Our results indicate that the parameters estimated by manipulating the iterative sensitivity-matrix based method converge to tissue's real hyperelastic parameters providing appropriate parameters are assigned to the hypothetical hyperelastic and regularization parameters. Iterative methods have therefore been proposed to compute proper hypothetical hyperelastic and regularization parameters. Accurate estimates of hyperelastic parameters of obscure breast pathology have been achieved even from imprecise measurements of displacements induced in the tissue by the ramp excitation.

Orthogonal Collocation Method for Solving the Diffusivity Equation: Application on Dual Porosity Reservoirs With Constant Pressure Outer Boundary

Fluid flow inside heterogeneous structure of dual porosity reservoirs is presented by two coupled partial differential equations (PDE). Finding an analytical solution for the diffusivity equations is tedious or even impossible in some circumstances due to the heterogeneity of dual porosity reservoirs. Therefore, in this study, orthogonal collocation method (OCM) is proposed for solving the governing equations in dual porosity reservoirs with constant pressure outer boundary. Since no analytical solution has been proposed for this system, validation is carried out by comparing the OCM-obtained results for “dual porosity reservoirs with circular no-flow outer boundary” with both exact analytical solution and real field data. Sensitivity analyses reveal that the OCM with 13 collocation points is a good candidate for prediction of pressure transient response (PTR) in dual porosity reservoirs. OCM predicts the PTR of a real field draw-down test with an absolute average relative deviation (AARD) of 0.9%. Moreover, OCM shows a good agreement with the analytical solution obtained by Laplace transform (AARD = 0.16%). It is worth noting that OCM requires a smaller computational effort. Thereafter, PTR of dual porosity reservoirs with a constant production rate in the wellbore and constant pressure outer boundary is simulated by OCM for wide ranges of operating conditions. Accuracy of OCM and its low required computational time justifies that this approximate method can be considered as a practical candidate for pressure transient analysis in dual porosity reservoirs.

Analytical study on the mode III stress fields due to blunt notches with cracks

AbstractThis work presents an analytical study on the stress fields induced by cracks nucleated at the tip of radiused notches under antiplane shear and torsion loadings. Closed‐form solutions for both shallow and deep notches are derived leveraging a combination of proper curvilinear coordinate systems and the complex potential method for antiplane elasticity. Based on the exact stress field solutions, convenient expressions for the stress intensity factors are derived.The accuracy of all the analytical formulations is verified by comparison with the results from a bulk of numerical analyses.

Effects of organic fertilization on soil properties and chamomile flower yield

The effects of different rates of organic fertilizers upon the yield of dry chamomile flowers were studied in an exact field trial setup on Luvisols in Podravina region, Croatia. The trial was set up according to the randomized block design with four replications. During three years of research (2013/2014, 2014/2015, and 2015/2016), changes in the soil chemical complex were monitored. Organic fertilization rendered significantly higher yields of dry chamomile flower than the control treatment. Organic fertilizers did not significantly affect soil pH, soil organic matter, and plant available phosphorus and potassium. The optimum amount of fertilizer for chamomile on this type of soil is 70 kg of nitrogen and 35 kg of plant available phosphorus and potassium. The study has also shown that the most effective parameter in the process is the weather conditions during the year, i.e., precipitation intensity, especially in the last few weeks prior to harvest.

Surface effects on an electrically permeable elliptical nano-hole or nano-crack in piezoelectric materials under anti-plane shear

An electrically permeable elliptical nano-hole or nano-crack embedded in an infinite piezoelectric material with surface effect is investigated based on the Gurtin–Murdoch surface/interface model, which is subjected to far-field anti-plane mechanical and in-plane electrical loads. The electric field inside the elliptical nano-hole has been taken into consideration, and exact electroelastic fields near the elliptical nano-hole are obtained by using the technique of conformal mapping. The size-dependent stress and electric displacement intensity factors at the crack tip are derived exactly for both electrically permeable and impermeable boundary conditions when the elliptical nano-hole reduces to the nano-crack. Numerical examples are illustrated to show the surface effects on the stress and electric displacement intensity factors of electrically permeable and impermeable cracks, and on the stress and electric field concentrations around the electrically permeable and impermeable holes. The results indicate that the size dependence of an electrically permeable nano-hole or nano-crack is entirely different from that of the electrically impermeable case.

Industrial Furnaces for Steel Processing – 90 Years of Continuous Improvement

Industrial furnaces are important facilities for the production of high quality metallic materials including melting, reheating, and heat treatment. The topics of the last 90 years are summarized for heat and mass transfer and furnaces for the reheating of cast steel (ingots, billets, blooms, and slabs) and for the recrystallization annealing of cold rolled strips. The fundamental task over decades is the calculation and simulation of the exact temperature field in metallic materials by analytical and at least numerical methods. Energy efficiency, use of different fuels, continuous improvement of quality, and productivity are also topics over the last nine decades. Actually, the improvement of the cooling sections of continuous annealing lines concerning higher cooling rate, flatness, and strip stability is a field of research and development.

Non-expanding Plebański–Demiański space-times

The aim of this work is to describe the complete family of non-expanding Plebański–Demiański type D space-times and to present their possible interpretation. We explicitly express the most general form of such (electro)vacuum solutions with any cosmological constant, and we investigate the geometrical and physical meaning of the seven parameters they contain. We present various metric forms, and by analyzing the corresponding coordinates in the weak-field limit we elucidate the global structure of these space-times, such as the character of possible singularities. We also demonstrate that members of this family can be understood as generalizations of classic B-metrics. In particular, the BI-metric represents an external gravitational field of a tachyonic (superluminal) source, complementary to the AI-metric which is the well-known Schwarzschild solution for exact gravitational field of a static (standing) source.

An accurate and efficient approach coupling quadrature element method and subregion generalized variational principle for fatigue crack growth modelling

Fatigue crack growth is modelled using a quadrature element method (QEM) in conjunction with a subregion generalized variational principle. Introducing the exact crack-tip stress field to the complementary energy subregion leads to accurate computation of stress intensity factors (SIFs), and applying the global high-order QEM to the potential energy subregion results in the least mesh effort and thus improved remeshing efficiency. With the aid of the fatigue crack growth criterion, structural fatigue life and crack path are predicted in an incremental manner. By specifying the remeshing rule that requires minimal effort, the entire growth process is modelled automatically. Several numerical examples are presented to demonstrate the effectiveness, accuracy and efficiency of the proposed approach.

Developing Field Test Procedures for Chloride Stress Corrosion Cracking in the Arabian Gulf

Oil and gas production and petrochemical plants in the Arabian Gulf are exposed to severe environmental conditions of high temperature and humidity. This makes these plants susceptible to chloride-induced stress corrosion cracking (CSCC). The laboratory testing fails to provide the exact field environmental conditions. A cost efficient field test setup for CSCC was designed and developed for the Arabian Gulf. The setup included designing self-sustained loading devices, samples, and sample racks. The samples were exposed to a stress equivalent to 80% and 100% of their yield strength. This paper describes the developed test procedures to establish testing with high level of accuracy and repeatability. It also discusses the design aspects and the challenges that were met.

Effects of Coronal Magnetic Field Structures on the Transport of Solar Energetic Particles

Abstract This Letter presents a model calculation of solar energetic particle (SEP) transport to test the sensitivity of the distribution of escaped SEPs in interplanetary space and dependence upon the details of the magnetic field structure in the corona. It is applied to a circumsolar event on 2011 November 3, in which SEPs are observed promptly after the solar event eruption by three spacecraft (the twin Solar TErrestrial RElations Observatories (STEREO-A and STEREO-B) and ACE) separated by more than 100° in longitude from each other. The corona magnetic field reconstructed from photosphseric field measurements using the PFSS method changes substantially before and after the solar eruption, especially around the active region. The locations of open field regions, separatrix surfaces including the heliospheric current sheet, and footpoints of magnetic field lines connected to the spacecraft location have shifted substantially. We inject 100 keV energetic electrons on the open field lines at 1.5 R s within the size of observed coronal mass ejections (CMEs) and follow their propagation in the corona and the interplanetary space. We find that with a perpendicular diffusion due to field line random walk equal to 10% of the supergranular diffusion rate, the overall distribution of escaped SEPs does not change much even though the region of open field lines from SEPs has changed. The result suggests that detailed small-scale coronal magnetic field structures and the exact magnetic field connection are not crucially important for observing SEPs in the interplanetary space.

Structure of interfaces at phase coexistence. Theory and numerics

We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the q-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in particular the theoretical predictions that below critical temperature the surplus of non-boundary colors appears in drops along a single interface, while for q > 4 at critical temperature there is formation of two interfaces enclosing a macroscopic disordered layer. These qualitatively different structures of the interfacial region can be discriminated through a measurement at a single point for different system sizes.

A family of metric gravities

.The goal of this paper is to take a completely fresh approach to metric gravity, in which the metric principle is strictly adhered to but its properties in local space-time are derived from conservation principles, not inferred from a global field equation. The global field strength variation then gains some flexibility, but only in the regime of very strong fields (2nd-order terms) whose measurement is now being contemplated. So doing provides a family of similar gravities, differing only in strong fields, which could be developed into meaningful verification targets for strong fields after the manner in which far-field variations were used in the 20th century. General Relativity (GR) is shown to be a member of the family and this is demonstrated by deriving the Schwarzschild metric exactly from a suitable field strength assumption. The method of doing so is interesting in itself because it involves only one differential equation rather than the usual four. Exact static symmetric field solutions are also given for one pedagogical alternative based on potential, and one theoretical alternative based on inertia, and the prospects of experimentally differentiating these are analyzed. Whether the method overturns the conventional wisdom that GR is the only metric theory of gravity and that alternatives must introduce additional interactions and fields is somewhat semantical, depending on whether one views the field strength assumption as a field and whether the assumption that produces GR is considered unique in some way. It is of course possible to have other fields, and the local space-time principle can be applied to field gravities which usually are weak-field approximations having only time dilation, giving them the spatial factor and promoting them to full metric theories. Though usually pedagogical, some of them are interesting from a quantum gravity perspective. Cases are noted where mass measurement errors, or distributions of dark matter, can cause one theory to mimic another implying that such estimates or distributions should be first obtained from weak-field measurements before being used to discriminate verification candidates. By this method theorists gain insight into the local constraints on space-time, and GR verification gains strong-field comparative objectives.

The method of generating functions in exact scalar field inflationary cosmology

The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most effective methods, viz., the method of generating functions for the construction of exact solutions in scalar field cosmology. We also include in the debate the superpotential method, which may be considered as the bridge to the slow roll approximation equations. Based on the review, we suggest a classification for the generating functions, and find a connection for all of them with the superpotential.