Three-dimensional Solution Research Articles

Three-dimensional massive Kiselev AdS black hole and its thermodynamics

We present an exact three-dimensional massive Kiselev AdS black hole solution. This Kiselev black hole is neither perfectly fluid, nor is it the quintessential solution, but the BTZ black hole modified by the anisotropic matter. This black hole possesses an essential singularity at its radial origin and a single horizon whose radius will increase monotonically when the parameter of the anisotropic matter field ω decreases. We calculate all thermodynamic quantities and find that the first law of thermodynamics of this massive Kiselev AdS black hole can be protected, while the consistent Smarr formula is only held in the extended thermodynamic phase space. After examining the sign of free energy, we conclude that there is no Hawking-Page transition since the massive Kiselev AdS black hole phase is always thermodynamically favored. Moreover, we study the phase transition between the Kiselev AdS black hole and BTZ black hole by considering the matchings for their temperature. We find that the Kiselev AdS black hole is still a thermodynamically more preferred phase, because it always has a smaller amount of free energy than the BTZ black hole, which seems to indicate that the anisotropic matter field may emerge naturally in BTZ black hole spacetime under some thermal fluctuations. We also show a first order phase transition between the Kiselev AdS black hole phase with and the black hole phase with . As the Kiselev AdS black hole has some notable features on the phase transition of black holes in three dimensions, it provides important clues to further investigate these both surprising and similar behaviors in four and higher dimensions.

Propagation of solitons in optical fibers with generalized Kudryashov’s refractive index

The propagation of optical solitons in optical fibers with the generalized Kudryashov’s refractive index is described by a high order nonlinear Schrödinger equation. The main feature is that the amplitude and width of the pulse can be changed with arbitrary power. By trial equation method, a series of propagation patterns of optical waves are obtained. In addition, the graphs of two-dimensional and three-dimensional solutions are illustrated, and then the existence of all those patterns of optical waves is proved.

Thermo-mechanical design optimization of symmetric and non-symmetric sandwich plates with ceramic-metal-ceramic functionally graded core to minimize stress, deformation and mass

This work explores the multiobjective design optimization of symmetric and non-symmetric sandwich plates with ceramic-metal-ceramic functionally graded (FG) core, along with ceramic faces (if included), under thermo-mechanical loadings. The FG core is made of two functionally graded material (FGM) layers, each with the volume fractions of the constituent phases defined by a power-law function through-thickness, with the interface between them metal-rich and the core outer surfaces ceramic-rich. In line with symmetric or non-symmetric sandwich plates, the design variables involve the thickness of each FGM layer of the core and the index of its power-law function, along with the thickness of each ceramic face. The thermal and mechanical problems are fully coupled using a layerwise mixed least-squares model with multi-field independent variables, including, most importantly, displacements, temperature and transverse stresses. The FG core z-continuous effective properties are also fully described by high-order z-expansions, as demonstrated adopting the rule of mixtures. The multiobjective optimization problem is solved by Direct MultiSearch derivative-free method, minimizing mass, transverse displacement and the stress field, measured by Tsai-Hill failure criteria, all together. Numerical results provide optimal symmetric and non-symmetric sandwich plates with ceramic-metal-ceramic FG core, considering distinct constituent materials and including three-dimensional approximate solutions for validation.

A refined plate theory for functionally graded carbon nanotube-reinforced plates with piezoelectric actuator

With the advantage of outstanding mechanical characteristics, carbon nanotube (CNT) is nowadays considered as one of the most ideal reinforcements for composite materials. Mechanical properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) structures have been extensively investigated in the published literature. However, analytical results on transverse shear stresses of smart FG-CNTRC plates subjected to electro-mechanical loadings are scarce in literature. To fill this gap, a refined plate theory is proposed for bending analysis of laminated FG-CNTRC plates integrated with a piezoelectric fiber reinforced composite (PFRC) actuator. The kinematic assumptions of the proposed plate theory are obtained by superimposing an efficient zigzag function on the first-order shear deformation theory. Laminated FG-CNTRC plates with four distribution types of CNT through the thickness are considered. The governing equations are obtained by using the principle of minimum potential energy and the Navier's method is used to solve the boundary value problem. The present results are compared with the three-dimensional (3D) elasticity solutions and the results computed by using the chosen models. Numerical results show that the proposed zigzag function can effectively improve the accuracy of proposed plate model in predicting the displacements and stresses. In order to understand clearly the static behaviors of smart FG-CNTRC plates, the influences of electro-mechanical loading, CNT distribution through the thickness direction, CNT volume fraction and span-to-thickness ratio are thoroughly investigated.

Frictional contact problem of a rigid charged indenter on two dimensional hexagonal piezoelectric quasicrystals coating

ABSTRACT This paper reports the frictional contact problem of a rigid charged indenter on two-dimensional (2D) hexagonal piezoelectric quasicrystals (PEQCs) coating. Using the rigorous operator theory and Almansi theorem, two sets of three-dimensional (3D) general solutions for 2D-hexagonal PEQCs are obtained. The frequency response functions (FRFs) for displacements and stresses of phonon and phason, electric potentials and electric displacements, which are the multifield responses of material under generalised unit point load in the Fourier domain, are obtained by applying double Fourier integral transforms to the general solutions and boundary conditions. The contact responses, such as pressures and stresses, are solved by the discrete convolution-fast Fourier transform technique (DC-FFT). Numerical results are given to reveal the influences of material parameters and loading conditions on the contact behaviour. The obtained 3D contact solutions are not only helpful further analysis and understanding of the coupling characteristics of phonon, phason and electric field, but also provide a reference basis for experimental analysis and material development.

Space Analyticity and Bounds for Derivatives of Solutions to the Evolutionary Equations of Diffusive Magnetohydrodynamics

In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier–Stokes equation. Such bounds are instructive in the numerical investigation of intermittency that is often observed in simulations, e.g., numerical study of vorticity moments by Donzis et al. (2013) revealed depletion of nonlinearity that may be responsible for smoothness of solutions to the Navier–Stokes equation. We employ an original method to derive analogous estimates for space derivatives of three-dimensional space-periodic weak solutions to the evolutionary equations of diffusive magnetohydrodynamics. Construction relies on space analyticity of the solutions at almost all times. An auxiliary problem is introduced, and a Sobolev norm of its solutions bounds from below the size in C3 of the region of space analyticity of the solutions to the original problem. We recover the exponents obtained earlier for the hydrodynamic problem. Moreover, the same approach is followed here to derive and prove similar a priori bounds for arbitrary-order space derivatives of the first-order time derivative of the weak MHD solutions.

Experimental and numerical investigations of the effect of pressure on combustion characteristics of Mg-based solid fuels

The present study is devoted to comprehensively evaluating the combustion performance of Mg-based (Magnesium/polytetrafluoroethylene/Viton) solid fuels in high-altitude operating environments. A small-scale sealed CO2 laser ignition experiment system is designed to produce different negative pressure environments. A high-speed camera (HSC) and an infrared thermal imager are used to cooperatively capture the burning process. The results obtained demonstrate that the area of the flame core zone and the flame temperature increase significantly as the pressure increases. It is conducive to the heat feedback of the gas phase reaction zone to the solid phase heating zone, resulting in an increase in the burning rate. As the Mg content increases, the flame temperature is decreased and the burning rate is increased. The burning rate for the Mg-based solid fuels is found to increase monotonically with ambient pressure and to follow the Vieille’s law in the pressure range of 0.02–0.1 MPa. Based on the experiment, a three-dimensional combustion-flow coupling solution model is established including the detailed aerobic combustion reaction kinetic model and the eddy dissipation concept (EDC) model. Numerical simulation results reveal that the content of incompletely reacted Mg increases as the pressure decreases. Conversely, the decreasing behavior of oxygen partial pressure at low pressure reduces the probability of reaction of Mg with O2, resulting in a dramatical decrease in the mass fraction of MgO. The scientific findings provide useful insight for the deep understanding of the combustion behavior of Mg-based solid fuels, and support for the increasing demands for both military and civilian applications.

The Structure of the Toronto Alexithymia Scale (TAS-20): A Meta-Analytic Confirmatory Factor Analysis.

Alexithymia is defined as the inability of persons to describe their emotional states, to identify the feelings of others, and a utilitarian type of thinking. The most popular instrument to assess alexithymia is the Toronto Alexithymia Scale (TAS-20). Despite its widespread use, an ongoing controversy pertains to its internal structure. The TAS-20 was originally constructed to capture three different factors, but several studies suggested different factor solutions, including bifactor models and models with a method factor for the reversely keyed items. The present study examined the dimensionality of the TAS-20 using summary data of 88 samples from 62 studies (total N = 69,722) with meta-analytic structural equation modeling. We found support for the originally proposed three-dimensional solution, whereas more complex models produced inconsistent factor loadings. Because a major source of misfit stems from translated versions, the results are discussed with respect to generalizations across languages and cultural contexts.

Structure and Zeatin Binding of the Peach Allergen Pru p 1.

Peach (Prunus persica) is among the fruits most frequently reported to cause food allergies. Allergic reactions commonly result from previous sensitization to the birch pollen allergen Bet v 1, followed by immunological cross-reactivity of IgE antibodies to structurally related proteins in peach. In this study, we present the three-dimensional NMR solution structure of the cross-reactive peach allergen Pru p 1 (isoform Pru p 1.0101). This 17.5 kDa protein adopts the canonical Bet v 1 fold, composed of a seven-stranded β-sheet and three α-helices enclosing an internal cavity. In Pru p 1, the inner surface of the cavity contains an array of hydroxyl-bearing amino acids surrounded by a hydrophobic patch, constituting a docking site for amphiphilic molecules. NMR-guided docking of the cytokinin molecule zeatin to the internal cavity of Pru p 1 provides a structure-based rationale for the effect that zeatin binding has on the protein’s RNase activity.

Investigating the Atomic and Mesoscale Interactions that Facilitate Spider Silk Protein Pre-Assembly.

Black widow spider dragline silk is one of nature's high-performance biological polymers, exceeding the strength and toughness of most man-made materials including high tensile steel and Kevlar. Major ampullate (Ma), or dragline silk, is primarily comprised of two spidroin proteins (Sp) stored within the Ma gland. In the native gland environment, the MaSp1 and MaSp2 proteins self-associate to form hierarchical 200-300 nm superstructures despite being intrinsically disordered proteins (IDPs). Here, dynamic light scattering (DLS), three-dimensional (3D) triple resonance solution NMR, and diffusion NMR is utilized to probe the MaSp size, molecular structure, and dynamics of these protein pre-assemblies diluted in 4 M urea and identify specific regions of the proteins important for silk protein pre-assembly. 3D NMR indicates that the Gly-Ala-Ala and Ala-Ala-Gly motifs flanking the poly(Ala) runs, which comprise the β-sheet forming domains in fibers, are perturbed by urea, suggesting that these regions may be important for silk protein pre-assembly stabilization.

The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis

This paper studies buckling problem of square nano-plates under uniform biaxial pressure through using three-dimensional nonlocal elasticity theory. Equations of stability are solved analytically for square nano-plates with simple supports using a Navier-type method. Critical buckling stress is presented for nano square plates with different thickness-length and nonlocal parameter-length ratios. The critical buckling stress is also reported using different local (classical) and nonlocal two-dimensional plate theories constructed essentially based on some simplifying assumptions. Comparison of the results of two-dimensional and three-dimensional theories for both local and nonlocal cases shows that the nonlocal two-dimensional plate theories are not as accurate as the local two-dimensional ones. This issue however reveals importance of the nonlocal three-dimensional solutions. Finally, through comparison of the numerical results with those obtained from molecular dynamic simulations, the value of the nonlocal parameter is calibrated for square graphene sheets. This parameter can be also used for the other nonlocal three-dimensional mechanical analyses of square graphene sheets to find accurate solutions.

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

NMR resonance assignments of the PR-10 allergens Act c 8 and Act d 8 from golden and green kiwifruit

Kiwifruits have become one of the most common food sources triggering allergic reactions. In patients suffering from birch pollen related food allergy, reactions result from initial sensitization to the birch (Betula verrucosa) pollen allergen Bet v 1, followed by immunological cross-reactivity to structurally homologous proteins in kiwifruit. Clinical symptoms range from scratching and itching of the oral cavity to more severe immunological reactions such as rhino conjunctivitis. In this work we assigned backbone and side chain 1H, 13C and 15N chemical shifts of the 17 kDa PR-10 allergens Act c 8.0101 and Act d 8.0101 from golden (Actinidia chinesis) and green (Actinidia deliciosa) kiwifruit by solution NMR spectroscopy. The chemical shift data confirm the characteristic Bet v 1 fold for both proteins, consisting of a seven-stranded antiparallel β-sheet interrupted by two short α-helices, along with a long C-terminal α-helix. Our data provide the basis for determining the three-dimensional solution structures of these proteins and characterizing their immunological cross-reactivity on a structural basis.

Emitter Location with Azimuth and Elevation Measurements Using a Single Aerial Platform for Electronic Support Missions.

Passive ground emitter geolocation techniques are essential to electronic warfare systems, as they provide threat warnings in hostile environments, while ensuring the electronic silence of the mission platform. Geolocation of enemy emitters indicates the position of and type of adversary troops, and allows for the use of guided munition against enemy targets. Three-dimensional geolocation solutions based on least squares and particle filter estimation, using only azimuth and elevation measurements, were considered. Three batch-processing and one instantaneous solution algorithms, i.e., using a single pulse or a single observation point, were developed and investigated. The performance of the proposed solutions was demonstrated by simulations. Results showed that the batch-processing solutions achieved acceptable accuracies with a sufficient number of observation points. The performance degraded with fewer observation points. The instantaneous geolocation solution improved performance with increasing observation points, i.e., working in the sequential mode, and therefore could approach the accuracy of the batch-processing solutions.

Hydroelastic behaviour of a submerged horizontal flexible porous structure in three-dimensions

A hydroelastic model is developed for the problem of linear wave interaction with a submerged horizontal flexible porous structure in three-dimensions. The generalized expansion formulae with orthogonal mode-coupling relations are derived by expanding Fourier cosine series in a channel width. Using eigensolutions, various aspects of hydroelastic wave behaviour in a channel with a porous plate submerged in finite water depth is investigated. Further, the usefulness of the expansion is analysed through a real physical problem of wave diffraction by a submerged flexible porous plate connected with mooting lines in three-dimensions. The accurateness of the three-dimensional solution is inspected and the hydroelastic behaviour of the submerged porous structure is analysed for oscillation modes, mooring stiffness, and porous-effect parameters on numerical assessment of reflection, dissipation coefficients, and plate displacements in different cases. The analysis of current hydroelastic behaviour will be beneficial for future design of a device for wave energy absorption in three-dimensions.

Speed limits of protein assembly with reversible membrane localization.

Protein assembly is often studied in a three-dimensional solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional surface. In a recent study, we quantified how proteins can exploit the reduced dimensionality of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent. We find that proteins can accelerate dimer formation due to an increase in relative concentration, driving more frequent collisions, which often win out over slow-downs due to diffusion. Our model contains two protein populations that dimerize with one another and use a distinct site to bind membrane lipids, creating a complex reaction network. However, by identifying two major rate-limiting pathways to reach an equilibrium steady-state, we derive an excellent approximation for the mean first passage time when lipids are in abundant supply. Our theory highlights how the "sticking rate" or effective adsorption coefficient of the membrane is central in controlling timescales. We also derive a corrected localization rate to quantify how the geometry of the system and diffusion can reduce rates of membrane localization. We validate and test our results using kinetic and particle-based reaction-diffusion simulations. Our results establish how the speed of key assembly steps can shift by orders-of-magnitude when membrane localization is possible, which is critical to understanding mechanisms used in cells.

A three-dimensional fractional solution for air contaminants dispersal in the planetary boundary layer

In this study, we investigated some closed-form solutions for solving atmospheric dispersion issues under variable atmospherical hypothesis, in a vertically positioned non-homogeneous planetary boundary-layer. In our context, a nonidentical expansion for the solution of the fractional advection-diffusion equation in a non-integer dimensional-space was examined. In a nutshell, a Sturm-Liouville eigenvalue problem with more reliable information concerning the initial value problem is discussed. The performance of the model was estimated by presenting numerical simulations against experimental data. Under these meteorological conditions, fractional-order models performed far better than those of the classical integer-order ones.

An Enhancement of the Warping Shear Functions of Refined Zigzag Theory

Abstract The paper presents an enhancement in Refined Zigzag Theory (RZT) for the analysis of multilayered composite plates. In standard RZT, the zigzag functions cannot predict the coupling effect of in-plane displacements for anisotropic multilayered plates, such as angle-ply laminates. From a computational point of view, this undesirable effect leads to a singular stiffness matrix. In this work, the local kinematic field of RZT is enhanced with the other two zigzag functions that allow the coupling effect. In order to assess the accuracy of these new zigzag functions for RZT, results obtained from bending of angle-ply laminated plates are compared with the three-dimensional exact elasticity solutions and other plate models used in the open literature. The numerical results highlight that the enhanced zigzag functions extend the range of applicability of RZT to the study of general angle-ply multilayered structures, maintaining the same seven kinematic unknowns of standard RZT.

Development of the consistent second-order plate theory for transversely isotropic plates and its analytical assessment from the three-dimensional perspective

In this paper, the consistent second-order plate theory is developed for transversely isotropic plates. It is validated against the three-dimensional elasticity theory using a well-known benchmark problem of a simply-supported rectangular plate subjected to symmetric transverse sinusoidal loading. The choice of the benchmark problem is based on the fact that it allows for an exact three-dimensional elasticity solution to be derived in closed form. In this study, a closed-form solution based on Elliot’s displacement potentials for transversely isotropic solids is specifically derived for validation purposes. Its equivalence to other closed-form analytical solutions is established. Expanding the closed-form analytical solution into a power-law series with respect to the non-dimensionalised plate thickness enables a direct term-by-term comparison with the consistent second-order plate theory solution and provides a valuable mechanism to validate the consistent plate theory for transversely isotropic plates in a purely analytical form. The term-by term comparison reveals that the first terms of the above power-law series coincide exactly with the expressions of the consistent second-order plate theory. In addition to the analytical validation, a numerical validation using the finite element method is performed. A comparative analysis of several plate theories for transversely isotropic plates demonstrates that the consistent plate theory can predict displacements and stresses in thick transversely isotropic plates with very high degree of accuracy, such that even for very thick plates with a thickness-to-length ratio of 0.5, the deviation from the three-dimensional elasticity solution is less than 1%.

Three-dimensional overall stress analysis for double-coated structure with equal coating thickness

The three-dimensional solution is derived in this article for the double-coated structure of the transversely isotropic material. The displacements and stresses are given by explicit expression, which will help researchers and designers gain insight into the impact of the properties of different coating materials on the structural performance. Numerical results show increasing the coating thickness, adjusting the elastic constants c13 and c33 of the coating material I can significantly reduce the maximum shear stress of the interface. In addition, theoretically, not only can the three-dimensional method predict the critical load and the failure area under minimum shear failure, but it also preliminary inference the bonding performance between different materials. Compared with the single-coating structure, the double-coating structure can not only accurately simulate the bonding layer between the coating and the substrate, but also improve the problem of interface stratification caused by the great difference of material properties.