Cylindrical Domain Research Articles

Structural Stability of Pseudo-Parabolic Equations for Basic Data

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data.

The hydromechanical coupled numerical method in pseudo-3D axisymmetric domain with cracks extension and coalescence applies to the decompression failure problem

The stress-strain state of the saturated porous media determines the behavior of fracturing, which defines the efficiency of developing tight oil, shale, coalbed, and thermal energy fields. Therefore, reliable hydromechanical coupled simulations with destruction reconstruction are critical.The proposed innovative simulator has a strong interrelation between fluid flow and rock deformation of porous media and realizes a fully coupled pseudo-transient numerical method by high-performance computing (HPC) tools. To increase the detail of the results in the problem, a finite difference numerical algorithm was implemented in the axisymmetric cylindrical domain, which reduces from three to two dimensions without loss of precision. Highly efficient parallelization using CUDA on the GPU computes meshes of up to one billion cells, allowing the simulation of a total core sample to sub-micrometer resolution in an appropriate time. The algorithm has been validated to find the exact solution to the cylinder problem. The proposed model accounts for cracks propagation with their coalescence within a single computational static grid, which keeps timing close to the continuous model.This comprehensive implementation enables solving industrial problems, such as modeling core sample damage during rapid decompression. High-resolution simulations help reconstruct fracture propagation, analyze the initial stress state, and identify critical damage factors. The comparison with the exact solution to the cylinder problem confirmed the reliability of the algorithm. The calculation results show a strong dependence of decompression failure on the coalescence and elongation of cracks, influenced significantly by the rock's cohesion. Microcracks length and distribution play a decisive role in the decompressive destruction behavior of the rock sample. For the first time, the simulations demonstrated the decompressive destruction of a core sample during an uncontrolled, rapid core retrieval operation.

Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains

The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection–diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Robin-type boundary condition involving convective and diffusive fluxes is imposed on the lateral surface. The limit problem for vanishing diffusion and the cylinder shrinking to an interval is a nonlinear first-order conservation law. For a time span that allows for a classical solution of this limit problem corresponding uniform pointwise and energy estimates are proven. They provide precise model error estimates with respect to the small parameter that controls the double viscosity-geometric limit. In addition, other problems with more higher Péclet numbers are also considered.

Estimations of global Mittag–Leffler bounds and synchronization for fractional-order permanent magnet synchronous motor systems

This article investigates the global Mittag-Leffler bounds (GM-LBs) and synchronization of fractional-order permanent magnet synchronous motors (FOPMSMs). To begin with, by using some appropriate generalized Lyapunov functions, the extremum principle of function and fractional differential inequalities, a few new bounds for the three-dimensional cylindrical and ellipsoidal domains and a rotatory parabolic body of FOPMSMs are estimated by utilizing the parameters in the systems, which improves the earlier studies and may conclude some new estimates. Moreover, linear feedback control strategies owning one or two inputs and fractional adaptive control owning both single input and single state are accepted to come true the global Mittag-Leffler synchronization (GM-LS) and global asymptotic synchronization (GAS) of two FOPMSMs. Some new criteria for the synchronization are acquired by utilizing some inequality approaches. Finally, the feasibility of the proposed control schemes is verified by numerical simulations.

Correctness of the mixed problem for degenerate multidimensional elliptic-parabolic equations

The initial-boundary value problem (Dirichlet problem) for general elliptic-parabolic equations of second order was first posed by G. Fichera. Further investigation of this problem was carried out in the monograph by O.A. Oleinik and E.V. Radkevich and the works by V.N. Vragov. In these works, the authors examined mixed problems for degenerate multidimensional elliptic equations. The articles by S.A. Aldashev focused on the correctness (in the sense of uniqueness of solvability) of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equations. A mixed problem for these equations has not been studied. In this paper, the authors demonstrate the uniqueness of solvability and obtain an explicit representation of the classical solution of the mixed problem for degenerate multidimensional elliptic-parabolic equations. The proposed method allows reducing the problem under study to a mixed problem for a degenerate multidimensional elliptic equation examined by S.A. Aldashev.

Scattering of elastic waves by a cluster of cylindrical inclusions: multiple scattering analysis and equivalent scatterer modeling

Abstract The two-dimensional scattering of elastic waves by a cluster of aligned circular cylindrical elastic inclusions embedded in a circular cylindrical domain of an infinitely extended elastic medium is analysed numerically. The analysis is based on a semi-analytical method where the scattered waves are expressed as the eigenfunction expansions of the time-harmonic displacement potentials and the expansion coefficients are determined by a numerical collocation technique. The wave fields within and around the cluster are demonstrated for different spatial arrangements of inclusions in the cluster. It is also examined if the scattering characteristics of the cluster can be simulated by a single equivalent scatterer which has the effective homogenized properties of the matrix/inclusion composite. As a result, it is shown that for sufficiently small inclusion radius-wavelength ratios, the scattering characteristics of the cluster are relatively insensitive to the spatial inclusion arrangements therein, and can be reasonably simulated by those of the equivalent scatterer.

Lp(Lq)-Maximal Regularity for Damped Equations in a Cylindrical Domain

Lp(Lq)-Maximal Regularity for Damped Equations in a Cylindrical Domain

Prandtl–Batchelor Flow in a Cylindrical Domain

Prandtl–Batchelor Flow in a Cylindrical Domain

Nearly Ideal Random Tiling with Dodecagonal Symmetry from Pentablock Quarterpolymers of the AB1CB2D Type.

Two-dimensional tiling manners as cross-sectional views of cylindrical domain assembly formed by pentablock quarterpolymers of the AB1CB2D type in bulk were investigated. Several binary and ternary blends from three mother polymers having different ϕB1/ϕB2 ratios (ϕB1 and ϕB2 are the volume fractions of the B1 and B2 blocks, respectively) represent nonperiodic but ordered triangle/square tilings, where the N3/N4 ratios (N3 and N4 are the numbers of triangles and squares in the observed area, respectively) are all close enough to the theoretical value of 4/√3 ≑ 2.31 for the dodecagonal quasicrystalline (DDQC) state, irrespective of the total number of polygons. The TEM images, having almost the same N3/N4 ratios, were proved to show 4- and 6-fold symmetries in terms of the angular appearance of equilateral polygon sides via image analyses. Among them, a ternary blend showed a nearly ideal random tiling pattern that is almost equivalent to the theoretically predicted tiling by SCFT. Moreover, the magnitude of phason strain estimated for a TEM image from the ternary blend was proved to be quite small when the observing area is narrow, while it deviates from the ideal quasicrystalline tiling with an increasing number of vertices in the observing area.

WUSCHEL-RELATED HOMEOBOX genes are crucial for normal vascular organization and wood formation in poplar

Vascular cambium in tree species is a cylindrical domain of meristematic cells that are responsible for producing secondary xylem (also called wood) inward and secondary phloem outward. The poplar (Populus trichocarpa) WUSCHEL (WUS)-RELATED HOMEOBOX (WOX) family members, PtrWUSa and PtrWOX13b, were previously shown to be expressed in vascular cambium and differentiating xylem cells in poplar stems, but their functions remain unknown. Here, we investigated roles of PtrWUSa, PtrWOX13b and their close homologs in vascular organization and wood formation. Expression analysis showed that like PtrWUSa and PtrWOX13b, their close homologs, PtrWUSb, PtrWUS4a/b and PtrWOX13a/c, were also expressed in vascular cambium and differentiating xylem cells in poplar stems. PtrWUSa also exhibited a high level of expression in developing phloem fibers. Expression of PtrWUSa fused with the dominant EAR repression domain (PtrWUSa-DR) in transgenic poplar caused retarded growth of plants with twisted stems and curled leaves and a severe disruption of vascular organization. In PtrWUSa-DR stems, a drastic proliferation of cells occurred in the phloem region between vascular cambium and phloem fibers and they formed islands of ectopic vascular tissues or phloem fiber-like sclerenchyma cells. A similar proliferation of cells was also observed in PtrWUSa-DR leaf petioles and midveins. On the other hand, overexpression of PtrWOX4a-DR caused ectopic formation of vascular bundles in the cortical region, and overexpression of PtrWOX13a-DR and PtrWOX13b-DR led to a reduction in wood formation without affecting vascular organization in transgenic poplar plants. Together, these findings indicate crucial roles of PtrWUSa and PtrWOX13a/b in regulating vascular organization and wood formation, which furthers our understanding of the functions of WOX genes in regulating vascular cambium activity in tree species.

Local solutions for nonhomogeneous Navier–Stokes equations with large flux

The local existence of solutions to nonhomogeneous Navier–Stokes equations in cylindrical domains with arbitrary large flux is demonstrated. The existence is proved by the method of successive approximations. To show the existence with the lowest possible regularity the special Besov spaces called the Sobolev–Slobodetskii spaces are used. The inflow and outflow are prescribed on the parts of the boundary which are perpendicular to the ‐axis. Since the inflow and outflow are positive the crucial point of this paper is to verify that ‐coordinate of velocity is also positive. Finally, we conclude the local existence such that the velocity belongs to , the gradient of pressure to and the density to , where .

The Role of Slip Velocity in Fractional MHD Casson Fluid Flow within Porous Cylinder

Numerous academics are intrigued by exploring the fractional Casson fluid model due to its enhanced precision compared to the traditional fluid model. However, many researchers have successfully tackled the analytical solution for the fractional fluid model while overlooking the impact of boundary slip. Hence, this study aims to tackle the challenge of describing the Casson fluid behaviour with fractional properties in a cylindrical domain, considering the influence of slip velocity at the boundaries. Furthermore, magnetohydrodynamics (MHD) had been introduced into the analysis and considered a porous medium resembling a blood clot or fatty plaque. The Caputo-Fabrizio fractional derivative is employed to establish the dimensionless governing equation. Subsequently, we solve it analytically using the Laplace transform in conjunction with finite Hankel transform techniques. A thorough examination follows the graphical presentation of the analytical solution in the context of relevant parameters. The findings illustrate those higher values of the Casson parameter, slip velocity parameter, Darcy number, and fractional parameter lead to an augmentation in fluid velocity. Conversely, an escalation in magnetic parameters causes a reduction in fluid velocity. These findings can be utilized to validate the accuracy of numerical results. The findings of this study hold considerable importance in enhancing our understanding of human blood flow, especially in scenarios where a velocity gradient occurs between blood particles and the stretching motion of arteries.

Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction

The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the cylindrical domains tends to infinity. This generalises an earlier work of Chipot et al. (Asymptot. Anal. 85(3–4) (2013) 199–227) where the linear case p = 2 is studied. Asymptotic behavior of all the higher eigenvalues of the linear case and the second eigenvalues of general case (using topological degree) for such problems is also studied.

On the solvability of a boundary value problem for a two-dimensional system of Navier-Stokes equations in a cone

Due to the fact that the Navier-Stokes equations are involved in the formulation of a large number of interesting problems that are important from an applied point of view, these equations have been the object of attention of mechanics, mathematicians and other scientists for several decades in a row. But despite this, many problems for the Navier-Stokes equation remain unexplored to this day. In this work, we are exploring the solvability of a boundary value problem for a two-dimensional Navier-Stokes system in a non-cylindrical degenerating domain, namely, in a cone with its vertex at the origin. Previously, we studied cases of the linearized Navier-Stokes system or non-degenerating cylindrical domains, so this work is a logical continuation of our previous research in this direction. To the above-mentioned degenerate domain we associate a family of non-degenerate truncated cones, which, in turn, are formed by a oneto-one transformation into cylindrical domains, where for the problem under consideration we established uniform a priori estimates with respect to changes in the index of the domains. Further, using a priori estimates and the Faedo-Galerkin method, we established the existence, uniqueness of solution in Sobolev classes, and its regularity as the smoothness of the given functions increases.

Effect of Finite Thermal Conductivity Bounding Walls on Darcy–Bénard Convection

Abstract Natural convection in fluid-saturated, horizontal porous-media is quintessential to many applications like geothermal reservoirs and solar thermal storage systems. Researchers have dedicated substantial effort over the years in pursuit of altering natural convection within a horizontal porous-media (Darcy–Bénard) system. Although significant research efforts have been directed toward understanding the effects of bounding walls in horizontal (Rayleigh–Bénard) convection systems, similar investigations for Darcy–Bénard convection systems are still lacking. Therefore, this study examines the effect of thermal properties of horizontal bounding plates on porous-media Nusselt number at high Rayleigh–Darcy numbers (105−107). Numerical simulations are performed by employing Darcy–Forchheimer model within a three-dimensional cylindrical computational domain to emulate Darcy–Bénard systems for two aspect ratios (1 and 2) and six different plate materials having nondimensional plate thicknesses of 0.02, 0.08, and 0.16. Polypropylene and compressed CO2 gas are chosen as solid and fluid phases for the porous media, respectively, that encompass a range of Darcy numbers (10−6−10−3). Findings reveal that when the ratio of thermal resistances of porous layer and plates falls below 4.61, the corrected Nusselt number deviates by more than 10% from the corresponding ideal Nusselt number with infinitely conducting bounding plates. The study also proposes a correction factor to estimate this deviation, which shows a good agreement with numerical results.

Existence of bounded solutions of fully nonlinear elliptic equations modeling the first passage time in cylindrical domains

Existence of bounded solutions of fully nonlinear elliptic equations modeling the first passage time in cylindrical domains

Effects of sidewall thermal condition on the formation of poloidal circulation in rotating three-dimensional convection

Axisymmetric and three-dimensional (3 D) simulations of natural convective flows in a Boussinesq fluid contained inside a shallow rotating cylindrical domain are conducted. There is a constant and uniform heat flux into the domain from the bottom boundary. The simulation results are analyzed to shed light on the role of sidewall thermal boundary conditions on formation of poloidal circulation. Insulated sidewall (3 D-ISW) and conducting sidewall (3 D-CSW) conditions are used for both 3 D and axisymmetric calculations. The axisymmetric results show that the flow spins up rapidly, forming poloidal circulation when the heat flux (related to Rayleigh number, Ra) and rotation rate (related to Ekman number, E) are chosen carefully, which is consistent with past studies. For given values of these two parameters, the poloidal circulation is observed in 3 D-CSW but not for 3 D-ISW. A retrograde wave rotating faster near the center compared to the periphery inhibits the formation of poloidal circulation in 3 D-ISW cases, and the flow is made of depth invariant vertical convective rolls. Furthermore, the poloidal circulation forms under 3 D-CSW condition only when the global Rossby number is Ro≃C/ε, where C is a constant, and this is observed empirically over the range of parameters considered for this study with an aspect ratio of ε for the computational domain. Hence, features like cyclone eye and eyewall are not always observed in 3 D-CSW cases over the range of Ra and E yielding these features in axisymmetric calculations. Thus, the formation of poloidal circulation in 3 D domain may have stringent dynamical constraints compared to the axisymmetric model.

Experimental investigation of thermal performance of vertical multitube cylindrical latent heat thermal energy storage systems

The multitube design in the shell-and-tube type latent heat thermal energy storage (LHTES) system has received intensive attention due to its promising benefits in enhancing heat storage efficiency. In this paper, single and multi-tube shell LHTES systems were experimentally investigated. First, this study experimentally compared the thermal characteristics between a multiple-tube heat exchanger (MTHX) and a single-tube heat exchanger (STHX). The STHX’s geometrical parameters coincided with a virtual cylindrical domain in the MTHX, being similar to the single-tube model formulated by simplifying the numerical solution to investigate the MTHX. The experimental data was then used to validate the simplified numerical model commonly used in the literature that converted the multi-tube problem to a single-tube model by formulating a virtual cylindrical domain for each tube in the MTHX system. The results showed that there was a noticeable difference in the thermal characteristics between the actual STHX and the virtual cylindrical STHX domain in the MTHX system. The comparison indicated that the simplified numerical model could not accurately reflect the thermal performance of the MTHX system. An experimental study or three-dimensional numerical modelling was required for the thermal analysis of the multi-tube problems. Second, the effect of tube number in the MTHX was experimentally investigated. It was found that an increase in tube number boosted both charging and discharging rates without inhibiting the natural convection. The five-tube configuration decreased the total charging and discharging duration by 50% compared to the two-tube one. Finally, the effect of heat transfer fluid (HTF) operating parameters on the system performance was evaluated on the five-tube MTHX system. The results revealed that the adoption of higher HTF temperature considerably improved the charging performance. The charging time decreased by up to 41% with the HTF temperature increasing from 70 to 80 °C. Meanwhile, a variation in the HTF flow rate from 5 to 20 L/min showed a more pronounced influence on charging than on discharging due to the different dominant heat transfer mechanisms.

Reaction-induced morphological transitions in a blend of diblock copolymers and reactive monomers: dissipative particle dynamics simulation.

The dissipative particle dynamics (DPD) method is applied to the morphological transitions of microphase-separated domains in a mixture of symmetric AB-diblock copolymers and reactive C-monomers, where polymerization and cross-linking reactions take place among C-monomers. The initial structure for the DPD simulation is an equilibrated cylindrical domain structure prepared by the density-biased Monte Carlo method with density profiles obtained from the self-consistent field theory. By introducing a cross-linking reaction among reactive C-monomers, we confirmed that the DPD simulation reproduces the morphological transitions observed in experiments, where the domain morphology changes due to segregation between A-blocks of diblock copolymers and cross-linking networks of C-monomers. When the cross-linking reaction of C-monomers is sufficiently fast compared to the deformation of the domains, the initial cylindrical domains are preserved, while the distance between the domains increases. On the other hand, when the formation of the cross-linking network is slow, the domains can deform and reconnect with each other in the developing cross-linking network. In this case, we observe morphological transitions from the initial domain morphology with a large-curvature interface to another domain morphology with a smaller-curvature interface, such as the transition from the cylindrical phase to the lamellar phase. We calculated the spatial correlations in the microphase-separated domains and found that such correlations are affected by the speed of the formation of the cross-linking network depending on whether the bridging between microphase-separated domains occurs in a nucleation and growth process or in a spinodal decomposition process.

On an approximate solution to an ill-posed mixed boundary value problem for the Laplace equation in a cylindrical domain with homogeneous conditions of the second kind on the lateral surface of the cylinder

On an approximate solution to an ill-posed mixed boundary value problem for the Laplace equation in a cylindrical domain with homogeneous conditions of the second kind on the lateral surface of the cylinder