Dimensional Boundary Research Articles

Three Dimensional Boundary Layer Flow of MHD Maxwell Nanofluid over a Non-Linearly Stretching Sheet with Nonlinear Thermal Radiation

Three Dimensional Boundary Layer Flow of MHD Maxwell Nanofluid over a Non-Linearly Stretching Sheet with Nonlinear Thermal Radiation

Nonlinear Imaging of Nanoscale Topological Corner States.

Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are insensitive to certain types of perturbations, thus naturally enhancing robustness of photonic circuitries. Conventionally, the N-dimensional bulk modes correspond to (N - 1)-dimensional boundary states. The higher-order bulk-boundary correspondence relates N-dimensional bulk to boundary states with dimensionality reduced by more than 1. A special interest lies in miniaturization of such higher-order topological states to the nanoscale. Here, we realize nanoscale topological corner states in metasurfaces with C6-symmetric honeycomb lattices. We directly observe nanoscale topology-empowered edge and corner localizations of light and enhancement of light-matter interactions via a nonlinear imaging technique. Control of light at the nanoscale empowered by topology may facilitate miniaturization and on-chip integration of classical and quantum photonic devices.

Chiral massive news: null boundary symmetries in topologically massive gravity

We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg ⊕ Virasoro algebra with a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.

Geometric model of the fracture as a manifold immersed in porous media

In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing fractures with complex geometries. We model the coupled fracture-porous media system where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside the fracture. We develop a model to examine the flow inside fractures with complex geometries and variable thickness on a Riemannian manifold. The fracture is represented as the normal variation of a surface immersed in R3. Using operators of Laplace–Beltrami type and geometric identities, we model an equation that describes the flow in the fracture. A reduced model is obtained as a low dimensional boundary value problem. We then couple the model with the porous media. Theoretical and numerical analyses have been performed to compare the solutions between the original geometric model and the reduced model in reservoirs containing fractures with complex geometries. We prove that the two solutions are close and, therefore, the reduced model can be effectively used in large scale simulators for long and thin fractures with complicated geometry.

On elliptic problems in domains with low dimensional boundaries

We study a solvability for some concrete boundary value problems in domains with a low dimensional boundary. Such boundaries are considered as a limit situation of a volume problem for which one or more parameters of a domain tend to their endpoint values. The solvability conditions in Sobolev-Slobodetskii spaces are given using the wave factorization concept for an alliptic symbol..

Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces

Higher-order topological phases (HOTPs) are systems with topologically protected in-gap boundary states localized at their (d-n)-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the so-called band inversion surfaces (BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra (a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.

Viscous Dissipation and Heat Transfer Effect on MHD Boundary Layer flow past a Wedge of Nano fluid Embedded in a Porous media

In this investigation the steady of laminar magnetohydrodynamic(MHD) heat and mass transfer two dimensional boundary layer nanofluid flow past a wedge embedded in a porous media in the availability of the viscous dissipation, thermophoresis and Brownian motion effects are taken into account. With the assistance of the similarity transformation, the governing partial differential equations (PDE) are transformed into nonlinear ordinary differential equations (ODE). The solution of the problem is solved numerically by using the MATLAB in built package solver bvp4c. The method's accuracy is examined against recently discussed results and outstanding agreement was reached. The impacts of the pertinent flow parameters are examined through graphs and tabular form.

Birational geometry of moduli spaces of configurations of points on the line

In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient $(\mathbb{P}^1)^n//PGL(2)$, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the Hilbert polynomial of $(\mathbb{P}^1)^n//PGL(2)$ in its natural embedding, and its group of automorphisms.

A Note on the Three Dimensional Dirac Operator with Zigzag Type Boundary Conditions

In this note the three dimensional Dirac operator A_m with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that A_m is self-adjoint in L^2(Omega ;{mathbb {C}}^4) for any open set Omega subset {mathbb {R}}^3 and its spectrum is described explicitly in terms of the spectrum of the Dirichlet Laplacian in Omega . In particular, whenever the spectrum of the Dirichlet Laplacian is purely discrete, then also the spectrum of A_m consists of discrete eigenvalues that accumulate at pm infty and one additional eigenvalue of infinite multiplicity.

Singular matrices arising in the MFS from certain boundary and pseudo-boundary symmetries

We consider the application of the method of fundamental solutions (MFS) to certain two–dimensional second order boundary value problems (BVPs). We assume that the domain of the problem under consideration is a regular polygon and that the sources in the MFS are placed uniformly on a circle concentric to and surrounding the polygon. For certain uniform distributions of the collocation points we prove that, for general classes of regular polygons, the MFS discretization leads to singular coefficient matrices.

Floquet second-order topological insulators in non-Hermitian systems

Second-order topological insulator (SOTI) is featured with the presence of $(d-2)$-dimensional boundary states in $d$-dimension systems. The non-Hermiticity induced breakdown of bulk-boundary correspondence (BBC) and the periodic driving on systems generally obscure the description of non-Hermitian SOTI. To prompt the applications of SOTIs, we explore the role of periodic driving in controllably creating exotic non-Hermitian SOTIs both for 2D and 3D systems. A scheme to retrieve the BBC and a complete description to SOTIs via the bulk topology of such nonequilibrium systems are proposed. It is found that rich exotic non-Hermitian SOTIs with a widely tunable number of 2D corner states and 3D hinge states and a coexistence of the first- and second-order topological insulators are induced by the periodic driving. Enriching the family of topological phases, our result may inspire the exploration to apply SOTIs via tuning the number of corner/hinge states by the periodic driving.

Carleson perturbations of elliptic operators on domains with low dimensional boundaries

We prove an analogue of a perturbation result for the Dirichlet problem of divergence form elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators of David, Feneuil and Mayboroda, which were developed to study geometric and analytic properties of sets with boundaries whose co-dimension is higher than 1. These operators are of the form −divA∇, where A is a weighted elliptic matrix crafted to weigh the distance to the high co-dimension boundary in a way that allows for the nourishment of an elliptic PDE theory. When this boundary is a d-Alhfors-David regular set in Rn with d∈[1,n−1) and n≥3, we prove that the membership of the harmonic measure in A∞ is preserved under Carleson measure perturbations of the matrix of coefficients, yielding in turn that the Lp-solvability of the Dirichlet problem is also stable under these perturbations (with possibly different p). If the Carleson measure perturbations are suitably small, we establish solvability of the Dirichlet problem in the same Lp space. One of the corollaries of our results together with a previous result of David, Engelstein and Mayboroda, is that, given any d-ADR boundary Γ with d∈[1,n−2), n≥3, there is a family of degenerate operators of the form described above whose harmonic measure is absolutely continuous with respect to the d-dimensional Hausdorff measure on Γ.

Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

Abstract Given n distinct points $\mathbf {x}_1, \ldots , \mathbf {x}_n$ in $\mathbb {R}^d$ , let K denote their convex hull, which we assume to be d-dimensional, and $B = \partial K $ its $(d-1)$ -dimensional boundary. We construct an explicit, easily computable one-parameter family of continuous maps $\mathbf {f}_{\varepsilon } \colon \mathbb {S}^{d-1} \to K$ which, for $\varepsilon> 0$ , are defined on the $(d-1)$ -dimensional sphere, and whose images $\mathbf {f}_{\varepsilon }({\mathbb {S}^{d-1}})$ are codimension $1$ submanifolds contained in the interior of K. Moreover, as the parameter $\varepsilon $ goes to $0^+$ , the images $\mathbf {f}_{\varepsilon } ({\mathbb {S}^{d-1}})$ converge, as sets, to the boundary B of the convex hull. We prove this theorem using techniques from convex geometry of (spherical) polytopes and set-valued homology. We further establish an interesting relationship with the Gauss map of the polytope B, appropriately defined. Several computer plots illustrating these results are included.

Stress state of an elastic rectangular domain under steady load

The dynamic elasticity problem for rectangular domain is presented at this paper. The conditions of ideal contact are given at the lateral sides and bottom edge of the domain; the upper edge is loaded by normal stress. Problem is formulated as the boundary value problem in steady-state case. It was necessary to find the wave field of the rectangular domain. The Fourier transform was applied to formulated problem and reduced it to one dimensional vector boundary problem. The last one was solved with the method based on matrix differential calculations which was successfully applied earlier to solve the analogous static problem Pozhylenkov O. V. (2019). According to this procedure of the solving the exact solution of the vector boundary problem was constructed in transform domain in the explicit form. Application of the inverse Fourier transform finalized the deriving of the stated problem solution. The analyses of wave field of rectangular domain depending on different load types, frequency values and domain size was done.

Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

<abstract> This paper studies the existence and uniqueness of solutions of a non local initial boundary value problem of a singular two dimensional nonlinear fractional order partial differential equation involving the Caputo fractional derivative by employing the functional analysis. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of obtaining the a priori bound relies on the construction of a suitable multiplicator. From the resulted a priori estimate, we can establish the solvability of the associated linear problem. Then, by applying an iterative process based on the obtained results for the associated linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the considered nonlinear problem. </abstract>

DEFECT FUNCTION MODELS FOR THE WAVE BOUNDARY LAYERS

The boundary layer flow induced by surface waves has been extensively investigated due to its significance in engineering applications such as sediment transport and hydrodynamic forces on subsea structures. Several forms of defect functions (referred to as DF hereafter) were developed in the past decades, e.g. Sleath (1970, 1982), Nielsen (1985, 2016) and etc., due to their good efficiency in the description of the velocity distribution in one dimensional wave boundary layer (WBL). In this work, two forms of DFs are proposed: (i) DF-I describes the velocity distributions and bottom shear stresses in phase space with 4 model parameters; (ii) DF-II describes the maximum WBL profile with 3 model parameters. A number of datasets to support the validation of the DFs were obtained through experimental and numerical tests. Two sets of experiments were conducted individually in a free-surface-wave flume located in Dalian University of Technology and an oscillating-flow flume located in the University of Western Australia. For the free surface wave tests, the velocity was measured.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/RK-z0Q8rTjk

Particle-Scale Reduction Analysis of CuFeMnO4 with Hydrogen for Chemical Looping Combustion

In this work, CuFeMnO4 (copper iron manganese oxide) oxygen carrier was characterized using differential scanning calorimetry/thermogravimetric analysis (TGA), in situ X-ray diffraction, and scanning electron microscopy–energy dispersive X-ray spectroscopy (EDS) to gain a clear elucidation of the chemical looping combustion reactions with H2 which is a component of synthesis gas. A reaction model which best described the experimental TGA reaction data was selected from the analysis. Intrinsic rate of reaction parameters obtained from the study could be used for designing a reactor for scale-up. A model with combined contributions from nucleation and growth model and dimensional phase boundary model was found to exhibit the best correlation with the experimental data. The analysis provided validation of intrinsic reaction rates and other rate parameters.

Thermal transport of bio-convection flow of micropolar nanofluid with motile microorganisms and velocity slip effects

The motivation of current research is to explore thermo-bioconvection micropolar liquid flow subject to motile microorganisms and nanomaterials. Rheological model characteristics of Maxwell viscoelasticity-based micropolar nanoliquid are considered for analysis. Slip mechanisms and stratification phenomenon are accounted. Heat and concentration diffusions are characterized by exploiting the Cattaneo-Christov fluxes for heat and mass. Aspects of thermophoresis, thermal radiation and Brownian motion are also accounted. The dimensional non-linear boundary value problems are rendered into the dimensionless ODE’s by utilizing admissible transformations and then tackled numerically by utilizing bvp4c technique via computational commercial software MATLAB. Significance of sundry variables against velocity, temperature, concentration of nanoparticles and microorganism’s concentration are described through graphs and numeric data.

Combining the 2.5D FE-BE method and the TMM method to study the vibro-acoustics of acoustically treated rib-stiffened panels

This paper is concerned with the prediction of the vibro-acoustic behavior of rib-stiffened panels treated with multiple layers of porous materials. The acoustically treated rib-stiffened panels are assumed to be uniform and infinitely long in one direction (the longitudinal direction) but the cross-section can have an arbitrary and often complicated shape. Although the two-and-half dimensional structural finite element method (2.5D FEM) and the two-and-half dimensional acoustic boundary element method (2.5D BEM) may be combined to perform the vibro-acoustic prediction, the presence of the multiple layers of acoustic treatment often makes the prediction too time-consuming. More efficient methods are required for such structures and the aim of this paper is to propose such a method. The rib-stiffened panel and the fluid domain containing the incident and reflected sound waves are modelled using 2.5D FEM-BEM while the acoustic treatment layer and the fluid domain containing the transmitted sound waves are dealt with, approximately, using the transfer matrix method (TMM). The coupling of TMM and 2.5D FEM-BEM is formulated in detail. Since the acoustically treated panel is assumed to be flat and baffled, the 2.5D BEM is based on the Rayleigh integral in the wavenumber domain. Meanwhile, the TMM is based on a two-dimensional Fourier transform which implies that the porous layers also extend to cover the baffle; the validity of this assumption is explored. The accuracy and efficiency of the method is compared with a full 2.5D FE-BE method for a homogeneous plate with attached layers of absorbent material. It is shown that the method proposed in this paper can reduce calculation time by about a factor of three compared with the full 2.5D FE-BE method. The proposed method is then applied to study the sound transmission loss (STL) of a typical rib-stiffened panel from a train carriage which is acoustically treated with different porous material layers, demonstrating that the design of the acoustic treatment can have a significant effect on the STL of the panel.

Numerical Solutions for Convective Boundary Layer Flow of Micropolar Jeffrey Fluid with Prescribe Wall Temperature

The steady two dimensional convective boundary layer flow of micropolar Jeffrey fluid past a permeable stretching sheet is studied in this paper. The governing boundary layer equation in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effects of Prandtl number, Deborah number, and material parameter with the boundary condition for microrotation, n = 0 (strong concentration of microelements) on the velocity, microrotation, temperature profiles as well as the skin friction and heat transfer coefficients are presented and discussed. An excellent agreement is observed between the present and earlier published results for some special cases. The results revealed that, the effect of Deborah number and stretching parameter are increased the heat transfer coefficient while the opposite trend is observed for the effects of material and velocity slip parameters. It was also observed that, the values of skin friction increased with the increment on the values of all studied parameters.