Cylindrical Boundary Conditions Research Articles

Dynamics of cylindrical crevice microbubbles

Microbubbles are theorized to form in crevices on mineralizations causing twinkling, a rapid color shift observed when imaging hard mineralizations with Doppler ultrasound. While the classic Rayleigh–Plesset equation and subsequent modifications describe bubble dynamics in a free field, they do not account for crevice boundaries. In this study, cylindrical boundary conditions were incorporated into the derivation of the Rayleigh–Plesset equation and validated experimentally. Cylindrical crevices with diameters ranging from 0.08–1.2 μm and depths of 1 μm were etched into a silicon wafer. Bubbles that formed in these crevices were photographed at high-speed through an inverted microscope while being driven with ultrasound at 0.75, 2.5, and 5 MHz. Experimentally, for all tested crevice sizes, the bubbles did not visibly grow. In contrast, computational results using standard water surface tension (72.5 mN/m) predicted the bubbles should grow ∼6 mm. However, when applying a higher surface tension that was measured on the silicon-water interface (∼3000 mN/m), the bubbles were only predicted to grow ∼1 nm, supporting the experimental findings. These results offer insight into the mechanism causing twinkling and provides avenues for future investigation into the effect of crevice size and shape on twinkling. [Work supported by NSF CAREER 1943937 and GRFP DGE1255832.]

Ternary Unitary Quantum Lattice Models and Circuits in 2+1 Dimensions.

We extend the concept of dual unitary quantum gates introduced in Phys. Rev. Lett. 123, 210601 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.210601 to quantum lattice models in 2+1 dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as building blocks of lattice models with periodic boundary conditions in time and space (corresponding to infinite temperature states), dynamical correlation functions exhibit a light ray structure. We also generalize solvable matrix product states introduced in Phys. Rev. B 101, 094304 (2020)PRBMDO2469-995010.1103/PhysRevB.101.094304 to two spatial dimensions with cylindrical boundary conditions, by showing that the analogous solvable projected entangled pair states can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out. We delineate and implement a numerical algorithm for computing such correlations by contracting the remaining tensors.

Estimation of Heat Diffusion in Human Tissue at Adverse Temperatures Using the Cylindrical Form of Bioheat Equation

Background: The assessment of the evolution or fall of the temperature distribution of all biological tissues, and particularly human in vivo tissues at adverse temperatures, is crucial because excess cold or heat can impair the human body and its physiological processes. However, this estimation through experimental investigations is challenging due to the ability of the human body to bear a wide range of unfavourable temperatures. Thus, it becomes imperative to frame a mathematical model and its solution for the measurement of the temperature distribution in the selected tissue. Method: The three-dimensional cylindrical bioheat equation, with initial and boundary conditions, was used to formulate a mathematical model. The model was solved using the variables-separable method. Results: The model was solved analytically, and MATLAB software was used for numerical calculations and a graphical representation. The model was applied to display the temperature distributions in human skin and in the head. Conclusions: The paper helps predict the distribution of heat and corresponding burn or cold injuries in human tissue well in advance of applying any thermal treatment such as targeted tumour hyperthermia or cryosurgery.

Simulation of sound propagation and calculation of its velocity in spherical and superellipsoidal particle systems

Discrete element method is used to simulate sound propagation in spherical and superellipsoidal particle systems and calculate the sound velocities under different boundary and stress conditions. Compressional and shear wave velocities at different axial and confining pressures for a conventional triaxial compressed spherical particle system under cylindrical boundary condition are calculated through time-of-flight method and analyzed using stiffness, effective medium theory (EMT), and granular solid hydrodynamics (GSH) theory. Results obtained through the time-of-flight method for a system under fixed boundary condition are consistent with the existing experimental results. The system stiffness calculated by branch vector and contact force can explain the variation of sound velocity with axial stress and confining pressure. For compressional velocities, the simulation results of spherical particle system at different axial stresses under isotropic compression in radial direction are consistent with the theoretical results provided by EMT and GSH theories. Compared with compressional velocities, shear velocities predicted by EMT are bigger than experiments, and shear modulus of theories improving upon EMT gives velocities in accordance with experiment. Moreover, the sound velocities of spherical and superellipsoidal particle systems are calculated under the same boundary and normal stress conditions to investigate the influence of particle shape on the sound velocity. The difference between compressional wave velocities in spherical and superellipsoidal particle systems is evident and is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The proposed methods of sound propagation simulation and sound velocity calculation can be used to investigate the elastic wave propagation in particle system, and can obtain the microscopic quantities that are difficult to obtain experimentally and theoretically. They can provide references for the study of EMT and GSH theories and further discuss the influence of shape-induced anisotropy on sound velocity.

Similarity solution of two-phase cylindrical Stefan solidification problem

The mathematical model of determining temperature fields in cylindrical domain with solidification process is represented. The solidification process of cylinder due to cooling is constructed by two-phase cylindrical Stefan problem for liquid and solid zones with freezing interface. Respect to strength of the heat sink at the center of cylindrical material boundary condition  is an important to determine temperature in solid domain. The analytical solution of the problem is introduced with method of similarity principle which enables us to reduce free boundary problem to ordinary differential equations. Temperature solutions of solid and liquid zones are represented by special function which called exponential integral equation. The free boundary at freezing interface and temperatures at two phases are determined. Lemmas about exponential integral functions are introduced and used to prove that obtained operator function is contraction operator. Upper boundness of the exponential integral function is checked graphically. It is shown that existence of uniqueness of solution exists.

A dynamic shell model for diagnostics of rotating machinery under periodic excitation

In this paper, a generalized dynamic model of a shell structure has been developed and utilized for diagnostics purposes. The dynamic model is three-dimensional, includes the effects of rotary inertia and shear deformation, and can handle moving loads in radial, tangential and axial directions. The model is utilized to determine in-plane radial displacements of the shell structure under concentrated radial loads for different boundary conditions. The periodic loads are constructed using harmonics obtained through the Fourier series expansion method. The modal expansion technique is implemented for calculation of the steady state forced response of the shell structure. A simplified acoustic radiation model is also implemented in conjunction with the dynamic shell model to predict the noise radiated from a rotating circular cylindrical shell structure under different kinematic, loading and boundary conditions. Moreover, forced vibration response and acoustic radiation predicted will be employed to reveal patterns in the signals that can potentially be used for diagnostics of rotating machinery applications. The shell model is derived using a comprehensive approach and thus can be used to model prevalent engineering applications ranging from electric motors to gears and bearings.

On the dynamics of rotating matrix cracked FG-GPLRC cylindrical shells via the element-free IMLS-Ritz method

Rotating cylindrical shells have been widely used in rotating machinery. The vibration characteristics of rotating composite cylindrical shells have a significant influence on the rotor dynamics. This paper provides a useful approach for the vibration analysis of a rotating functionally graded (FG) graphene nanoplatelets (GPLs) reinforced composite (GPLRC) cylindrical shell with matrix cracks. GPLs and matrix cracks are distributed in multilayer FG-GPLRC shells. The modified Halpin-Tsai model and self-consistent model are employed to determine the effective materials properties and stiffness degradation of the composite shell. The energy functional of rotating FG-GPLRC cylindrical shells are obtained using the first-order shear deformation theory (FSDT). Based on the improved moving least-squares Ritz (IMLS-Ritz) approximation, the discrete vibration equations of rotating FG-GPLRC cylindrical shells are derived. The accuracy of the IMLS-Ritz results is examined by comparing the natural frequencies with those presented in the previously published papers. Then the effects of crack density parameter, rotating speed, GPLs parameters, weight fraction, size and geometry, as well as the geometry of the cylindrical shell and boundary conditions on the critical rotating speed and natural frequency are examined comprehensively.

Mott transition and magnetism in a fragile topological insulator

We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of strong correlations, such as the Mott-insulator transition and magnetism, on a known model hosting fragile topology. We show that in the nonmagnetic case, fragile topology, along with the twisted boundary states, is stable with interactions below a critical interaction strength. Above this interaction strength, a transition to the Mott insulating phase occurs, and the twisted boundary states disappear. Furthermore, by applying a homogeneous magnetic field, the fragile topology is destroyed. However, we show that a magnetic field can induce a topological phase transition which converts a fragile topological insulator to a Chern insulator. Finally, we study ferromagnetic solutions of the fragile topological model.

Gaussian beam scattering by an infinite cylinder with a spherical inclusion

An analytical method of analyzing the electromagnetic scattering of a Gaussian beam by an infinitely long circular cylinder with a spherical inclusion is presented. The fields within different regions are expanded in terms of appropriate cylindrical or spherical vector wave functions. By applying the integral representation of spherical vector wave functions over cylindrical ones, boundary conditions and projection procedure, the unknown expansion coefficients are determined. For a localized beam model, numerical results of the total scattered field and normalized field intensity distribution are shown, and the scattering properties are discussed briefly.

Low-velocity impact response of sandwich cylindrical panels with nanotube-reinforced and metal face sheet in thermal environment

ABSTRACTEmploying an analytical method, non-linear low-velocity impact response of carbon nanotube (CNT)-reinforced sandwich cylindrical panels in thermal environments is analysed. Two types of core (i.e. homogenous and functionally graded) are considered for sandwich panels. The face sheets of sandwich panels are multi-layer which consist of CNT-reinforced composite (CNTRC) and metal layers. Micromechanical models are used to estimate the material properties of CNTRCs. A higher-order shear deformation theory with a von Kármán-type of kinematic non-linearity provides the equations of motion. Temperature-dependent material properties are used to include the thermal effects. The equations of motion are solved using a two-step perturbation technique. Existing numerical results in the literature are used to validate the present method. The effect of nanotube volume fraction, material property gradient, impactor initial velocity, geometrical parameters of cylindrical panel, temperature change and edge boundary condition on the impact response of cylindrical panel structures is discussed. The quantitative results and analytical formulations can be helpful in better designing of CNTRC structures subjected to low-velocity impact in thermal environments.

Axisymmetric analytical solutions for a heterogeneous multi-ferroic circular plate subjected to electric loading

ABSTRACTIn the present article, responses of an electrically loaded heterogeneous circular plate of transversely isotropic multi-ferroic materials are investigated. The axisymmetric problem is solved by adopting the direct displacement method developed by the second author. The corresponding generalized displacement functions are obtained through a step-by-step integration procedure. The coupling magneto-electro-elastic fields in the plate, which exactly satisfy the upper and lower boundary conditions and approximately meet the cylindrical boundary condition, are explicitly expressed. Numerical calculations are performed for two particular plates to investigate the influence of material heterogeneity.

Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition

This paper aims at studying the shear behavior of homogeneous granular materials by conventional triaxial test. The work is performed both in laboratory tests and by discrete element method simulations. Conventional triaxial tests are performed on glass beads packing, while a cylindrical rigid wall boundary condition based on lame formula and a series of procedures are proposed to simulate the conventional triaxial test. The experimental results on dry and saturated glass beads samples have been studied to find out the effect of saturation condition on the shear behavior. The comparisons between experimental and numerical results show that the numerical model can reproduce deviatoric curves satisfactorily in experimental conditions as long as experimental sample remains cylindrical. It correctly describes the volumetric strains of a numerical sample up to the peak value. Additionally, a parametric study on the influence of main micromechanical parameters has been carried out, which has been compared to experimental tests with glass beads of different textures. The comparison highlights the significant effect of friction coefficients and rolling resistance coefficients on global behavior of granular materials.

Dimers on the [formula omitted] lattice

In this work, we obtain explicit expression of the number of close-packed dimers (perfect matchings) of the 33.42 lattice with cylindrical boundary condition. Particularly, we show that the entropy of 33.42 lattice is the same for cylindrical and toroidal boundary conditions.

Dimer problem for some three dimensional lattice graphs

Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K2×C4×Pn))≈(−1.171⋅n−1.1223+3.146)n, and log(M(K2×P4×Pn))≈(−1.164⋅n−1.196+2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy.

Young’s Modulus Variation of Carbon Nanotubes Due to Defects Associated with Atomic Reconstruction of Random Vacancies

This paper studies the effect of three different types of defects on the Young’s modulus of zigzag and armchair single-walled carbon nanotubes. The defects are randomly introduced into the structure with a maximum distribution density of 2%. The defects include monovacancies, before and after reconstruction of dangling bonds, resulting finally to the Stone-Wales defect. As the length of model effects computation time significantly, finite element models are created in pristine and very short tube lengths to investigate the effect of model length on the results obtained. The investigation shows that the introduction of defects generally weakens the elastic strength of tubes but to rather different degrees. However, the structure is capable of restoring its elastic strength by rearranging its atoms in form of the Stone-Wales defect. The use of shorter nanotube models on the other hand can lead to accurate results if appropriate cylindrical boundary conditions are defined.

A unified approach to the asymptotic topological indices of various lattices

In this paper, we present a unified approach to the asymptotic topological indices of various lattices. Moreover, we propose the various topological indices per vertex problem for lattice systems and show that the various topological indices per vertex of lattices are independent of the toroidal, cylindrical, and free boundary conditions. Our result is a generalization of some earlier results.

Asymptotic Laplacian-energy-like invariant of lattices

Let μ1⩾μ2⩾⋯⩾μn denote the Laplacian eigenvalues of a graph G with n vertices. The Laplacian-energy-like invariant, denoted by LEL(G)=∑i=1n-1μi, is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.

Asymptotic incidence energy of lattices

The energy of a graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. As an analogue to E(G), the incidence energy IE(G), defined as the sum of the singular values of the incidence matrix of G, is a much studied quantity with well known applications in chemical physics. In this paper, based on the results by Yan and Zhang (2009), we propose the incidence energy per vertex problem for lattice systems, and present the closed-form formulae expressing the incidence energy of the hexagonal lattice, triangular lattice, and 33.42 lattice, respectively. Moreover, we show that the incidence energy per vertex of lattices is independent of the toroidal, cylindrical, and free boundary conditions. In particular, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis approach with the help of calculational software.

Model carcinogen adsorption dynamics of DNA gel

We have derived theoretical equations describing the adsorption of carcinogen to gels in an immersion medium containing carcinogens. The theory was developed for a cylindrical boundary condition under the assumption of a carcinogen diffusion-limited process combined with the “moving boundary picture (Furusawa et al., 2007)”. The time course of the adsorbed carcinogen layer thickness and that of the carcinogen concentration in an immersion medium were expressed by a set of scaled variables, and the asymptotic behavior in the initial stage was derived. Experiments based on the theory were performed using a DNA gel sandwiched between a set of coverglasses in a medium containing acridine orange (AO). The boundary between the AO-adsorbed gel layer and AO-nonadsorbed gel layer was traced during the immersion. The time courses of the AO-adsorbed gel layer thickness and the AO concentration in the immersion medium were well explained by the theory, and the number ratio of the total AO molecules to the adsorption sites in the DNA gel was determined.

Exact finite-size corrections and corner free energies for the [formula omitted] universality class

We consider the partition functions of the anisotropic dimer model on the rectangular (2M−1)×(2N−1) lattice with (a) free and (b) cylindrical boundary conditions with a single monomer residing on the boundary. We express (a) and (b) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the free energy for both cases (a) and (b). We confirm the conformal field theory prediction for the corner free energy of these models, and find the central charge is c=−2. We also show that the dimer model on the cylinder with an odd number of sites on the perimeter exhibits the same finite-size corrections as on the plane.