Propagation for KPP bulk-surface systems in a general cylindrical domain

ABSTRACTSurface and bulk electronic structure of the ordered NiAl alloy were measured using angle resolved photoelectron spectroscopy. The measured bulk d-bands (Ni like) were observed to be narrower than theoretically calculated d band widths which are 20 to 40% wider (depending upon what is used as a measure of the width). At least two surface states were observed on both the (110) and (111) surfaces. The nature of these surface states and their relationship to the bulk band structure is discussed. Dispersion of bulk phonons was measured by neutron scattering and fitted with a fourth nearest neighbor Born-von Karman model. Dipole active surface phonons on the (110) and (111) surfaces were observed by inelastic electron scattering and the frequencies also calculated assuming a truncated bulk surface. The calculated surface modes present a qualitative picture of the atomic displacement at each surface and also show that the surface phonon energy and intensity depends upon the structure of the surface.

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$L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

Advances in Difference Equations ◽

10.1186/s13662-020-03054-5 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Carlos Lizama ◽

Marina Murillo-Arcila

Keyword(s):

Acoustic Waves ◽

Maximal Regularity ◽

Bubble Radius ◽

Fourier Multipliers ◽

Cylindrical Domain ◽

Lebesgue Spaces ◽

Regularity Problem ◽

Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

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A Boundary Estimate for Singular Sub-Critical Parabolic Equations

International Mathematics Research Notices ◽

10.1093/imrn/rnaa351 ◽

2020 ◽

Author(s):

Ugo Gianazza ◽

Naian Liao

Keyword(s):

Modulus Of Continuity ◽

Weak Solutions ◽

Parabolic Equations ◽

Boundary Point ◽

Cylindrical Domain ◽

Boundary Estimate ◽

Critical Range ◽

Type Integral ◽

Wiener Type ◽

Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

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Interaction of hydrogen with the bulk, surface and subsurface of crystalline RuO2 from first principles

Physics Open ◽

10.1016/j.physo.2021.100059 ◽

2021 ◽

Vol 7 ◽

pp. 100059

Author(s):

Ankita Jadon ◽

Carole Rossi ◽

Mehdi Djafari-Rouhani ◽

Alain Estève ◽

David Pech

Keyword(s):

First Principles ◽

Bulk Surface

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A new approach to memory and logic-cylindrical domain devices

10.1145/1478559.1478617 ◽

1969 ◽

Cited By ~ 2

Author(s):

A. H. Bobeck ◽

R. F. Fischer ◽

A. J. Perneski

Keyword(s):

Cylindrical Domain ◽

New Approach

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The bulk, surface and corner free energies of the anisotropic triangular Ising model

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0713 ◽

2020 ◽

Vol 476 (2234) ◽

pp. 20190713

Author(s):

Rodney J. Baxter

Keyword(s):

Free Energy ◽

Ising Model ◽

Partition Function ◽

Temperature Series ◽

Isotropic Case ◽

Series Expansions ◽

Exact Results ◽

Free Energies ◽

Bulk Surface ◽

Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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Theory of bulk, surface and interface phase transition kinetics in thin films

The Journal of Chemical Physics ◽

10.1063/1.1760737 ◽

2004 ◽

Vol 121 (2) ◽

pp. 1038-1049 ◽

Cited By ~ 15

Author(s):

Ellen H. G. Backus ◽

Mischa Bonn

Keyword(s):

Thin Films ◽

Phase Transition ◽

Surface And Interface ◽

Interface Phase ◽

Bulk Surface ◽

Phase Transition Kinetics

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Cut finite element methods for coupled bulk–surface problems

Numerische Mathematik ◽

10.1007/s00211-015-0744-3 ◽

2015 ◽

Vol 133 (2) ◽

pp. 203-231 ◽

Cited By ~ 27

Author(s):

Erik Burman ◽

Peter Hansbo ◽

Mats G. Larson ◽

Sara Zahedi

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

Bulk Surface

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Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

Journal of Applied Mechanics ◽

10.1115/1.4007475 ◽

2013 ◽

Vol 80 (2) ◽

Cited By ~ 1

Author(s):

D. Zhou ◽

S. H. Lo

Keyword(s):

Cross Section ◽

Chebyshev Polynomial ◽

Numerical Solutions ◽

Twist Angle ◽

Ritz Method ◽

Three Dimensional ◽

Cylindrical Domain ◽

Linear Elasticity Theory ◽

Boundary Functions ◽

Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

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