scholarly journals Properties of size-dependent models having quasiperiodic boundary conditions

2018 ◽  
Vol 33 (01) ◽  
pp. 1850008 ◽  
Author(s):  
E. Cavalcanti ◽  
C. A. Linhares ◽  
A. P. C. Malbouisson
Keyword(s):  
Phase Transition ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Thermal Equilibrium ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Minimal Length ◽  
Thermally Induced ◽  
Size Dependent ◽  
Aharonov Bohm

Boundary condition effects are explored for size-dependent models in thermal equilibrium. Scalar and fermionic models are used for [Formula: see text] (films), [Formula: see text] (hollow cylinder) and [Formula: see text] (ring). For all models, a minimal length is found, below which no thermally-induced phase transition occurs. Using quasiperiodic boundary condition controlled by a contour parameter [Formula: see text] ([Formula: see text] is a periodic boundary condition and [Formula: see text] is an antiperiodic condition), it results that the minimal length depends directly on the value of [Formula: see text]. It is also argued that this parameter can be associated to an Aharonov–Bohm phase.

scholarly journals Isospectral sets for boundary value problems on the unit interval

1988 ◽  
Vol 8 (8) ◽  
pp. 301-358 ◽  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Liouville Equation ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Unit Interval ◽  
Trace Function ◽  
Sturm Liouville ◽  
Real Self

AbstractWe analyse isospectral sets of potentials associated to a given ‘generalized periodic’ boundary condition in SL(2, R) for the Sturm-Liouville equation on the unit interval. This is done by first studying the larger manifold M of all pairs of boundary conditions and potentials with a given spectrum and characterizing the critical points of the map from M to the trace a + d Isospectral sets appear as slices of M whose geometry is determined by the critical point structure of the trace function. This paper completes the classification of isospectral sets for all real self-adjoint boundary conditions.

scholarly journals Computation of Flutter of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code

1998 ◽  
Author(s):  
Shanhong Ji ◽  
Feng Liu
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Unsteady Flows ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Multiple Passage ◽  
Parallel Code

A quasi-three-dimensional multigrid Navier-Stokes solver on single and multiple passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades. The conventional “direct store” method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the Message Passing Interface (MPI) standard is developed for multiple passage computations. In the parallel multiple passage computations, the phase-shifted periodic boundary condition is converted to simple in-phase periodic condition. Euler and Navier-Stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel code. It is found that the parallel code offers almost linear speedup with multiple CPUs. In addition, significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple passage computations due to the use of in-phase periodic boundary conditions as compared to that in the single passage computations with phase-lagged periodic boundary conditions via the “direct store” method. The parallel Navier-Stokes code is also used to calculate the flow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors.

scholarly journals FCC-BCC Phase Transition in Iron under a Periodic Boundary Condition

1999 ◽  
Vol 40 (11) ◽  
pp. 1306-1313 ◽  
Author(s):  
Masato Shimono ◽  
Hidehiro Onodera ◽  
Tetsuro Suzuki
Keyword(s):  
Phase Transition ◽  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Bcc Phase

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals A new time-delayed periodic boundary condition for discrete element modelling of railway track under moving wheel loads

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Huiqi Li ◽  
Glenn McDowell ◽  
John de Bono
Keyword(s):  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Discrete Element ◽  
Contact Forces ◽  
Railway Track ◽  
Discrete Element Modelling ◽  
Fixed Boundary ◽  
Element Modelling ◽  
New Time

Abstract A new time-delayed periodic boundary condition (PBC) has been proposed for discrete element modelling (DEM) of periodic structures subject to moving loads such as railway track based on a box test which is normally used as an element testing model. The new proposed time-delayed PBC is approached by predicting forces acting on ghost particles with the consideration of different loading phases for adjacent sleepers whereas a normal PBC simply gives the ghost particles the same contact forces as the original particles. By comparing the sleeper in a single sleeper test with a fixed boundary, a normal periodic boundary and the newly proposed time-delayed PBC (TDPBC), the new TDPBC was found to produce the closest settlement to that of the middle sleeper in a three-sleeper test which was assumed to be free of boundary effects. It appears that the new TDPBC can eliminate the boundary effect more effectively than either a fixed boundary or a normal periodic cell. Graphic abstract

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

1953 ◽  
Vol 49 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Boundary Condition ◽  
Thermal Properties ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
The Moon ◽  
Non Linear

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

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