Acoustical Dispersion in Periodic Microwave Structures

1975 ◽  
Vol 53 (4) ◽  
pp. 360-371 ◽  
Author(s):  
O. A. Aboul-Atta ◽  
E. Tomchuk
Keyword(s):  
Numerical Methods ◽  
Numerical Procedure ◽  
Frequency Dispersion ◽  
Design Parameters ◽  
Variational Theory ◽  
Microwave Structures ◽  
Basic Equations ◽  
High Degree ◽  
Operational Modes ◽  
Special Curve

The theory, the design, and the numerical results relevant to the acoustical frequency dispersion band of periodic microwave structures are discussed. Experimental Brillouin diagrams for the acoustical band of different structures exhibit a neat fitting to a special curve. This curve coincides with the qualitative analysis of resonators chain coupled (distant coupling included) together both capacitively and inductively. Discrete points on the curve are obtained analytically using the variational theory. Those points which correspond to the eigenvalues of only one period of the structure are analyzed and explained in terms of boundary conditions. Numerical methods for calculating these eigenvalues to a high degree of accuracy are either already available or can easily be programed. These programs are easily modified so that various other design parameters may be evaluated simultaneously. The basic equations are derived and the appropriate technique developed for a model of distant coupling up to the second neighbor. Comments on the numerical procedure, on the accuracy, and on the practicality of the different operational modes are given.

scholarly journals Creating better superconductors by periodic nanopatterning

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Milan Allan ◽  
Mark H Fischer ◽  
Oliver Ostojic ◽  
Arjo Andringa
Keyword(s):  
Thin Films ◽  
Transition Temperature ◽  
Numerical Methods ◽  
Model Calculation ◽  
Lattice Mismatch ◽  
Specific Pattern ◽  
Design Parameters ◽  
Phonon Coupling ◽  
Electron Phonon Coupling ◽  
Correct Design

The quest to create superconductors with higher transition temperatures is as old as superconductivity itself. One strategy, popular after the realization that (conventional) superconductivity is mediated by phonons, is to chemically combine different elements within the crystalline unit cell to maximize the electron-phonon coupling. This led to the discovery of NbTi and Nb_33Sn, to name just the most technologically relevant examples. Here, we propose a radically different approach to transform a ‘pristine’ material into a better (meta-) superconductor by making use of modern fabrication techniques: designing and engineering the electronic properties of thin films via periodic patterning on the nanoscale. We present a model calculation to explore the key effects of different supercells that could be fabricated using nanofabrication or deliberate lattice mismatch, and demonstrate that specific pattern will enhance the coupling and the transition temperature. We also discuss how numerical methods could predict the correct design parameters to improve superconductivity in materials including Al, NbTi, and MgB_22.

Dynamic Characteristics of Planar Compliant Parallel-Guiding Mechanisms

2008 ◽  
Author(s):  
Wenjing Wang ◽  
Yueqing Yu
Keyword(s):  
Numerical Methods ◽  
Rigid Body ◽  
Natural Frequency ◽  
Dynamic Modeling ◽  
Dynamic Characteristics ◽  
Compliant Mechanisms ◽  
Design Parameters ◽  
Dynamic Effects ◽  
Body Model ◽  
Rigid Body Model

Dynamic effects are very important to improving the design of compliant mechanisms. An investigation on the dynamic characteristics of planar compliant parallel-guiding mechanism is presented. Based on the pseudo-rigid-body model, the dynamic model of planar compliant parallel-guiding mechanisms is developed using the numerical methods at first. The natural frequency is then calculated, and frequency characteristics of this mechanism are studied. The numerical results show the accuracy of the proposed method for dynamic modeling of compliant mechanisms, and the relationships between the natural frequency and design parameters are analyzed clearly.

Analysis of Airfoil Trailing Edge Heat Transfer and Its Significance in Thermal-Mechanical Design and Durability

2005 ◽  
Author(s):  
F. J. Cunha ◽  
M. T. Dahmer ◽  
M. K. Chyu
Keyword(s):  
Mechanical Design ◽  
Thermal Characteristics ◽  
Metal Temperature ◽  
Design Parameters ◽  
Trailing Edge ◽  
Aerodynamic Loss ◽  
Expansion Waves ◽  
Detail Design ◽  
Turbine Airfoils ◽  
High Degree

The trailing edge section of modern high-pressure turbine airfoils is an area that requires a high degree of attention from turbine performance and durability standpoints. Aerodynamic loss near the trailing edge includes expansion waves, normal shocks and wake shedding. Thermal issues associated with trailing edge are also very complex and challenging. To maintain effective cooling ensuring metal temperature below design limit is particularly difficult, as it needs to be implemented in a relatively small area of the airfoil. To date little effort has been devoted to advancing the fundamental understanding of the thermal characteristics in airfoil trailing edge regions. Described in this paper are the procedures leading to closed-form, analytical solutions for temperature profile for four most representative trailing edge configurations. The configurations studied are: (1) solid wedge shape without discharge, (2) wedge with slot discharge, (3) wedge with discrete-hole discharge, and (4) wedge with pressure-side cutback slot discharge. Comparison among these four cases is made primarily in the context of airfoil metal temperature and resulting cooling effectiveness. Further discussed in the paper are the overall and detail design parameters for preferred trailing edge cooling configurations as they affect turbine airfoil performance and durability.

scholarly journals The Evaluation Of Algorithms For Determination Of The Reliability Index

2015 ◽  
Vol 61 (3) ◽  
pp. 133-147 ◽  
Author(s):  
A. Dudzik ◽  
U. Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Numerical Procedure ◽  
Vertical Displacement ◽  
Design Parameters ◽  
State Function ◽  
Structural Failure

AbstractThe study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

Planar distributions of dislocations

1968 ◽  
Vol 305 (1482) ◽  
pp. 387-404 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Crack Nucleation ◽  
Physical Phenomenon ◽  
Continuous Distribution ◽  
Numerical Procedure ◽  
Physical Reality ◽  
Cleavage Crack ◽  
Planar Arrays ◽  
High Degree

Many problems in metal physics can be adequately described by planar arrays of dislocations, and in analysing them there are two extreme types of approach: either all the dislocations can be regarded as discrete entities, when a numerical procedure must in general be adopted, or they may be smeared into a continuous distribution, when a simple analytical solution is usually available. The present paper introduces a procedure whereby the majority of the dislocations in an array are smeared into a continuous distribution, while those that are intimately concerned with the particular physical phenomenon under consideration are allowed to remain discrete. The main advantage of this approach is that it allows for ease of solution, while preserving a high degree of physical reality. Particular types of dislocation array are considered, the accuracy of the method being demonstrated by comparing, where possible, the results with those obtained assuming that all the dislocations are discrete. Both singular integral equation and potential theory techniques are employed, and the results are applied in a brief discussion of the problem of cleavage crack nucleation in crystalline solids.

Analysis of Airfoil Trailing Edge Heat Transfer and Its Significance in Thermal-Mechanical Design and Durability

2005 ◽  
Vol 128 (4) ◽  
pp. 738-746 ◽  
Author(s):  
F. J. Cunha ◽  
M. T. Dahmer ◽  
M. K. Chyu
Keyword(s):  
Mechanical Design ◽  
Thermal Characteristics ◽  
Metal Temperature ◽  
Design Parameters ◽  
Trailing Edge ◽  
Aerodynamic Loss ◽  
Expansion Waves ◽  
Detail Design ◽  
Turbine Airfoils ◽  
High Degree

The trailing edge section of modern high-pressure turbine airfoils is an area that requires a high degree of attention from turbine performance and durability standpoints. Aerodynamic loss near the trailing edge includes expansion waves, normal shocks, and wake shedding. Thermal issues associated with trailing edge are also very complex and challenging. To maintain effective cooling ensuring metal temperature below design limit is particularly difficult, as it needs to be implemented in a relatively small area of the airfoil. To date, little effort has been devoted to advancing the fundamental understanding of the thermal characteristics in airfoil trailing edge regions. Described in this paper are the procedures leading to closed-form, analytical solutions for temperature profile for four most representative trailing edge configurations. The configurations studied are: (1) solid wedge shape without discharge, (2) wedge with slot discharge, (3) wedge with discrete-hole discharge, and (4) wedge with pressure-side cutback slot discharge. Comparison among these four cases is made primarily in the context of airfoil metal temperature and resulting cooling effectiveness. Further discussed in the paper are the overall and detail design parameters for preferred trailing edge cooling configurations as they affect turbine airfoil performance and durability.

NUMERICAL EVALUATION OF FEM WITH APPLICATION TO THE 1-D ADVECTION–DIFFUSION PROBLEM

2002 ◽  
Vol 12 (02) ◽  
pp. 205-228 ◽  
Author(s):  
GIANCARLO SANGALLI
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
General Framework ◽  
Numerical Evaluation ◽  
Numerical Procedure ◽  
Diffusion Problem ◽  
Empirical Justification ◽  
Eigenvalue Computation ◽  
Advection Diffusion

In this paper we present a numerical procedure to evaluate the efficiency of finite element numerical methods. We improve some of the ideas proposed in previous works and give a partly theoretical, partly empirical justification in a general framework. The proposed procedure performs an eigenvalue computation, and requires the knowledge of the behavior of the exact operator in order to choose proper norms for the evaluations. In the experiments we focus our attention on the 1-D advection–diffusion problem: we show that our numerical procedure actually gives very sharp indications about the optimality of the tested numerical methods.

Estimation of Effective Effort from Catch-at-Age Data

1993 ◽  
Vol 50 (11) ◽  
pp. 2421-2428 ◽  
Author(s):  
J. E. Paloheimo ◽  
Yong Chen
Keyword(s):  
Age Groups ◽  
Simulated Data ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
A Value ◽  
Basic Equations ◽  
Highly Correlated ◽  
High Degree ◽  
Two Age Groups

We present a method for estimating effective efforts or fishing mortality rates based on a linearized version of the catch equation. Catch-at-age for at least two age groups over a series of years is required. The method presupposes a value for natural mortality rate (M). The method is validated using simulated data with an appropriate error structure. The algorithm always converges to a set of effective efforts that are compatible with the known catches. Nevertheless, the solution to the basic equations is not unique although the different solutions are typically highly correlated. If the M assumed by the algorithm is the same as the actual M the iterated effective efforts are typically very close to the true effective efforts or fishing mortality rates. If the assumed M is too high or too low the pattern of effective efforts is still recovered to a high degree of accuracy, typically 0.90 < r < 1.00, even though M may be off by as much as 60%. When data for three or more age groups are available the method is extended to at least squares procedure that takes into account the increasing uncertainty of catches with age.

COMPUTING MINKOWSKI SUMS OF PLANE CURVES

1995 ◽  
Vol 05 (04) ◽  
pp. 413-432 ◽  
Author(s):  
ANIL KAUL ◽  
RIDA T. FAROUKI
Keyword(s):  
Algebraic Curve ◽  
Numerical Procedure ◽  
The Other ◽  
Minkowski Sum ◽  
Plane Curves ◽  
Parametric Curves ◽  
Implicit Equation ◽  
Minkowski Sums ◽  
High Degree ◽  
The Given

The Minkowski sum of two plane curves can be regarded as the area generated by sweeping one curve along the other. The boundary of the Minkowski sum consists of translated portions of the given curves and/or portions of a more complicated curve, the “envelope” of translates of the swept curve. We show that the Minkowski-sum boundary is describable as an algebraic curve (or subset thereof) when the given curves are algebraic, and illustrate the computation of its implicit equation. However, such equations are typically of high degree and do not offer a practical basis for tracing the boundary. For the case of polynomial parametric curves, we formulate a simple numerical procedure to address the latter problem, based on constructing the Gauss maps of the given curves and using them to identifying “corresponding” curve segments that are to be summed. This yields a set of discretely-sampled arcs that constitutes a superset of the Minkowski-sum boundary, and can be regarded as a planar graph. To extract the true boundary, we present a method for identifying and “trimming” away extraneous arcs by systematically traversing this graph.

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