Interface acoustic waves in piezoelectric bi-crystalline structures of specific types

2005 ◽  
Vol 461 (2056) ◽  
pp. 895-911 ◽  
Author(s):  
A. N Darinskii ◽  
M Weihnacht
Keyword(s):  
Acoustic Waves ◽  
The Other ◽  
Imaginary Component ◽  
Sufficient Condition ◽  
Bulk Wave ◽  
Piezoelectric Crystal ◽  
Piezoelectric Media ◽  
Crystalline Structures ◽  
Material Constants ◽  
Bulk Waves

The paper discusses the properties of the acoustic waves guided by an interface inside piezoelectric media. The interfaces of two types have been considered: (i) an infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry; (ii) rigidly bonded crystals whose piezoelectric coefficients differ by sign while the other material constants are identical. Several general theorems have been proved regarding the existence of interface acoustic waves (IAWs) propagating more slowly than bulk waves. In particular, a sufficient condition for the existence of such ‘slow’ IAWs has been derived. The propagation of leaky IAWs has been studied. Special attention has been paid to the analysis of the situation when the imaginary component of the leaky IAW velocity vanishes, resulting in the appearance of non-attenuating IAWs travelling faster than the slow transverse bulk wave. The computations performed for LiNbO 3 and LiTaO 3 illustrate general conclusions.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals Equipartitioning and balancing points of polygons

Pythagoras ◽  
2010 ◽  
Vol 0 (71) ◽  
Author(s):  
Shunmugam Pillay ◽  
Poobhalan Pillay
Keyword(s):  
General Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

scholarly journals Two examples related to conical energies

2022 ◽  
Vol 47 (1) ◽  
pp. 261-281
Author(s):  
Damian Dąbrowski
Keyword(s):  
Singular Integral ◽  
Recent Article ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
The Other ◽  
Independent Interest ◽  
Sufficient Condition ◽  
Lipschitz Graphs ◽  
Big Pieces

In a recent article (2021) we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

Mathematical methods for the characterization of ultrasound in anisotropic materials

2000 ◽  
Vol 78 (9) ◽  
pp. 803-821 ◽  
Author(s):  
B O'Neill ◽  
R Gr. Maev
Keyword(s):  
Wave Propagation ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Anisotropic Materials ◽  
Bulk Wave ◽  
Mathematical Methods ◽  
Theoretical Methods ◽  
The Past ◽  
Fundamental Equations

Although the fundamental equations for the propagation of elastic and acoustic waves in anisotropic materials have not changed in more than a 100 years, the last few decades have seen a surge in interest in the topic. Much of this interest stems from the growing need for characterization of an increasing number of exotic materials. The intent of this paper is to review, for the benefit of beginning researchers in acoustics and ultrasonics, the fundamental phenomena related to elastic wave propagation in anisotropic media. We also present the most common and interesting theoretical methods developed over the past 20 years to model bulk wave propagation in such media. The methods discussed include plane wave superpositions, ray asymptotic theory, paraxial beams, and Green's functions. More peripheral issues, including anisotropic effects combined with various other exotic effects, are dealt with in the bibliography. PACS No.: 43.90

Trustworthy Government and Legitimating Beliefs

2019 ◽  
pp. 362-384
Author(s):  
Margaret Levi
Keyword(s):  
Decision Making ◽  
State Building ◽  
The Other ◽  
Sufficient Condition ◽  
Goods And Services ◽  
Moral Economies ◽  
The Government ◽  
The Relationship ◽  
Advanced Democracies

A trustworthy government is one that keeps its promises (or has exceptionally good reasons why it fails to), is relatively fair in its decision-making and enforcement processes, and delivers goods and services. A legitimate government is one that appeals to widely accepted justifications for its selection, maintenance, and policies. Investigations across history and countries reveal that the more trustworthy the government, the more likely it is to evoke observation of its laws and acquiescence to policies. Less clear is the link between perceptions that government is trustworthy and beliefs that it is legitimate, at least in countries claiming or trying to be democratic. Being trustworthy in practices and outcomes may contribute to perceptions of government legitimacy. However, trustworthiness is, at best, a necessary but not sufficient condition for legitimating beliefs. This chapter explores the relationship between the trustworthiness of government and its legitimacy by considering cases from both advanced democracies and state-building efforts. It argues that current democracies may need to refashion their moral economies—the extra-market reciprocal rights and obligations that link populations, governments, corporations, and all the other various organizations that make up the society—if they are to reestablish strong grounds for legitimacy.

Orthogonal Fractional Factorial Plans

1980 ◽  
Vol 29 (3-4) ◽  
pp. 143-160 ◽  
Author(s):  
Rahul Mukerjee
Keyword(s):  
Broad Class ◽  
Existence Results ◽  
Fractional Factorial ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equal Frequency ◽  
Other Hand ◽  
Necessary And Sufficient ◽  
Generally True

This paper shows that the criterion of proportional frequency for (unblocked) orthogonal fractional factorial plans, as suggested by some previous authors, is not generally true. On the other hand, the criterion of equal frequency has been established as a necessary and sufficient condition in the general case. Some other properties of orthogonal fractional factorial plans have been investigated. A necessary and sufficient condition for designs involving two or more blocks has also been presented. A broad class of non-existence results follow.

Uncertainty Regarding Interpretation of the “Negligence Rule” and Its Implications for the Efficiency of Outcomes

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Satish K. Jain
Keyword(s):  
Subjective Probability ◽  
The Other ◽  
Sufficient Condition ◽  
Subjective Probabilities ◽  
Necessary And Sufficient Condition ◽  
Liability Rule ◽  
Important Conclusion ◽  
Standard Version ◽  
Necessary And Sufficient ◽  
Negligence Rule

AbstractThere are two ways that the negligence rule is interpreted. Under one interpretation a negligent injurer is liable for the entire harm to the victim; and under the other interpretation a negligent injurer is liable only for that part of the harm which can be ascribed to his negligence. Both these versions are efficient. However, if there is uncertainty regarding whether the court will be employing the full liability version or the incremental liability version for determining the liability of a negligent injurer, notwithstanding the fact that both the versions are efficient, inefficiency is possible. It is shown in the paper that a necessary and sufficient condition for efficiency in all cases is that the subjective probability with which the injurer expects the standard version to be employed must be greater than or equal to the subjective probability with which the victim expects the standard version to be employed. For the subset of applications without complementarities in the cares of the two parties and which are such that the total social costs are minimized at a unique care-configuration, it is shown that efficiency obtains regardless of the subjective probabilities with which the parties expect the two versions. One very important conclusion that emerges from the analysis of this paper is that when courts employ more than one liability rule, even if all the employed rules are efficient, the efficiency of all outcomes cannot be taken for granted merely on the ground of the efficiency of the employed rules.

Periodicity Conditions for Third-Order Nonlinear With Application to Wave Propagation in Relaxing Media

2007 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
M. Mahinfalah ◽  
J. Christopherson ◽  
A. Khazaei ◽  
G. Nazari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Water Waves ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Rapid Convergence ◽  
Third Order ◽  
Specific Equation

It is known that wave propagation in nonlinear continues media, such as acoustic waves in solids, water waves, and solitary waves in arteries, can be reduced to a third order ordinary differential equations. They can be cast in a general third order ODE as x‴‴‴+f(t,x,x′,x″)=0. However, having an ODE as a reduced model for a phenomenon expressible by a partial differential equation lacks a proof to grantee for having a periodic solution. A third-order existence theorem has been proven to establish the sufficient conditions of periodicity for the above general third-order ODE. However, the equation is too general. In this paper we examine the following more specific equation x‴‴‴+g1(x′)x″+g2(x)x′+g(x,x′,t)=e(t). and prove a new theorem to establish the sufficient condition for its periodicity. To obtain the periodicity conditions, the Schauder’s fixed-point theorem is implemented. A numerical method is also developed for rapid convergence.

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