Nonlinear self-excited acoustic oscillations within fixed boundaries

1982 ◽  
Vol 123 ◽  
pp. 267-281 ◽  
Author(s):  
Jakob J. Keller
Keyword(s):  
Time Lag ◽  
Sound Radiation ◽  
Acoustic Oscillations ◽  
Viscous Effects ◽  
Arbitrary Boundary ◽  
Order Analysis ◽  
First Order ◽  
Fundamental Understanding ◽  
Fixed Boundaries ◽  
Special Case

In §1 a brief discussion of the general problem of self-excited acoustic oscillations within fixed boundaries is given. I n §2 a second-order analysis is developed for the special case of rectangular cavities. A nonlinear wave equation is derived for essentially arbitrary boundary conditions. The analysis can be extended to other cavity geometries provided that the first-order solutions can be expressed in closed form. Various applications of the analysis are discussed in §3. It turns out that two-dimensional problems of self-excited oscillations generally lead to nonlinear equations containing terms with a time lag. It is anticipated that the time lag (rather than viscous effects or sound radiation) represents the key to a fundamental understanding of the character of the oscillations and the variety of modes appearing in self-excited resonators.

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

First Order Analysis for Automotive Body Structure Design-Part 2: Joint Analysis Considering Nonlinear Behavior

2004 ◽  
Author(s):  
Yasuaki Tsurumi ◽  
Hidekazu Nishigaki ◽  
Toshiaki Nakagawa ◽  
Tatsuyuki Amago ◽  
Katsuya Furusu ◽  
...  
Keyword(s):  
Nonlinear Behavior ◽  
Structure Design ◽  
Joint Analysis ◽  
Body Structure ◽  
Order Analysis ◽  
First Order ◽  
Automotive Body

Microscale Flow Pumping Inspired by Rhythmic Tracheal Compressions in Insects

2011 ◽  
Author(s):  
Yasser Aboelkassem ◽  
Anne E. Staples ◽  
John J. Socha
Keyword(s):  
Tracheal Tube ◽  
Incompressible Flows ◽  
Time Lag ◽  
Viscous Effects ◽  
Single Cycle ◽  
Single Model ◽  
Microscale Flow ◽  
Valveless Pumping ◽  
Viscous Incompressible Flows ◽  
Rhythmic Contractions

Inspired by the physiological network of insects, which have dimensions on the order of micrometers to millimeters, we study the airflow within a single model insect tracheal tube. The tube undergoes localized rhythmic wall contractions. A theoretical analysis is given to model the airflow within the tracheal tube. Since flow motions at the microscale are dominated mainly by viscous effects, and the tube has radius, R, that is much smaller than its length, L, (i.e. δ = R/L ≪ 1), lubrication theory for axisymmetric, viscous, incompressible flows at low Reynolds number (Re ∼ δ) is used to model the problem mathematically. Expressions for the velocity field, pressure gradient, wall shear stress and net flow produced by the driving tube wall contractions are derived. The effect of the contraction amplitudes, time lag, and spacing between two sequences of contractions on the time-averaged net flow over a single cycle of wall motions is investigated. The study presents a new, insect-inspired mechanism for valveless pumping that can guide efforts to fabricate novel microfluidic devices that mimic these physiological systems. A x-ray image that shows the tracheal network of the respiratory system of an insect (Carabid beetle) and the associated locations of these rhythmic contractions are shown in figure (1) to promote this study.

Radiant Panel Columns Magnetostrictive Transducers of Forced Vibration

2012 ◽  
Vol 588-589 ◽  
pp. 359-363
Author(s):  
Jian Ping Sun ◽  
Jian Xin Wang
Keyword(s):  
Forced Vibration ◽  
Radiation Effect ◽  
Optimization Methods ◽  
Motion Model ◽  
Spring Rate ◽  
Order Analysis ◽  
First Order ◽  
Radiant Panel ◽  
Magnetostrictive Transducer

the columns of magnetostrictive transducer for the object, the establishment of a Radiant Panel in magnetostrictive rods through the spring of motion model, gives a method for solving first-order analysis and solutions, discusses the spring rate on radiation effect of amplitude. On reasonable determination of Radiant Panel structure, the size of the transducer, and optimization methods.

scholarly journals Application of a three-step approach for prediction of combustion instabilities in industrial gas turbine burners

2017 ◽  
Vol 1 ◽  
pp. JCW78T
Author(s):  
Dmytro Iurashev ◽  
Giovanni Campa ◽  
Vyacheslav V. Anisimov ◽  
Ezio Cosatto ◽  
Luca Rofi ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Time Lag ◽  
High Amplitude ◽  
Combustion Regime ◽  
Industrial Test ◽  
Distributed Model ◽  
Combustion Instabilities ◽  
Acoustic Oscillations ◽  
Analytical Time

Abstract Recently, because of environmental regulations, gas turbine manufacturers are restricted to produce machines that work in the lean combustion regime. Gas turbines operating in this regime are prone to combustion-driven acoustic oscillations referred as combustion instabilities. These oscillations could have such high amplitude that they can damage gas turbine hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion chambers.

scholarly journals First-order analysis of optical flow in monkey brain.

1992 ◽  
Vol 89 (7) ◽  
pp. 2595-2599 ◽  
Author(s):  
G. A. Orban ◽  
L. Lagae ◽  
A. Verri ◽  
S. Raiguel ◽  
D. Xiao ◽  
...  
Keyword(s):  
Optical Flow ◽  
Monkey Brain ◽  
Order Analysis ◽  
First Order

Uniqueness, definability and interpolation

1988 ◽  
Vol 53 (2) ◽  
pp. 554-570 ◽  
Author(s):  
Kosta Došen ◽  
Peter Schroeder-Heister
Keyword(s):  
Proof Theory ◽  
Interpolation Theorem ◽  
Order Logic ◽  
First Order Logic ◽  
General Notion ◽  
Structural Part ◽  
First Order ◽  
First Case ◽  
Additional Constant ◽  
Special Case

This paper is meant to be a comment on Beth's definability theorem. In it we shall make the following points.Implicit definability as mentioned in Beth's theorem for first-order logic is a special case of a more general notion of uniqueness. If α is a nonlogical constant, Tα a set of sentences, α* an additional constant of the same syntactical category as α and Tα, a copy of Tα with α* instead of α, then for implicit definability of α in Tα one has, in the case of predicate constants, to derive α(x1,…,xn) ↔ α*(x1,…,xn) from Tα ∪ Tα*, and similarly for constants of other syntactical categories. For uniqueness one considers sets of schemata Sα and derivability from instances of Sα ∪ Sα* in the language with both α and α*, thus allowing mixing of α and α* not only in logical axioms and rules, but also in nonlogical assumptions. In the first case, but not necessarily in the second one, explicit definability follows. It is crucial for Beth's theorem that mixing of α and α* is allowed only inside logic, not outside. This topic will be treated in §1.Let the structural part of logic be understood roughly in the sense of Gentzen-style proof theory, i.e. as comprising only those rules which do not specifically involve logical constants. If we restrict mixing of α and α* to the structural part of logic which we shall specify precisely, we obtain a different notion of implicit definability for which we can demonstrate a general definability theorem, where a is not confined to the syntactical categories of nonlogical expressions of first-order logic. This definability theorem is a consequence of an equally general interpolation theorem. This topic will be treated in §§2, 3, and 4.

Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad

2021 ◽  
Author(s):  
Behnam Malakooti ◽  
Mohamed Komaki ◽  
Camelia Al-Najjar
Keyword(s):  
Risk Behaviors ◽  
Empirical Studies ◽  
Dispersion Theory ◽  
Dispersion Models ◽  
Decision Making Under Risk ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Out Of Sample ◽  
Mean Variance ◽  
Special Case

Many studies have spotlighted significant applications of expected utility theory (EUT), cumulative prospect theory (CPT), and mean-variance in assessing risks. We illustrate that these models and their extensions are unable to predict risk behaviors accurately in out-of-sample empirical studies. EUT uses a nonlinear value (utility) function of consequences but is linear in probabilities, which has been criticized as its primary weakness. Although mean-variance is nonlinear in probabilities, it is symmetric, contradicts first-order stochastic dominance, and uses the same standard deviation for both risk aversion and risk proneness. In this paper, we explore a special case of geometric dispersion theory (GDT) that is simultaneously nonlinear in both consequences and probabilities. It complies with first-order stochastic dominance and is asymmetric to represent the mixed risk-averse and risk-prone behaviors of the decision makers. GDT is a triad model that uses expected value, risk-averse dispersion, and risk-prone dispersion. GDT uses only two parameters, z and zX; these constants remain the same regardless of the scale of risk problem. We compare GDT to several other risk dispersion models that are based on EUT and/or mean-variance, and identify verified risk paradoxes that contradict EUT, CPT, and mean-variance but are easily explainable by GDT. We demonstrate that GDT predicts out-of-sample empirical risk behaviors far more accurately than EUT, CPT, mean-variance, and other risk dispersion models. We also discuss the underlying assumptions, meanings, and perspectives of GDT and how it reflects risk relativity and risk triad. This paper covers basic GDT, which is a special case of general GDT of Malakooti [Malakooti (2020) Geometric dispersion theory of decision making under risk: Generalizing EUT, RDEU, & CPT with out-of-sample empirical studies. Working paper, Case Western Reserve University, Cleveland.].

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