Isochronous anharmonic oscillations

1998 ◽  
Vol 76 (8) ◽  
pp. 645-657 ◽  
Author(s):  
Pirooz Mohazzabi
Keyword(s):  
General Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
One To One ◽  
Anharmonic Oscillations ◽  
Special Case

The problem of a particle oscillating without friction on a curve in a vertical plane (referred to as a vertical curve) is addressed. It is shown that there are infinitely many asymmetric concave vertical curves on which oscillations of a particle remain isochronous. The general equation of these curves is derived, and a one-to-one correspondence between these curves and one-dimensional potentials is established. The results are compared with the existing literature, and an interesting nontrivial special case is discussed. Some issues regarding interpretation of the results in the context of action and angle variables are also addressed. PACS No. 03.20

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

CONTINUOUS PIECEWISE LINEAR FUNCTIONS

2005 ◽  
Vol 10 (1) ◽  
pp. 77-99 ◽  
Author(s):  
CHARALAMBOS D. ALIPRANTIS ◽  
DAVID HARRIS ◽  
RABEE TOURKY
Keyword(s):  
Piecewise Linear ◽  
Continuous Functions ◽  
Linear Functions ◽  
Dimensional Euclidean Space ◽  
Piecewise Linear Functions ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Mathematical Background ◽  
Linear Regressions ◽  
Special Case

The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on them-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean formwhereX=(X1,X2, …,Xm) is some random vector, {Ej}j∈Jis a finite family of finite sets.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Thermal conduction in a quasi-stationary one-dimensional lattice system

2019 ◽  
Vol 33 (17) ◽  
pp. 1950178
Author(s):  
Mohammad Khorrami ◽  
Amir Aghamohammadi
Keyword(s):  
Heat Transfer ◽  
Ising Model ◽  
Diffusion Equation ◽  
Thermal Conduction ◽  
Nearest Neighbor ◽  
Entropy Change ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Special Case

A system of nearest-neighbor interaction on a one-dimensional lattice is investigated, which has a quasi-stationary (and position-dependent) temperature profile. The rates of heat transfer and entropy change, as well as the diffusion equation for the temperature are studied. A q-state Potts model, and its special case, a two-state Ising model, are considered as an example.

scholarly journals Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities

2020 ◽  
pp. 2050024 ◽  
Author(s):  
Andrei Velicu
Keyword(s):  
Hardy Inequality ◽  
Root Systems ◽  
Dunkl Operators ◽  
Hardy Inequalities ◽  
One Dimensional ◽  
Hardy Type Inequalities ◽  
Rellich Inequality ◽  
Nirenberg Inequality ◽  
Special Case ◽  
The Hardy Inequality

In this paper, we study various forms of the Hardy inequality for Dunkl operators, including the classical inequality, [Formula: see text] inequalities, an improved Hardy inequality, as well as the Rellich inequality and a special case of the Caffarelli–Kohn–Nirenberg inequality. As a consequence, one-dimensional many-particle Hardy inequalities for generalized root systems are proved, which in the particular case of root systems [Formula: see text] improve some well-known results.

Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

1999 ◽  
Vol 51 (5) ◽  
pp. 915-935 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Christoph Leuenberger
Keyword(s):  
Unit Circle ◽  
Complex Flow ◽  
One Dimensional ◽  
Holomorphic Motions ◽  
Strictly Convex ◽  
Fixed Domain ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
The One ◽  
Special Case

AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.

A nonlinear unsteady one-dimensional theory for wings in extreme ground effect

1980 ◽  
Vol 98 (1) ◽  
pp. 33-47 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Ground Effect ◽  
Vortex Sheet ◽  
Unsteady Motion ◽  
The Body ◽  
Order Ordinary Differential Equation ◽  
One Dimensional ◽  
First Order ◽  
Gap Flow ◽  
Normal Distance ◽  
Special Case

Flow induced by a body moving near a plane wall is analysed on the assumption that the normal distance from the wall of every point of the body is small compared to the body length. The flow is irrotational except for the vortex sheet representing the wake. The gap-flow problem in the case of unsteady motion is reduced to a nonlinear first-order ordinary differential equation in the time variable. In the special case of steady flow, some known results are recovered and generalized. As an illustration of the unsteady theory, the problem is solved of a flat plate falling toward the ground under its own weight, while moving forward at uniform speed.

scholarly journals Modulated oscillations in many dimensions

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110551 ◽  
Author(s):  
S. C. Olhede
Keyword(s):  
Physical Oceanography ◽  
Time Varying ◽  
Signal Component ◽  
One Dimensional ◽  
The Common ◽  
The Difference ◽  
Common Signal ◽  
Multivariate Signals ◽  
Special Case ◽  
Signal Models

Modulated oscillations are described via their time-varying amplitude and frequency. For multivariate signals, there is structure in the signal beyond this local amplitude and frequency defined for each signal component, in turn describing the commonality of the components. The multivariate structure encodes how the common oscillation is present in each component signal. This structure will also be evolving. I review the special case of the representation of both bivariate and trivariate oscillations. Additionally, existing results on the general multivariate oscillation are covered. I discuss the difference between a model of a multivariate oscillation compared with other common signal models of phenomena observed in several channels, and how their properties are different. I show how for the multivariate signal the global dimensionality of the signal is built up from local one-dimensional contributions, and introduce the purely unidirectional signal, to quantify how any given signal is different from the closest such signal. I illustrate the properties of the derived representation of the multivariate signal with synthetic examples, and discuss the representation of data from observations in physical oceanography.

Gravity-induced wrinkle lines in vertical membranes

1981 ◽  
Vol 375 (1762) ◽  
pp. 307-325 ◽  
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Prime Objective ◽  
Flow Through ◽  
Flexible Membranes ◽  
The One

A theory is presented for the behaviour under self-weight of inextensible but perfectly flexible membranes supported in a vertical plane. Slack in the membrane manifests itself in the formation of (curved) wrinkle lines whose determination is the prime objective. The equilibrium and strain conditions are derived and solutions are given for several simple cases. It is shown that the wrinkle lines satisfy the one-dimensional diffusion equation and hence there are analogies, for example, with heat flow through a slab.

scholarly journals Causality and passivity in elastodynamics

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150256 ◽  
Author(s):  
Ankit Srivastava
Keyword(s):  
Fourier Transforms ◽  
Constitutive Relations ◽  
Higher Order ◽  
Causal Effects ◽  
Passive System ◽  
One Dimensional ◽  
The Real ◽  
Analogous Question ◽  
Derivatives Of ◽  
Special Case

What are the constraints placed on the constitutive tensors of elastodynamics by the requirements that the linear elastodynamic system under consideration be both causal (effects succeed causes) and passive (system does not produce energy)? The analogous question has been tackled in other areas but in the case of elastodynamics its treatment is complicated by the higher order tensorial nature of its constitutive relations. In this paper, we clarify the effect of these constraints on highly general forms of the elastodynamic constitutive relations. We show that the satisfaction of passivity (and causality) directly requires that the hermitian parts of the transforms (Fourier and Laplace) of the time derivatives of the constitutive tensors be positive semi-definite. Additionally, the conditions require that the non-hermitian parts of the Fourier transforms of the constitutive tensors be positive semi-definite for positive values of frequency. When major symmetries are assumed these definiteness relations apply simply to the real and imaginary parts of the relevant tensors. For diagonal and one-dimensional problems, these positive semi-definiteness relationships reduce to simple inequality relations over the real and imaginary parts, as they should. Finally, we extend the results to highly general constitutive relations which include the Willis inhomogeneous relations as a special case.

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