Elastohydrodynamic Squeeze Films Between Two Cylinders in Normal Approach

1970 ◽  
Vol 92 (2) ◽  
pp. 292-301 ◽  
Author(s):  
K. Herrebrugh
Keyword(s):  
Integral Equation ◽  
Bifurcation Point ◽  
Present Problem ◽  
Proper Treatment ◽  
Elasticity Equations ◽  
Single Integral ◽  
The One

In this approach the fundamental hydrodynamic and elasticity equations that govern the problem are reduced to one single integral equation. Although the resulting integral equation in the present problem is at first sight similar in form to the one governing the steady rolling problem, on closer consideration it appears that the former constitutes a different type of equation, which is mainly characterized by the existence of a bifurcation point not occurring in the equation for steady rolling. By proper treatment of this complication, solutions also in the range of conditions where deformation may be expected to be large are obtained.

Solving the Incompressible and Isothermal Problem in Elastohydrodynamic Lubrication Through an Integral Equation

1968 ◽  
Vol 90 (1) ◽  
pp. 262-270 ◽  
Author(s):  
K. Herrebrugh
Keyword(s):  
Integral Equation ◽  
Film Thickness ◽  
Numerical Solution ◽  
Analytic Functions ◽  
Large Range ◽  
Nonlinear Function ◽  
Elastohydrodynamic Lubrication ◽  
Elasticity Equations ◽  
Single Integral ◽  
Constant Viscosity

It will be shown that the hydrodynamic and elasticity equations in elastohydrodynamic lubrication can be coupled to one single integral equation of the following form: H(x)=f(x)−T∫abK(x,ξ)F{H(ξ)}dξ in which f(x) and K(x, ξ) are both known analytic functions inside [a, b], and F(H) is in general a nonlinear function of the dimensionless film thickness. A numerical solution of this integral equation for constant viscosity is presented for a large range of loading conditions.

An efficient approach to the seismogram synthesis for a basin structure using propagation invariants

1996 ◽  
Vol 86 (2) ◽  
pp. 379-388 ◽  
Author(s):  
H. Takenaka ◽  
M. Ohori ◽  
K. Koketsu ◽  
B. L. N. Kennett
Keyword(s):  
Integral Equation ◽  
Inverse Fourier Transform ◽  
Linear Equations ◽  
Computation Time ◽  
Reduction Technique ◽  
Final Solution ◽  
Space Domain ◽  
New Approach ◽  
Simultaneous Linear Equations ◽  
Single Integral

Abstract The Aki-Larner method is one of the cheapest methods for synthetic seismograms in irregularly layered media. In this article, we propose a new approach for a two-dimensional SH problem, solved originally by Aki and Larner (1970). This new approach is not only based on the Rayleigh ansatz used in the original Aki-Larner method but also uses further information on wave fields, i.e., the propagation invariants. We reduce two coupled integral equations formulated in the original Aki-Larner method to a single integral equation. Applying the trapezoidal rule for numerical integration and collocation matching, this integral equation is discretized to yield a set of simultaneous linear equations. Throughout the derivation of these linear equations, we do not assume the periodicity of the interface, unlike the original Aki-Larner method. But the final solution in the space domain implicitly includes it due to use of the same discretization of the horizontal wavenumber as the discrete wavenumber technique for the inverse Fourier transform from the wavenumber domain to the space domain. The scheme presented in this article is more efficient than the original Aki-Larner method. The computation time and memory required for our scheme are nearly half and one-fourth of those for the original Aki-Larner method. We demonstrate that the band-reduction technique, approximation by considering only coupling between nearby wavenumbers, can accelerate the efficiency of our scheme, although it may degrade the accuracy.

Dr. Tuke's Addeess As President of the Section of Psychology

1873 ◽  
Vol 19 (87) ◽  
pp. 485-487
Keyword(s):  
Mental Disease ◽  
The Other ◽  
Proper Treatment ◽  
Moral Management ◽  
The Moment ◽  
The One

The proper treatment of mental disease must always be considered as involving two distinct divisions. In the one, “moral” management, it is necessary to gain regard and willing obedience, to check wayward impulse, to beat away disturbing fears, to cheer the despairing, to restrain, not by force, bat by patience and firmness, the angry and the violent, and to catch the moment in which the swiftly wavering mind may be brought to rest, and its balance permanently retained. The other division embraces the correct employment of hygienic and purely medical remedial agents.

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

Argument Structure and Morphology

2019 ◽  
Author(s):  
Jim Wood ◽  
Neil Myler
Keyword(s):  
Argument Structure ◽  
Word Formation ◽  
The Other ◽  
Proper Treatment ◽  
Structure And Morphology ◽  
Theoretical Approaches ◽  
The One ◽  
Theoretical Issues

The topic “argument structure and morphology” refers to the interaction between the number and nature of the arguments taken by a given predicate on the one hand, and the morphological makeup of that predicate on the other. This domain turns out to be crucial to the study of a number of theoretical issues, including the nature of thematic representations, the proper treatment of irregularity (both morphophonological and morphosemantic), and the very place of morphology in the architecture of the grammar. A recurring question within all existing theoretical approaches is whether word formation should be conceived of as split across two “places” in the grammar, or as taking place in only one.

Symmetry-breaking bifurcation for the one-dimensional Hénon equation

2019 ◽  
Vol 21 (01) ◽  
pp. 1750097
Author(s):  
Inbo Sim ◽  
Satoshi Tanaka
Keyword(s):  
Symmetry Breaking ◽  
Bifurcation Point ◽  
Global Bifurcation ◽  
One Dimensional ◽  
Bifurcation Points ◽  
Connected Set ◽  
Hénon Equation ◽  
The One ◽  
Symmetry Breaking Bifurcation

We show the existence of a symmetry-breaking bifurcation point for the one-dimensional Hénon equation [Formula: see text] where [Formula: see text] and [Formula: see text]. Moreover, employing a variant of Rabinowitz’s global bifurcation, we obtain the unbounded connected set (the first of the alternatives about Rabinowitz’s global bifurcation), which emanates from the symmetry-breaking bifurcation point. Finally, we give an example of a bounded branch connecting two symmetry-breaking bifurcation points (the second of the alternatives about Rabinowitz’s global bifurcation) for the problem [Formula: see text] where [Formula: see text] is a specified continuous parametrization function.

Bound state QED effects from the Schrödinger equation

1992 ◽  
Vol 70 (8) ◽  
pp. 670-682 ◽  
Author(s):  
Tao Zhang ◽  
Lixin Xiao ◽  
Roman Koniuk
Keyword(s):  
Integral Equation ◽  
Scattering Amplitudes ◽  
Principal Quantum Number ◽  
Bound State ◽  
Renormalization Scheme ◽  
Dirac Particles ◽  
Feynman Gauge ◽  
The One ◽  
Qed Effects ◽  
Bound State Qed

We present a new relativistic bound-state formalism for two interacting Fermi–Dirac particles. The kernel of the integral equation for the bound-state system is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. The method is illustrated through calculations of the hyperfine and fine splittings of positronium up to order α5. Our calculations of the one-loop contributions are carried out in the explicitly covariant Feynman gauge. We also present new results for the hyperfine and fine splittings in positronium to order α5 for arbitrary principal quantum number n, which are easily obtained owing to the virtue of conceptual and calculational simplicity of our formalism. In addition, we present the one-loop renormalization scheme in our formalism.

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