scholarly journals Exact solution to the steady-state dynamics of a periodically modulated resonator

APL Photonics ◽  
2017 ◽  
Vol 2 (7) ◽  
pp. 076101 ◽  
Author(s):  
Momchil Minkov ◽  
Yu Shi ◽  
Shanhui Fan
Keyword(s):  
Exact Solution ◽  
Steady State

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

Drawing of Tubes

1980 ◽  
Vol 47 (4) ◽  
pp. 736-740 ◽  
Author(s):  
D. Durban
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Radial Flow ◽  
Material Behavior ◽  
Wall Friction ◽  
Flow Rule ◽  
Flow Conditions ◽  
Steady State Flow ◽  
Linear Hardening ◽  
Von Mises

The process of the tube drawing between two rough conical walls is analyzed within the framework of continuum plasticity. Material behavior is modeled as rigid/linear-hardening along with the von-Mises flow rule. Assuming a radial flow pattern and steady state flow conditions it becomes possible to obtain an exact solution for the stresses and velocity. Useful relations are derived for practical cases where the nonuniformity induced by wall friction is small. A few restrictions on the validity of the results are discussed.

Exact Dynamics in a Model of the Bimolecular Reaction A+B→ 0

1992 ◽  
Vol 290 ◽  
Author(s):  
Eric Clément ◽  
Patrick Leroux-Hugon ◽  
Leonard M. Sander
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Initial Conditions ◽  
Finite Size ◽  
Bimolecular Reaction ◽  
Reaction Model

AbstractWe have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.

A Numerical Method for Heat Conduction Problems

1974 ◽  
Vol 96 (3) ◽  
pp. 307-312 ◽  
Author(s):  
M. J. Reiser ◽  
F. J. Appl
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Steady State ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Singular Integral ◽  
Integral Method ◽  
Two Dimensional ◽  
Convection Boundary ◽  
Steady State Heat

A singular integral method of numerical analysis for two-dimensional steady-state heat conduction problems with any combination of temperature, gradient, or convection boundary conditions is presented. Excellent agreement with the exact solution is illustrated for an example problem. The method is used to determine the solution for a fin bank with convection.

An exact electrostatic shock solution for a collisionless plasma

1970 ◽  
Vol 4 (3) ◽  
pp. 549-561 ◽  
Author(s):  
A. Smith
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Energy Equation ◽  
Collisionless Plasma ◽  
Debye Length ◽  
Elementary Functions ◽  
One Dimensional ◽  
Particle Distributions ◽  
Vlasov Equations ◽  
Shock Solution

An exact solution to the steady-state Vlasov equations and Poisson's equation for a one-dimensional plasma of electrons and protons is obtained by splitting the energy equation into two integral equations for the trapped particle distributions. This solution has the properties that the number densities and electric potential are moiiotonic functions of space and do most of their changing over a distance of the order of the Debye length for electrons. The distributions are everywhere differentiable in phase space and are Maxwellian-like, and in terms of elementary functions. Evidence is given to support stability for restricted shock strengths.

Scaling Analysis of a Moving Point Heat Source in Steady-State on a Semi-Infinite Solid

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Patricio F. Mendez ◽  
Yi Lu ◽  
Ying Wang
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Numerical Models ◽  
Scaling Analysis ◽  
Point Heat Source ◽  
Maximum Width ◽  
Characteristic Values ◽  
First Time

This paper presents a systematic scaling analysis of the point heat source in steady-state on a semi-infinite solid. It is shown that all characteristic values related to an isotherm can be reduced to a dimensionless expression dependent only on the Rykalin number (Ry). The maximum width of an isotherm and its location are determined for the first time in explicit form for the whole range of Ry, with an error below 2% from the exact solution. The methodology employed involves normalization, dimensional analysis, asymptotic analysis, and blending techniques. The expressions developed can be calculated using a handheld calculator or a basic spreadsheet to estimate, for example, the width of a weld or the size of zone affected by the heat source in a number of processes. These expressions are also useful to verify numerical models.

scholarly journals A note on “Taylor–Couette flow of a generalized second grade fluid due to a constant couple”

2010 ◽  
Vol 15 (2) ◽  
pp. 155-158 ◽  
Author(s):  
C. Fetecau ◽  
A. U. Awan ◽  
M. Athar
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
New Form ◽  
Second Grade Fluids

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

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