Interfacial phenomenon for one-dimensional equation of forward-backward parabolic type

1996 ◽  
Vol 171 (1) ◽  
pp. 379-394 ◽  
Author(s):  
Vladimir N. Grebenev
Keyword(s):  
Parabolic Type ◽  
Interfacial Phenomenon ◽  
One Dimensional ◽  
Dimensional Equation

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

scholarly journals Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

2019 ◽  
Vol 21 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Alberto Boscaggin ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Boundary Value ◽  
Periodic Problem ◽  
Nodal Solutions ◽  
Shooting Technique ◽  
One Dimensional ◽  
Dimensional Equation

By using a shooting technique, we prove that the quasilinear boundary value problem [Formula: see text] where [Formula: see text] is a ball and [Formula: see text], has more and more pairs of nodal solutions on growing of the parameter [Formula: see text]. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

Large Amplitude Pulsatile Water Flow Across an Orifice

1975 ◽  
Vol 97 (1) ◽  
pp. 92-95 ◽  
Author(s):  
E. L. Yellin ◽  
C. S. Peskin
Keyword(s):  
Large Amplitude ◽  
Heart Valves ◽  
Equation Of Motion ◽  
Separated Flows ◽  
Prosthetic Heart Valves ◽  
One Dimensional ◽  
Water Flows ◽  
Lumped Parameter ◽  
Dimensional Equation ◽  
The One

The pressure-flow relations of large amplitude pulsatile water flows across an orifice have been investigated theoretically and experimentally. By retaining the unsteady term in the one-dimensional equation of motion, and by allowing the jet area to be a function of distance in the continuity equation, a lumped parameter relationship between pressure drop and flow has been developed which reflects the influence of inertia and dissipation. The results are applicable to the analysis of natural and prosthetic heart valves under normal and pathologic conditions. Within the physiologically possible conditions of frequency and flow rate, unsteady separated flows exhibit the same energy losses as comparable steady separated flows. Thus, the flow is quasi-steady, even when the waveforms and temporal relations indicate a significant inertial influence.

Wave packets, resonant interactions and soliton formation in inlet pipe flow

1993 ◽  
Vol 252 ◽  
pp. 1-30 ◽  
Author(s):  
Igor V. Savenkov
Keyword(s):  
Wave Packets ◽  
Three Dimensional ◽  
Short Wave ◽  
Nonlinear Interactions ◽  
Two Dimensional ◽  
Inlet Pipe ◽  
One Dimensional ◽  
Resonant Interactions ◽  
Dimensional Equation ◽  
Axisymmetric Disturbances

The development of disturbances (two-dimensional non-linear and three-dimensional linear) in the entrance region of a circular pipe is studied in the limit of Reynolds number R → ∞ in the framework of triple-deck theory. It is found that lower-branch axisymmetric disturbances can interact in the resonant manner. Numerical calculations show that a two-dimensional nonlinear wave packet grows much more rapidly than that in the boundary layer on a flat plate, producing a spike-like solution which seems to become singular at a finite time. Large-sized, short-scaled disturbances are also studied. In this case the development of axisymmetric disturbances is governed by single one-dimensional equation in the form of the Korteweg-de Vries and Benjamin-Ono equations in the long- and short-wave limits respectively. The nonlinear interactions of these disturbances lead to the formation of solitons which can run both upstream and downstream. Linear three-dimensional wave packets are also calculated.

scholarly journals Radial Imbibition in Paper under Temperature Differences

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 86
Author(s):  
Abel López-Villa ◽  
Abraham Medina ◽  
F. J. Higuera ◽  
Jonatan R. Mac Intyre ◽  
Carlos Alberto Perazzo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Porous Material ◽  
Radial Temperature ◽  
Temperature Variations ◽  
One Dimensional ◽  
Blotting Paper ◽  
Dimensional Equation ◽  
The One ◽  
Account Temperature

Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and surface tension in order to find the one-dimensional equation for the imbibition fronts. Experiments using blotting paper showed a good fit between the experimental data and theoretical profiles through the estimation of a single parameter.

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