The 2D problem of linear waves generated by an arbitrary pressure distribution <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mi>x,t</mml:mi><mml:mo>)</mml:mo></mml:math> on a uniform viscous stream of finite depth <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math> is
examined. The surface displacement <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B6;</mml:mi></mml:math> is expressed correct to <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>O(</mml:mo><mml:mi>&#x03BD;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> terms, for small viscosity
 <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03BD;</mml:mi></mml:math>, with a restriction on <mml:math id="E6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mi>x,t</mml:mi><mml:mo>)</mml:mo></mml:math>. For <mml:math id="E7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x,t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>&#x03C9;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>, exact forms of the steady-state propagating waves are next obtained for all 
 <mml:math id="E8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>x</mml:mi></mml:math> and not merely for <mml:math id="E9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>x</mml:mi><mml:mo>&#x226B;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> which form a wave-quartet or a wave-duo amid local disturbances. The long-distance asymptotic forms are then shown to be uniformly valid for large <mml:math id="E10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math>. For numerical and other purposes, a result essentially due to Cayley is used successfully to express these asymptotic forms in a series of powers of powers of <mml:math id="E11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> or <mml:math id="E12" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> with coefficients expressed directly in terms of nonviscous wave frequencies and amplitudes. An approximate thickness of surface boundary layer is obtained and a numerical study is undertaken to bring out the salient features of the exact and asymptotic wave motion in question.

Arghya Bandyopadhyay

A study of the waves and boundary layers due to a surface pressure on a uniform stream of a slightly viscous liquid of finite depth

A one-dimensional model is proposed for the simulations of resistance spot
welding, which is a common industrial method used to join metallic plates by electrical
heating. The model consists of  the Stefan problem, in enthalpy form, coupled  with
the equation of charge conservation for the electrical potential. The temperature
dependence of the density, thermal conductivity, specific heat, and electrical
conductivity are taken into account, since the process generally involves a large
temperature range, on the order of 1000 K. The model is general enough to
allow for the welding of plates of different thicknesses or dissimilar materials and
to account for variations in the Joule heating through the material
thickness due to the dependence of electrical resistivity on the
temperature. A novel feature in the model is the inclusion of the effects of interface
resistance between the plates which is also assumed to  be temperature dependent.
In addition to constructing the model, a finite difference scheme for its numerical
approximations is described, and representative computer simulations are depicted.
These describe welding processes involving different interface resistances,
different thicknesses, different materials, and different voltage forms.
The differences in the process due to AC or DC currents are depicted as well.

K. T. Andrews

L.  Guessous

S.  Nassar

S. V. Putta

M.  Shillor

A one-dimensional spot welding model

This paper generalizes the classical spline using a new construction of spline coalescence
hidden variable fractal interpolation function (CHFIF). The derivative of a
spline CHFIF is a typical fractal function that is self-affine or non-self-affine
depending on the parameters of a nondiagonal iterated function system. Our construction
generalizes the construction of Barnsley and Harrington (1989), when the construction
is not restricted to a particular type of boundary conditions. Spline CHFIFs
are likely to be potentially useful in approximation theory due to
effects of the hidden variables and these effects are demonstrated through suitable examples
in the present work.

A. K. B. Chand

G. P. Kapoor

Spline coalescence hidden variable fractal interpolation functions

We consider two quasistatic frictionless contact problems forpiezoelectric bodies. For the first problem the contact ismodelled with Signorini's conditions and for the second one ismodelled with normal compliance. In both problems the material'sbehavior is electroelastic and the adhesion of the contactsurfaces is taken into account and is modelled with a surfacevariable, the bonding field. We provide variational formulationsfor the problems and prove the existence of a unique weak solutionto each model. The proofs are based on arguments of time-dependentvariational inequalities, differential equations, and fixed point.Moreover, we prove that the solution of the Signorini contactproblem can be obtained as the limit of the solution of thecontact problem with normal compliance as the stiffnesscoefficient of the foundation converges to infinity.

Mircea  Sofonea

Rachid  Arhab

Raafat  Tarraf

Analysis of electroelastic frictionless contact problems withadhesion

We consider a general nonlinear age-structured population model with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> interacting species. We deduce the characteristic function in the form of a determinant of an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-by-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> matrix. Then we formulate some biologically meaningful sufficient conditions for the stability (resp., instability) of positive stationary solutions of the system.

Jozsef Z. Farkas

On the linearized stability of age-structured multispecies populations

Costas arrays are not only useful in radar engineering, but they
also present many interesting, and still open, mathematical
problems. This work collects in it all important knowledge about
them available today: some history of the subjects, density
results, construction methods, construction algorithms with full
proofs, and open questions. At the same time all the necessary
mathematical background is offered in the simplest possible format
and terms, so that this work can play the role of a reference for
mathematicians and mathematically inclined engineers interested in the field.

Konstantinos Drakakis

A review of Costas arrays

A fourth-order nonlinear evolution equation is derived from amicroscopic model for surface diffusion, namely, the continuumsolid-on-solid model. We use the method developed by Varadhan forthe computation of the hydrodynamic scaling limit of nongradientmodels. What distinguishes our model from other models discussedso far is the presence of two conservation laws for the dynamicsin a nonperiodic box and the complex dynamics that is notnearest-neighbor interaction. Along the way, a few steps have tobe adapted to our new context. As a byproduct of our main result,we also derive the hydrodynamic scaling limit of a perturbation ofthe continuum solid-on-solid model, a model that incorporates bothsurface diffusion and surface electromigration.

Anamaria  Savu

Hydrodynamic scaling limit of continuum solid-on-solid model

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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

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Journal of Applied Mathematics - Table of contents 2006

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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal of Applied Mathematics