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Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation.
The Lorentz gauge condition makes them hyperbolic equations with the null form.
To handle the divergence-free property, a Coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically.
The scheme for the Maxwell Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show.
In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition.
The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector.
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Ground-based sensors are already used to record temperature, wind speed, humidity, air density, and rainfall, but they gauge conditions only at ground level, says How.
The desirable property of PADM is that it turns the surface of constraints into a local attractor because its constraint propagation system becomes second-order parabolic independently of the gauge conditions employed.
But unlike blood, urine and other bodily fluids, relatively little research has gone into using sweat to gauge conditions inside our bodies.
As L.A. Unified works through "growing pains" to revamp its evaluation process, Lucia said, his group sought to gauge conditions in other California school districts.
Also given is the conditional gauge theorem conditioned according to Martin kernels and the limiting behaviors of theh-conditional stable process, wherehis a positive harmonic function ofXD.
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