Perturbation homogeneous

In Fig. 5.20 one can see the rather rapid transition of the deterministic system from the slightly perturbed homogeneous fixed point (H) to the inhomogeneous filamentary one (I). This illustrates that for the given parameters the only stable solution, apart from a trivial, non-conducting fixed point, is an inhomogeneous steady state. 

Bornemann, F. A. Homogenization in Time of Singularly Perturbed Conservative Mechanical Systems. Manuscript (1997) 146pp... 

The evolution of spall in a body subject to transient tensile stresses is complex. A state of homogeneous tensile stress is intrinsically unstable and small perturbations in the material microstructure (microcracks, inclusions, etc.) can lead to the opening of voids and initiation of the spall process. 

The shock-compression pulse carries a solid into a state of homogeneous, isotropic compression whose properties can be described in terms of perfect-crystal lattices in thermodynamic equilibrium. Influences of anisotropic stress on solid materials behaviors can be treated as a perturbation to the isotropic equilibrium state. ... 

If the perturbation is a homogeneous electric field F, the perturbation operator P i (eq. (10.17)) is the position vector r and P2 is zero. As.suming that the basis functions are independent of the electric field (as is normally the case), the first-order HF property, the dipole moment, from the derivative formula (10.21) is given as (since an HF wave function obeys the Hellmann-Feynman theorem)... 

An Experimental Study Using Feed Perturbations for a Free-Radically Initiated Homogeneous Polymerization in a Continuous-Flow Stirred-Tank Reactor... 

Finally, in order to ensure an homogeneous treatment of all excited states at the variational level, the MCSCF calculation should be averaged on the states under investigation. The lowest eigenfunetions of the MCSCF Hamiltonian will provide the zeroth-order wavefunetions to build the perturbation on. 

Figure 8.11 Evidence of cross-diffusional effects. The homogeneous distribution of species 2 (dashed line, top) is perturbed by a coexisting gradient of species 1 (bottom).

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