This information measure, herein dubbed the variational information, meaningfully assigns a numerical bit-value to arbitrary state transitions of physical systems. ❋ Mumon (2005)
"Anytime you see some kind of variational depth in a rock like this, you interpret it to mean there is some kind of chemical alteration that has taken place since the rock was first exposed on the surface," Squyres explained. ❋ Unknown (2010)
I suspect there is some extremal principle here, where the tuning is some variational principle on a partition function which results in a greatest upper bound on the measure of complexity which can exist in a local region. ❋ Unknown (2010)
Calculating integrals and minimizing functions for many-parameter variational wave functions of semiconductor nanostructures in very high magnetic fields was much more on my mind. ❋ Unknown (2007)
Neither would they seem necessarily to be only convenient mathematical fictions, as, for example, are the physically impossible dynamical evolutions of a system one integrates over in the variational derivation of the Euler-Lagrange equations, for, as we have remarked, many physicists and philosophers seem eager to find such a construction for the purpose of bestowing substantive and clear ontic status on singular structure. ❋ Curiel, Erik (2009)
Of particular importance here is the application of the variational principle to the QM of such systems. ❋ Sean (2008)
Each form is reachable by small, selectable variational steps from simpler forms. ❋ Unknown (2006)
Rather, they suggest that the pre-variationists held two variational beliefs that the transformationists did not: (1) that organisms inherit the traits of their parents regardless of their adaptive value and (2) that differential survival is relevant to species adaptation. ❋ Unknown (2006)
Now evidently Dembski has read Cosma Shalizi's critique of an earlier version of this paper here, but for the life of me, other than admitting Shalizi is right that Dembski's "variational information" really is a special case of the more general Rényi information, I can't find anything "revised" in this paper. ❋ Mumon (2005)
I should try to develop a Green's function variational method for three-body scattering problems, like low-energy neutron-deuteron scattering, while warning me ominously, that he himself had tried and failed. ❋ Unknown (1999)
In short order we had recast the Rayleigh-Ritz variational theorem for the groundstate energy in terms of the density n (r) instead of the many electron wave function, leading to what is now called the Hohenberg Kohn (HK) variational principle. ❋ Unknown (1999)
Bloembergen, on the recently discovered, so-called Knight shift of nuclear magnetic resonance, and, in this connection, returning to my old love of variational methods, developed a new variational approach to the study of wavefunctions in periodic crystals. ❋ Unknown (1999)
I told Schwinger briefly of my very modest efforts using variational principles. ❋ Unknown (1999)
We developed a theory for the energy band structure of electrons for periodic potentials, harking back to my earlier experience with scattering, Green's functions and variational methods. ❋ Unknown (1999)
Wavefunctions for these excitations were proposed and their computed variational energies found to match the experimental activation energy for the parallel conductance in the plateau regions. ❋ Unknown (1999)
It was not exact at all, but rather a well-known variational technique for approximating the ground state of strongly-interacting many-body systems. ❋ Unknown (1999)
Together we derived from the HK variational principle what are now known as the Kohn-Sham (KS) equations, which have found extensive use by physicists and chemists, including members of my group. ❋ Unknown (1999)
Green's function variational principles during the war for wave-guides, optics and nuclear physics (Soon afterwards Green's functions played an important role in his Nobel-Prize-winning work on quantum electrodynamics). ❋ Unknown (1999)
Some six months later, when I had obtained some partial, very unsatisfactory results, I looked for alternative approaches and soon found a rather elementary formulation, later known as Kohn's variational principle for scattering, and useful for nuclear, atomic and molecular problems. ❋ Unknown (1999)
