A Completeness Study on Certain 2×22\times2 Lax Pairs Including Zero Terms

We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all $2\times2$ Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms within the Lax matrices to be zero. We cover all possible Lax pairs of this type and find a new third order equation that can be reduced to special cases of the non-autonomous lattice KdV and lattice modified KdV equations among others

Algorithmic Thermodynamics

Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In particular, suppose we fix a universal prefix-free Turing machine and let X be the set of programs that halt for this machine. Then we can regard X as a set of 'microstates', and treat any function on X as an 'observable'. For any collection of observables, we can study the Gibbs ensemble that maximizes entropy subject to constraints on expected values of these observables. We illustrate this by taking the log runtime, length, and output of a program as observables analogous to the energy E, volume V and number of molecules N in a container of gas. The conjugate variables of these observables allow us to define quantities which we call the 'algorithmic temperature' T, 'algorithmic pressure' P and algorithmic potential' mu, since they are analogous to the temperature, pressure and chemical potential. We derive an analogue of the fundamental thermodynamic relation dE = T dS - P d V + mu dN, and use it to study thermodynamic cycles analogous to those for heat engines. We also investigate the values of T, P and mu for which the partition function converges. At some points on the boundary of this domain of convergence, the partition function becomes uncomputable. Indeed, at these points the partition function itself has nontrivial algorithmic entropy.Comment: 20 pages, one encapsulated postscript figur

Rising protectionist threat creates risks for Texas

Expanding trade has brought jobs and business to Texas, but has left the state particularly vulnerable to antitrade actions. Texas would suffer greatly if the U.S. and other countries implement protectionist measures.Economic conditions - Texas ; International trade ; Free trade ; North American Free Trade Agreement

Density functional theory study of Fe(II) adsorption and oxidation on goethite surfaces

We study the interactions between Fe(II) aqua complexes and surfaces of goethite (alpha-FeOOH) by means of density functional theory calculations including the so-called Hubbard U correction to the exchange-correlation functional. Using a thermodynamic approach, we find that (110) and (021) surfaces in contact with aqueous solutions are almost equally stable, despite the evident needlelike shape of goethite crystals indicating substantially different reactivity of the two faces. We thus suggest that crystal anisotropy may result from different growth rates due to virtually barrierless adsorption of hydrated ions on the (021) but not on the (110) surface. No clear evidence is found for spontaneous electron transfer from an adsorbed Fe(II) hex-aqua complex to a defect-free goethite substrate. Crystal defects are thus inferred to play an important role in assisting such electron transfer processes observed in a recent experimental study. Finally, goethite surfaces are observed to enhance the partial oxidation of adsorbed aqueous Fe(II) upon reaction with molecular oxygen. We propose that this catalytic oxidation effect arises from donation of electronic charge from the bulk oxide to the oxidizing agent through shared hydroxyl ligands anchoring the Fe(II) complexes on the surface

A Monolithically Fabricated Combinatorial Mixer for Microchip-Based High-Throughput Cell Culturing Assays

We present an integrated method to fabricate 3- D microfluidic networks and fabricated the first on-chip cell culture device with an integrated combinatorial mixer. The combinatorial mixer is designed for screening the combinatorial effects of different compounds on cells. The monolithic fabrication method with parylene C as the basic structural material allows us to avoid wafer bonding and achieves precise alignment between microfluidic channels. As a proof-of-concept, we fabricated a device with a three-input combinatorial mixer and demonstrated that the mixer can produce all the possible combinations. Also, we demonstrated the ability to culture cells on-chip and performed a simple cell assay on-chip using trypan blue to stain dead cells

Subspace representations in ab initio methods for strongly correlated systems

We present a generalized definition of subspace occupancy matrices in ab initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT, which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT+U in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies and ionic forces is preserved. We illustrate the effect of this formalism in a DFT+U study using self-consistently determined projectors.Comment: 15 pages, 8 figures. This version (v2) matches that accepted for Physical Review B on 15th April 201

Generalized Wannier functions: a comparison of molecular electric dipole polarizabilities

Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization. Nonorthogonal generalized Wannier functions (NGWFs) [Skylaris et al., Phys. Rev. B 66, 035119 11 (2002); Skylaris et al., J. Chem. Phys. 122, 084119 (2005)] may also be optimized in situ, in the process of solving for the ground-state density. We explore the relationship between NGWFs and orthonormal, maximally localized Wannier functions (MLWFs) [Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997); Souza, Marzari, and Vanderbilt, ibid. 65, 035109 (2001)], demonstrating that NGWFs may be used to compute electric dipole polarizabilities efficiently, with no necessity for post-processing optimization, and with an accuracy comparable to MLWFs.Comment: 5 pages, 1 figure. This version matches that accepted for Physical Review B on 4th May 201