A proof of the Benjamin-Feir instability

The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms of the spatial and temporal Hamiltonian structure of the water-wave problem. A proof, within the Hamiltonian framework, of instability of the Stokes periodic wavetrain is presented. A Hamiltonian center-manifold analysis reduces the linear stability problem to an ordinary differential eigenvalue problem on ℝ⁴. A projection of the reduced stability problem onto the tangent space of the 2-manifold of periodic Stokes waves is used to prove the existence of a dispersion relation Λ(λ,σ, I ₁, I ₂)=0 where λ ε ℂ is the stability exponent for the Stokes wave with amplitude I ₁ and mass flux I ₂ and σ is the “sideband’ or spatial exponent. A rigorous analysis of the dispersion relation proves the result, first discovered in the 1960's, that the Stokes gravity wavetrain of sufficiently small amplitude is unstable for F ε (0,F₀) where F ₀ ≈ 0.8 and F is the Froude number.     

Complexes of Formaldehyde and α-Dicarbonyls with Hydroxylamine: FTIR Matrix Isolation and Theoretical Study

The interactions of formaldehyde (FA), glyoxal (Gly) and methylglyoxal (MGly) with hydroxylamine (HA) isolated in solid argon and nitrogen were studied using FTIR spectroscopy and ab initio methods. The spectra analysis indicates the formation of two types of hydrogen-bonded complexes between carbonyl and hydroxylamine in the studied matrices. The cyclic planar complexes are stabilized by O–H⋯O(C), and C–H⋯N interactions and the nonplanar complexes are stabilized by O–H⋯O(C) bond. Formaldehyde was found to form with hydroxylamine, the cyclic planar complex and methylglyoxal, the nonplanar one in both argon and nitrogen matrices. In turn, glyoxal forms with hydroxylamine the most stable nonplanar complex in solid argon, whereas in solid nitrogen, both types of the complex are formed.     

Alpha-plutonium's polycrystalline elastic moduli over its full temperature range

alpha-plutonium's volume-corrected polycrystal elastic moduli were measured between 18 K and the upper limit of its occurrence, near 400 K. The two independent moduli for a polycrystal-bulk and shear-behave smoothly, indicating no phase transition. Both moduli show the same 50% increase on cooling, an order of magnitude larger than in other metals. The Debye temperature obtained from low-temperature elastic moduli, 207 K, significantly exceeds most previous estimates. The Gruneisen parameter gamma=5.3, obtained from the temperature dependence of the bulk modulus, is intermediate among previous estimates using other approaches, alpha-plutonium's Poisson ratio nu is low: 0.18, nearly temperature independent, and its small decrease on warming opposes usual behavior. The high gamma, large but equal bulk modulus and shear modulus fractional stiffening on cooling, and near-temperature-invariant nu are attributed to a single mechanism: 5-f electron localization-delocalization.     

CH stretching vibration of N-methylformamide as a sensitive probe of its complexation: infrared matrix isolation and computational study

The complexes between trans-N-methylformamide (t-NMF) and Ar, N(2), CO, H(2)O have been studied by infrared matrix isolation spectroscopy and/or ab initio calculations. The infrared spectra of NMF/Ne, NMF/Ar and NMF/N(2)(CO,H(2)O)/Ar matrices have been measured and the effect of the complexation on the perturbation of t-NMF frequencies was analyzed. The geometries of the complexes formed between t-NMF and Ar, N(2), CO and H(2)O were optimized in two steps at the MP2/6-311++G(2d,2p) level of theory. The four structures, found for every system at this level, were reoptimized on the CP-corrected potential energy surface; both normal and CP corrected harmonic frequencies and intensities were calculated. For every optimized structure the interaction energy was partitioned according to the SAPT scheme and the topological distribution of the charge density (AIM theory) was performed. The analysis of the experimental and theoretical results indicates that the t-NMF-N(2) and CO complexes present in the matrices are stabilized by very weak N-H···N and N-H···C hydrogen bonds in which the N-H group of t-NMF serves as a proton donor. In turn, the t-NMF-H(2)O complex present in the matrix is stabilized by O-H···O(C) hydrogen bonding in which the carbonyl group of t-NMF acts as a proton acceptor. Both, the theoretical and experimental results indicate that involvement of the NH group of t-NMF in formation of very weak hydrogen bonds with the N(2) or CO molecules leads to a clearly noticeable red shift of the CH stretching wavenumber whereas engagement of the CO group as a proton acceptor triggers a blue shift of this wavenumber.     

Variational Convergence of Gradient Flows and Rate-Independent Evolutions in Metric Spaces

We study the asymptotic behaviour of families of gradient flows in a general metric setting, when the metric-dissipation potentials degenerate in the limit to a dissipation with linear growth. We present a general variational definition of BV solutions to metric evolutions, showing the different characterization of the solution in the absolutely continuous regime, on the singular Cantor part, and along the jump transitions. By using tools of metric analysis, BV functions and blow-up by time rescaling, we show that this variational notion is stable with respect to a wide class of perturbations involving energies, distances, and dissipation potentials. As a particular application, we show that BV solutions to rate-independent problems arise naturally as a limit of p-gradient flows, p >?1, when the exponents p converge to 1.     

Practical methods for including torsional anharmonicity in thermochemical calculations on complex molecules: the internal-coordinate multi-structural approximation

Many methods for correcting harmonic partition functions for the presence of torsional motions employ some form of one-dimensional torsional treatment to replace the harmonic contribution of a specific normal mode. However, torsions are often strongly coupled to other degrees of freedom, especially other torsions and low-frequency bending motions, and this coupling can make assigning torsions to specific normal modes problematic. Here, we present a new class of methods, called multi-structural (MS) methods, that circumvents the need for such assignments by instead adjusting the harmonic results by torsional correction factors that are determined using internal coordinates. We present three versions of the MS method: (i) MS-AS based on including all structures (AS), i.e., all conformers generated by internal rotations; (ii) MS-ASCB based on all structures augmented with explicit conformational barrier (CB) information, i.e., including explicit calculations of all barrier heights for internal-rotation barriers between the conformers; and (iii) MS-RS based on including all conformers generated from a reference structure (RS) by independent torsions. In the MS-AS scheme, one has two options for obtaining the local periodicity parameters, one based on consideration of the nearly separable limit and one based on strongly coupled torsions. The latter involves assigning the local periodicities on the basis of Voronoi volumes. The methods are illustrated with calculations for ethanol, 1-butanol, and 1-pentyl radical as well as two one-dimensional torsional potentials. The MS-AS method is particularly interesting because it does not require any information about conformational barriers or about the paths that connect the various structures.     

Quasi-two-dimensional organic superconductors: A review

Quasi-two-dimensional organic superconductors are reviewed. These systems exhibit many interesting phenomena, including reduced dimensionality, strong electron - electron and electron - phonon interactions and the proximity of antiferromagnetism, insulator states and superconductivity. Moreover, it has been possible to measure the electronic bands of many of the organics in great detail, in contrast to the situation in other well-known systems in which similar phenomena occur. The crystal structure and normal-state properties of the organics are described before the experimental evidence is presented for and against exotic superconductivity mediated by antiferromagnetic fluctuations. Finally, three instances of field-induced unconventional superconductivity are described.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.