Trivial, strongly minimal theories are model complete after naming constants

We prove that if is any model of a trivial, strongly minimal theory, then the elementary diagram is a model complete -theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are -decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is .

     

Correlation functions of the chiral Potts chain from conformal field theory and finite-size corrections

We study the incommensurate phase of the N = 3 superintegrable chiral Potts chain by computing the leading finite-size corrections to the low-lying energy levels. These results are used to study the asymptotic behavior of the correlation functions. In particular we analyze the difference between the regions above and below the self-dual point.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

A comparison of parabolic wave theories for linearly elastic solids

The Schrödinger equation describes a theory for propagating scalar waves which is frequently termed a parabolic theory. This theory has been demonstrated to provide a paraxial, or narrow-angled, approximation to the theory of acoustic wave propagation, described by the Helmholtz equation, by a variety of seemingly different procedures. Several authors have considered the question of an approximation to the time harmonic equations of linear elastodynamics, which is parabolic in the above described sense. Since none of the deivation procedures employed can be termed rigorous, and since the results of these procedures are different, the validity of each of the theories is suspect and all should be considered further. In this paper we consider three parabolic theories of elastodynamics; by Hudson, by Landers and Claerbout, and by McCoy; and apply them in turn to a computational experiment that can be solved in the perturbation limit using the exact equations of elastodynamics. The principal conclusion achieved is that an approximate theory for propagating vector waves must be based on a representation of the vector wave field, that explicitly incorporates different wave speeds for the dilitational and rotational components, if predictions of the approximate theory are to approach those of the exact formulation for narrow angles.     

Unraveling anharmonic effects in the vibrational predissociation spectra of H5O2(+) and its deuterated analogues

The nature of anharmonic couplings in the H(5)O(2)(+) "Zundel" ion and its deuterated isotopologues is investigated through comparison of their measured and calculated vibrational spectra. This follows a recent study in which we reported spectra for H(5)O(2)(+), D(5)O(2)(+), and D(4)HO(2)(+) from ～600 to 4000 cm(-1), as well as H(4)DO(2)(+) in the OH and OD stretching regions [ J. Phys. Chem. B 2008 , 112 , 321 ]. While the assignments of the higher-energy transitions associated with the fundamentals of the exterior OH and OD motions are relatively straightforward, difficulties arise in the assignment of the lower-frequency regions that involve displacement of the bridging proton, especially for the isotopically mixed species. Here we revisit the Ar-tagged isotopomers, and report the low energy action spectrum of H(4)DO(2)(+) for the first time, as well as present significantly improved spectra for the D(4)HO(2)(+) and D(5)O(2)(+) systems. Band assignments are clarified in several cases using IR-IR hole-burning. We then investigate the physical origin of the anharmonic effects encoded in these spectra using a recently developed technique in which the anharmonic frequencies and intensities of transitions (involving up to two quanta of excitation) are evaluated using the ground state probability amplitudes [ J. Phys. Chem. A 2009 , 113 , 7346 ] obtained from diffusion Monte Carlo simulations. This approach has the advantage that it is applicable to low-symmetry systems [such as (HDO)H(+)(OH(2))] that are not readily addressed using highly accurate methods such as the multiconfigurational time-dependent Hartree (MCTDH) approach. Moreover, it naturally accommodates an intuitive evaluation of the types of motion that contribute oscillator strength in the various regions of the spectrum, even when the wave function is intrinsically not separable as a product of low-dimensional approximate solutions. Spectra for H(5)O(2)(+), D(5)O(2)(+), H(4)DO(2)(+), and D(4)HO(2)(+) that are calculated by this approach are shown to be in excellent agreement with the measured spectra for these species, leading to reassignments of two of the bands in the intramolecular bending region of D(4)HO(2)(+).     

Modelling rotations,vibrations, and rovibrational couplings in astructural molecules – a case study based on the H+5 molecular ion

One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H⁺₅. Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H⁺₅, this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H⁺₅ is gained via variational nuclear motion and diffusion Monte Carlo computations and by the analysis of the wavefunctions they provide. The modelling results describing the transition from the zero barrier limit to the large barrier limit should prove to be useful for the important class of molecules and molecular ions that contain two weakly coupled internal rotors.     

Decreased Water Mobility Contributes To Increased α-Synuclein Aggregation**

The solvation shell is essential for the folding and function of proteins, but how it contributes to protein misfolding and aggregation has still to be elucidated. We show that the mobility of solvation shell H₂O molecules influences the aggregation rate of the amyloid protein α-synuclein (αSyn), a protein associated with Parkinson's disease. When the mobility of H₂O within the solvation shell is reduced by the presence of NaCl, αSyn aggregation rate increases. Conversely, in the presence CsI the mobility of the solvation shell is increased and αSyn aggregation is reduced. Changing the solvent from H₂O to D₂O leads to increased aggregation rates, indicating a solvent driven effect. We show the increased aggregation rate is not directly due to a change in the structural conformations of αSyn, it is also influenced by a reduction in both the H₂O mobility and αSyn mobility. We propose that reduced mobility of αSyn contributes to increased aggregation by promoting intermolecular interactions.