On the density expansion of spectral lineshapes

We compare two types of expansions (in the density of perturbers) of collisionally broadened spectral lineshapes. The first is the more conventional frequency-domain expansion of Fano whereas the second is made in the time domain. In the impact limit they both predict a simple lorentzian line shape but otherwise they yield very different results upon trunction. Our calculations indicate that the time-domain expansion is more adequate and should be preferred.     

Two-dimensional near-ultraviolet spectroscopy of aromatic residues in amyloid fibrils: a first principles study

We report a first principles study of two dimensional electronic spectroscopy of aromatic side chain transitions in the 32-residue β-amyloid (Aβ(9-40)) fibrils in the near ultraviolet (250-300 nm). An efficient exciton Hamiltonian with electrostatic fluctuations (EHEF) algorithm is used to compute the electronic excitations in the presence of environmental fluctuations. The through-space inter- and intra-molecular interactions are calculated with high level quantum mechanics (QM) approaches, and interfaced with molecular mechanics (MM) simulations. Distinct two dimensional near ultraviolet (2DNUV) spectroscopic signatures are identified for different aromatic transitions, and the couplings between them. 2DNUV signals associated with the transition couplings are shown to be very sensitive to the change of residue-residue interactions induced by residue mutations. Our simulations suggest that 2DNUV spectra could provide a useful local probe for the structure and kinetics of fibrils.     

Stochastic Liouville equations for coherent multidimensional spectroscopy of excitons

Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath modulation model of a dimer and a four-state jump bath model of a single chromophore). Slow Gaussian-Markovian spectral diffusion of a symmetric dimer induces new peaks which are damped as the dipole moment is equilibrated. These effects require an explicit treatment of the bath and may not be described by lower-level theories such as the Redfield equations, which eliminate the bath.     

Probing interactions between core-electron transitions by ultrafast two-dimensional x-ray coherent correlation spectroscopy

Two-dimensional x-ray correlation spectra (2DXCS) obtained by varying two delay periods in a time-resolved coherent all-x-ray four-wave-mixing measurement are simulated for the N 1s and O 1s transitions of aminophenol. The necessary valence and core-excited states are calculated using singly and doubly substituted Kohn-Sham determinants within the equivalent-core approximation. Sum-over-states calculations of the 2DXCS signals of aminophenol isomers illustrate how novel information about electronic states can be extracted from the 2D spectra. Specific signatures of valence and core-excited states are identified in the diagonal and off-diagonal peaks arising from core transitions of the same and different types, respectively.     

Probing multiple core-hole interactions in the nitrogen K-edge of DNA base pairs by multidimensional attosecond X-ray spectroscopy. A simulation study

Two-dimensional X-ray correlation spectroscopy (2DXCS) signals of the isolated DNA bases and Watson-Crick base pairs which contain multiple absorbing nitrogen atoms are calculated. Core-hole excited states are calculated using density functional theory with the B3LYP functional and 6-311G** basis set. Sum over states calculations of the signals reveal changes in cross-peak intensities between hydrogen-bonded and stacked base pairs. Nucleobase analogues are proposed for investigating base-stacking and hydrogen-bonding interactions.     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

Modified Eulerian–Lagrangian formulation for hydrodynamic modeling

We present the modified Eulerian–Lagrangian (MEL) formulation, based on non-divergent forms of partial differential balance equations, for simulating transport of extensive quantities in a porous medium. Hydrodynamic derivatives are written in terms of modified velocities for particles propagating phase and component quantities along their respective paths. The particles physically interpreted velocities also address the heterogeneity of the matrix and fluid properties. The MEL formulation is also implemented to parabolic Partial Differential Equations (PDE’s) as these are shown to be interchangeable with equivalent PDE’s having hyperbolic – parabolic characteristics, without violating the same physical concepts. We prove that the MEL schemes provide a convergent and monotone approximation also to PDE’s with discontinuous coefficients. An extension to the Peclet number is presented that also accounts for advective dominant PDE’s with no reference to the fluid velocity or even when this velocity is not introduced.In Sorek et al. [27], a mathematical analysis for a linear system of coupled PDE’s and an example of nonlinear PDE’s, proved that the finite difference MEL, unlike an Eulerian scheme, guaranties the absence of spurious oscillations. Currently, we present notions of monotone interpolation associated with the MEL particle tracking procedure and prove the convergence of the MEL schemes to the original balance equation also for discontinuous coefficients on the basis of difference schemes approximating PDE’s. We provide numerical examples, also with highly random fields of permeabilities and/or dispersivities, suggesting that the MEL scheme produces resolutions that are more consistent with the physical phenomenon in comparison to the Eulerian and the Eulerian–Lagrangian (EL) schemes.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).