Long-range Coefficient Research Articles

Limit Theorem for a Rough Differential Equation with a Negative Long-Range Random Coefficient

Limit Theorem for a Rough Differential Equation with a Negative Long-Range Random Coefficient

Fourier-transform spectroscopy and global deperturbation treatment of the A1Σu+ and b3Πu states of K2 in the entire bound energy range.

Rotationally resolved Fourier-transform spectra of laser-induced fluorescence A1Σu+∼b3Πu→X1Σg+ of K2 molecules were recorded and analyzed, yielding 4053 term values of the spin-orbit (SO) coupled A ∼ b complex of the 39K2 isotopologue with ∼0.01 cm-1 accuracy. Their compilation with 1739 term values from previously published sources allowed them to cover the energy range [9955, 17 436] cm-1 from the bottom of the lower-lying b3Πu state up to the vicinity of the atomic asymptote 4s2S12 + 4p2P12, with a rotational quantum number J ∈ [0, 149]. The experimental data were processed by a direct 6 × 6 coupled-channel (CC) deperturbation treatment, which accounted explicitly for both SO and electronic-rotational interactions between all six e-symmetry states: A1Σu+(0u+), b3Πu(0u+,1u,2u), c3Σu(1u), and B1Πu(1u). The initial parameters of the global deperturbation model have been estimated in the framework of abinitio electronic structure calculations applying multi-reference configuration-interaction and coupled-clusters methods. The interatomic potentials analytically defined for A and b states, as well as SO-splitting of the triplet b state and A ∼ b SO-coupling functions, have been particularly refined to fit the 5792 term values of the 39K2 isotopologue, whereas the rest parameters were fixed on their abinitio values. The resulting mass-invariant parameters of the 6 × 6 CC model reproduced the overall rovibronic term energies of the A ∼ b complex of 39K2 with accuracy, which is well within the experimental errors. The quality of the deperturbation analysis was independently confirmed by comparison with the present obtained 705 and 14 term values of respective 39K41K and 41K2 isotopologues, as well as by agreement between measured and predicted relative intensity distributions in long A ∼ b → X(vX) band progressions. This deperturbation analysis provided the refined dissociation energy Tdis = 17 474.569(5) cm-1 and the long-range coefficient C3Σ = 5.501(4) × 105 cm-1 Å3 relevant to the non-relativistic atomic limit 4s + 4p. The derived Tdis yielded the accurate well depth De = 4450.910(5) cm-1 for the ground X1Σg+ state, whereas the new C3Σ value yielded the improved estimates for atomic K(4p2P12;32) radiative lifetimes, τ12 = 26.67(3) and τ32 = 26.32(3) ns.

Neutron scattering studies on ionic diffusion behaviors of superionic α-Cu2−δ Se

We present studies on crystal structure and ionic diffusion behaviors of superionic Cu2−δ Se (δ = 0, 0.04, and 0.2) by utilizing neutron powder diffraction and quasi-elastic neutron scattering. In the superionic phase, the structural model with Cu ions occupying the Wyckoff sites of 8c and 32f provides the best description of the structure. As the content of Cu increasing in Cu2−δ Se, the Cu occupancy increases on the 32f site but decreases on the 8c site. Fitting to the quasi-elastic neutron scattering spectra reveals two diffusion modes: the localized diffusion between the 8c and 32f sites and the long-range diffusion between the adjacent 8c sites using the 32f site as a bypass. Between 430 and 650 K, we measured that the compound with more Cu content exhibits a larger long-range diffusion coefficient. Temperature in this range does not affect the long-range diffusion process obviously. Our results suggest the two diffusion modes cooperative and, thus, provide a microscopic understanding of the ionic diffusion of the Cu ions in superionic Cu2−δ Se.

Interaction Potential for NaCs for Ultracold Scattering and Spectroscopy.

We obtain the interaction potential for NaCs by fitting to experiments on ultracold scattering and spectroscopy in optical tweezers. The central region of the potential has been accurately determined from Fourier transform spectroscopy at higher temperatures, so we focus on adjusting the long-range and short-range parts. We use coupled-channel calculations of binding energies and wave functions to understand the nature of the molecular states observed in ultracold spectroscopy and of the state that causes the Feshbach resonance used to create ultracold NaCs molecules. We elucidate the relationships between the experimental quantities and features of the interaction potential. We establish the combinations of experimental quantities that determine particular features of the potential. We find that the long-range dispersion coefficient C6 must be increased by about 0.9% to 3256(1)Eha06 to fit the experimental results. We use coupled-channel calculations on the final potential to predict bound-state energies and resonance positions.

Long-range dispersion C6 coefficient for SF6 dimer: Experimental and theoretical study.

The long-range dispersion C6 coefficient for the SF6 dimer is experimentally measured using a technique that uses the expansion of a supersonic pulse jet into a vacuum. A dynamic model of the jet enables us to correlate the position of the maximal peak in the time-of-flight spectrum with the initial conditions of the experiment and the parameters of the intermolecular interaction potential. Due to the low temperature of the jet target, the C6 coefficient can be extracted directly from the experimental results. Theoretical calculation of the C6 dispersion coefficient is also performed by using linearly approximated explicitly correlated coupled-cluster singles and doubles (CCSD(F12)) method with the subsequent utilization of the Casimir-Polder formula. Good agreement of experimental and theoretical results confirms the reliability of results.

Highly sensitive photoassociation spectroscopy of ultracold 23Na133Cs molecular long-range states below the 3S1/2 + 6P3/2 limit**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304203), the ChangJiang Scholars and Innovative Research Team in the University of the Ministry of Education of China (Grant No. IRT13076), the National Natural Science Foundation of China (Grant Nos. 91436108,

We present high resolution photoassociation spectroscopy of ultracold 23Na133Cs molecules in a long-range c3Σ+ state below the (3S1/2 + 6P3/2) asymptote. We perform photoassociation spectroscopy in a dual-species magneto-optical trap (MOT) and detect the photoassociation resonances using trap-loss spectroscopy. By fitting the experimental data with the semi-classical LeRoy–Bernstein formula, we deduce the long-range molecular coefficient C6 and derive the empirical potential energy curve in the long-range region.

Can Tai Chi training impact fractal stride time dynamics, an index of gait health, in older adults? Cross-sectional and randomized trial studies.

PurposeTo determine if Tai Chi (TC) has an impact on long-range correlations and fractal-like scaling in gait stride time dynamics, previously shown to be associated with aging, neurodegenerative disease, and fall risk.MethodsUsing Detrended Fluctuation Analysis (DFA), this study evaluated the impact of TC mind-body exercise training on stride time dynamics assessed during 10 minute bouts of overground walking. A hybrid study design investigated long-term effects of TC via a cross-sectional comparison of 27 TC experts (24.5 ± 11.8 yrs experience) and 60 age- and gender matched TC-naïve older adults (50–70 yrs). Shorter-term effects of TC were assessed by randomly allocating TC-naïve participants to either 6 months of TC training or to a waitlist control. The alpha (α) long-range scaling coefficient derived from DFA and gait speed were evaluated as outcomes.ResultsCross-sectional comparisons using confounder adjusted linear models suggest that TC experts exhibited significantly greater long-range scaling of gait stride time dynamics compared with TC-naïve adults. Longitudinal random-slopes with shared baseline models accounting for multiple confounders suggest that the effects of shorter-term TC training on gait dynamics were not statistically significant, but trended in the same direction as longer-term effects although effect sizes were very small. In contrast, gait speed was unaffected in both cross-sectional and longitudinal comparisons.ConclusionThese preliminary findings suggest that fractal-like measures of gait health may be sufficiently precise to capture the positive effects of exercise in the form of Tai Chi, thus warranting further investigation. These results motivate larger and longer-duration trials, in both healthy and health-challenged populations, to further evaluate the potential of Tai Chi to restore age-related declines in gait dynamics.Trial registrationThe randomized trial component of this study was registered at ClinicalTrials.gov (NCT01340365).

Interacting He and Ar atoms: Revised theoretical interaction potential, dipole moment, and collision-induced absorption spectra

Coupled cluster quantum chemical calculations of the potential energy surface and the induced dipole surface are reported for the He-Ar van der Waals collisional complex. Spectroscopic parameters are derived from global analytical fits while an accurate value for the long-range dipole coefficient D7 is obtained by perturbation methods. Collision-induced absorption spectra are computed quantum mechanically and compared with existing measurements.

High Sensitivity Measurement and Accurate Analysis of the Vibrational Spectroscopy Near the (6S1/2+6P3/2) Dissociation limit for 1g State of Cs2

The photoassociation spectroscopic data of the long-range molecular 1g state of Cs 2 in the asymptotic range red detuned [-5.02, -2.45 cm -1 ] to the (6S 1/2 +6P 3/2 ) dissociation limit detected using photon counting technique are presented and 18 new high-lying vibrational energy levels are obtained. Fitting experimental data to the improved LeRoy–Bernstein (LRB) formula, we have obtained the long-range molecular coefficient c 3 with a high precision and also demonstrated the necessity of the improved LRB formula for more precise c 3 coefficient by analyzing the residual from fitting procedure.

CrRb: A molecule with large magnetic and electric dipole moments

We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule 52Cr-87Rb, and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient (C6=1770 a.u.) has an expected error of 3%. The ground state 6Sigma+ molecule at its equilibrium separation has a permanent electric dipole moment of de (Re=3.34 A) = 2.90 D. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of 100-1000.

Two-Dimensional Continuum Percolation Threshold as a Function of the Radius of the Diffusing Particles

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing diffusion in the presence of immobile obstacles is the percolation threshold, where long-range conducting paths disappear and the long-range diffusion coefficient therefore goes to zero. The thresholds are well-known for point diffusing particles on various lattices or the continuum. But for diffusing particles of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. For the triangular lattice, the threshold is known to be highly sensitive to the size of the diffusing particle [Saxton, Biophys J 64 (1993) 1053], but lattice calculations give very low resolution. Here high-resolution results are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, and tested for percolation by examining bond percolation on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest diffusing particle that can cross a set of obstacles at a prescribed number density. For the simplest case, random overlapping obstacles, the analytical solution is known and the Monte Carlo results agree with it quantitatively. When the obstacles are disks with a 1/r⊥12 repulsion, the percolating diameter is around 10% lower than for overlapping obstacles. Disks with a 1/r⊥6 or 1/r⊥18 repulsion behave similarly. The results are used to find the thresholds for lipids, and for proteins of various diameters. (Supported by NIH grant GM038133)

The van der Waals coefficients between carbon nanostructures and small molecules: A time-dependent density functional theory study

We employ all-electron ab initio time-dependent density functional theory based method to calculate the long-range dipole-dipole dispersion coefficient, namely, the van der Waals (vdW) coefficient (C(6)) between fullerenes and finite-length carbon nanotubes as well as between these structures and different small molecules. Our aim is to accurately estimate the strength of the long-range vdW interaction in terms of the C(6) coefficients between these systems and also compare these values as a function of shape and size. The dispersion coefficients are obtained via Casimir-Polder relation. The calculations are carried out with the asymptotically correct exchange-correlation potential-the statistical average of orbital potential. It is observed from our calculations that the C(6) coefficients of the carbon nanotubes increase nonlinearly with length, which implies a much stronger vdW interaction between the longer carbon nanostructures compared with the shorter ones. Additionally, it is found that the values of C(6) and polarizability are about 40%-50% lower for the carbon cages when compared with the results corresponding to the quasi-one-dimensional nanotubes with equivalent number of atoms. From our calculations of the vdW coefficients between the small molecules and the carbon nanostructures, it is observed that for H(2), the C(6) value is much larger compared with that of He. It is found that the rare gas atoms have very low values of vdW coefficient with the carbon nanostructures. In contrast, it is found that other gas molecules, including the ones that are environmentally important, possess much higher C(6) values. Carbon tetrachloride as well as chlorine molecule show very high C(6) values with themselves as well as with the carbon nanostructures. This is due to the presence of the weakly bound seven electrons in the valence state for the halogen atoms, which makes these compounds much more polarizable compared with the others.

Direct Measurement of the Cs2 0u+ (P3/2) High-Lying Vibrational Spectroscopy Using Photon Counting

We report on the photoassociation of cold Cs atoms giving spectroscopy data of the 0 u + long-range molecular state in the asymptotic range of [-6.2, -2.5 cm -1 ] close to the 6S 1/2 +6P 3/2 dissociation limit using photon counting technique. 24 new high-lying vibrational levels of the 0 u + long-range state are identified to lead to the formation of excited molecules in the photoassociation process. Fitting experimental data to improved LeRoy–Bernstein formula, we obtain long-range molecular coefficient with a high precision.

Determinants of the long-range apparent diffusion coefficient in the human lung: collateral channels or intra-acinar branching?

to the editor: We have given considerable thought to the study by Bartel and colleagues ([1][1]) in an attempt to reconcile their simulation of the long-range apparent diffusion coefficient (LRADC) obtained from hyperpolarized helium-3 experiments in human lungs, with our own simulation using

Percolation Thresholds for Diffusing Particles of Nonzero Radius: Circular Obstacles in the Two-dimensional Continuum

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing diffusion in the presence of immobile obstacles is the percolation threshold, where long-range connected paths disappear and the long-range diffusion coefficient D goes to zero. To describe obstructed diffusion, it is more accurate to find the threshold directly than to extrapolate a low-density expansion in the obstacle concentration to find the concentration at which D = 0. The thresholds are well-known for point diffusing particles on various lattices or the continuum. But for particles of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Earlier results [Saxton, Biophys J 64 (1993) 1053] for the triangular lattice showed a very rapid decrease in the threshold as the radius of the diffusing particle increases, but a lattice model gives very low resolution. The current work finds the percolation threshold for circular obstacles in the two-dimensional continuum as a function of the radius of the diffusing species. The thresholds are obtained by a Monte Carlo method based on the Voronoi diagram for the obstacles. Each Voronoi bond is by definition the path equidistant from the nearest pair of obstacles, so the separation of that pair determines whether a diffusing particle of a given diameter can traverse that bond. For point obstacles, then, one can choose a threshold corresponding to the diameter of the diffusing particle, set the conductivity of all bonds narrower than that diameter to zero and all wider bonds to one, and test for bond percolation on the resulting Voronoi diagram. The results are used to find the thresholds for lipids and for proteins of different diameters. (Supported by NIH grant GM038133)

Persistence of travelling waves in a generalized Fisher equation

Travelling waves of the Fisher equation with arbitrary power of nonlinearity are studied in the presence of long-range diffusion. Using analogy between travelling waves and heteroclinic solutions of corresponding ODEs, we employ the geometric singular perturbation theory to prove the persistence of these waves when the influence of long-range effects is small. When the long-range diffusion coefficient becomes larger, the behaviour of travelling waves can only be studied numerically. In this case we find that starting with some values, solutions of the model lose monotonicity and become oscillatory.

Physical study of dynamics in fully hydrated phospholipid bilayers

We studied the thermotropic phase behavior of a phospholipid membrane bilayer of dimyristoylphosphatidylcholine (DMPC) under excess water conditions. We also investigated the effect induced by the antimicrobial peptide, gramicidin D (GrD), when inserted into the membrane bilayer. Several techniques were used to collect information on different properties and various spatial and temporal regimes, including differential scanning calorimetry, fixed energy window neutron scattering, pulsed-field gradient nuclear magnetic resonance and molecular dynamics simulations. We obtained data on the main phase transition (gel–liquid crystalline) temperature of the bilayer system and on the long-range diffusion coefficient for both phospholipids and hydration water. Moreover, we demonstrated the effect of transition on microscopic molecular mobility, perpendicular and parallel to the membrane plane. The influence of gramicidin on these properties is also discussed.

Time-dependent density-functional-theory calculation of the van der Waals coefficientC6of alkali-metal atoms Li, Na, K; alkali-metal dimersLi2,Na2,K2; sodium clustersNan; and fullereneC60

We have employed time-dependent density-functional theory (TDDFT) to calculate the long-range dipole-dipole dispersion coefficient (van der Waals coefficient) ${C}_{6}$ of alkali-metal atoms Li, Na, K; alkali-metal atom dimers ${\mathrm{Li}}_{2}$, ${\mathrm{Na}}_{2}$, ${\mathrm{K}}_{2}$; sodium clusters containing even number of atoms ranging from 2 to 20 atoms; and fullerene ${\text{C}}_{60}$. The dispersion coefficient is obtained via Casimir-Polder expression which relates it to the frequency dependent linear polarizability at imaginary frequencies. The frequency-dependent polarizabilities are calculated by employing TDDFT-based complete sum-over-states expressions for the atoms, and direct TDDFT linear response theory for the closed shell dimers and clusters.

The Role of Collateral Paths in Long-range Diffusion of 3He in Lungs

The hyperpolarized (3)He long-range diffusion coefficient (LRDC) in lungs is sensitive to changes in lung structure due to emphysema, reflecting the increase in collateral paths resulting from tissue destruction. However, no clear understanding of LRDC in healthy lungs has emerged. Here we compare LRDC measured in healthy lungs with computer simulations of diffusion along the airway tree with no collateral connections. Computer simulations of diffusion of spatially modulated spin magnetization were performed in computer-generated, symmetric-branching models of lungs and compared with existing LRDC measurements in canine and human lungs. The simulations predict LRDC values of order 0.001 cm(2)/sec, approximately 20 times smaller than the measured LRDC. We consider and rule out possible mechanisms for LRDC not included in the simulations: incomplete breath hold, cardiac motion, and passage of dissolved (3)He through airway walls. However, a very low density of small (micron) holes in the airways is shown to account for the observed LRDC. It is proposed that LRDC in healthy lungs is determined by small collateral pathways.

Measuring Collateral Pathways in Health via 3He MRI

IntroductionThere has been recent interest in the use of 3He diffusion MRI because of the close correlations of the imaging measure with tissue morphometry. The long‐range diffusion coefficient (LRDC) has been shown to be a measure of collateral pathways in emphysema, but little is known of the role of collaterals in the LRDC in health. A recent publication attempted to explain the LRDC by simulations within single lung acini, without collateral pathways.MethodsWe measured the LRDC of 3He ex‐vivo in 4 human donor lungs that were rejected for transplantation and in 3 pig lungs, which are known to have greatly reduced collateral ventilation. We also simulated the interacinar diffusion of 3He (at 2‐cm diffusion distances) via the diffusion equation in a strictly branching model of human lung with no collateral pathways. (Airway radii, lengths, and branching angles were taken from detailed, morphometric literature.)ResultsLRDC in pig lungs (0.004 cm2/s) was 4x lower than in the human lungs (0.022 cm2/s), implying that collateral pathways can play a significant role in the measurements. The robustly tested simulations revealed a surprisingly low LRDC (24x lower than the measured value), implying that diffusion via the airway tree alone (no collaterals) cannot account for the measured value in healthy lung. A surprisingly small number of 5‐μ pores is shown to account for the discrepancy.