Long-range Region Research Articles

Long-range transcription factor binding sites clustered regions may mediate transcriptional regulation through phase-separation interactions in early human embryo

In mammals, during the post-fertilization pre-implantation phase, the expression of cell type-specific genes is crucial for normal embryonic development, which is regulated by cis-regulatory elements (CREs). TFs control gene expression by interacting with CREs. Research shows that transcription factor binding sites (TFBSs) reflect the general characteristics of the regulatory genome. Here, we identified TFBSs from chromatin accessibility data in five stages of early human embryonic development, and quantified transcription factor binding sites-clustered regions (TFCRs) and their complexity (TC). Assigning TC values to TFCRs has made it possible to assess the functionality of these regulatory elements in a more quantitative way. Our findings reveal a robust correlation between TFCR complexity and gene expression starting from the 8Cell stage, which is when the zygotic genome is activated in humans. Furthermore, we have defined long-range TFCRs (LR-TFCRs) and conjecture that LR-TFCRs may regulate gene expression through phase-separation mechanisms during the early stages of human embryonic development.

Molecular dynamics simulation of interaction between NaOH solution and AgCo/C electrode

Using carbon-supported silver-cobalt (AgCo/C) electrode as the electrocatalyst in fuel cell (FC), it has good electrocatalytic performance for NaOH solution (aq), however, the mechanism of the interaction between aq and AgCo/C electrode is not clear. In this work, layered models (L1, L2, L3) of the interaction between them were constructed, and molecular dynamics (MD) simulation was carried out using Materials Studio (MS) software to explore their interaction rule and reveal the interaction mechanism. At 298 K, the results showed that the interaction force between aq and AgCo/C electrode is mutually attracted, and the order of the absolute value of the interaction energy is L3 ≫ L2 > L1, indicating that the electrocatalytic effect of the composite electrode with 4 carbon-supporter layers is obviously stronger than that of the composite electrode with 3 and 2 carbon-supporter layers, which is consistent with the experimental conclusion. Their interaction inhibits the diffusion of Na+ ions and water molecules− in aq. There is no bonding between AgCo(AgCo/C)-OH−(aq) and AgCo(AgCo/C)-Na+(aq) in the short-range region, while there is non-bonding in the long-range region. Bond formation is a common occurrence between H2O(aq)-OH−(aq) in the short-range region, but it is weak in the long-range region. Research and development of cathode materials for fuel cells will be supported by these theoretical results.

Toward Consistent Predictions of Core/Valence Ionization Potentials and Valence Excitation Energies by MRSF-TDDFT.

Optimizing exchange-correlation functionals for both core/valence ionization potentials (cIPs/vIPs) and valence excitation energies (VEEs) at the same time in the framework of MRSF-TDDFT is self-contradictory. To overcome the challenge, within the previous "adaptive exact exchange" or double-tuning strategy on Coulomb-attenuating XC functionals (CAM), a new XC functional specifically for cIPs and vIPs was first developed by enhancing exact exchange to both short- and long-range regions. The resulting DTCAM-XI functional achieved remarkably high accuracy in its predictions with errors of less than half eV. An additional concept of "valence attenuation", where the amount of exact exchange for the frontier orbital regions is selectively suppressed, was introduced to consistently predict both VEEs and IPs at the same time. The second functional, DTCAM-XIV, exhibits consistent overall prediction accuracy at ∼0.64 eV. By preferentially optimizing VEEs within the same "valence attenuation" concept, a third functional, DTCAM-VAEE, was obtained, which exhibits improved performance as compared to that of the previous DTCAM-VEE and DTCAM-AEE in the prediction of VEEs, making it an attractive alternative to BH&HLYP. As the combination of "adaptive exchange" and "valence attenuation" is operative, it would be exciting to explore its potential with a more tunable framework in the future.

Deciphering the dynamical chromosome structural reorganizations in human neural development

Understanding the mechanisms of cell-fate determination in neural development is pivotal for advancing regenerative medicine and addressing neurodegenerative diseases. Cell-fate determination is controlled by the underlying gene expression networks, which are further regulated by the three-dimensional chromosome structures. During neural development, chromosomes progressively adapt their structures to accommodate the requisite gene expressions. However, elucidating the pathways of chromosome structural dynamics during these transitions remains a grand challenge. In this study, we employed the data-driven coarse-grained molecular dynamics simulations, coupled with the nonequilibrium landscape-switching model, to quantify the chromosome structural dynamics during human neural development. We focused on a simplified human neural developmental system, comprising of cell differentiation, reprogramming, and transdifferentiation among the neural progenitor cell (NPC), the glia cell, and the neuron cell. We identified significant large-scale chromosome structural reorganizations during cell-state transitions. From the chromosome structural perspective, the transdifferentiation processes between the glia and neuron cells exhibited nonmonotonic behaviors characterized by an initial increase followed by a subsequent decrease in cell stemness. The transdifferentiation appeared to share the same routes of differentiation after passing through the NPC. Additionally, our findings revealed that the chromosome structural dynamical pathways at the scale of topologically associating domains exhibited little overlap, in contrast to the ones at the long-range regions. This suggests that the active, ATP-driven molecular processes play dominant roles in modulating topologically associating domain (TAD) structures, while the compartmental segregation in chromosomes is primarily governed by the passive phase separation. Our study offers a theoretical exploration of neural cell-fate determination from the chromosome structural perspective, paving a way for potential applications in neuroregeneration. Published by the American Physical Society 2024

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System.

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

H2O-HCN complex: A new potential energy surface and intermolecular rovibrational states from rigorous quantum calculations.

In this work the H2O-HCN complex is quantitatively characterized in two ways. First, we report a new rigid-monomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetry-adapted perturbation theory based on density functional theory method. The PES is based on 2833 abinitio points computed employing the aug-cc-pVQZ basis set, utilizing the autoPES code, which provides a site-site analytical fit with the long-range region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O-HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum bound-state methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged ground-state geometry of H2O-HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed ground-state rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O-HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.

Quantifying the large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition of cell cycle.

Cell cycle is known to be regulated by the underlying gene network. Chromosomes, which serve as the scaffold for gene expressions, undergo significant structural reorganizations during mitosis. Understanding the mechanism of the cell cycle from the chromosome structural perspective remains a grand challenge. In this study, we applied an integrated theoretical approach to investigate large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition. We observed that the chromosome structural expansion and adaptation of the structural asphericity do not occur synchronously and attributed this behaviour to the unique unloading sequence of the two types of condensins. Furthermore, we observed that the coherent motions between the chromosomal loci are primarily enhanced within the topologically associating domains (TADs) as cells progress to the G1 phase, suggesting that TADs can be considered as both structural and dynamical units for organizing the three-dimensional chromosome. Our analysis also reveals that the quantified pathways of chromosome structural reorganization during the mitosis-to-G1 phase transition exhibit high stochasticity at the single-cell level and show nonlinear behaviours in changing TADs and contacts formed at the long-range regions. Our findings offer valuable insights into large-scale chromosome structural dynamics after mitosis.

Atomic mixing mechanisms in nanocrystalline Cu/Ni composites under continuous shear deformation and thermal annealing

Molecular dynamics (MD) simulations are used to reveal the mechanisms of defect substructure evolution and atomic mixing in nanocrystalline Cu/Ni composites under severe shear deformation and subsequent thermal annealing. A continuous shear scheme of MD simulation utilizing an on-the-fly periodic boundary adjustment approach enables it to reach any large shear strain. The comprehensive evaluation on the evolution of dislocation structures at various strain states indicates partial dislocation-mediated plastic deformation and triple junction slide via partial dislocation nucleation and emission from triple junctions and grain boundaries. The analysis of atomic structures in unique mixing regions suggests that triple junction sliding can result in a long-range region of atomic mixing facilitated by net dislocation flux, which is the key mechanism of atomic mixing in nanocrystalline Cu/Ni composite under severe shear, while dislocation emissions at interfaces result in short-range mixing. It is also found that thermal annealing causes the evolution of non-equilibrium defect substructures which assists atomic mixing.

Long-range ab initio potential energy surface for the ground electronic state of the ozone molecule with the accurate dissociation asymptote

In this work an excellent agreement was achieved between the empirical (9230.08 ± 4.85 cm−1) and theoretical (9230.70 cm−1) values of the first dissociation limit (De) of O3. Ab initio multireference calculations were performed for the first time using the extended complete active space [CAS(24,15)] reference in the icMRCI(Q) method combined with the extrapolation to the complete basis set limit [CBS(56Z)] and with the inclusion of the spin–orbit coupling between 9 multiplet electronic states approaching De. Finally, the full-dimensional potential energy surface was developed in the scattering coordinates for the long-range region toward De at this level of theory.

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions.

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. This study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C-O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10-11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

Quantum computations in heavy noble-gas hydride cations: Reference energies and new spectroscopic data

Computational quantum chemistry has become a powerful tool with a wide range of possibilities to solve chemical-physical problems. As a result of this, the interest in the applications of computational quantum chemistry has expanded considerably, and has opened up novel research opportunities. In particular, those related to the characterization of heavy-atoms complexes, as most electronic structure calculations for such systems struggle with the problem posed by the large number of electrons present in them, and consequently, the introduction of relativistic effects. The present study performed an exhaustive assess to characterized the uncommon NgH+ (Ng = Kr, Xe, and Rn) hydride cations in order to provide accurate rovibrational data of their isotopes to assist in the laboratory characterization or even their astronomical detection. Scalar relativistic effects were included, and the ground and first electronically exited states potential curves were obtained from benchmark ab initio CCSD(T)/CBS and MRCI+Q electronic structure calculations. Next, such interaction potentials, correctly extended to long-range asymptotic regions, were employed in quantum bound state calculations and molecular spectroscopic constants were determined for the most abundance 84Kr, 132Xe, and 222Rn isotopes. Our results were discussed in comparison with available experimental and previous theoretical estimates, aiming to treat accuracy issues. The new sets provide reference data that could serve for spectroscopic characterization of such low abundance and high radioactive species.

Hyperconnectivity of Two Separate Long-Range Cholinergic Systems Contributes to the Reorganization of the Brain Functional Connectivity during Nicotine Withdrawal in Male Mice.

Chronic nicotine results in dependence with withdrawal symptoms on discontinuation of use, through desensitization of nicotinic acetylcholine receptors and altered cholinergic neurotransmission. Nicotine withdrawal is associated with increased whole-brain functional connectivity and decreased network modularity; however, the role of cholinergic neurons in those changes is unknown. To identify the contribution of nicotinic receptors and cholinergic regions to changes in the functional network, we analyzed the contribution of the main cholinergic regions to brain-wide activation of the immediate early-gene Fos during withdrawal in male mice and correlated these changes with the expression of nicotinic receptor mRNA throughout the brain. We show that the main functional connectivity modules included the main long-range cholinergic regions, which were highly synchronized with the rest of the brain. However, despite this hyperconnectivity, they were organized into two anticorrelated networks that were separated into basal forebrain-projecting and brainstem-thalamic-projecting cholinergic regions, validating a long-standing hypothesis of the organization of the brain cholinergic systems. Moreover, baseline (without nicotine) expression of Chrna2, Chrna3, Chrna10, and Chrnd mRNA of each brain region correlated with withdrawal-induced changes in Fos expression. Finally, by mining the Allen Brain mRNA expression database, we were able to identify 1755 gene candidates and three pathways (Sox2-Oct4-Nanog, JAK-STAT, and MeCP2-GABA) that may contribute to nicotine withdrawal-induced Fos expression. These results identify the dual contribution of the basal forebrain and brainstem-thalamic cholinergic systems to whole-brain functional connectivity during withdrawal; and identify nicotinic receptors and novel cellular pathways that may be critical for the transition to nicotine dependence.

Long-range and short-range dihadron correlations in central PbPb collisions at (s_NN )=5.02 TeV and centrality 40-50%

This paper reports the first measurement of charged particle elliptic flow in Pb-Pb collisions at (s_NN ) = 5.02T eV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed on more than 20,000 events in 40-50% centrality class on both long-range 2 < || < 4 and short-range || < 1 regions. The two-particle correlation method is used over long-range region, in the transverse momentum range of 1 < p_T < 1.5GeV , and the elliptic flow signals, given by v_n =(V_n ) , are v_2 = 0.17 0.01,v_3 = 0.07 0.01,v_4 = 0.04 0.01,v_5 = 0.03 0.01. Since V_1 is obtained as -0.0013, it does not have a square root value. In addition, for n=2-4, it is found that v_n increases as p_T increases. The Q-vectors method is also used to determine the values of v_2. The magnitudes of the Q-vectors are fitted to a function. The values of v_2 produced by the two methods are compared and discussed. At the end, the vectors are used to analyse high-energy jet particles.

A variationally improved Hulburt-Hirschfelder analytical potential energy function for diatomic molecules

In this paper, a variationally improved Hulburt-Hirschfelder (VIHH) analytical potential energy function (APEF) is presented and tested. The VIHH potential is composed of the remedy function and the improved Hulburt-Hirschfelder (IHH) APEF which possesses the same explicit parameters () with VIHH potential. Potential energy curves (PECs) for the ground electronic states of HI, HBr and KLi molecules have been modeled by the VIHH analytical potential, and it suggests that the VIHH potential is in good agreement of Rydberg-Klein-Rees (RKR) potential points and is superior to the original Hulburt-Hirschfelder (HH) potential, IHH potential and Morse potential, especially in the dissociation and the long-range region. The vibrational energy levels for the ground electronic state of the HI, HBr, and KLi molecules are obtained by numerically solving the radial Schrödinger equation using the LEVEL program for the case of the Morse potential, HH potential, IHH potential and the VIHH potential functions. The comparison for both vibrational energy levels and VIHH potential functions shows better agreement with the experimental data than the other potential functions. Comparing with IHH potential, the VIHH potential which included the remedy function has better physical behavior in the long-range region and the is effective for vanishing the invalid barrier.

Three-branch attention deep model for hyperspectral image classification using cross fusion

ABSTRACT Deep learning has achieved impressive success in computer vision,especially remote sensing. It is well known that different deep models are ableto extract different kinds of features from remote sensing images. For example,the convolutional neural networks (CNN) can extract neighbourhood spatialfeatures in the short-range region, the graph convolutional networks (GCN) canextract structural features in the middle- and long-range region, and the encoder-decoder(ED) can obtain the reconstruction features from an image. Thus, it is challenging to design a modelthat can combine the different models to extract fused features in ahyperspectral image classification task. To this end, this paper proposes athree-branch attention deep model (TADM) for the classification ofhyperspectral images. The model can be divided into three branches: graphconvolutional neural network, convolutional neural network, and deepencoder-decoder. These three branches first extract structural features,spatial-spectral joint features and reconstructed encoded features fromhyperspectral images, respectively. Then, a cross-fusion strategy and an attentionmechanism are employed to automatically learn the fusion parameters andcomplete the feature fusion. Finally,the hybrid features are fed into a standard classifier for pixel-levelclassification. Extensive experiments on two real-world hyperspectral datasets (Houstonand Trento) demonstrate the effectiveness and superiority of the proposedmethod. Compared with other baseline classification methods, such as FuNet-Cand Two-Branch CNN(H), proposed method achieves the highest classificationresults. Specifically, overall classification accuracies of 93.25% and 95.84%were obtained on the Houston and Trento data, respectively.

A neural network potential energy surface for the Li + LiNa → Li2 + Na reaction and quantum dynamics study from ultracold to thermal energies.

An improved fundamental invariant neural network (FI-NN) approach for representing a potential energy surface (PES) involving permutation symmetry is introduced in this work. In this approach, FIs are regarded as symmetric neurons, thus avoiding complex preprocessing of training set data, especially when the training set contains gradient data. In this work, the improved FI-NN method, combined with simultaneous fitting of the energy and gradient strategy, is used for constructing a global accurate PES of a Li2Na system (root-mean-square error of 12.20 cm-1). The potential energies and the corresponding gradients are calculated by a UCCSD(T) method with effective core potentials. Based on the new PES, the vibrational energy levels and the corresponding wave functions of Li2Na molecules are calculated using an accurate quantum mechanics method. To accurately describe the cold or ultracold reaction dynamics of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction, the long-range region of the PES in both the reactant and product asymptotes is represented by an asymptotically correct form. A statistical quantum model (SQM) is used to study the dynamics of the ultracold Li + LiNa reaction. The calculated results are in good agreement with the exact quantum dynamics results (B. K. Kendrick, J. Chem. Phys., 2021, 154, 124303), which indicates that the dynamics of the ultracold Li + LiNa reaction can be well described by the SQM approach. The time-dependent wave packet calculations are performed for the Li + LiNa reaction at thermal energies, and the characteristic of differential cross-sections confirms that the reaction follows the complex-forming reaction mechanism.

Long-range transport and potential source regions of PM2.5 during the autumn season in Edirne, Türkiye

The variation in daily Particulate Matter 2.5 (PM2.5) concentrations was studied in Edirne city center from September 1, 2019 to November 30, 2019 (autumn season). The values of daily PM2.5 concentrations were between 5.65 and 77.59 μg m-3. The values of PM2.5 concentration had the highest average value on Tuesdays compared to other days. The mean value of daily PM2.5 concentrations on Tuesdays was 23.41 μg m-3. The backward trajectories were computed and clustered by applying the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. The backward trajectories clustered in eight major clusters during the autumn. In Cluster 4 (C4), which has more short-range transport according to the other seven clusters, the mean value of PM2.5 concentrations was 19.52 μg m-3. The mean value of PM2.5 concentrations was 28.11 μg m-3 in C8 (3.3%), which has more long-range transport than the other seven clusters. Potential source areas of PM2.5 have been determined by the Potential Source Contribution Function (PSCF) model. The results of PSCF analyses illustrated that the north, northeast, south, and southeast regions of the sampling area as major potential source areas for PM2.5. The results obtained in this study can make important contributions to the evaluation of PM2.5 concentration in the region in terms of health and long-range transport.

Correlated barrier charge hopping and non-Debye relaxation in columbite MnNb2O6

A comprehensive study on the mechanism of ac-charge transport and dielectric relaxation in the MnNb2O6 columbite system has been reported. Thermally driven, Arrhenius-like behaviour of the ac-conductivity is predominant at temperatures above 300 K in the frequency range 50 Hz–5 MHz with activation energies lying between 0.45 and 0.38 eV. Besides, a quadratically decreasing trend in the activation energy is evident as given by: = A + Bf + Cf 2 with the constants A (0.413 eV), B (0.023 eV Hz−1) and C (−0.004 eV Hz−2). The measured data is analysed using the Double power law to explain the dispersive behaviour of electrical conductivity. These studies also provide evidence for the correlated-barrier hopping (CBH) conduction mechanism of charge carriers for temperatures in the range 173–473 K. Further, the temperature dependence of frequency exponent, s(T) displays two distinct regions both of which are associated with the CBH mechanism with slopes K−1 and K−1 in Region-I (173–300 K) and the slope K−1 with non-linear variation of s 2 in Region-II (300–473 K). However, the second region is more dominated by thermally activated Arrhenius-like behaviour. The dynamical response of complex electric modulus spectra and the corresponding analysis using Kohlrausch-Williams-Watts method reveals the presence of a non-Debye type relaxation process with decay function exponent β lying between 0.794 and 0.840. This inference of the non-Debye type relaxation process is further supported by depressed semicircles in Nyquist plots and the higher magnitude of full width half maximum (FWHM) (≈1.44 decades) of the normalized master cusp vs compared to the FWHM ( = 1.14 decades) for ideal Debye behaviour. Both short-range and long-range conductivity regions are ubiquitous in with a pronounced distribution of relaxation times (s) with temperature. This study further leads to the estimation of activation energy of charge carriers, E M = 0.44 eV which is in consonance with .

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

We investigate the interplay between the Kondo effect and the ferromagnetism by an one dimension Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under Lacroix basis.The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from density matrix renormalization group (DMRG). For system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field $h$. A fitting formula is proposed to perfectly fits the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.