Mean-field Density Research Articles

Freezing of a soft-core fluid in a one-dimensional potential: Predictions based on a pressure-balance equation.

Using concepts from classical density functional theory, we investigate the freezing of a two-dimensional system of ultrasoft particles in a one-dimensional external potential, a phenomenon often called laser-induced freezing (LIF). In the first part of the paper, we present numerical results from free minimization of a mean-field density functional for a system of particles interacting via the GEM-4 potential. We show that the system does indeed display a LIF transition, although the interaction potential is markedly different from the cases studied before. We also introduce a suitably defined effective density within the potential wells ρ[over ¯]_{eff} as a control parameter of LIF, rather than the amplitude of the external potential as in the common LIF scenario. In the second part, we suggest a theoretical description of the onset of LIF which is based on the pressure-balance equation relating the pressure tensor and the external potential. Evaluating this equation for the modulated liquid phase at effective density ρ[over ¯]_{eff} and combining it with the (known) stability threshold of the corresponding bulk fluid, we can predict the critical effective density or, equivalently, the potential amplitude related to the onset of LIF. Our approach yields very good results for the model at hand and it is transferable, in principle, to other model systems.

Transverse temperature interfaces in the Katz-Lebowitz-Spohn driven lattice gas.

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T>T_{c} and T_{c}, respectively, where T_{c} indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. To explain this particle density accumulation near the interface, we have measured the steady-state current in the KLS model at T>T_{c} and found it to decay as 1/T. In analogy with TASEP systems containing "slow" bonds, we argue that transport in the high-temperature subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. This blockage is induced by the extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_{c}, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region.

Entropic Effects in Solvent-Free Bidisperse Polymer Brushes Investigated Using Density Functional Theories.

Solvent-free polymer-functionalized nanoparticles form a special type of colloid composed of inorganic cores self-suspended by their grafted coronas. In the absence of intervening solvent molecules, the fluidity of the system is provided by these tethered polymers as they fill the space. Here, we study the structure and interaction of neighboring polymer-grafted surfaces in the solvent-free condition using mean-field density functional theories. For opposing flat surfaces, the brush configuration and the associated energy landscape are semianalytically investigated given the incompressibility of the tethered entropic chains. The effect of brush polydispersity (including variations in both chain length and surface grafting density) is considered by two bidisperse models corresponding to different physical scenarios: one for opposing brushes uniformly mixed with two species at a fixed grafting density, and the other for opposing brushes with distinct chain lengths and grafting densities. The space-filling capabilities of the neighboring coronas differ not only by their ratio of radii of gyration for the composing polymers but also by their ratio of grafting densities. We show that the system energy depicts a steric repulsion as the brushes are compressed, which is typical for hairy particles in a solvent. However, as the interwall separation increases, the cooperative stretching of the chains leads to an entropic attraction between them, a unique characteristic of solventless systems. The corresponding brush profiles change from a bell-like shape to a more step-function-like feature as the interwall spacing increases significantly. The interwall separation associated with the overall free energy minimum therefore characterizes the favorable interparticle spacing for solvent-free polymer-functionalized particles. The limiting accessible parameter space of polymer sizes and grafting densities subjected to the space-filling constraint is comprehensively explored for representative interparticle spacing characterizing the compressed, relaxed, and stretched regimes for a given polymer species, respectively. Such information would be useful for guiding the design of experimental solvent-free polymer-functionalized nanoparticles.

Investigation of proton emission using deformed relativistic mean field densities

The proton emission in neutron deficient nuclei with [Formula: see text] has been investigated within the framework of axially deformed relativistic mean field (RMF) theory using NL3 and density-dependent DD-ME1 and DD-ME2 parameters. The quasi-bound states from which the proton emission is probable are determined. The RMF densities are folded with the M3Y effective nucleon–nucleon interaction to obtain the nuclear potential. The total interaction potential consisting of nuclear, Coulomb and centrifugal potentials is used to calculate the proton decay half-lives using the Wentzel–Kramers–Brillouin (WKB) approximation. For this, we have used the [Formula: see text], [Formula: see text] being the single-particle energy of the decaying proton near the Fermi surface. The calculated proton decay half-lives for different nuclei are in consonance with experimental data.

Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: Case of spherical colliding nuclei

In the present work, the influence of the nuclear matter density on the DF potential and on the Coulomb barrier parameters is studied systematically for collisions of spherical nuclei. The value of the parameter BZ=ZPZT/(AP1/3+AT1/3) (estimating the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. We have introduced self-consistent relativistic mean field (RMF) density in the present analysis. For the nucleon-nucleon effective interaction, the M3Y forces with the finite range exchange term and density dependence are employed. The above barrier fusion cross sections are calculated within the framework of the trajectory model with surface friction. Results are compared with the previous study in which the nuclear density came from the Skyrme Hartree-Fock (HF) calculations and with the high precision experimental data. This comparison demonstrates that i) agreement between the theoretical and experimental cross sections obtained with RMF and HF densities is of the same quality and ii) the values of the only adjustable parameter (friction strength) obtained with RMF and HF densities strongly correlate with each other.

Analysis with relativistic mean-field density distribution of elastic scattering cross-sections of carbon isotopes (10–14,16C) by various target nuclei

A microscopic study of elastic scattering of carbon isotopes from different target nuclei at various incident energies is presented by using density distributions derived for 10–14,16C nuclei using relativistic mean field (RMF) theory. To obtain the real part of the optical potential, the double folding model is used. Woods–Saxon potential is used for the imaginary part. The theoretical results are discussed and compared with each other as well as with the experimental data. It is seen that the agreement between theoretical results and experimental data is very good. Also, new global equations for the imaginary potentials of the 10–14,16C nuclei are derived from the results of the theoretical analysis.

Energy-weighted density matrix embedding of open correlated chemical fragments.

We present a multiscale approach to efficiently embed an ab initio correlated chemical fragment described by its energy-weighted density matrices and entangled with a wider mean-field many-electron system. This approach, first presented by Fertitta and Booth [Phys. Rev. B 98, 235132 (2018)], is here extended to account for realistic long-range interactions and broken symmetry states. The scheme allows for a systematically improvable description in the range of correlated fluctuations out of the fragment into the system, via a self-consistent optimization of a coupled auxiliary mean-field system. It is discussed that the method has rigorous limits equivalent to the existing quantum embedding approaches of both dynamical mean-field theory and density matrix embedding theory, to which this method is compared, and the importance of these correlated fluctuations is demonstrated. We derive a self-consistent local energy functional within the scheme and demonstrate the approach for hydrogen rings, where quantitative accuracy is achieved despite only a single atom being explicitly treated.

Effect of the nucleon-nucleon interaction on the fusion cross-section within the relativistic mean field formalism

We establish a relationship between the nucleon-nucleon interaction potential and the nuclear fusion reaction cross-sections at low energies. The axially deformed self-consistent relativistic mean field is used with the non-linear NL3* interaction parameter set. The Wong formula is used to estimate the fusion cross-section for 58Ni + 58Ni and 48Ca + 238U systems, which are known to display fusion hindrance phenomena. The results of the application of the nucleus-nucleus optical potential for the fusion cross-section from the recently developed effective relativistic NN-interaction (R3Y) potential is compared with the well-known, phenomenological M3Y potential. The results obtained from our present calculation for the R3Y interaction are reasonable good as compared to the M3Y potential concerning the available experimental at barrier energies. The present analysis pursues a full microscopic studies of fusion process at low energies by taking the R3Y potential along with the relativistic mean field density instead of taking the M3Y interaction within the double folding approach.

Coarse-Grained Modelling and Temperature Effect on the Morphology of PS-b-PI Copolymer.

Spontaneous spatial organization behavior and the aggregate morphology of polystyrene-block-polyisoprene (PS-b-PI) copolymer were investigated. Molecular dynamic (MD) and mesoscopic simulations using the dynamic of mean field density functional theory (DDF) were adopted to investigate the morphology changes exhibited by this block copolymer (BCP). In the mesoscopic simulations, several atoms in repeating units were grouped together into a bead representing styrene or isoprene segments as a coarse-grained model. Inter-bead interactions and essential parameters for mesoscopic models were optimized from MD simulations. Study indicated that morphology alternations can be induced in this system at annealing temperature of 393, 493, and 533 K. From our simulations, lamellar, bicontinuous, and hexagonally packed cylindrical equilibrium morphologies were achieved. Our simulated morphologies agree well with the reported experimental evidence at the selected temperature. The process of aggregate formation and morphology evolution were concretely clarified.

Iterative approaches to the self-consistent nuclear energy density functional problem

Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF's parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order.

Time-crystal ground state and production of gravitational waves from QCD phase transition * * A.A and A.M. acknowledge support by the NSFC(11875113), the Shanghai Municipality(KBH1512299), and by Fudan University(JJH1512105). R.P. was partially supported by the Swedish Research Council, contract numbers 621-2013-428 and 2016-05996, by CONICYT grant MEC80170112 (Chile), as well as by the European Research Council (ERC) under the European

We propose a novel mechanism for the production of gravitational waves in the early Universe that originates from the relaxation processes induced by the QCD phase transition. While the energy density of the quark-gluon mean-field is monotonously decaying in real time, its pressure undergoes a series of violent oscillations at the characteristic QCD time scales that generate a primordial multi-peaked gravitational waves signal in the radio frequencies’ domain. The signal is an echo of the QCD phase transition that is accessible by planned measurements at the FAST and SKA telescopes.

Proton emission from the drip-line nuclei I-Bi using the WKB approximation with relativistic mean-field densities * * Supported by the Department of Science and Technology, Govt. of India (EMR/2015/002517)

We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z = 53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativistic mean-field formalism (E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin (WKB) barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated half-lives are in good agreement with the experimental results for all emitters considered in this study.

Random phase approximation for the non-uniform Yukawa fluid

Mean-field density functional theory can be used to estimate the free energy of non-uniform fluids. The second functional derivative with respect to density of the free energy is related to the direct correlation function of the fluid and, in principle, this can be inverted to find an improved approximation for the pair correlation function and hence the free energy, the so-called ‘random phase approximation’. If the repulsive molecular interaction is approximated by the local density approximation and the attractive interaction is assumed to be of the Yukawa form, the problem reduces to that of finding the eigenvalues of Schrödinger-like equations, which, for certain models (such as the ‘Φ4 model’), can be done analytically in the planar case. The relationship between this approach and field theoretical treatment of the vapour-liquid interface is discussed. The ultraviolet divergence of the expression can be eliminated by separating the first term in the expansion, although quantitative results still depend on the behaviour of the attractive potential in the repulsive core. In the case of a spherical droplet of radius R, correction terms to the free energy involving lnR appear due to (i) cluster translational invariance, (ii) the unstable mode corresponding to droplet growth, and (iii) capillary waves. The net effect of these terms is to modify the classical expression for the nucleation rate by a factor proportional to R4/3.

Relativistic mean-field approach for Λ,Ξ , and Σ hypernuclei

We systematically study the properties of single-$\mathrm{\ensuremath{\Lambda}},\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Sigma}}$ hypernuclei within the framework of relativistic mean-field model. The $YN$ coupling constants are constrained according to the experimental data and previous theoretical efforts. By adding a hyperon to $^{40}\mathrm{Ca}$, we investigate its mean-field potentials, single-hyperon levels, density distributions, and binding energies, where the consequences of introducing different types of hyperons ($\mathrm{\ensuremath{\Lambda}},{\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Sigma}}}^{+,0,\ensuremath{-}}$) are examined. In general, the $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Sigma}}}^{0}$ hyperons show similar behaviors in bulk properties since both of them are electroneutral and have similar coupling constants; ${\mathrm{\ensuremath{\Xi}}}^{0}$ hyperon owns the shallowest mean-field potential well with the most extended density distribution; and Coulomb interactions play vital roles in the charged ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}},\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Sigma}}}^{+}$ hyperons. As a result, those hyperons have different impurity effects on the nuclear core $^{40}\mathrm{Ca}$. The $\ensuremath{\omega}YY$ tensor couplings are included and show remarkable effects on the spin-orbit splitting which even change the level ordering of $\mathrm{\ensuremath{\Xi}}$ hyperon. Finally, the single-hyperon binding energy of hypernuclei generally increases with the mass number. However, there is a turning point for ${\mathrm{\ensuremath{\Sigma}}}^{+}$ hypernuclei at $_{{\mathrm{\ensuremath{\Sigma}}}^{+}}^{91}\mathrm{Nb}$ where the binding energy begins to decrease. This is mainly due to the increasing Coulomb repulsive potential at large proton numbers.

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACTConfinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. II. The interplay between molecular packing and orientational order.

As in Paper I of this series of papers [S. M. Cattes et al., J. Chem. Phys. 144, 194704 (2016)], we study a Heisenberg fluid confined to a nanoscopic slit pore with smooth walls. The pore walls can either energetically discriminate specific orientations of the molecules next to them or are indifferent to molecular orientations. Unlike in Paper I, we employ a version of classical density functional theory that allows us to explicitly account for the stratification of the fluid (i.e., the formation of molecular layers) as a consequence of the symmetry-breaking presence of the pore walls. We treat this stratification within the White Bear version (Mark I) of fundamental measure theory. Thus, in this work, we focus on the interplay between local packing of the molecules and orientational features. In particular, we demonstrate why a critical end point can only exist if the pore walls are not energetically discriminating specific molecular orientations. We analyze in detail the positional and orientational order of the confined fluid and show that reorienting molecules across the pore space can be a two-dimensional process. Last but not least, we propose an algorithm based upon a series expansion of Bessel functions of the first kind with which we can solve certain types of integrals in a very efficient manner.

Morphology of Fluids Confined in Physically Reconstructed Mesoporous Silica: Experiment and Mean Field Density Functional Theory.

Three-dimensional physical reconstruction of the random mesopore network in a hierarchically structured, macroporous-mesoporous silica monolith via electron tomography has been used to generate a lattice model of amorphous, mesoporous silica. This geometrical model has subsequently been employed in mean field density functional theory (MFDFT) calculations of adsorption and desorption. Comparison of the results with experimental sorption isotherms for nitrogen at 77 K shows a good qualitative agreement, with both experiment and theory producing isotherms characterized by type H2 hysteresis. In addition to the isotherms, MFDFT provides the three-dimensional density distribution for the fluid in the porous material for each state studied. We use this information to map the phase distribution in the mesopore network in the hysteresis region. Phase distributions on the desorption boundary curve are compared to those on the adsorption boundary curve for both fixed pressure and fixed density, revealing insights into the relationship between phase distribution and hysteresis.

Ring polymers are much stronger depleting agents than linear ones

ABSTRACTWe investigate the conformations and shapes of circular polymers close to planar, hard walls as well as the ensuing ring–wall and polymer-induced wall–wall interactions in ring polymer solutions. We derive, by means of Monte Carlo simulations, the effective interaction potential between the centres of mass of flexible, unknotted ring polymers and a hard wall for different polymerisation degrees N. Adopting the coarse-grained description of ring polymers as ultrasoft, penetrable spheres, mean-field density functional theory is then employed in order to examine ring polymer solutions under confinement. We demonstrate that, below the semi-dilute regime, ring polymers structure close to walls much more strongly than their linear counterparts, their density profiles featuring pronounced oscillations. Moreover, the polymer-induced depletion potential between the two walls exhibits an oscillatory profile reminiscent of hard-sphere systems, with oscillations that intensify upon increasing polymer concentration. The obtained form of the depletion interaction is shown to be qualitatively different in comparison to the case of linear polymer solutions at the corresponding densities.

Astrophysical S-factor of some (p, γ) Reactions

We have studied the important astrophysical S-factor for 36 known p-nuclei with (p, γ) reactions at low energy in the mass region A $\approx $ 74–196. This is done by folding the density-dependent M3Y (DDM3Y) interaction with spherical relativistic mean field (RMF) densities. The densities are obtained from different parameter sets such as G1, G2, NL1, NL2, NL3*, NL-SH, DD-ME1, DD-ME2 and DD-PC1. The independence of the S-factor on different densities is discussed and compared with experimental data and with NON-SMOKER calculations whenever available.

Magnetic Properties of Metal–Organic Coordination Networks Based on 3d Transition Metal Atoms

The magnetic anisotropy and exchange coupling between spins localized at the positions of 3d transition metal atoms forming two-dimensional metal–organic coordination networks (MOCNs) grown on a Au(111) metal surface are studied. In particular, we consider MOCNs made of Ni or Mn metal centers linked by 7,7,8,8-tetracyanoquinodimethane (TCNQ) organic ligands, which form rectangular networks with 1:1 stoichiometry. Based on the analysis of X-ray magnetic circular dichroism (XMCD) data taken at T = 2.5 K, we find that Ni atoms in the Ni–TCNQ MOCNs are coupled ferromagnetically and do not show any significant magnetic anisotropy, while Mn atoms in the Mn–TCNQ MOCNs are coupled antiferromagnetically and do show a weak magnetic anisotropy with in-plane magnetization. We explain these observations using both a model Hamiltonian based on mean-field Weiss theory and density functional theory calculations that include spin–orbit coupling. Our main conclusion is that the antiferromagnetic coupling between Mn spins and the in-plane magnetization of the Mn spins can be explained by neglecting effects due to the presence of the Au(111) surface, while for Ni–TCNQ the metal surface plays a role in determining the absence of magnetic anisotropy in the system.