Average Atomic Density Research Articles

SOFIA FEEDBACK Survey: The Pillars of Creation in [C ii] and Molecular Lines

We investigate the physical structure and conditions of photodissociation regions (PDRs) and molecular gas within the Pillars of Creation in the Eagle Nebula using SOFIA FEEDBACK observations of the [C ii] 158 μm line. These observations are velocity resolved to 0.5 km s−1 and are analyzed alongside a collection of complimentary data with similar spatial and spectral resolution: the [O i] 63 μm line, also observed with SOFIA, and rotational lines of CO, HCN, HCO+, CS, and N2H+. Using the superb spectral resolution of SOFIA, APEX, CARMA, and BIMA, we reveal the relationships between the warm PDR and cool molecular gas layers in context of the Pillars’ kinematic structure. We assemble a geometric picture of the Pillars and their surroundings informed by illumination patterns and kinematic relationships and derive physical conditions in the PDRs associated with the Pillars. We estimate an average molecular gas density cm−3 and an average atomic gas density n H ∼ 1.8 × 104 cm−3 and infer that the ionized, atomic, and molecular phases are in pressure equilibrium if the atomic gas is magnetically supported. We find pillar masses of 103, 78, 103, and 18 M ⊙ for P1a, P1b, P2, and P3, respectively, and evaporation times of ∼1–2 Myr. The dense clumps at the tops of the pillars are currently supported by the magnetic field. Our analysis suggests that ambipolar diffusion is rapid and these clumps are likely to collapse within their photoevaporation timescales.

Characterization of breast tissues in density and effective atomic number basis via spectral X-ray computed tomography

Objective. Differentiation of breast tissues is challenging in X-ray imaging because tissues might share similar or even the same linear attenuation coefficients μ. Spectral computed tomography (CT) allows for more quantitative characterization in terms of tissue density (ρ) and effective atomic number (Z eff) by exploiting the energy dependence of μ. The objective of this study was to examine the potential of ρ/Z eff decomposition in spectral breast CT so as to explore the benefits of tissue characterization and improve the diagnostic accuracy of this emerging 3D imaging technique. Approach. In this work, 5 mastectomy samples and a phantom with inserts mimicking breast soft tissues were evaluated in a retrospective study. The samples were imaged at three monochromatic energy levels in the range of 24–38 keV at 5 mGy per scan using a propagation-based phase-contrast setup at SYRMEP beamline at the Italian national synchrotron Elettra. Main results. A custom-made algorithm incorporating CT reconstructions of an arbitrary number of spectral energy channels was developed to extract the density and effective atomic number of adipose, fibro-glandular, pure glandular, tumor, and skin from regions selected by a radiologist. Significance. Preliminary results suggest that, via spectral CT, it is possible to enhance tissue differentiation. It was found that adipose, fibro-glandular and tumorous tissues have average effective atomic numbers (5.94 ± 0.09, 7.03 ± 0.012, and 7.40 ± 0.10) and densities (0.90 ± 0.02, 0.96 ± 0.02, and 1.07 ± 0.03 g cm−3) and can be better distinguished if both quantitative values are observed together.

Mathematical Modeling: Cisplatin Binding to Deoxyribonucleic Acid

The discovery of the cisplatin drug attracted considerable research attention as scientists strove to understand the drug’s mechanism in the human body that is responsible for destroying cancer cells, particularly the coordination between the cisplatin drug and deoxyribonucleic acid. Here, the binding energies of a cisplatin molecule relative to double-stranded deoxyribonucleic acid are obtained. The interactions of the system are determined by performing double integrals, and the analytical expressions are derived from the Lennard–Jones function and the continuum approximation; here, it is assumed that a discrete atomic structure might be replaced by surfaces with a constant average atomic density. The results observed that the cisplatin molecule is binding to the double-stranded deoxyribonucleic acid at either the minor or major grooves. By minimizing the interaction energies between the cisplatin molecule and the minor and major grooves, for arbitrary distances λ and arbitrary tilt angles φ from the axis of the helix of the double-stranded deoxyribonucleic acid, the binding energies are determined, and their values are ≈−6 and ≈−12.5 (kcal/mol), respectively. Thus, we may deduce that the major groove in double-stranded deoxyribonucleic acid is the most preferred groove for linking with the cisplatin molecule. The current analysis might help in the equivalent continuum modeling of deoxyribonucleic acids and nanocomposites.

Three-color reflections in one-dimensional ordered and disordered atomic lattices with trapped N-type cold atoms.

Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N0 (1 + Δk). When the random number Δk = 0 (the atomic density Nk(z)) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase (N k+(z) with Δk > 0) or decrease (N k-(z) with Δk < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k+(z)/N k (z) (N k-(z)/N k (z)) with the random distribution of lattice cells with N k+(z) (N k-(z)). When a cluster of disordered lattice cells with N k+(z) and N k-(z) is located at the front or tail of the atomic lattice, reflection symmetry can be broken. However, the symmetry and robustness can be well preserved with the random fluctuation of the average atomic density in each lattice cell.

CDFTPY: A python package for performing classical density functional theory calculations for molecular liquids

Classical density functional theory (CDFT) provides a rigorous theoretical framework for the statistical mechanics based analysis of many-body systems. This approach has proven to be successful in simulations of mono-atomic, i.e. simple liquids, and there is an ongoing theoretical effort in extending it to more complex polyatomic, molecular liquid systems. Sharing these developments in the form of open-source and easily accessible codes could greatly benefit these efforts. In this work, we present python-based CDFT code that contains both conventional Reference Interaction Site Model (RISM) and recently developed renormalized site density theory (RSDFT) approach. The current implementation is focused on ion solvation - the problem of both fundamental and practical importance. It allows the calculation of individual ions as well as comparative analysis across a range of interaction parameters. Program summaryProgram Title: cdftpyCPC Library link to program files:https://doi.org/10.17632/p8dsgz5n4g.1Developer's repository link:https://github.com/opencdftLicensing provisions: GPLv3Programming language: python 3.9+Nature of problem: Computational modeling of molecular liquids at the atomistic level of resolution is an important capability across many scientific areas. Classical density functional theory (CDFT) approaches this problem by building statistical mechanics model of the system in terms of its average atomic (site) density. Such an approach can provide orders of magnitudes improvements in efficiency compared to conventional molecular dynamics simulations, but requires special treatment of multi-scale interactions in a molecular liquid. A practical utility of our open-source python based implementation of CDFT is the study the problem solvation of ions or Lennard-Jones particles.Solution method: Python package developed in this work provides two CDFT implementations for molecular liquids - renormalized site density functional theory and reference interaction site model. It enables calculations of thermodynamic and structural properties related to solvation of spherical solutes. The nonlinear integral equations associated with the two methods are solved iteratively, utilizing Fast Fourier Transform (FFT) for the calculation of the numerically intensive convolution integrals. The resulting code provides near instantaneous evaluation of the solvated properties of individual solutes and high-throughput screening across the range of different solute parameters.

Dynamic evolution of expanding Bose–Einstein condensates in the presence of a three-dimensional random optical speckle potential

We study the diffusion of an expanding Bose–Einstein condensate released from a harmonic trap in a three-dimensional speckle disorder potential. To this end, we use the first Born approximation and examine the density profiles at short and long times. Analytical results are presented in different regimes. The evolution of the density profiles in space and time is deeply examined. We find that at long times and for a fixed disorder strength, the profile of the average atomic density decreases in power law. The time evolution of the typical size of the condensate is explored numerically.

Phase-field crystal simulation of evolution of liquid pools in grain boundary pre-melting regions

Abstract Pre-melting is a phenomenon that below the melting point the liquid-like structure appears at the grain- boundary while the grain interior remains a crystal structure. The phase-field crystal method was employed to investigate the early evolution of the liquid pools in pre-melting regions, mainly involving four structural transformations: solid−solid state → small droplet → large liquid pool → homogeneous liquid melting. The microscopic morphology and free energy variation with different average atomic densities demonstrate that the average atomic density is sensitive to the morphological characteristics of liquid pools. Both two-dimensional and three-dimensional simulation results show that the amplitude reduction of order parameters can promote the order−disorder transition of grain boundaries, causing pre-melting in the edge dislocation aggregation. The relationship between the average atomic density and the width of the liquid pools is verified from thermodynamics, which provides a prerequisite for the application of high-temperature strain in the later stage to some extent.

Structure of glycerol-Mg2+-smectites/vermiculites complex based on molecular dynamics and implementation of the model for X-ray diffraction modeling

Smectites and vermiculites can be distinguished from each other after Mg2+-saturation and solvation with glycerol (GLY). Smectites generally expand to c.a. 18 Å, forming a two-layer complex, while vermiculites to c.a. 14.5 Å, forming a one-layer complex. Additionally, the distribution of layer charges within one population of crystallites can lead to mixed-layered one−/two-GLY layer complexes. Thus far, the model of the GLY intercalate has not been implemented in programs used for XRD modeling of clay minerals. The aim of this study was to obtain a model of the structure of Mg2+-GLY-smectite/vermiculite with the help of molecular dynamic (MD) simulations.A wide range of GLY and H2O contents, in the simulated structures of montmorillonites with charges: 0.3, 0.5, and 0.75 per half unit cell (phuc), and beidellite with a charge of 0.75 phuc, were considered.The average atomic density profiles along the z-direction were calculated for all of the simulations. Subsets corresponding to certain basal spacings (plateaus) were chosen as representative for one- and two-layer intercalates. The electronic density profiles of GLY, H2O, and Mg2+ ions were fitted with Gaussian functions. The purpose of the work was to minimize the number of functions in order to achieve a maximally simple, yet flexible model of the interlayer structures.It was possible to determine relationships between positions of the atomic distributions and the basal spacings. All the relationships were implemented in Sybilla and BGMN computer programs. The new model of the complex was used for fitting of diffractograms of Mg2+-montmorillonites and Mg2+-vermiculite with different layer charges.

Bond-order bond energy model for alloys

We introduce a novel way to parameterize alloy energies in the form of a bond-order bond energy model. There, a bond order function models the transition between competing phases and switches their respective bond energies on and off. For the case of the Ni-Cr-Mo alloys investigated here, which assume face- or body-centered cubic structures, we propose a sigmoidal switching function fitted to the c/a ratio of “Bain-like” cells. With that, the model does an excellent job in describing the DFT-calculated alloy energies. We also show that the average atomic charge density can vary considerably as a function of composition, which can significantly modify alloy bond energies from simple expectation. The fitted bond energies can among others be used to determine phase diagrams, where we find excellent agreement with previous assessments in the solid range for Ni-Cr and Cr-Mo phase diagrams once the necessary entropy terms are added. They also allow quantitative, composition-dependent calculation of chemical potentials, which we use to determine vacancy formation energies in binary NiCr alloys for configurations that have been energy-minimized with Monte Carlo simulations. We show that the resulting regime of negative formation energies is a sign for thermodynamic instability of the underlying crystal and lies in the two-phase concentration range in the phase diagram, resulting in a holistic picture that unites defect and phase stability through the fully quantitative link between stoichiometry and chemical potentials enabled by the proposed bond energy model.

A facility for production and laser cooling of cesium isotopes and isomers

We report on the design, installation, and test of an experimental facility for the production of ultra-cold atomic isotopes and isomers of cesium. The setup covers a broad span of mass numbers and nuclear isomers, allowing one to directly compare chains of isotopes and isotope/isomer pairs. Cesium nuclei are produced by fission or fusion-evaporation reactions using primary proton beams from a 130 MeV cyclotron impinging upon a suitable target. The species of interest is ejected from the target in ionic form, electrostatically accelerated, mass separated, and routed to a science chamber. Here, ions are neutralized by implantation in a thin foil, and extracted by thermal diffusion. A neutral vapor at room temperature is thus formed and trapped in a magneto-optical trap. Real-time fluorescence imaging and destructive absorption imaging provide information on the number of trapped atoms, their density, and their temperature. Tests with a dedicated beam of 133Cs+ ions at 30 KeV energy confirm neutralization, evaporation, and laser cooling to 150 μK, with an average atomic density of 1010 cm−3. Availability of cold and dense atomic samples of Cs isotopes and isomers opens new avenues for high-precision measurements of isotopic and isomeric shifts thereby gaining deeper insight into the nuclear structure, as well as for sensitive measurements of isotopes’ concentration ratios in trace quantities. The facility also constitutes the core for future experiments of many-body physics with nuclear isomers.

Elastic constants of stressed and unstressed materials in the phase-field crystal model

A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.

Suction Energy for Double-Stranded DNA Inside Single-Walled Carbon Nanotubes

Summary Deoxyribonucleic acid (DNA) and carbon nanotubes (CNTs) constitute hybrid materials with the potential to provide new components with many applications in various technology areas, such as molecular electronics, field devices and medical applications. Using classical applied mathematical modelling, we investigate the suction force experienced by a double-stranded DNA (dsDNA) molecule which is assumed to be located on the axis near an open end of a semi-infinite single-walled CNT. We employ both the 6-12 Lennard-Jones potential and the continuum approximation, which assumes that a discrete atomic structure can be replaced by a surface with constant average atomic density. While most research in the area is dominated by molecular dynamics simulations, here we use elementary mechanical principles and classical applied mathematical modelling techniques to formulate explicit analytical criteria and ideal model behaviour. We observe that the suction behaviour depends on the radius of the CNT, and we predict that it is less likely for a dsDNA molecule to be accepted into the CNT when the value of the tube radius is ${&lt;}12.9$ Å. The dsDNA molecule will be accepted into the CNT for radii lager than 13 Å, and we show that the optimal single-walled CNT necessary to fully enclose the DNA molecule has a radius of 13.56 Å, which approximately corresponds to the chiral vector numbers (20, 20). This means that the ideal single-walled CNT to be used to encapsulate a dsDNA is (20, 20) which has the required radius of 13.56 Å.

Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications

In many nanotechnology areas, there is often a lack of well-formed conceptual ideas and sophisticated mathematical modeling in the analysis of fundamental issues involved in atomic and molecular interactions of nanostructures. Mathematical modeling can generate important insights into complex processes and reveal optimal parameters or situations that might be difficult or even impossible to discern through either extensive computation or experimentation. We review the use of applied mathematical modeling in order to determine the atomic and molecular interaction energies between nanoscale objects. In particular, we examine the use of the 6-12 Lennard-Jones potential and the continuous approximation, which assumes that discrete atomic interactions can be replaced by average surface or volume atomic densities distributed on or throughout a volume. The considerable benefit of using the Lennard-Jones potential and the continuous approximation is that the interaction energies can often be evaluated analytically, which means that extensive numerical landscapes can be determined virtually instantaneously. Formulae are presented for idealized molecular building blocks, and then, various applications of the formulae are considered, including gigahertz oscillators, hydrogen storage in metal-organic frameworks, water purification, and targeted drug delivery. The modeling approach reviewed here can be applied to a variety of interacting atomic structures and leads to analytical formulae suitable for numerical evaluation.

Atomic density effects on temperature characteristics and thermal transport at grain boundaries through a proper bin size selection.

This study focuses on the proper characterization of temperature profiles across grain boundaries (GBs) in order to calculate the correct interfacial thermal resistance (ITR) and reveal the influence of GB geometries onto thermal transport. The solid-solid interfaces resulting from the orientation difference between the (001), (011), and (111) copper surfaces were investigated. Temperature discontinuities were observed at the boundary of grains due to the phonon mismatch, phonon backscattering, and atomic forces between dissimilar structures at the GBs. We observed that the temperature decreases gradually in the GB area rather than a sharp drop at the interface. As a result, three distinct temperature gradients developed at the GB which were different than the one observed in the bulk solid. This behavior extends a couple molecular diameters into both sides of the interface where we defined a thickness at GB based on the measured temperature profiles for characterization. Results showed dependence on the selection of the bin size used to average the temperature data from the molecular dynamics system. The bin size on the order of the crystal layer spacing was found to present an accurate temperature profile through the GB. We further calculated the GB thickness of various cases by using potential energy (PE) distributions which showed agreement with direct measurements from the temperature profile and validated the proper binning. The variation of grain crystal orientation developed different molecular densities which were characterized by the average atomic surface density (ASD) definition. Our results revealed that the ASD is the primary factor affecting the structural disorders and heat transfer at the solid-solid interfaces. Using a system in which the planes are highly close-packed can enhance the probability of interactions and the degree of overlap between vibrational density of states (VDOS) of atoms forming at interfaces, leading to a reduced ITR. Thus, an accurate understanding of thermal characteristics at the GB can be formulated by selecting a proper bin size.

Energy behaviour for DNA translocation through graphene nanopores

Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6–12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b of the hole that gives the minimum energy. By minimizing the interaction energy, we observe that the single-strand DNA and double-strand DNA molecules penetrate through a graphene nanopore when the pore radii b> 7.8Å and b> 12.7Å, respectively. Our results can be adopted to offer new applications in the atomic surface processes and electronic sensing.

Three model shapes of Doxorubicin for liposome encapsulation.

Targeted drug delivery provides a possible method for the transfer of drug molecules into cancer cells. Liposomes together with a drug, such as Doxorubicin (DOX) inside the liposomes, can be formed as a nano-capsule. In this study, we are interested in finding a favorable size of liposome and an appropriate shape of DOX cluster: sphere, cylinder or ellipsoid. Using mathematical modeling, the interaction energy of the system is obtained from the Lennard-Jones potential and the continuum assumption which assumes that discrete atomic structure can be replaced by an average atomic density spread over a surface. The numerical results show that the spherical shape gives the lowest energy at the equilibrium configuration amongst the three shapes. In the case of equivalent surface areas, the spherical shape gives the energy lower than -4,000 kJ/mol at the equilibrium while the energies for the other cases do not come close to this level. Further in the case of a liposome of 50 nm in radius, the sphere of radius 49.726 nm, equivalent to 31,072 nm(2) surface area, gives the minimum energy at -6,642 kJ/mol. However, an equivalent cylindrical shape is not possible due to geometric constraints. The lowest minimum energy for the ellipsoid occurs for equal major and minor axes, namely for the spherical case. The results presented here are a first step in the design and implementation of a drug molecule for a targeted drug delivery system.

C60 fullerene binding to DNA

Fullerenes have attracted considerable attention in various areas of science and technology. Owing to their exceptional physical, chemical, and biological properties, they have many applications, particularly in cosmetic and medical products. Using the Lennard-Jones 6-12 potential function and the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities, we determine the binding energies of a C60 fullerene with respect to both single-strand and double-strand DNA molecules. We assume that all configurations are in a vacuum and that the C60 fullerene is initially at rest. Double integrals are performed to determine the interaction energy of the system. We find that the C60 fullerene binds to the double-strand DNA molecule, at either the major or minor grooves, with binding energies of −4.7 eV or −2.3 eV, respectively, and that the C60 molecule binds to the single-strand DNA molecule with a binding energy of −1.6 eV. Our results suggest that the C60 molecule is most likely to be linked to the major groove of the dsDNA molecule.

Determination of optimal nanotube radius for single‐strand deoxyribonucleic acid encapsulation

The molecular interactions between a single-strand deoxyribonucleic acid (ssDNA) molecule and a carbon nanotube (CNT) are modelled to determine the suction force experienced by the DNA which is assumed to be located on the axis near the open end of a single-walled CNT (SWCNT). They determine the optimal nanotube radius for encapsulation, that is, the radius of the nanotube with the lowest interaction energy. The expression for the molecular interaction energy is derived from the 6–12 Lennard-Jones potential together with the continuum approach, which assumes that a discrete atomic structure can be replaced by a line or a surface with constant average atomic density. It was found that an ssDNA can be encapsulated inside a SWCNT with a radius larger than 8.2 A, and it is shown that the optimal SWCNT needed to fully enclose the DNA molecule has a radius of 8.8 A, which approximately corresponds to the chiral vector numbers (13, 13). This means that if it is wished to encapsulate the ssDNA into a CNT, an ideal SWCNT to do this is (13, 13) which has the required radius of 8.8 A.

Influence of ion-to-atom ratio on the microstructure of evaporated molybdenum thin films grown using low energy argon ions

The authors report the effect of argon ion to molybdenum atom ratio (r) on the microstructure of low energy (70 eV) argon ion assisted electron beam evaporated Mo thin films. Surface roughness, morphology, and crystallinity of Mo films are found to strongly depend on “r.” Increase of “r” from 0 to 100 induces gradual loss in crystallinity, reduction in surface roughness and systematic increase in density of the film. For “r” ∼ 100, average atomic density of the film approaches the bulk value (97%) with lowest surface roughness. Further, increasing “r” up to 170 reduces the atomic density, increases roughness, and increase in crystallinity induced by low energy Ar ion beam. The observed surface roughness and grain size determined by x-ray reflectivity and glancing incidence x-ray diffraction correlate well with atomic force microscopy measurements. This study demonstrates that for r = 100 one gets lowest roughness Mo film with highest density and nearly amorphous microstructure. The growth model is discussed by structural zone model.

Encapsulation of a Chloroform Molecule in a Peptide Nanotube

We determine the encapsulation of a chloroform molecule into a D,L-Ala cyclopeptide nanotube by investigating the interaction energy between the two molecular structures. We employ the Lennard-Jones potential and a continuum approach which assumes that the atoms are evenly distributed over the molecules providing average atomic densities. Our result demonstrates that the encapsulation depends on the size of the molecule and the internal diameter of the peptide nantube. In particular, the on-axis chloroform molecule is only accepted into a peptide nanotube whose internal radius is greater than 5 ?. If located near the edge of the nanotube, then it is unlikely that the chloroform molecule will enter the nanotube. This is due to the energy valley that the molecule will need to overcome to move past the edge into the open end of the nanotube.