Coalescence Point Research Articles

Plain Capping for Improved Accuracy of Approximate One- and Two-Electron Densities at Two-Particle Coalescence Points.

The values of the one-electron and intracule densities at two-particle coalescence points that enter the expressions for relativistic corrections to energies of Coulombic systems cannot be efficiently computed with sufficient accuracy from approximate wave functions expressed in terms of cuspless basis functions such as the explicitly correlated Gaussians. A new approach to alleviation of this problem, called plain capping, is proposed. Unlike those offered by the previously published formalisms, such as the expectation value identities and integral transforms, the accuracy improvements effected by the plain capping are attained with negligible computational effort and minimum programming. In the case of the on-top two-electron densities, whose accurate computation is particularly costly, the plain capping constitutes the only viable means of error reduction available at present.

Neutral diversity in experimental metapopulations

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth–death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given number of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.

Graphene nanowalls formation investigated by Electron Energy Loss Spectroscopy

The properties of layered materials are significantly dependent on their lattice orientations. Thus, the growth of graphene nanowalls (GNWs) on Cu through PECVD has been increasingly studied, yet the underlying mechanisms remain unclear. In this study, we examined the GNWs/Cu interface and investigated the evolution of their microstructure using advanced Scanning transmission electron microscopy and Electron Energy Loss Spectroscopy (STEM-EELS). GNWs interface and initial root layers of comprise graphitic carbon with horizontal basal graphene (BG) planes that conform well to the catalyst surface. In the vertical section, the walls show a mix of graphitic and turbostratic carbon, while the latter becomes more noticeable close to the top edges of the GMWs film. Importantly, we identified growth process began with catalysis at Cu interface forming BG, followed by defect induction and bending at ‘coalescence points’ of neighboring BG, which act as nucleation sites for vertical growth. We reported that although classical thermal CVD mechanism initially dominates, growth of graphene later deviates a few nanometers from the interface to form GNWs. Nascent walls are no longer subjected to the catalytic action of Cu, and their development is dominated by the stitching of charged carbon species originating in the plasma with basal plane edges.

Coalescent point process of branching trees in a varying environment

Coalescent point process of branching trees in a varying environment

Growth Mechanism and Film Properties of Atomic-Layer-Deposited Titanium Oxysulfide

Titaniumoxysulfide (TiOxSy) is a technologically-relevant material for batteries, catalysis and, the area of our focus: photovoltaics. One of the key merits of TiOxSy is the wide range of electrical conductivity and optical absorption that can be achieved by tuning its composition. In this contribution, we present a supercycle-based ALD approach for TiOxSy which combines ALD of amorphous TiO2 and semimetallic two-dimensional (2D) TiS2, and uses tetrakis(dimethylamido)titanium (TDMATi), H2O and H2S as precursors. While ALD with supercycles is generally acknowledged to give a high level of control over film composition, in this case of TiOxSy we show through a variety of in-situ techniques that many effects occur during the ALD supercycles that strongly affect the film growth and resulting film properties. Yet, by understanding and taking these effects into account, the supercycle process allows for accurate tailoring between pure TiOx and TiSx. The effects of study focus mainly on exchange reactions and the film crystal morphology and its effect on the growth rate. Exchange reactions: QMS measurements show that during supercycle ALD, strong exchange reactions occur during the H2O dosing step, where exchange occurs between underlying TiSx and H2O, resulting in the formation of TiOx and release of H2S. The exchange reactions and their effect on the film growth were studied in-depth using in-situ SE. From these studies, it was found that during ALD TiO2 cycles on TiSx, the exchange reactions behave similarly at 100 and 150 °C, while being more pronounced at 200 °C. Specifically, at 100 and 150 °C, the reactions persist for about seven cycles and stop once approximately 3−4 Å of TiO2 has grown, while at 200 °C, the reactions are more prominent and persist for about nine cycles and stop once approximately 5 Å of TiO2 has grown. This TiO2 forms both through back-oxidation of underlying TiSx and by ALD of TiO2 on top. These exchange effects are thus less prominent at lower growth temperatures, facilitating more accurate control over composition. Film crystallinity: Interestingly, the pure ALD TiO2 and TiS2 processes yield films of very different morphology. Whereas ALD TiO2 at these temperatures results in smooth, amorphous films that grow with a constant growth-per-cycle (GPC), in the case of pure ALD 2D-TiSx the growth process is more intricate: Electron microscopy shows that these 2D films initially have crystal growth that occurs laterally, up to the point of coalescence where the 2D layers start to grow out of plane. As ALD growth on the sideplanes of the 2D material is much faster, the GPC of these films keeps increasing as the film thickness progresses. When combining ALD TiO2 and TiS2 in a supercycle, the TiO2 cycles interrupt the growth of the 2D TiS2 crystals. This not only leads to a lower crystallinity of the film, but due to suppression of the reactive 2D-TiS2 edges, also the GPC is strongly reduced. As such, this effect has a strong influence on the resulting film thickness and composition, which is markedly different than would be expected than on the basis of the constituent ALD cycles in the supercycle.Based on the insights, we present a model that can explain the relation between supercycle ratio, deposition temperature and the resulting film properties. This enables the control over film conductivity over six orders of magnitude, where Hall measurements show that S-rich films exhibit both higher carrier densities and carrier mobility. Similary, controlling the composition allows tuning the optical properties between opaque, semimetallic 2D-TiS2 and transparent, dielectric TiO2 with a bandgap a little over 3 eV.Since exchange reactions and film crystallinity are common factors in ALD films, we expect these results to be of broader interest to the ALD community, for those preparing multicomponent materials using supercycles Figure 1

Influence of the temperature gradient and the pulling velocity on solidification cracking susceptibility during welding: A phase field study

The influence of the temperature gradient and the pulling velocity on solidification cracking susceptibility (SCS) during welding is studied by simulating the liquid channel evolution with a quantitative phase field model. Increasing the pulling velocity or decreasing the temperature gradient increases the pressure drop from the dendrite tip to the coalescence point, leading to an increase in SCS. Decreasing the primary dendrite arm spacing (PDAS) decreases the permeability of the liquid channel and the liquid channel length at the same time, resulting in a decrease in the pressure drop and SCS when the PDAS is small. Consideration of the PDAS dependency on the temperature gradient and the pulling velocity influences the value of the pressure drop but does not change the tendency of SCS. The conclusions are also valid for an alloy with strong back diffusion. As the temperature gradient and the pulling velocity within the melt pool are controlled by process parameters, the findings from this work provide a theoretical basis to optimize process parameters to avoid solidification cracking.

The sixth Painlevé equation as isomonodromy deformation of an irregular system: monodromy data, coalescing eigenvalues, locally holomorphic transcendents and Frobenius manifolds

The sixth Painlevé equation PVI is both the isomonodromy deformation condition of a 2-dimensional isomonodromic Fuchsian system and of a 3-dimensional irregular system. Only the former has been used in the literature to solve the nonlinear connection problem for PVI, through the computation of invariant quantities . We prove a new simple formula expressing the invariants p jk in terms of the Stokes matrices of the irregular system, making the irregular system a concrete alternative for the nonlinear connection problem. We classify the transcendents such that the Stokes matrices and the p jk can be computed in terms of special functions, providing a full non-trivial class of 3-dim. examples such that the theory of non-generic isomonodromy deformations of Cotti et al (2019 Duke Math. J. 168 967–1108) applies. A sub-class of these transcendents realises the local structure of all the 3-dim Dubrovin–Frobenius manifolds with semisimple coalescence points of the type studied in Cotti et al (2020 SIGMA 16 105). We compute all the monodromy data for these manifolds (Stokes matrix, Levelt exponents and central connection matrix).

Improving the performance of fermionic neural networks with the Slater exponential Ansatz

AbstractIn this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron‐nuclear and electron–electron distances, which provides faster convergence of target ground‐state energies due to a better description of the interparticle interaction in the vicinities of the coalescence points, while the accuracies of results, obtained with original and input‐modified FermiNets are similar due to high expressiveness of underlying neural network. Our analysis of learning curves indicates on the possibility to obtain accurate energies with smaller batch sizes using arguments of the bagging approach. In order to obtain even more accurate results for the ground‐state energies, we propose an extrapolation scheme for estimating Monte Carlo integrals in the limit of an infinite number of points. Numerical tests for a set of molecules demonstrate a good agreement with the results of the original FermiNets approach (achieved with larger batch sizes than required by our approach) and with results of the coupled‐cluster singles and doubles with perturbative triples (CCSD(T)) method that are calculated in the complete basis set limit.

Diffusion-controlled annihilation A+B→0: Coalescence, fragmentation, and collapse of nonidentical A-particle islands submerged in the B-particle sea.

We present a systematic analysis of diffusion-controlled interaction and collapse of two nonidentical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ and a relatively large initial ratio of island-to-sea concentrations, the evolution dynamics of the island-sea-island system demonstrates remarkable universality and, depending on the system dimension, is determined unambiguously by two dimensionless parameters Λ=N_{0}^{+}/N_{Ω} and q=N_{0}^{-}/N_{0}^{+}, where N_{0}^{+} and N_{0}^{-} are the initial particle numbers in the larger and smaller of the islands, respectively, and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. We find that at each fixed 0<q≤1, there are threshold values Λ_{★}(q) and Λ_{s}(q)≥Λ_{★}(q) that depend on the dimension and separate the domains of individual death of each of the islands Λ<Λ_{★}(q), coalescence and subsequent fragmentation (division) of a two-centered island Λ_{★}(q)<Λ<Λ_{s}(q), and collapse of a single-centered island formed by coalescence Λ>Λ_{s}(q). We demonstrate that regardless of d, the trajectories of the island centers are determined unambiguously by the parameter q, and we reveal a detailed picture of the evolution of islands and front trajectories with an increase in Λ, focusing on the scaling laws of evolution at the final collapse stage and in the vicinity of starting coalescence and fragmentation points.

Three-dimensional unsteady axisymmetric vortex solutions to the Bellamy-Knights equation and the distribution of boundary conditions

The Bellamy-Knights equation gives three-dimensional unsteady axisymmetric incompressible vortex solutions that are disconnected from the known exact steady solutions. In this paper, by introducing a new parameter that allows a change of the time scale, the Bellamy-Knights equation is transformed into an integro-differential equation that continuously connects with the equation for steady vortices. The new equation is viewed as describing the one-dimensional motion of a particle under conserved and nonconserved forces and leads to new regular solutions, in which the particle initially undergoes almost sinusoidal oscillations around the minimum of potential followed by a very rapid approach to the extrema of the potential. The regular solutions distribute discretely in the space of boundary conditions and are classified into types that are specified by the pattern of sequence of small and large oscillations of the axial component of velocity. Extending the solutions to singular ones, the boundary conditions for solutions of the same type are shown to form a continuous one-dimensional set, which we call a branch. The set of branches forms dense self-similar patterns with accumulation points, some of which coalesce to a single point. In an arbitrary neighborhood of the accumulation or coalescent point, any two distinct boundary conditions whose distance in the space of boundary conditions is arbitrarily small give mutually distinctive solutions with a finite difference at some region of the spatial distance. This feature of the equations signifies the extreme sensitivity of inflowing vortex solutions to boundary conditions.

Two-particle coalescence conditions revisited

The notion of the nth order local energy, generated by the nth power of the Hamiltonian, has been introduced. The nth order two-particle coalescence conditions have been derived from the requirements that the nth order local energy at the coalescence point is non-singular and equal to the nth power of the Hamiltonian eigenvalue. The first condition leads to energy-independent constraints. The second one is state-specific. The analysis has been done using a radial, one-dimensional, model Hamiltonian. The model is valid in the asymptotic region of . The coalescence conditions set the relations between the expansion coefficients of the radial wave function into a power series with respect to r.

Wave function identity: A new symmetry for 2-electron systems in an electromagnetic field

Stationary-state Schr{\"o}dinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schr{\"o}dinger-Pauli theory Hamiltonian with a symmetrical binding potential, we report a new symmetry operation of the electronic coordinates. The symmetry operation is such that it leads to the equality of the transformed wave function to the wave function. This equality is referred to as the Wave Function Identity. The symmetry operation is a two-step process: an interchange of the spatial coordinates of the electrons whilst keeping their spin moments unchanged, followed by an inversion. The Identity is valid for arbitrary structure of the binding potential, arbitrary electron interaction of the form $w(|{\bf{r}} - {\bf{r}}'|)$, all bound electronic states, and arbitrary dimensionality. It is proved that the exact wave functions satisfy the Identity. On application of the permutation operation for fermions to the identity, it is shown that the parity of the singlet states is even and that of triplet states odd. As a consequence, it follows that at electron-electron coalescence, the singlet state wave functions satisfy the cusp coalescence constraint, and triplet state wave functions the node coalescence condition. Further, we show that the parity of the singlet state wave functions about all points of electron-electron coalescence is even, and that of the triplet state wave functions odd. The Wave Function Identity and the properties on parity, together with the Pauli principle, are then elucidated by application to the $2$-dimensional $2$-electron `artificial atoms' or semiconductor quantum dots in a magnetic field in their first excited singlet $2^{1}S$ and triplet $2^{3} S$ states.

SECURITY DYNAMIC OF THE STRATEGIC NUCLEAR BALANCE IN SYSTEMS THEORY AND THE CONCEPT OF CENTRES OF GRAVITY

The general concepts and understandings of the international security environment in the 21st century have become more complex owing to a multitude of factors spanning both traditional and novel security domains. In the current era, nuclear security in particular has continued to exist in its paramount role of importance. The following paper explores the defined state of the “strategic nuclear balance” as a state extant within the systemic approach towards international security. Based upon previous research in defining the state through core concepts fundamental to systems theory and supporting concepts such as those of centres of gravity, this paper aims to further expand contemporary understandings and illustrate a point of coalescence. Thereby the given study demonstrates how based upon key postulations in the understanding of the security concept in systems theory and centres of gravity of both physical and non-physical nature within a system, a combined novel model can be extrapolated, which demonstrates the security dynamic in the “strategic nuclear balance” between major global nuclear armed state actors.

Coalescence of ultrathin films by atomic layer deposition or chemical vapor deposition: Models of the minimum thickness based on nucleation and growth rates

Ultrathin, pinhole-free, and atomically smooth films are essential for future development in microelectronic devices. However, film morphology and minimum thickness are compromised when growth begins with the formation of islands on the substrate, which is the case for atomic layer deposition or chemical vapor deposition (CVD) on relatively unreactive substrates. Film morphology at the point of coalescence is a function of several microscopic factors, which lead to measurable, macroscopic rates of island nucleation and growth. To quantify the effect of these rates on the morphology at the point of coalescence, we construct two models: (1) a Monte Carlo simulation generates the film height profile from spatially random nucleation events and a constant island growth rate; simulated films resemble AFM images of the physical films; (2) an analytical model uses Poisson point statistics to determine the film thickness required to cover the last bare site on the substrate as a function of the nucleation rate and growth rate. Both models predict the same maximum thickness required to reach 99% coverage and reveal a power law relationship between the maximum thickness and the ratio of the nucleation rate divided by the growth rate. The Monte Carlo simulation further shows that the roughness scales linearly with thickness at coverages below 100%. The results match well with experimental data for the low-temperature CVD of HfB2 on Al2O3 substrates, but there are significant discrepancies on SiO2 substrates, which indicate that additional surface mechanisms must play a role.

When Elasticity Affects Drop Coalescence.

The breakup and coalescence of drops are elementary topological transitions in interfacial flows. The breakup of a drop changes dramatically when polymers are added to the fluid. With the strong elongation of the polymers during the process, long threads connecting the two droplets appear prior to their eventual pinch-off. Here, we demonstrate how elasticity affects drop coalescence, the complement of the much studied drop pinch-off. We reveal the emergence of an elastic singularity, characterized by a diverging interface curvature at the point of coalescence. Intriguingly, while the polymers dictate the spatial features of coalescence, they hardly affect the temporal evolution of the bridge. These results are explained using a novel viscoelastic similarity analysis and are relevant for drops created in biofluids, coating sprays, and inkjet printing.

Study on microstructure wax evolution behavior of waxy crude oil during cooling

The microcosmic characteristics of wax evolution of waxy crude-oil directly affect the heat transfer process of crude-oil. A microscopic experiment was carried out on the wax deposit process of waxy crude-oil by polarized light microscopy. The phase change characteristics of wax crystals during wax deposit process were analyzed, and the process of wax crystal precipitation was quantitatively analyzed by the image analysis software ImageProPlus. The results show that the wax deposit process mainly includes wax crystal nucleation, growth and bonding, which together lead to the formation of wax crystal network. The sample oil particle number and the wax crystal area fraction curves have inflection points at 41 ? and 38?, respectively, which are caused by different carbon number alkane content and wax crystal bonding. By analyzing the particle size and particle area curves, it is known that nucleation precipitation and growth are alternately dominant in the early stage of wax crystal growth. Through the wax roundness study, it is found that the growth of wax crystals in the early stage is mainly in the longitudinal direction, and the growth in the late stage is not directional. According to the phase change process of wax crystal, it is proposed that the temperature of the crude-oil with porous media grid structure is coalescence point. By using the position point tracking of wax crystal and analysis of the variation characteristics of microscopic parameters, the coalescence point temperature of the sample crude-oil in this experiment is 38?.

Nonreciprocal and even Willis couplings in periodic thermoacoustic amplifiers

Thermoacoustic amplifiers are analyzed in the framework of nonreciprocal Willis coupling. The closed form expressions of the effective properties are derived, showing that an applied temperature gradient causes the appearance of a nonreciprocal Willis coupling. Even and nonreciprocal Willis couplings are exhibited already in the first-order Taylor expansion of the solution and are of equal modulus but opposite sign, thus suggesting that the even Willis coupling is a reaction to the nonreciprocity introduced by the temperature gradients. These Willis couplings cause a coalescence point in the $k$ space, which deviates from $\text{Re}(k)=0$ (with $k$ the wave number) and is thus a zero-group-velocity point, as well as the opening of an amplification gap at low frequency. Effective parameters and scattering properties are found in excellent agreement with experimental results. This article paves the way to further control the acoustic waves at very low frequencies with nonreciprocal systems.

On-top description of the effect of excitation on electron correlation with quasiparticles

A spectrum of $\mathrm{\ensuremath{\Delta}}$-correlon quasiparticles is proposed to describe the excitation effect on electron correlation. The proposed quasiparticle description is based on the comparison of the pair-correlation functions of the excited and ground states at the special coalescence points of the configurational space. The complex form of the $\mathrm{\ensuremath{\Delta}}$-correlon wave function allows us to naturally separate regions with the excitation suppression of correlation (ESC $\mathrm{\ensuremath{\Delta}}$-correlon), where correlation is stronger in the ground state, from those with the excitation enhancement of correlation (EEC $\mathrm{\ensuremath{\Delta}}$-correlon), where correlation is stronger in the excited state. The proposed $\mathrm{\ensuremath{\Delta}}$-correlon approach is applied to characterize the important single excitations with the competition of ``anticorrelation squeezing'' and ``enhanced-correlation spreading'' of the two-electron distribution. The former feature characterizes single valence excitations of the ionic nature and this leads to the prevailing of the ESC effect in this type of excitations. In turn, the enhanced-correlation spreading characterizes single Rydberg excitations, which leads to the prevailing of the EEC effect in this type of excitations. The proposed $\mathrm{\ensuremath{\Delta}}$-correlon quasiparticles are studied both analytically and numerically. The analytical expressions for the on-top correlation functions are obtained with the two-determinantal two-electron model of the active site of an excitation. The two-dimensional contour plots of the ESC and EEC $\mathrm{\ensuremath{\Delta}}$-correlons obtained for the lowest vertical valence ionic and Rydberg excitations in the prototype molecules ${\mathrm{H}}_{2}, {\mathrm{N}}_{2}$, and ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ from the highly correlated wave functions confirm, in general, the trends in the relative correlation strength deduced from the model.

Symmetric evolution, coherence and violation of Leggett–Garg inequalities

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a parity-time () symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e. the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett–Garg inequality tests show maximal violation about the EPs.

Influence of hydrodynamic interactions among multiple bubbles on convective heat transfer in nucleate boiling

To clear the effects of the hydrodynamic interactions among neighboring vapor bubbles on the saturated pool boiling heat transfer, artificial nucleation sites with several cavity arrangements were manufactured on the substrate surface and measured liquid temperatures near heated substrate by a miniature thermocouple probe with 10 kHz. The surface temperature of heated substrate was measured by an infrared camera with 1 kHz and bubble dynamics were simultaneously visualized by a high-speed video camera with 5 kHz and 10 kHz, respectively. The liquid temperature fluctuations, measured with micro thermocouple 100 μm and 10 μm above the substrate surface, were compared among each other and with the transient temperature fields obtained through IR measurements. Results showed that the hydrodynamic interaction among neighboring bubbles causes the liquid convection, that was only detected 100 µm above the boiling surface. Generally, the degree of liquid temperature fluctuations at 10 μm height and different arrangements of nucleation sites was under 1 K. Here the superheated sublayer in the vicinity of the boiling surface was generally not affected by the convection. Only when the coalescence from two neighboring nucleation sites occurred and the liquid-vapor interface nearly reached the substrate, a steep temperature drop over 2 K was detected. It was concluded that the viscous sublayer stably exists during boiling of water in lower heat flux conditions. To enhance the convective heat transfer in nucleate boiling, coalesced bubble needs to peel off the viscous sublayer during its deformation. Based on the measurements in this study, this peel-off effect only happens when the coalescence point is less than 1 mm above the heated surface.