Minimum Energy Configuration Research Articles

Geometric parameter control for tunable resonance frequencies in asymmetric nanodots: equilibrium states and dynamic response

Through numerical simulations, we delve into the examination of the equilibrium state and dynamic response of asymmetric nanodots. Within these nanodots, we identify two distinct equilibrium states—single domain and vortex. Our findings reveal a direct correlation between the number and frequencies of peaks and the minimum energy configuration, which is contingent upon the physical parameters of the system. This observation implies the potential to intentionally manipulate a desired set of frequencies by precisely controlling the geometric parameters of the system.

On the Strong Binding Affinity of Gold-Graphene Heterostructures with Heavy Metal Ions in Water: A Theoretical and Experimental Investigation.

Minimum energy configurations in 2D material-based heterostructures can enable interactions with external chemical species that are not observable for their monolithic counterparts. Density functional theory (DFT) calculations reveal that the binding energy of divalent toxic metal ions of Cd, Pb, and Hg on graphene-gold heterointerfaces is negative, in contrast to the positive value associated with free-standing graphene. The theoretical predictions are confirmed experimentally by Surface Plasmon Resonance (SPR) spectroscopy, where a strong binding affinity is measured for all the heavy metal ions in water. The results indicate the formation of a film of heavy metal ions on the graphene-gold (Gr/Au) heterointerfaces, where the adsorption of the ions follows a Langmuir isotherm model. The highest thermodynamic affinity constant K = 3.1 × 107 L mol-1 is observed for Hg2+@Gr/Au heterostructures, compared to 1.1 × 107 L mol-1 and 8.5 × 106 L mol-1 for Pb2+@Gr/Au and Cd2+@Gr/Au, respectively. In the case of Hg2+ ions, it was observed a sensitivity of about 0.01°/ppb and a detection limit of 0.7 ppb (∼3 nmol L-1). The combined X-ray photoelectron spectroscopy (XPS) and SPR analysis suggests a permanent interaction of all of the HMIs with the Gr/Au heterointerfaces. The correlation between the theoretical and experimental results indicates that the electron transfer from the graphene-gold heterostructures to the heavy metal ions is the key for correct interpretation of the enhanced sensitivity of the SPR sensors in water.

Study on the spectral characteristics and chemical structure of Taixi Anthracite

Taixi anthracite is a rare form of coal in both China and the world, characterized by low ash, sulfur, phosphorus, high carbon content, conductivity, and calorific value. Our team employed a solid-phase microwave method [1] to graphitize Taixi anthracite and graft it with natural rubber to create a composite with outstanding properties. However, since the molecular structure of Taixi anthracite was unknown, establishing a molecular model for the reaction becomes crucial for the functionalization of anthracite. In this study, By combining elemental analysis, nuclear magnetic resonance carbon spectroscopy, Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy, the molecular carbon content of Taixi anthracite is 89 %, the XBP value is 0.37, and the chemical formula of the lowest relative molecular weight of Taixi anthracite is C181H77O4NS0.1. The results of computer simulation show that Taixi anthracite is assembled into coal macromolecular structure by 10 molecular structure units of 5 kinds of coal according to 2:1:2:2:3 ratio, and the geometric optimization, annealing simulation and inverse verification are carried out. The aggregation model is established by using X-ray diffraction data and computer simulation techniques.we innovatively constructed five groups of macromolecular structure units of Taixi anthracite to characterize the results and simulate the minimum energy configuration of single chains and aggregate states. This research provides a molecular-level theoretical basis for the functionalization of Taixi anthracite.

Compliant frame geometry for DEMES-based gripper and flapping wing actuators: A comprehensive design study

Dielectric elastomer minimum energy structures (DEMES) have attracted significant attention in the recent past because of their ability to switch between multiple equilibrium states. The DEMES is formed when a pre-stretched elastomer film adheres to an inextensible frame and is further allowed to attain an equilibrium configuration as a result of energy minimization. While several researchers have investigated; both theoretically and experimentally, the underlying mechanics of DEMES, a majority of them deploy simplistic boundary frames (square/rectangular/circular) to obtain the requisite minimum energy configuration. In this paper, we demonstrate that this seemingly restrictive choice of using simplistic frame geometries can be given away by designing more complex-shaped compliant frames capable of producing useful modes of deformation. To demonstrate this idea, two prototypes; namely, the four-arm gripper actuator and the flapping-wing actuator, are studied numerically and experimentally. In both cases, a single compliant frame is used to realize the respective configuration, thus circumventing the need to assemble multiple MES on a common platform. In tandem, we investigate the role of reinforcements in (a) controlling the warping in MES and (b) maximizing actuation in the desired mode of deformation. Finite element analysis are carried out using the ABAQUS to determine the equilibrium configuration of the actuators, and subsequently their electromechanical behavior. Experimental investigations involve the utilization of the commercially available VHB 4910 acrylic tape in conjunction with PET frames and 3D-printed reinforcements. Excellent qualitative agreement is achieved between the numerical predictions and the experimental observations. Finally, we allude to a few innovative frame architectures leading the MES of engineering interest.

Interacting dust grains in complex plasmas: Ion wake formation and the electric potential

Dust grains have been used as minimally invasive probes to determine plasma parameters including the plasma density, temperature, and electric field in a plasma discharge. However, the dust grains in a plasma generate local potential disturbances due to the collection of charge and the subsequent electrostatic interactions between the dust and charged plasma particles. Dust grains in close proximity to one another exhibit interesting non-reciprocal interactions and self-organize into structures such as one-dimensional filamentary chains, two-dimensional “zigzags,” and three-dimensional helices, among others. The formation of these structures suggests that although the dust grains may be less invasive than traditional plasma probes, the disturbance to the local plasma environment introduced by dust grains is non-trivial. Commonly used analytic forms of the electric potential describing complex plasmas have failed to resolve the near-dust region, and as a result are insufficient to provide insight about the formation of complex dust structures. Here, we use an N-body simulation to compute the electric potential from ion densities near various dust grain configurations. We provide an alternative description to the standard analytic model for the electric potential of dust and ion wakes based on a Gaussian shaped cloud of ions. The electric potential obtained from simulations is used to identify minimum energy configurations for two and three dust grains. It is further demonstrated that the minimum potential region identified for N dust grains and their associated ion wakes does not predict the minimum-energy configuration of N + 1 dust grains.

Wrinkling of fluid deformable surfaces.

Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic processes. We here consider wrinkling of fluid deformable surfaces. In contrast with thin elastic sheets, with in-plane and out-of-plane elasticity, these surfaces are characterized by in-plane viscous flow and out-of-plane elasticity and have been established as model systems for biomembranes and cellular sheets. We use this hydrodynamic theory and numerically explore the formation of wrinkles and their coarsening, either by a continuous reduction of the enclosed volume or bythe continuous increase of the surface area. Both lead to almost identical results for wrinkle formation and the coarsening process, for which a scaling law for the wavenumber is obtained for a broad range of surface viscosity and rate of change of volume or area. However, for large Reynolds numbers and small changes in volume or area, wrinkling can be suppressed and surface hydrodynamics allows for global shape changes following the minimal energy configurations of the Helfrich energy for corresponding reduced volumes.

Zigzag phase transition of electrons confined within a thin annulus region

We consider a semiclassical approach to study the possible stabilization of a zigzag phase for a system of interacting electrons confined within a thin annulus region with infinite inner/outer walls. The electrons are considered spinless and interact via the standard Coulomb interaction potential. The classical minimum energy configuration of the system due to the Coulomb repulsion between electrons is accurately determined by using the simulated annealing method. As the number of electrons increases we see the appearance and stabilization of a two-ring structure with zigzag patterns. Further increase of the number of electrons appears to eventually lead to the collapse of the two-ring zigzag structure. A simple quantum treatment of the nodal features of the free many-particle wave function shows the appearance of nodal domain patterns that are consistent with the zigzag features that were observed in the classical model.

Adsorption of dihalogen molecules X2 (X = F, Cl, Br and I) on the Fe/W(110) substrate

We report on spin-polarized density-functional theory study of adsorption of dihalogen molecules X2 (X = F, Cl, Br and I) on the Fe/W(110) substrate, i.e., X2/Fe/W(110) systems. We considered different molecular orientations and adsorption sites of the halogens and obtained their corresponding ground-state structures. We obtained initial molecular orientation (IMO) and initial adsorption site (IAS), i.e., IMO-IAS combinations that give the minimum energy configurations for each of the X2/Fe/W(110) systems. Our results shows that all the molecules studied in this work are chemisorbed on the Fe surface. Also, the halogen atoms may be adsorbed dissociatively on the hollow sites in such a way that an X2 separates into two X atoms with each of the atoms located at two nearby hollow sites. Similarly, we found IMO-IAS combinations which resulted in a non-dissociative adsorption. In the latter, the pre-relaxed IMO-IAS is maintained even after the structural relaxation. The most stable configuration for the X2 dihalogen molecule in this case is either the top or bridge site while the halogen is in perpendicular orientation to the Fe surface. We conclude therefore that, the final relaxed configurations of the X2 halogen depends on the IMO through which is deposited on the Fe/W(110) substrate. The trend in the adsorption energy EA for the most stable configurations for the dissociative adsorption is EA (F) > EA (Cl) > EA (Br) > EA (I). The trend of EA for non-dissociative adsorption is similar to that of dissociative adsorption, however, the latter is the more energetically favorable. Electronic structure calculations show hybridization between the p and d orbitals of X and Fe atoms respectively. Furthermore, we have found antiferromagnetic coupling between the interfacial W atoms and the Fe overlayer atoms while ferromagnetic coupling is found between the halogens and the Fe atoms. Our work represents a detailed study of adsorption properties of highly reactive halogens in contact with the Fe/W(100) surface.

Bonobo Optimizer: A New Tool Toward the Global Optimization of Small Atomic Clusters.

In the realm of structural and bonding investigations within chemical systems, elucidating global minimum energy configurations stands as a paramount goal. As the systems increase in size and complexity, this pursuit becomes progressively challenging. Herein, we introduce Bonobo optimizer (BO), a metaheuristic algorithm inspired by the social and reproductive behaviors of bonobos, to the domain of chemical problem solving. Focusing on small carbon clusters, this study systematically evaluates BO's performance, showcasing its robustness and efficiency. Parametric studies highlight the algorithm's adaptability, consistently converging to global minimum structures. Rigorous statistical validation supports the results, and a comparative analysis against established global optimization algorithms underlines BO's superior efficiency. This exploration extends the applicability of BO to the optimization of atomic clusters, providing a promising avenue for future advancements in computational chemistry.

Exploring odd-even sensitivity in m.OnO.m liquid crystal compounds: A comprehensive study using DFT analysis

In this article, a comprehensive investigation into a series of liquid crystalline compounds belonging to the α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) family has been conducted to unravel their intricate molecular characteristics. The computational investigations employing DFT/B3LYP/6-311G(d,p) level delve into the odd–even effect, exploring how the presence of spacer units influences the structural, electronic, and vibrational properties of these compounds. Optimization analyses reveal the minimum energy configurations, offering valuable insights into spatial arrangements and symmetry. Visualization of molecular structures emphasizes a distinctive odd–even effect, with compounds exhibiting either U-shaped or Z-shaped configurations based on the parity of spacer units. Charge distribution maps further elucidate electronic intricacies, showcasing the interplay of charges among different atoms. Thermodynamic properties and frontier orbital analysis providing a nuanced understanding of the compounds behavior. NLO parameters exhibited a consistent odd–even effect. Potential Energy Distribution (PED), IR, and Raman spectra analysis, provided a detailed symphony of stretching, bending, and torsional motions. UV–Vis absorption spectra uncover distinctive electronic transitions within each compound. In essence, this research sheds light on the profound impact of spacer units, shaping the structural, electronic, and vibrational characteristics of the liquid crystalline compounds. The odd–even effect emerges as a central theme, weaving a captivating narrative of molecular dynamics within this intriguing class of materials.

Exploring the bounds of methane catalysis in the context of atmospheric methane removal

Methane, a potent greenhouse gas, is a significant contributor to global warming, with future increases in its abundance potentially leading to an increase of more than 1∘C by 2050 beyond other greenhouse gases if left unaddressed. To remain within the crucial target of limiting global warming to 1.5 ∘C, it is imperative to evaluate the potential of methane removal techniques. This study presents a scoping analysis of different catalytic technologies (thermal, photochemical and electrochemical) and materials to evaluate potential limitations and energy requirements. An analysis of mass transport and reaction rates is conducted for atmospheric methane conversion system configurations. For the vast majority of catalytic technologies, the reaction rates limit the conversion which motivates future efforts for catalyst development. An analysis of energy requirements for atmospheric methane conversion shows minimum energy configurations for various catalytic technologies within classic tube or parallel plate architectures that have analogs to ventilation and industrial fins. Methane concentrations ranging from 2 ppm (ambient) to 1000 ppm (sources, such as wetlands, fossil-fuel extraction sites, landfills etc) are examined. The study finds that electrocatalysis offers the most energy efficient approach (∼0.2 GJ tonne−1 CO2e) for new installations in turbulent ducts, with a total energy intensity < 1 GJ tonne−1 CO2e. Photocatalytic methane removal catalysts are moderately more energy intensive (∼2 GJ tonne−1 CO2e), but could derive much of their energy input from ‘free’ solar energy sources. Thermal systems are shown to be excessively energy intensive ( > 100 GJ tonne−1), while combining photovoltaics with electrochemical catalysts (∼1 GJ tonne−1 CO2e) have comparable energy intensity to photocatalytic methane removal catalysts.

On a mathematical theory for the crystallography of shear transformations in metals: Unification of mechanisms

A theory for shear transformations in crystalline materials linking their Crystallography, atomic-scale mechanisms and Thermodynamics is introduced. The lattice and transformation function are treated as vector space and functions respectively to overcome shortcomings of classical matrix-based theories for martensite crystallography. The extremum principle is used to obtain the atomic paths minimising and maximising the energy from all possible solutions, therefore explaining which sequences are more Thermodynamically feasible. The face-centred cubic (FCC)→body-centred cubic (BCC) transformation in Fe is used as case study. The theory predicts that the average values of the extrema correspond to the crystallography, shear magnitude, interface defects and habit planes of main transformations in Fe, i.e. Widmanstätten Ferrite, Bainite, lath martensite, plate and lenticular martensite. Bainite represents the macroscopic average minimum energy configuration, whereas Widmanstätten Ferrite corresponds to a local and discrete minimum energy configuration. Lath martensite corresponds to the average shear configurations minimising atomic displacements when there is no other driving force, e.g. diffusion, whereas the maximum energy configurations correspond to plate and lenticular martensite forming twin pairs. Targeted results for the FCC→hexagonal close-packed lattice transformation are presented to demonstrate the robustness of the theory. The predictions are combined with elasticity theory to compute the Driving Force and predict the start temperatures – therefore connecting for the first time – local and macroscopic crystallographic features with the Thermodynamics of shear-controlled structures in Fe. This work presents new results towards addressing longstanding challenges in Materials Science such as theoretically demonstrating that Bainite is a shear transformation.

SHEEP, a Signed Hamiltonian Eigenvector Embedding for Proximity

Signed network embedding methods allow for a low-dimensional representation of nodes and primarily focus on partitioning the graph into clusters, hence losing information on continuous node attributes. Here, we introduce a spectral embedding algorithm for understanding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Inspired by a physical model, we construct our embedding as the minimum energy configuration of a Hamiltonian dependent on the distance between nodes and locate the optimal embedding dimension. We show through a series of experiments on synthetic and empirical networks, that our method (SHEEP) can recover continuous node attributes showcasing its main advantages: re-configurability into a computationally efficient eigenvector problem, retrieval of ground state energy which can be used as a statistical test for the presence of strong balance, and measure of node extremism, computed as the distance to the origin in the optimal embedding.

Misfit and the mechanism of high temperature and low stress creep of Ni-base single crystal superalloys

The present work proposes a new elementary deformation mechanism which governs high temperature and low stress creep of single crystal superalloys (SXs), where the misfit between the γ- and the γ′-phase plays a central role. In the coherent two phase SX microstructure, there is a tendency to minimize the overall elastic strain energy. This is accomplished by the formation of dislocation networks in the γ-phase close to the γ/γ’-interfaces. The stress fields of the network dislocations and misfit stresses accommodate each other to keep the overall strain energy of the system at a minimum. Previous work has shown that dynamic recovery is associated with knitting-out reactions, where dislocations from the network shear the γ’-phase and annihilate with dislocations of opposite sign on the other side of the γ’-phase region. Due to the presence of the misfit this results in an increase of elastic strain energy which is counteracted by coupled knitting-in reactions where newly arriving γ-channel dislocations re-establish the minimum energy configuration. Here we provide microstructural evidence for knitting-out and knitting-in reactions and show that while these reactions clearly occur, dislocation network spacings stay constant. The misfit between the γ- and the γ′-phase accounts for a constant network spacing. Dislocation networks are not static but represent dynamic steady state equilibrium structures in an evolving microstructure. Knitting regular networks requires climb processes which are suggested to be rate controlling. This new view of high temperature and low stress creep mechanism of SXs allows to rationalize previous results published in the literature.

Maxwell-scalar system and scalar field with impurity: Novel approach to find nontrivial solutions

In this work, we investigate a Maxwell-scalar model that couples the scalar and gauge fields through the electric permittivity and another model, in which the scalar field lives in the presence of impurity. By considering a single spatial dimension, we determine the conditions under which the model with impurity can be seen as an effective model for the Maxwell-scalar system, having similar solutions. This correspondence shows that the impurity can be used to describe the presence of a charge density, and we use it to verify that the impurity-free case, which supports minimum energy configurations, is related to the case of point charges. We also investigate a class of impurities which modifies the core of the scalar field, and find the corresponding nontrivial charge densities and electric fields. In particular, the asymptotic behavior in terms of the impurity is also studied, leading to solutions exhibiting long-range or quasi-compact profile.

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals.

In its original version, the Thomson problem consists of the search for the minimum-energy configuration of a set of point-like electrons that are confined to the surface of a two-dimensional sphere () that repel each other according to Coulomb's law, in which the distance is the Euclidean distance in the embedding space of the sphere, i.e., . In this work, we consider the analogous problem where the electrons are confined to an n-dimensional flat Clifford torus with n = 1, 2, 3. Since the torus can be embedded in the complex manifold , we define the distance in the Coulomb law as the Euclidean distance in , in analogy to what is done for the Thomson problem on the sphere. The Thomson problem on a Clifford torus is of interest because supercells with the topology of a Clifford torus can be used to describe periodic systems such as Wigner crystals. In this work, we numerically solve the Thomson problem on a square Clifford torus. To illustrate the usefulness of our approach, we apply it to Wigner crystals. We demonstrate that the equilibrium configurations we obtain for large numbers of electrons are consistent with the predicted structures of Wigner crystals. Finally, in the one-dimensional case, we analytically obtain the energy spectrum and the phonon dispersion law.

Global optimization and structural analysis of Coulomb and logarithmic potentials on the unit sphere using a population-based heuristic approach

Global optimization of high-dimensional non-convex functions arises in many important applications and researches. In this paper, we focus on the minimum energy configuration problem on the unit sphere, whose goal is to determine the minimum-energy configuration of N particles interacting via the standard Coulomb potential or the discrete logarithmic potential on the unit sphere. This is a classic global optimization problem with many important applications in mathematics, physics, biology and chemistry, and is one of the 18 great mathematical problems for the twenty-first century listed by the Fields Medal winner (Smale, 1998). To determine the minimum-energy configuration for these two potential functions, we propose a population-based global optimization algorithm that combines a two-phase local optimization method with early-stopping strategy, a random perturbation operator, a distance-based population update strategy using a novel distance function to measure the difference between solutions, and a population rebuilding method. Computational results show that the proposed algorithm is very competitive compared to the best known results in the literature. In particular, it improves the best-known result for one instance of the classic Thomson problem (i.e., N=360) widely studied in the literature. The configurations of instances with up to N=500 particles are systematically optimized for the first time by the proposed algorithm for the discrete logarithmic potential. The comparative study shows that the putative optimal configurations have a high similarity for the Coulomb and logarithmic potentials and that the defects play an important role in reducing the energy of configuration. The energies of particles on the putative optimal configurations are analyzed for the studied logarithmic potential.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface.

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom, , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds of and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped with , , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Energetics of Interfaces and Strain Partition in GaN/AlN Pseudomorphic Superlattices

We present the results of a twofold experimental and computational study of (0001) GaN/AlN multilayers forming pseudomorphic superlattices. High-Resolution Transmission Electron Microscopy (HRTEM) shows that heterostructures with four c-lattice parameters thick GaN Quantum Wells (QW) are misfit-dislocation free. Accurate structural data are extracted from HRTEM images via a new methodology optimizing the residual elastic energy stored in the samples. Total energy calculations are performed with several models analogous to the experimental QWs with increasing thicknesses of GaN, whereas this of the AlN barrier is kept fixed at n = 8 c-lattice parameters. With vanishing external stresses, minimum energy configurations of the studied systems correspond to different strain states. Linear elasticity accurately yields the corresponding lattice parameters, suppressing the need for on-purpose total energy calculations. Theoretically justified parabolic fits of the excess interfacial energy yield the values of interfacial stress and elastic stiffness as functions of the GaN QW thickness. Total species-projected densities of states and gap values extracted from there allow deciphering the effect of the evolving strain on the electronic structure of the superlattice. It is found that the gap energy decreases linearly with increasing the strain of the QW. These results are briefly discussed in the light shed by previous works from the literature.

Collective formation of misfit dislocations at the critical thickness for equilibrium nanowire heterostructures

In this work we model the evolution of strain energy during different growth stages of heterostructure nanowires. We find that the minimum energy configuration changes abruptly from fully elastically strained to partially relaxed at the critical thickness. The transition at the critical thickness, when the crystal growth is close to equilibrium, is associated with a collective formation event of misfit dislocations. These insights are based on a technique developed to simulate misfit dislocations in a finite element framework, incorporating both elastic and plastic relaxation in a stationary heterostructure. We argue that these results have general relevance for mismatched heterostructures.