Nodes Of Lattice Research Articles

THE COMPUTER MODEL EXPERIMENT FOR STUDYING MECHANISMS OF FORMATION OF RADIATION-STIMULATED DEFECTS IN MAGNESIUM-ALUMINUM SPINEL

In the work in the Geant 4 software a computer model of the experiment on the study of the efficiency of formation of radiation-stimulated defects in magnesium aluminum spinel under irradiation with high-energy electrons and gamma quanta was developed. Under irradiation with electrons it was found that defects in the crystal lattice of spinel arise both under direct knocking out of atoms from the nodes and under photonuclear reactions. For energies of primary electrons of 25… 30 MeV the efficiency of formation of defects due to photonuclear reactions is several times higher compared to direct knocking out of atoms from the nodes of the crystal lattice. Under irradiation of samples with monoenergetic gamma quanta it was found that the efficiency of formation of defects is an order of magnitude higher than under irradiation with electrons of the same energy due to processes of photofission of nuclei.

The Kinetics of Polymer Brush Growth in the Frame of the Reaction Diffusion Front Formalism

We studied the properties of a reaction front that forms in irreversible reaction–diffusion systems with concentration-dependent diffusivities during the synthesis of polymer brushes. A coarse-grained model of the polymerization process during the formation of polymer brushes was designed and investigated for this purpose. In this model, a certain amount of initiator was placed on an impenetrable surface, and the “grafted from” procedure of polymerization was carried out. The system consisted of monomer molecules and growing chains. The obtained brush consisted of linear chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions only. The simulations were carried out for high rafting densities of 0.1, 0.3, and 0.6 and for reaction probabilities of 0.02, 0.002, and 0.0002. Simulations were performed by means of the Monte Carlo method while employing the Dynamic Lattice Liquid model. Some universal behavior was found, i.e., irrespective of reaction rate and grafting density, the width of the reaction front as well as the height of the front show for long times the same scaling with respect to time. During the formation of the polymer layer despite the observed difference in dispersion of chain lengths for different grafting densities and reaction rates at a given layer height, the quality of the polymer layer does not seem to depend on these parameters.

Conceptual model of electrostatic non-ionizing air filter

Abstract Many infectious diseases such as SARS-CoV-2, rhinovirus, adenovirus, and influenza are transmitted through small respiratory droplets and various filtration systems are used to reduce the risk of airborne infection. Here, we develop a conceptual model of a filter, which is based on the electrostatic deposition of air droplets potentially containing pathogens. Within the model, we explore the effect of polarization of neutral spherical droplets moving in an air flow past cylindrical electrodes. The strength of electric field they produce is low enough to eliminate corona discharge and minimize air ionization, but high enough to capture the droplets. Based on the proposed model, we calculate the filtration efficiency in a quasi-continuous approximation. Also, we conduct numerical simulations of the deposition of respiratory droplets on a compact periodic array of cylindrical electrodes located at the nodes of a square lattice. The droplets with a radius of 10-20 μm pose the greatest threat in spreading the respiratory infections, and as we demonstrate, the proposed system is very effective in capturing droplets of this size, specifically, for a filter element with a width of about 5 mm, the filtration efficiency exceeds 90%.

Mechanical Properties and Energy Absorption Characteristics of Additively Manufactured Lattice Structures of a High‐Temperature Titanium Matrix Composite

Lightweight lattice structure is of great significance in the fields of aerospace thermal protection and energy absorption. In this study, compressive properties and energy‐absorbing characteristics of additively manufactured body‐centered cubic (BCC) lattice structures of a high‐temperature titanium matrix composite (TMC) are investigated systematically. It is found that compressive strength increases monotonically as either lattice strut diameter or temperature increases. With lattice strut diameter increasing from 1.0 to 1.5 and 2.0 mm, strength increases from 78 to 94 and 108 MPa at room temperature (RT) and from 71 to 104 and 123 MPa at 650 °C. Unexpectedly, specific energy absorption (SEA) capability increases as strut diameter decreases, although also increases as temperature increases. BCC lattice structure with a strut diameter of 1.0 mm presents the highest SEA being up to 13.7 MJ m−3 at RT and 142 MJ m−3 at 650 °C. And sphericizing the lattice nodes is found incapable of enhancing strength and SEA. Besides, numerical simulation is used to demonstrate the compressive stress and strain fields, in order to explain the fracture modes and SEA capability of individual BCC lattice structures. This study provides deep insights into the mechanical properties and energy absorption behavior of additively manufactured lattice structures of TMCs.

ANALYTICAL DESCRIPTION AND ALGORITHM OF CALCULATIONS OF MECHANICS OF STRUCTURES WITH BERNOULLI – EULER BEAMS USING SCAS KIDY

The problems of developing a universal analytical description and algorithm for automatic computer calculations of dynamics, statics and kinetostatics of mechanical models of structures including a beam lattice are considered. This can be calculations of transient processes, steady-state free and forced oscillations, determination of equilibrium positions and stress-strain states under static and dynamic loads, etc. The structure itself can be flat or spa- tial, stationary or moving on a plane or in space. Various instruments and devices can be attached to it. Arbitrary connections can be taken into ac- count. It is shown how it is possible to succinctly, using a special language for preparing computer data, analytically describe a part of a structure rep- resenting a beam lattice. Based on the theory of elasticity of Bernoulli-Euler beams, 2 forms of the canonical representation of the potential energy of an elastic beam are obtained. This makes it possible to introduce into the language of description of mechanical models of the special computer algebra system KiDyM (SCAS KiDyM) a new beam element, for which the position of the coordinate systems associated with the extreme sections is indi- cated. The positions of these sections are determined by lattice nodes, like solid bodies. Angular and linear coordinates of such solid bodies give gen- eralized coordinates of the mechanical model. An algorithm has been developed for the formation of elements adopted to describe mechanical models in SCAS KiDyM. Thus, the elastic structure of the mechanical model is formed. Using the available tools in this program, equations of dynamics and statics are automatically constructed, that is, a mathematical model is formed, and dynamic and static calculations can be carried out. The proposed method is demonstrated in detail on the example of calculating the deformation of an elastic lattice, with is the basis of a UAV (unmanned aerial vehi- cle). The results are compared with calculations using the ANSYS program

EFFECT OF Rh-DOPING ON THE OPTICAL ABSORPTION OF THE (001) BaTiO<sub>3</sub> SURFACE

Barium titanate is one of the most studied perovskite materials due to its substitution ability at both nodes of the crystal lattice, high dielectric constant, and stability. It has many outstanding characteristics, especially ferroelectric and dielectric properties, which can be improved by alloying, making this material suitable for a wide range of applications. In this paper, the effect of Rh doping on the structural, optical properties and electronic density of states of this compound is investigated. According to our calculations, Rh doping is a method that helps to increase the ability of BaTiO3 to absorb more light and reduce the excess potential required for water oxidation. Calculations of the electronic density of states were carried out using the hybrid functional HSE06. The analysis of optical properties was performed on the basis of matrix elements with a transient dipole moment. Studies have confirmed that the (001) BaTiO3 surface with terminated TiO2 has significant potential for use as a catalyst. Rh doping leads to an expansion of the spectrum of absorbed light over the entire visible range.

METHODS OF INFLUENCE ON THE SYSTEM TO CHANGE THE ENERGY STATE OF SUBSTANCE: EXPERIENCE, STATE OF THE ISSUE

Methods of influencing the system, the ultimate goal of which is to destruct the natural structure of the material, can be divided as mechanical, physical, chemical, biological and complex. The changing the energy state of a substance is called activation. The current scientific field of ultradispersed materials and physical and chemical processes caused by dispersion is created by the researches of many scientists. Detailed consideration for the increasing reactivity of a solid substance compared to the change in its specific surface area during its mechanical activation showed that the share attributable to the growth of the specific surface area is only a few percent of the mechanical activation effect. The other part is due to the accumulation of defects in the crystals during the grinding process. According to the law of conservation of energy, when a crystal splits, the potential energy of interaction between lattice nodes is transferred to uncompensated surface energy. In addition, the value of the specific surface energy depends on the type of flat lattice used to split the crystal. Therefore, the activation processes and the application of the substance in the active state are relevant in the development of modern binders and concretes. The purpose of the article is to analyse the advantages and disadvantages of the existing methods of influencing the system with the ultimate goal of destruction of the natural structure of the material to changing the energy state of the substance, i.e. its activation. Conclusions. During the destruction of solids, the formation of new cleavage surfaces is accompanied by the breaking of bonds between the substance structural elements and the transition of the potential bond energy into surface energy. Ceteris paribus, the higher the ionic charges and the smaller the distance between them (between adjacent flat grids in the lattice), the greater the value of σ. In addition, the value of the specific surface energy depends on the type of flat grids used to split the crystal. It is worth mentioning that not all methods of activation for binder and concrete (soluble) mixtures are currently implemented on an i industry level. This is due to various reasons. The main method of activation used on an industry level is mechanochemical activation in various types of mills.

Quantum field theory at finite temperature for 3D periodic backgrounds

The one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised in terms of the scattering data, allowing to compute the quantum vacuum interaction energy between nodes at zero temperature, as well as the total Helmholtz free energy, the entropy, and the Casimir pressure between nodes at finite non-zero temperature. Some examples of periodic potentials built from the repetition in one of the three spatial dimensions of the same punctual or compact supported potential are addressed: a stack of parallel plates constructed by positioning δδ′ -functions at the lattice nodes, and an ‘upside-down tiled roof’ of parallel two-dimensional Pöschl–Teller wells centred at the nodes. They will be called generalised Dirac comb and Pöschl–Teller comb, respectively. Positive one-loop quantum corrections to the entropy appear for both combs at non-zero temperatures. Moreover, the Casimir force between the lattice nodes is always repulsive for both chains when non-trivial temperatures are considered, implying that the primitive cell increases its size due to the quantum interaction of the phonon field.

THE ROLE OF ATOMIC SCATTERING FACTORS IN DETERMINING THE MINERAL COMPOSITION OF THE BAZHENOV SUITE'S ROCKS

For the first time, it was demonstrated, that the use of standard atomic-structural parameters of minerals in X-ray diffraction (XRD) analysis to determine the phase composition in the Bazhenov suite's core is incorrect and most often leads to inaccurate information when calculating their quantitative ratio. In particular, by decomposing the XRD — based quantitative data on the mineral composition of the core of the Bazhenov suite into the main rock-forming oxides and further comparing them with reliable X-ray fluorescence spectrometry (XRF) data, an unsatisfactory convergence between them was established. At the same time, significant differences in the results of XRD and XRF have been shown in terms of oxides of silicon, sodium, magnesium, potassium, and iron, both at large and small mass fractions. It has been found that even with perfect XRD, achieved by optimizing the standard mineral structure parameters (lattice period, crystallite size, crystal lattice microdistortion, absorption coefficient, crystallographic texture, background) and achieving a very high degree of convergence (more than 95%) of experimental and theoretical diffractograms, the differences between oxide forms are still significant. It is shown, that the results of XRD of Bazhenov suite are questioned due to detected inconsistencies in oxide forms. Using the analysis of multiple factors and data from diffractograms of many samples, it has been established that the identified differences are primarily caused by the use of incorrect initial atomic-structure parameters of minerals in modeling. It is shown that rock minerals in the Bazhenov suite are primarily characterized by significant changes in the values of atomic scattering factors and significant displacements of atomic positions in the nodes of the crystal lattice, caused by the action of the high pressures and temperatures in the formation. For the first time, the XRD algorithm that has been developed, is presented and implemented in Bazhenov suite rocks, with consideration of the state of atoms in the analyzed mineral. Furthermore, it was found that the authors XRD approach enables the identification and quantification of the Bazhenov suite minerals with a relatively low content, which are challenging to identify during traditional XRD.

Efficient and exquisite concurrent optimization of hierarchical structures with non-uniform eccentric body centered cubic lattice

To obtain lightweight structures with desirable mechanical performances and to enlarge the design space, this work presents an innovative concurrent optimization methodology for the precise inverse design of micro lattices and the modeling of hierarchical structures. The inverse design of micro lattices with continuously changing anisotropic properties is achieved by offsetting the center nodes of eccentric body centered cubic lattices (EBCC) to designated locations. Simultaneously, the macro material distribution is adjusted utilizing 3D density-based topology optimization method. To enhance the computation efficiency and significantly amplify the versatility in optimization design, a Parameterized Interpolation for Anisotropic Lattice material (PIAL) is established based on elastic stiffness matrices of micro lattices with 21 independent components. Specifically, a cubic multinomial function is employed to construct a direct correlation between micro topology configurations and equivalent elasticities of the EBCC lattices. Several numerical examples of compliance optimization are carried out to confirm the validity of the proposed approach. Concurrently, Additive Manufacturing (AM) using AlSi10Mg is adopted to manufacture the obtained hierarchical structures, which exhibit well-improved mechanical performance, as confirmed by experimental testing, when compared to the classical density-graded structures.

Tuning collective actuation of active solids by optimizing activity localization.

Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then condensates on a small fraction of the vibrational modes, the selection of which obeys non trivial rules rooted in the nonlinear part of the dynamics. So far, the complexity of the selection mechanism has limited the design of specific actuation. Here, we investigate numerically how localizing activity to a fraction of modes enables the selection of non-trivial collective actuation. We perform numerical simulations of an agent-based model on triangular and disordered lattices and vary the concentration and the localization of the active agents on the lattice nodes. Both contribute to the distribution of the elastic energy across the modes. We then introduce an algorithm, which, for a given fraction of active nodes, evolves the localization of the activity in such a way that the energy distribution on a few targeted modes is maximized - or minimized. We illustrate on a specific targeted actuation, how the algorithm performs as compared to manually chosen localization of the activity. While, in the case of the ordered lattice, a well-educated guess performs better than the algorithm, and the latter outperform the manual trials in the case of the disordered lattice. Finally, the analysis of the results in the case of the ordered lattice leads us to introduce a design principle based on a measure of the susceptibility of the modes to be activated along certain activation paths.

Modeling and Visualizing the Dynamic Spread of Epidemic Diseases—The COVID-19 Case

Our aim is to provide an insight into the procedures and the dynamics that lead the spread of contagious diseases through populations. Our simulation tool can increase our understanding of the spatial parameters that affect the diffusion of a virus. SIR models are based on the hypothesis that populations are “well mixed”. Our model constitutes an attempt to focus on the effects of the specific distribution of the initially infected individuals through the population and provide insights, considering the stochasticity of the transmission process. For this purpose, we represent the population using a square lattice of nodes. Each node represents an individual that may or may not carry the virus. Nodes that carry the virus can only transfer it to susceptible neighboring nodes. This important revision of the common SIR model provides a very realistic property: the same number of initially infected individuals can lead to multiple paths, depending on their initial distribution in the lattice. This property creates better predictions and probable scenarios to construct a probability function and appropriate confidence intervals. Finally, this structure permits realistic visualizations of the results to understand the procedure of contagion and spread of a disease and the effects of any measures applied, especially mobility restrictions, among countries and regions.

Статистичний метод визначення параметрів поля зсувних напружень в площині ковзання в багатокомпонентному сплаві

A method has been developed in which atomic sizes misfit and elastic modulus misfit at crystal lattice nodes are considered as discrete random variables and the definition of their dispersion allows to obtain analytical expressions for standard deviations and correlation lengths of the short- and long-wave components of stochastic shear stress field created by solute atoms in the glide plane in a multicomponent alloy. This makes it possible to significantly reduce the amount of calculations when determining the shear stress field parameters. The developed method was applied to calculate these parameters for the CrCoNiFeMn alloy. The calculated parameters were well correlated with similar parameters determined from the analysis of shear stress distributions in the glide plane, which were calculated by the method of direct summation of solute atoms contributions. In addition, it was found that there are separate effective crystal lattice distortions for the short- and long-wave components that differ from the average distortion that was proposed earlier. This results from the fact that these components are determined by solute atoms with different distance from the glide plane. Effective distortion is greater, the greater this distance from the glide plane. In addition, there is no single empirical constant for all alloy to determine the yield strength as a function of their shear modulus and average distortion. But the proposed method makes it possible to determine the main parameters of the shear stress field in a specific multicomponent alloy. These parameters can be used to calculate the yield strength of this alloy. Keywords: shear stress, multicomponent alloy, glide plane, solid solution.

On polarization of Smith-Purcell radiation from a photonic crystal slab

We analyze the polarization of radiation arising during the pass of a relativistic electron over a 2D photonic crystal slab consisting of subwavelength particles arranged at the nodes of a flat rectangular lattice. It is shown that the contribution of the parallel and perpendicular polarizations depends on the direction of propagation of the radiation, the bifurcation of the maxima is due to the contribution of the perpendicular polarization, while the asymmetry of the angular distribution is due to the contribution of the parallel polarization.

Vectorial finite-difference-based lattice Boltzmann method: Consistency, boundary schemes and stability analysis

In this paper we propose a vectorial finite-difference-based lattice Boltzmann method (FD-LBM), which unifies several different numerical schemes for the incompressible Navier–Stokes equations. By using the Maxwell iteration, we analyze the consistency under the diffusive scaling. In the situation that the widely used bounce-back or “anti-bounce-back” boundary schemes are not applicable, a new boundary scheme is developed to accompany the vectorial method. It is shown that the scheme has second-order accuracy when the boundary is located at the middle of two neighboring lattice nodes. We also prove the numerical stability of the vectorial method on periodic domains and the vectorial method together with the boundary scheme on bounded domains. Several numerical experiments for 2D & 3D flow problems with straight and curved boundaries validate the stability and accuracy of the vectorial LBM with the proposed boundary scheme.

Orientation texturing and static magnetic response of multi-core particle containing limited number of superparamagnetic nanocores

In this paper, we study the orientational texturing and static magnetization of a small multi-core particle (MCP) that includes a few immobilized superparamagnetic particles (SPPs). We focus on the consideration of the MCPs containing 7 and 8 SPPs, which are located randomly or at the nodes of a simple cubic lattice. The results are obtained using Monte Carlo computer simulations. It is shown that intensive dipole–dipole interaction leads to the formation of an orientational texturing of the SPP’s magnetic moments, which strongly depends on the location of the SPPs inside the MCP. The magnetization laws of MCPs are compared with the continuous medium magnetostatics. For strongly interacting SPPs there is a big difference between the simulation results for the magnetization of the MCPs with cubic structure and the magnetization of continuous system of SPPs located in simple cubic lattice. The magnetization of the MCP for each specific random location of the SPPs also differs from the magnetization of continuous media of SPP gas, however, the average value of the MCP magnetization coincides with the continuous media magnetostatics.

Optimizing mixing in the Rudner–Levitov lattice

Here we discuss the optimization of mixing in finite linear and circular Rudner–Levitov lattices (Su–Schrieffer–Heeger lattices with a dissipative sublattice). We show that the presence of exceptional points in the systems’ spectra can lead to drastically different scaling of the mixing time with the number of lattice nodes, varying from quadratic to logarithmic. When operating in the region between maximal and minimal exceptional points, it is always possible to restore logarithmic scaling by choosing the initial state of the chain. Moreover, for the same localized initial state and values of parameters, a longer lattice might mix much faster than the shorter one. Also we demonstrate that an asymmetric circular Rudner–Levitov lattice can preserve logarithmic scaling of the mixing time for an arbitrarily large number of lattice nodes.

Defect sensitivity mitigation in the compressive mechanical response of two-phase lattice metamaterials

Engineered materials commonly referred to as metamaterials are materials that offer appealing features such as customisable stiffness and strength, auxetic behaviour and energy absorption. This work focuses on the classical 2D lattice metamaterial configuration with regular triangular unit cell. A combination of two dissimilar materials is employed in the design process: the primary material that constitutes the lattice structure is composed of thermoplastic polyurethane (TPU), while an incompressible silicone serves as the secondary material, completely filling selected lattice cells. In order to investigate the mechanical response of such lattices to intrinsic defects, geometric imperfections are intentionally introduced. Three distinct types of geometric anomalies, i.e. curvature of some elements, lateral shift of some lattice nodes, and reduced beam thickness, are randomly introduced. Additively manufactured perfect and defective lattices are subjected to compressive loading for both empty and silicone filled cases. Overall, the results reveal that the lattices show a significant improvement with the assumed reinforcing filling pattern, helping to prevent the buckling of the beams under compression and enhancing the load bearing capacity of the structure at higher deformations. Finite element (FE) analyses are performed to validate the experimental results, demonstrating how the filling pattern enhances the mechanical response of the lattices.

Квантові ефекти пікноядерних реакцій у компактних зорях: Нові квазізв’язані стани та спектроскопія

Quantum effects in pycnonuclear reactions in compact stars at zero temperatures are studied with high precision. The reaction 16O + 16O was analyzed using the method of multiple internal reflections. The study of such reactions requires full consideration of quantum fluxes in the internal nuclear region. This reduces the rate and number of pycnonuclear reactions up to 1.8 times. This leads to the appearance of new states (which we call quasibound states) where the compound nuclear system is formed with maximal probability. As shown, the minimal energy of such a state is slightly higher than the energy of zero-mode oscillations in the lattice nodes in the pycnonuclear reaction, however, the probability of the formation of a compound system in a quasibound state is significantly greater than the corresponding probability in a state of zero-mode oscillations. It is reasonable to say that the frequency of reactions in quasi-bound states is more likely than in states of zero-mode oscillations. This can lead to significant changes in estimates of reaction rates in stars.

Новая модель течения жидкости на базе метода решетчатых уравнений больцмана для сред со сложной геометрической структурой

Modelling porous media finds its application in many industries and human life, namely from the oil industry and construction to washing dishes. The article considers the processes of filtrating single-phase liquid through a porous structure, the description of which is based on lattice Boltzmann method in two-dimensional space. The problem of taking into account the structure of a simulated porous medium when applying the algorithm of lattice Boltzmann equations has many solutions. Nevertheless, at the microlevel, large errors in approximating the pore boundaries can occur, due to the fact that the lattice sites are assumed to be absolutely liquid or absolutely impenetrable. The paper proposes a model in which the lattice nodes are considered to be partially permeable. Partial permeability in this case refers to having a proportion of solids in the lattice site. As a result, it is possible to derive an equation that obeys the laws of mass and momentum conservation, the validity of which has been proven empirically. Due to the equation symmetry, it can be easily used not only on a plane, but also in three-dimensional space.The new lattice Boltzmann method can be employed, for example, in modelling water filtration through sandy soils, which is used in calculating subsidence of the foundations