Chains Of Spheres Research Articles

A non-autonomous fractional granular model: Multi-shock, Breather, Periodic, Hybrid solutions and Soliton interactions

This paper explores a novel generalized one-dimensional fractional order Granular equation with the effect of periodic forced term. This type of equation arises in different area of mathematical physics with several rough materials in engineering applications. By taking into account of external forces in combination with Hertz constant law and the long wave approximation principle, we construct the fractional order one-dimensional crystalline chain of elastic spheres. A suitable transformation is implemented to convert the fractional order equation to a regular equation. The Hirota’s bilinear approach is used to secure solutions for kink and anti-kink types shock solutions. In order to find periodic and solitary wave solutions, the Granular model is converted to approximate KdV model. The newly developed solutions exhibit a range of interesting dynamics due to the existence of an external force and the roughness effect. Many hybrid solutions are created by taking a long wave limit of a fraction of the exponential and trigonometrical functions in the bilinear form of the granular model. The hybrid solutions show different superposed wave shapes with lumps, kinks and breathers. The dynamical interaction of these solutions are further illustrated graphically. Furthermore, the system’s stability is assessed using perturbation techniques in order to comprehend its resilience and possible uses in granular particles in real-world situations, guaranteeing their dependability in a range of circumstances.

Entropy-Driven Crystallization of Hard Colloidal Mixtures of Polymers and Monomers.

The most trivial example of self-assembly is the entropy-driven crystallization of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. Inspired by the difference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. As a first result, a more precise determination of the melting point for freely jointed chains of tangent hard spheres is extracted. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres, as quantified by the Voronoi polyhedron, is systematically more spherical and more symmetric compared to that of spheres belonging to chains. In turn, the local environment of the ordered phase is more symmetric and more spherical compared to that of the initial random packing, demonstrating the entropic origins of the phase transition. In general, increasing the polymer content reduces the degree of crystallinity and increases the melting point to higher volume fractions. According to the present findings, relative concentration is another determining factor in controlling the phase behavior of hard colloidal mixtures based on polymers.

Axisymmetric Slow Rotation of Coaxial Soft/Porous Spheres.

The steady low-Reynolds-number rotation of a chain of coaxial soft spheres (each with an impermeable hard core covered by a permeable porous layer) about the axis in a viscous fluid is analyzed. The particles may be unequally spaced, and may differ in the permeability and inner and outer radii of the porous surface layer as well as angular velocity. By using a method of boundary collocation, the Stokes and Brinkman equations for the external fluid flow and flow within the surface layers, respectively, are solved semi-analytically. The particle interaction effect increases as the relative gap thickness between adjacent particles or their permeability decreases, which can be significant as the gap thickness approaches zero. A particle's hydrodynamic torque is reduced (its rotation is enhanced) when other particles rotate in the same direction at equivalent or greater angular velocities, but increases (its rotation is hindered) when other particles rotate in the opposite direction at arbitrary angular velocities. For particles with different radii or permeabilities, the particle interaction has a greater effect on smaller or more permeable particles than on larger or less permeable particles. For the rotation of three particles, the presence of the third particle can significantly affect the hydrodynamic torques acting on the other two particles. For the rotation of numerous particles, shielding effects between particles can be substantial. When the permeability of porous layers is low, relative fluid motion is barely felt by the hard cores of the soft particles. The insights gained from this analysis on the effects of interactions among rotating soft particles may be of great importance in many physicochemical applications of colloidal suspensions.

Targeting Manganese Amidinate and ß-Ketoiminate Complexes as Precursors for Mn-Based Thin Film Deposition.

With a focus on Mn based organometallic compounds with suitable physico-chemical properties to serve as precursors for chemical vapor deposition (CVD) and atomic layer deposition (ALD) of Mn-containing materials, systematic synthetic approaches with ligand variation, detailed characterization, and theoretical input from density functional theory (DFT) studies are presented. A series of new homoleptic all-nitrogen and mixed oxygen/nitrogen-coordinated Mn(II) complexes bearing the acetamidinate, formamidinate, guanidinate and ß-ketoiminate ligands have been successfully synthesized for the first time. The specific choice of these ligand classes with changes in structure and coordination sphere and side chain variations result in significant structural differences whereby mononuclear and dinuclear complexes are formed. This was supported by density functional theory (DFT) studies. The compounds were thoroughly characterized by single crystal X-ray diffraction, magnetic measurements, mass spectrometry and elemental analysis. To evaluate their suitability as precursors for deposition of Mn-based materials, the thermal properties were investigated in detail. Mn(II) complexes possessing the most promising thermal properties, namely Bis(N,N'-ditertbutylformamidinato)manganese(II) (IV) and Bis(4-(isopropylamino)pent-3-en-2-onato)manganese(II) (ßIII) were used in reactivity studies with DFT to explore their interaction with oxidizing co-reactants such as oxygen and water which will guide future CVD and ALD process development.

Coupling Gold Nanospheres into Nanochain Constructs for High-Contrast, Longitudinal Photoacoustic Imaging.

Structural parameters play a crucial role in determining the electromagnetic and thermal responses of gold nanoconstructs (GNCs) at near-infrared (NIR) wavelengths. Therefore, developing GNCs for reliable, high-contrast photoacoustic imaging has been focused on adjusting structural parameters to achieve robust NIR light absorption with photostability. In this study, we introduce an efficient photoacoustic imaging contrast agent: gold sphere chains (GSCs) consisting of plasmonically coupled gold nanospheres. The chain geometry results in enhanced photoacoustic signal generation originating from outstanding photothermal characteristics compared to traditional gold contrast agents, such as gold nanorods. Furthermore, the GSCs produce consistent photoacoustic signals at laser fluences within the limits set by the American National Standards Institute. The exceptional photoacoustic response of GSCs allows for high-contrast photoacoustic imaging over multiple imaging sessions. Finally, we demonstrate the utility of our GSCs for molecular photoacoustic cancer imaging, both in vitro and in vivo, through the integration of a tumor-targeting moiety.

Prediction of azeotropes position of refrigerant mixtures using the PHSC EoS

The work aims is predict the azeotropes' position in refrigerant mixtures using the Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). The vapor-liquid equilibrium (VLE) of seventeen binary refrigerant mixtures has been correlated using two model-adjustable parameters. The results show that the proposed model can calculate the bubble and dew points of binary systems, accurately. The average ARD value of binary VLE calculations has been obtained 1.28 %. The azeotropes pressure and composition of binary mixtures have been predicted using the PHSC EoS with the average ARD values of 1.043 % and 2.23 %, respectively. The maximum relative deviation has been observed for R717+R125 systems with two azeotropes points; ARDx=12.2 %. The performance of the PHSC EoS has been evaluated by predicting the azeotropes position of ternary mixtures. The PHSC EoS results have been compared to three cubic-based EoSs containing the PR-vdW, PR-BM, and PR-MHV2-NRTL models. The results show that the PHSC EoS can predict the ternary VLE data and azeotropes position satisfactory. The relative absolute deviation does not exceed 1.7 % for the azeotropes pressure. The PHSC EoS can be used as a robust and efficient model for the prediction of the azeotropes' position in binary and ternary refrigerant mixtures. Prediction of azeotropic composition helps us to find promising refrigerant candidates in the pre-design stage of the desired apparatus.

Empirical formulas for predicting the energy attenuation behavior of primary stress waves in 1D composite chain of viscoelastic spheres

One-dimensional composite chain of viscoelastic spheres are potential candidates for novel impact buffers. Understanding the energy attenuation behavior of primary stress waves in the composite chain of viscoelastic spheres is the premise for high-performance impact buffers design. Although the current research included viscoelasticity into the motion equations of spheres, most of them were limited to homogeneous chains. Moreover, the models of discrete system could not give the explicit expressions of the key factors governing the energy attenuation of primary stress waves. The absence of explicit formulas for the key factors hindered efficient optimization design of impact buffers constructed by one-dimensional composite chain of viscoelastic spheres. In this study, empirical formulas for predicting the input amplitude, the attenuation coefficient of the contact force and the transmission coefficient at the interface were constructed. Multivariate nonlinear regression method and dimensional constraint were applied to ensure that all the empirical formulas only employ the impact velocity and the parameters of the used spheres as independent variables. Intermediate factor was introduced for individual key factor to evaluate the accuracy of the empirical formula. Though the groups of empirical formulas have degraded performance in the low range of the intermediate factors, their accuracy in quantitatively predicting the energy attenuation behavior of the stress waves in one-dimensional composite chain of viscoelastic spheres deserves satisfactory.

Модель "трубок-слоев" намагничиваемой цепочки шаров: магнитные свойства, оценка гиперусиления поля между шарами

A chain of granules is the magnetic flux conductive channel in the magnetized granular material. Experimental data on magnetic fluxes were obtained for eight conditional cores (different relative radii rc / R = 0.2--0.9) of the magnetized chain of spheres making it possible to establish the magnetic flux data for seven "pipe-layers" of the rp / R = 0.25--0.85 average radius. In the H magnetized field strength range from 10 to 50--55 kA/m, field dependences of this parameter and of the more universal parameter (independent of the radius of the spheres in the chain) of the magnetic flux density, i.e., magnetic induction in each "pipes", are close to the linear ones. Thus, the values of their magnetic permeability μp which are individual for different "pipes", turn out to be essentially constant in this range of H, which also carries important information about how many times the local field intensity h between the spheres exceeds the value of H. At rp / R ≤ 0.4, the h values are exceeding by an order of magnitude or more the H value, and at rp / R > > 0.4 and up to the periphery of the inter-sphere --- by several times. The μp = h / H decreasing dependence on rp / R, which is of interest in solving problems of the materials fine magnetic separation (using the magnetized matrix media), obeys the inverse quadratic function, and the field inhomogeneity level to the inverse cubic function

Magnetic Properties of Tube-Layers of Magnetized Chains of Spheres: Monitoring by Measured Magnetic Core Parameters

Magnetic Properties of Tube-Layers of Magnetized Chains of Spheres: Monitoring by Measured Magnetic Core Parameters

Densest packing of flexible polymers in 2D films.

How dense objects, particles, atoms, and molecules can be packed is intimately related to the properties of the corresponding hosts and macrosystems. We present results from extensive Monte Carlo simulations on maximally compressed packings of linear, freely jointed chains of tangent hard spheres of uniform size in films whose thickness is equal to the monomer diameter. We demonstrate that fully flexible chains of hard spheres can be packed as efficiently as monomeric analogs, within a statistical tolerance of less than 1%. The resulting ordered polymer morphology corresponds to an almost perfect hexagonal triangular (TRI) crystal of the p6m wallpaper group, whose sites are occupied by the chain monomers. The Flory scaling exponent, which corresponds to the maximally dense polymer packing in 2D, has a value of ν = 0.62, which lies between the limits of 0.50 (compact and collapsed state) and 0.75 (self-avoiding random walk).

Magnetic properties of pipe-layers of magnetized chain of spheres: a control based on measured magnetic properties of its cores

The use of circular contour sensors on printed circuit boards placed between contacting spheres with radius R in the magnetized chain of balls makes it possible to measure magnetic microflows in the chain along its cores of different radius r c . Thus, it becomes possible to obtain information about the magnetic properties of not only the cores of the chain themselves, but also its pipe quasi-functional layers limited by adjacent sensors. It is the purpose of the work. According to the magnetic flux measured with the help of well-recommended contour sensors (eight: from r c /R from 0.2 to 0.9) at magnetizing fi eld intensity in the range of 10–55 kA/m, magnetic flux is established along seven pipe-layers of relative radius r p /R (from 0.25 to 0.85). The values χ p of their magnetic susceptibility were found, as the r p /R values increase χ p -values decrease according to the inverse power dependence with a power degree equals 2.4. The values of the demagnetizing factor are set and functionally approximated for pipe-layers in relatively short chains of different lengths (with a number of spheres from 2 to 8). The obtained information expands idea about magnetization a chain of granules as the basic element of the granular medium. This information is useful in detailing the characteristics of such heterogeneous media used to solve scientific and practical problems, in particular, to clarify the conditions for building zones that are responsible for the magnetic capture of magnetoactive particles between granules of working elements (matrix type) of polygradient magnetic separators and analyzers.

Topological magnon modes of a chain of magnetic spheres in a waveguide

We study topological features of a bipartite chain of magnetic spheres embedded in a rectangular metallic waveguide. The coherently coupled chain via the waveguide mode can host two topologically distinct phases identified by the Zak phase. A finite chain supports a pair of doubly degenerate topological edge states within the gap when the intercoupling dominates over the intracoupling, demonstrating that despite the strong coupling to the waveguide mode, the bulk-edge correspondence still holds. The nontrivial (trivial) topological phase is determined by the intracell and intercell coupling of magnetic spheres which depend on the separation, the external magnetic inductions, and the waveguide dimensions. Magnetically tunable topological magnon modes may enable unprecedented topological photonic devices.

Special features of diagnostics of magnetic properties of “pipe-layer” chains of spheres

Circuit sensor contours created by using the technology of printed circuit boards and placed between spheres of radius R that are in contact allow measuring magnetic (micro-)fluxes Φc over the cores of different radii rc in a magnetized chain of spheres, which are basic elements of a granular medium. The main goal is to obtain information about the magnetic properties of the “pipe-layers” of a magnetized chain of spheres as a quasi-continuous magnet by virtue of the fact that such step-by-step data Φc can also be used to directly judge the step-by-step changes in magnetic fluxes along the “pipe-layers” (limited by adjacent circuit sensors). According to the data Φc, measured using eight sensors (from rc/R = 0.2 to rc/R = 0.9 at steps of 0.1), magnetic fluxes Φp were obtained along seven thin “pipe-layers” of different relative radii rp/R (from 0.25 to 0.85). The Φp data were obtained using chains in which the number of spheres (from 2 to 12) and the intensity of the magnetizing field varied (from 10 to 55 kA/m). The induction values in each of the “pipe-layers” were found and characterized. The values of their magnetic permeability were also found, which reflect the magnitude of the excess field intensity between the granules in comparison with the intensity of the magnetization field, which is of fundamental importance, for example, in matters of fine magnetic separation.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres.

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

Universal flow-induced orientational ordering of colloidal rods in planar shear and extensional flows: Dilute and semidilute concentrations

The design of flow processes to build a macroscopic bulk material from rod-shaped colloidal particles has drawn considerable attention from researchers and engineers. Here, we systematically explore and show that the characteristic strain rate of the flow universally determines the orientational ordering of colloidal rods. We employed the fluctuating lattice Boltzmann method by simulating hydrodynamically interacting Brownian rods in a Newtonian liquid moving under various flow types. By modeling a rigid rod as a chain of nonoverlapping solid spheres with constraint forces and torque, we elucidate rigid rod dynamics with an aspect ratio (L/d) either 4.1 or 8.1 under various rotational Péclet number (Per) conditions. The dynamics of colloidal rods in dilute (nL3=0.05) and semidilute suspensions (nL3=1.1) were simulated for a wide range of Per (0.01<Per<1000) under shear flows including Couette and Poiseuille flows in a planar channel geometry, and an extensional and mixed-kinematics flow in a periodic four-roll mill geometry, where n is the number density, and d and L are the diameter and length of the rod, respectively. By evaluating the degree of orientational alignment of rods along the flows, we observed that there is no significant difference between flow types, and the flow-induced ordering of rods depends on the variation of Per up to moderate Per (Per<100). At a high Per (Per>100), the degree of orientational ordering is prone to diversify depending on the flow type. The spatial inhomogeneity of the strain-rate distribution leads to a substantial decrease in the orientational alignment at high Per.

Hybrid Carbon Sphere Chain-MnO2 Nanorods as Bifunctional Oxygen Electrocatalysts for Rechargeable Zinc-Air Batteries.

It is now recognized that the development of self-supported and efficient bifunctional air cathodes via the direct growth of earth-abundant catalysts onto the surface of the conductive collector would be a cutting-edge strategy to reduce interfacial resistance, enhance the mechanical tenure, and reduce the final weight and cost of manufacturing of rechargeable Zn-air batteries (ZABs). This work reports an innovative self-supported precious metal-free electrode, comprising carbon sphere chains (CSCs) directly grown onto a carbon paper (CP) substrate, wherein the CSCs have a functionalized surface bearing carbon nanobud defects, oxygen functional groups, and high-density MnO2 hierarchical nanorods (NRs), uniformly coating the surface of CSCs. Not only is the metal-free functionalized CSC catalyst functional for both the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) but its combination with MnO2 NRs impressively enhances the ORR/OER activities. A homemade ZAB assembled with functionalized CSC/MnO2 air cathode can successfully power a timer for a period of 17 days with no voltage loss, whereas two series-connected ZABs can light up 39 red light-emitting diode (LED) bulbs. The self-supported and earth-abundant-based CSC/MnO2 materials open up an opportunity for lightweight and cost-effective ZABs and metal-air batteries in general.

Polarizabilities and electric field-induced forces in periodic two-component linear dielectric sphere chains

Idealized single-stranded linear chains of dielectric spheres in a dielectric medium can be used as a model system for electric field-induced particle chaining in complex systems, such as electrorheological fluids. The polarizability of the spheres in the chains and the interparticle (bonding) forces between them determine the macroscopic (e.g. dielectric, rheological) behavior of the bulk. We have derived new analytical equations for the bonding forces in a linear, bidisperse chain, where two components with different sizes form a periodic structure. The force equations were obtained on the basis of local field strength at the particle sites by taking into account the interactions beyond the nearest neighbors within the chain. The dependence of the bonding force and the local field strength on the ratio of particle sizes was investigated. As an application the dielectric permittivity of a bulk model system with bidisperse chains was calculated using the Clausius–Mossotti equation.

Results of magnetometry of spheres’ chains as basic structural elements of a granulated material

During the magnetization of a granulated material with back filling of ferromagnetic spheres, the chains of contacting granules (spheres) serve as self-sufficient conductors of the magnetic flux. Each of such chains is characterized by a pronounced redistribution of the magnetic flux along its cross section. If in the chain of spheres with radius R the conditional core with radius r is selected, and then this core is surrounded by a loop placed between the contacting spheres in order to measure magnetic flux, it has been found that an increase in r decreases the thread density (magnetic induction). The data for magnetic flux are given for a different relative radius r/R of the cores of two chains differing only in R. For this purpose, the sensors created in the form of circular circuits based on thin printed circuit boards have been used. According to recorded magnetic flux, the detailed information on magnetic induction within the cores and their magnetic permeability under the magnetization of the chains in a solenoid has been obtained. It has been shown that as the ratio r/R increases, i.e., with the thickening in the conditional cores and the corresponding increase in magnetic flux, both magnetic induction and magnetic permeability significantly reduce. The complete mutual agreement of the corresponding r/R-dependence of magnetic induction and magnetic permeability is demonstrated for both chains, what indicates the potential in applying the results obtained for the chains of spheres of other radii.

Dynamic breakage of double glass spheres chain subjected to impacting loading

Strain energy releasing due to local failure plays an important role in the dynamic breakage of the brittle medium. A series of experiments are conducted based on the Split Hopkinson pressure bar (SHPB) device. Two contact modes, i.e. the rigid contact between two spheres and the elastic contact between the sphere and the impact/support bar, are introduced by using the double sphere chain sample. Two methods, e.g. the Infrared temperature measurement (ITMS) method and the Digital image correlation (DIC) method, are utilized to trace the fracture sequence of the chain samples under impact velocity 5.0–13.0 m/s. The effects of strain energy releasing to the force-displacement curves, the temperature rising process, and the broken products of the chain samples are demonstrated in detail. Releasing of strain energy causes a delayed recompression process, and the delayed time decreases with increasing of impact velocity, which was caused by the formation and releasing of local strain in elastic contact mode. The approaches to evaluate the effects of strain energy releasing are then proposed to analyze the force-displacement curves and the temperature rising process. The elevated temperature is estimated to be a linear relationship to ε˙2/3. It is of great significance for the profound understanding of the failure mechanism of sphere aggregates.

Routing multiple flow channels for additive manufactured parts using iterative cable simulation

Many prior works highlight the potential of additive manufacturing (AM) for flow components. Examples include hydraulic manifolds with multiple crossing flow channels that guide separate fluid flows in a single part. Creating the 3D geometry of such complex parts can be challenging. Designers must consider functional requirements, such as minimizing the channels’ length, creating smooth channel paths, and preventing overlaps between channels for different fluid flows. Furthermore, designers must adhere to manufacturing restrictions specific to the chosen AM technology. Critical overhangs inside channels must be avoided for processes such as laser powder bed fusion by adapting the shape of channel cross-sections. However, such production-related design changes can cause overlaps between different channels and require re-adjusting the channel paths. Consequently, routing several flow channels is often challenging when manually designing parts for AM. This work aims to automate the routing of multiple channels considering the AM overhang restriction. The presented approach models flow channels as virtual cables defined by a chain of particles (connected by line segments) and collision spheres (located at the cable particles). The cable line segments describe the path or centerline of channels, while the cable collision spheres approximate the required space of each channel. The cables are initialized as straight lines between the channel inlets and outlets and iteratively subjected to geometric-based constraints, e.g., to minimize the cables’ length and smoothen their paths. The collision spheres are used to detect overlaps between channels for different flows and repel the affected cables from each other. The radii of the collision spheres are iteratively updated to consider the adaption of cross-sections for AM. After the iterative cable simulation convergences, the cable paths are used to generate a detailed 3D part design. A case study applies the approach to a hydraulic manifold fabricated using laser powder bed fusion of stainless steel. The study demonstrates the automated design and production of customized design variants.