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By using Gaussian98 package at BPW91 6-31g(d,p) level combined a genetic algorithm (GA) simulation, we have studied the lowest energy structural and electronic properties of the Al_nN (n=2-13) clusters. The ground-state structures, the charge transfers from Al to N site, HOMO-LUMO gap and the covalent, ionic and metallic nature with cluster size and atomic structure are investigated. Al₇N, Al₉N and Al₁₂N cluster is found particularly stable among the Al_nN clusters.

First-principles calculations are employed to investigate the structural and elastic properties, formation enthalpies and chemical bonding features as well as hardness values of chromium tetraboride $({\mathrm{\text{CrB}}}_4)$ with different structures. The lattice parameters, Poisson’s ratio and $B/G$ ratio are also derived. Our calculations indicate that the orthorhombic structure with Pnnm symmetry is the most energetically stable one for CrB₄. Except for ${\mathrm{\text{WB}}}_{4}P{6}_3/mmc$ structure with imaginary frequencies, another six new structures are investigated through the full phonon dispersion calculations. Their mechanical and thermodynamic stabilities are also studied by calculating the elastic constants and formation enthalpies. Our calculations show that the thermodynamic stabilities of all these ${\mathrm{\text{CrB}}}_4$ phases can be enhanced under high pressure. The large shear moduli, Young’s moduli and hardness values indicate that these ${\mathrm{\text{CrB}}}_4$ phases are potential hard materials. Analyses of the densities of states (DOSs) and electron localization functions (ELFs) provide further understandings of the chemical and physical properties of these ${\mathrm{\text{CrB}}}_4$ phases. It is observed that the large occupations and high strengths of the B–B covalent bonds are important for the stabilities, incompressibility and hardnesses of these ${\mathrm{\text{CrB}}}_4$ phases.

To investigate the configurations and the electrical performance of the Pb–I films, the geometries and electronic properties of the Pb${}_n$I and Pb${}_n$I₂ (n = 1–6) clusters are calculated by density functional theory at the GGA/PBE functional. The results reveal that I atoms prefer to occupy the symmetrical positions which are far from the centers of the Pb${}_n$ clusters. The Pb₂I₂ clusters are more structurally stable than the neighbors by the average binding energy. The PbI, Pb₃I, PbI₂, Pb₄I₂ and Pb₆I₂ clusters are more dynamically stable than their neighbors by the HOMO–LUMO gaps. The adsorption capacity of an I atom on the Pb₂ cluster is the strongest compared to those of the other Pb${}_n$ (n = 1–6) clusters. NBO analysis reveals that the 5p orbital of I atoms in the Pb–I clusters acquires more electrons than the 5s orbital loses.

To understand sulfide inclusions in the steel industry, the structures, stabilities, electronic and magnetic properties of the Mn${}_n$S and Mn${}_{n-1}$S₂ (n=1–6) clusters are investigated by using first-principles. The results show that the S atoms prefer to occupy the outside surface center of the Mn${}_n$ (n = 3–6) clusters. Chiral isomers are occurred to the Mn₅S₂ isomers. The Mn₂S, Mn₂S₂ clusters are more stable than their neighbors. However, the MnS, S₂, and Mn₅I₂ clusters possess higher dynamic stability than their neighbors by the HOMO–LUMO gaps. The Mn${}_n$S and Mn${}_{n-1}$S₂ (n = 1–6) clusters prefer to spontaneous generation by Gibbs free energy. A few 4s orbital electrons of Mn atoms transferred to the S atoms by Mülliken population analysis. For the other Mn${}_n$S (n = 1–6) clusters, the spin density (17.256) of the ground-state Mn₆S clusters is the largest. For the Mn${}_{n-1}$S₂ (n = 1–6) clusters, the total spin (9.604) of the ground-state Mn₂S₂ cluster is the largest.

Transition metal (Mn, Fe, Co and Ni)-doped tungsten oxides nanoparticles with magnetic properties may be applied in various catalysts such as water treatment as they are easy to be recycled. Structural, electronic and magnetic properties of TM_n@W${}_{12}$O${}_{36}$ (TM=Mn, Fe, Co and Ni, n=1–4) clusters have been calculated at PBE level. The results reveal that the centers of the TM${}_{1-3}$ clusters are in accordance with that of the W${}_{12}$O${}_{36}$ clusters while the TM₄ clusters deviate obviously from the center of the W${}_{12}$O${}_{36}$ cages. All TM_n@W${}_{12}$O${}_{36}$ clusters exhibit slightly less structural stability and obviously more chemical reactivity than the W${}_{12}$O${}_{36}$ clusters. Mülliken spin densities of a TM atom embedded are almost kept except for the Ni@W${}_{12}$O${}_{36}$ clusters. The spin densities of TM_n clusters in the TM₃@W${}_{12}$O${}_{36}$ and TM₄@W${}_{12}$O${}_{36}$ clusters are offset. The magnetic TM modification strategy is helpful to design recyclable tungsten oxide catalysts.

The boron nitrides as excellent sensors are adopted to detect some harmful gases. The adsorption sites and lengths of the boron nitrides are very important to improve the adsorption capacity. The structures, stabilities and electronic properties of the COB_mN_m and CO@B_mN_m ($m=48$, 96 and 144) nanotubes with different lengths have been investigated by using density functional theory. The longer B_mN_m, COB_mN_m and CO@B_mN_m clusters are more stable. The adsorption of the CO molecules at the ends of B_mN_m nanotubes competes with the insertion of the CO molecules in the B_mN_m nanotubes. The COB_mN_m clusters exhibit higher chemical reactivity than the CO@B_mN_m clusters. The lengths of the B_mN_m nanotubes have little effect on the chemical reactivity of the nanotubes. The charge transfer amounts of the O atoms increase while those of the C atoms of the COB_mN_m and CO@B_mN_m clusters are almost the same with the increase of cluster lengths. The CO molecules lose fewer electrons ($0.174|\mathrm{\text{e}}|$, $0.164|\mathrm{\text{e}}|$, $0.158|\mathrm{\text{e}}|$) to the B_mN_m nanotubes of the COB_mN_m clusters while the CO molecules obtain fewer electrons ($-0.028|\mathrm{\text{e}}|$, $-0.045|\mathrm{\text{e}}|$, $-0.045|\mathrm{\text{e}}|$) from the B_mN_m nanotubes of the CO@B_mN_m clusters.

The structures, stability, electronic and magnetic properties of the TM@Si${}_{12}$C${}_{12}$ clusters have been calculated by using PBE functional. The results indicate that only for the TM@Si${}_{12}$C${}_{12}$ (TM$=$Zn, Y, Ag, Cd, Lu, Au and Hg) clusters, TM atoms are nearly located at the center of the Si${}_{12}$C${}_{12}$ cages. As for other TM@Si${}_{12}$C${}_{12}$ clusters, TM atoms approach one side of the Si${}_{12}$C${}_{12}$ cages. The structural stability of the Ti@Si${}_{12}$C${}_{12}$, Ti@Si${}_{12}$C${}_{12}$, Zr@Si${}_{12}$C${}_{12}$, Nb@Si${}_{12}$C${}_{12}$, Hf@Si${}_{12}$C${}_{12}$, Ta@Si${}_{12}$C${}_{12}$, W@Si${}_{12}$C${}_{12}$ and Os@Si${}_{12}$C${}_{12}$ is higher than that of the Si${}_{12}$C${}_{12}$ cages. All TM@Si${}_{12}$C${}_{12}$ clusters display covalent bond characteristics. The spins of the TM atoms in the TM@Si${}_{12}$C${}_{12}$ cages are dramatically quenched and only the V@Si${}_{12}$C${}_{12}$ and Cr@Si${}_{12}$C${}_{12}$ clusters remain −1.474 ${\mu }_B$ and 1.638 ${\mu }_B$, respectively.

Metal doping is considered as an effective method to stabilize the structures and optimize the properties of boron clusters. The structures and electronic properties of the ${\mathrm{\text{TMB}}}_{36}$ clusters have been calculated at the Perdew–Burkle–Ernzerhof (PBE) level. The results reveal that the Cu atoms for the ${\mathrm{\text{CuB}}}_{36}$ clusters unexpectedly enter the ${\mathrm{\text{B}}}_{36}$ clusters. Ti, V, Co, Ni, Zr, Hf, Ta and W can obviously increase the structural stability of pristine ${\mathrm{\text{B}}}_{36}$ clusters. The Ti, Cr, Fe, Ni and Zn; Y, Ru and Ag; Lu, Ta, Ir and Au-adsorbed ${\mathrm{\text{B}}}_{36}$ clusters display higher kinetic activity than other ${\mathrm{\text{B}}}_{36}$ clusters. The d orbital electrons of the TM atoms will significantly affect the distributions of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) states of pristine ${\mathrm{\text{B}}}_{36}$ clusters. All the TM–B bonds of the ${\mathrm{\text{TMB}}}_{36}$ clusters display covalent characters.

In countries where the earthquake has devastating effects, new buildings should be earthquake-resistant. For this, soil surveys and structure natural vibration frequencies should be considered. In this study, regardless of the ground period, the fluid damper has been modeled numerically to decrease the natural vibration frequency of the structure. In fluid dampers, mechanical energy is converted into heat energy. The fluid damper was exposed to the same structure frequency value during an earthquake of 10, 20, 30, 40, 50, and 60s for four different building heights (6–12–18–24m) and the temperature and velocity distribution of the fluid damper was examined with the help of the COMSOL multiphysics. The temperature changes in the fluid damper for the 6m high building that has the lowest structure natural vibration period (highest frequency) were observed to be the highest. It has been determined that during the vibration, fluid passes through the micro channel between the piston and the outer surface of the fluid damper and reaches high temperatures and velocities because of the viscous heating effect.

Transition metal substitution can expand the applications of tungsten oxides in chemical sensors, catalysts, and other fields. In order to highlight the effect of TM substitution on the electronic properties of tungsten oxide clusters, the configurations, electronic properties and dipole magnitudes of ${\mathrm{\text{TMW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ and ${\mathrm{\text{TM}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ (TM = Ni, Pd and Pt; $n=2-6$) clusters have been investigated via the density functional theory. The structures of ${\mathrm{\text{TMW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ and ${\mathrm{\text{TM}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ clusters inherit those of ${\mathrm{\text{W}}}_n{\mathrm{\text{O}}}_{3n}$ ($n$ = 2–6) clusters to some extent except for ${\mathrm{\text{Pd}}}_2{\mathrm{\text{W}}}_2{\mathrm{\text{O}}}_{12}$, ${\mathrm{\text{Pt}}}_2{\mathrm{\text{W}}}_2{\mathrm{\text{O}}}_{12}$, ${\mathrm{\text{Pd}}}_2{\mathrm{\text{W}}}_3{\mathrm{\text{O}}}_{15}$, and ${\mathrm{\text{Pt}}}_2{\mathrm{\text{W}}}_3{\mathrm{\text{O}}}_{15}$ clusters. ${\mathrm{\text{NiW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ clusters exhibit higher thermodynamic stability than the other ${\mathrm{\text{TMW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ and ${\mathrm{\text{TM}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ clusters. ${\mathrm{\text{NiW}}}_2{\mathrm{\text{O}}}_9$, ${\mathrm{\text{NiW}}}_4{\mathrm{\text{O}}}_{15}$, ${\mathrm{\text{Ni}}}_2{\mathrm{\text{O}}}_6$, ${\mathrm{\text{Ni}}}_2{\mathrm{\text{W}}}_4{\mathrm{\text{O}}}_{18}$, ${\mathrm{\text{PdW}}}_3{\mathrm{\text{O}}}_{12}$, ${\mathrm{\text{PdW}}}_5{\mathrm{\text{O}}}_{18}$, ${\mathrm{\text{Pd}}}_2{\mathrm{\text{WO}}}_9$, ${\mathrm{\text{Pd}}}_2{\mathrm{\text{W}}}_4{\mathrm{\text{O}}}_{18}$, ${\mathrm{\text{PtWO}}}_6$, ${\mathrm{\text{PtW}}}_4{\mathrm{\text{O}}}_{15}$, ${\mathrm{\text{Pt}}}_2{\mathrm{\text{O}}}_6$, ${\mathrm{\text{Pt}}}_2{\mathrm{\text{W}}}_4{\mathrm{\text{O}}}_{18}$ clusters display more kinetically stable than adjacent ${\mathrm{\text{TMW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ and ${\mathrm{\text{TM}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ clusters. The Mülliken charge transfer amount of ${\mathrm{\text{Pt}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ clusters is more than that of other ${\mathrm{\text{TMW}}}_{n-1}{\mathrm{\text{O}}}_{3n}$ and ${\mathrm{\text{TM}}}_2{\mathrm{\text{W}}}_{n-2}{\mathrm{\text{O}}}_{3n}$ clusters except for ${\mathrm{\text{Pt}}}_2{\mathrm{\text{W}}}_4{\mathrm{\text{O}}}_{18}$ clusters.

Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall transcendental stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. The present paper gives the first ever derivation of the Bernoulli–Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

The main purpose of this paper is to examine the influence of time delay associated with a semi-active variable viscous (SAVV) damper on the response of seismically excited linear and nonlinear structures. The maximum time delay is estimated on the basis of stability criteria, which consist of analyses of structural modal properties. Numerical computation of the critical time delay is performed by using dichotomic approach, which is based on multiple solving of the eigenvalue problem. Simulation results indicate that variable dampers can be effective in reducing the seismic response of structures, and that time-delay effects are important factors in control design of seismically excited structures. Furthermore, simulation results show degradation of performance whenever the actual delay exceeds the calculated critical time delay, which shows the accuracy and reliability of the proposed approach.

Small Angle Neutron Scattering (SANS) and Small Angle X-ray Scattering (SAXS), anong other available techniques, are the nost sought after techniques for studying the sizes and shapes of nanoparticles. The contrast between particle and its surrounding is different for X-rays and neutrons. Thus a combined SANS and SAXS study, at times, provides information about the core and the shell structure of nanoparticles. This paper gives an introduction to the techniques of SANS and SAXS and shows results of a study of core-shell structure for a micelle (nanaoparticle of organic material).

A global search on the lowest-energy structures of the medium-sized silver clusters Ag_n(n = 21–34) was performed by using a genetic algorithm (GA) coupled with a tight-binding (TB) method. Structures, binding energies per atom, second differences in energies, the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO), and fragmentation behaviors of Ag_n(n = 21–34) are investigated by using DFT method. The calculated results show that the neutral silver clusters prefer to decay by evaporation of a monomer except a small sized silver cluster (Ag₄), which favors a dimmer evaporation. For the collision induced dissociation of cationic silver clusters, decaying a silver atom is found to be the dominant fragmentation channel. But for some small sized cationic silver clusters, a neutral dimmer evaporation is found to be energetically favorable. Our calculated results are consistent with previous studies.

The geometries, electronic structures and energies of small TiSi_n species (n = 1–8) and their anions were systematically investigated by G4 theory. The ground-state structures of these clusters are presented herein. For neutral TiSi_n (n = 1–8), the spin multiplicities of the ground-state structures are singlet, with the exception of n = 2, which exists in a triplet state. For anionic TiSi_n^-, the spin multiplicities of the ground-state structures are doublet, with the exception of n = 2, which is quartet. The adiabatic electron affinities for TiSi_n are estimated to be 1.31 eV (TiSi), 1.46 eV (TiSi₂), 1.53 eV (TiSi₃), 1.71 eV (TiSi₄), 2.06 eV (TiSi₅), 2.16 eV (TiSi₆), 2.20 eV (TiSi₇) and 2.39 eV (TiSi₈). In comparison with the available experimental data, the calculated adiabatic electron affinities differ from experimental values by an average absolute deviation of only 0.03 eV. Additionally, the dissociation energies of Ti atoms from TiSi_n, and Si atoms from TiSi_n and Si_n clusters are estimated to examine relative stabilities.

4D printing is a fast-developing technique which enables the transformation of shape, property, and function after a structure is manufactured. Here the ’fourth dimension’ refers to a time-dependent deformation, and thus 4D printing technique is closely related to the mechanical design strategies of materials and structures. This review concentrates on the recent progress of fundamental mechanical theories, analytical methods, and designing tools, for three categories of designing principles in 4D printing. The first type of 4D printing relies on active materials that respond to external stimuli. The second type includes a wide range of 4D-printed innovative structures, where the automatic actuation mainly comes from a combination of different deformation mechanisms. The third type of 4D printing focuses on mechanical designs related to the manufacturing process. The classification bridges the gaps between materials, microarchitectures, and large-scale structures, while some 4D printing strategies might involve more than one aforementioned design principle. This review provides reference and guidance for future 4D printings with customized deformation modes and multiple functionalities.

The contemporary epoch in human history is characterised by unprecedented levels of discourses on structural violence and an urge to interrogate, deconstruct and dismantle the oppressive structures. Different subaltern sections which have hitherto remained subjugated or even invisible have found in the notion of equity a way to emancipate themselves, not just as individuals, but also as collectives. This historical background has facilitated a re-reading of Gandhi from multiple perspectives and made him a centre of renewed interest in his approach to equity. While on one side, Gandhi has been hailed as a crusader against various power structures such as imperialism, racism, casteism, class dominance and even patriarchy, the limitations in his approach towards those oppressive structures have also been subjected to deep and informed critiques. While critiques which problematise his approach to oppressive structures like Ambedkar’s critique of Gandhi on the caste question and the Marxist critiques on him on the class question have been prevalent for some time yet, the contemporary assertions of different social identities have sparked off newer debates focusing on Gandhi’s approach towards oppressive structures. The best example is the burgeoning critical readings on his work in South Africa, which has been hailed as a glorious struggle against apartheid by historiographers and biographers sympathetic to him but being increasingly read from a Black perspective in terms of its reinforcement of racism. These discursive critiques find their practical manifestations in movements such as the ongoing “Black Lives Matter” movement, where Gandhi as an icon is being denounced. Against this backdrop, this chapter tries to determine whether there is a unique Gandhian approach to oppressive structures. If it is there, how far it is useful in the struggles for equity being waged by the different subaltern sections. Also, an attempt is made to historically situate the various critical readings on Gandhi, and critically examine how far they can help in reclaiming the radical-rebellious part in Gandhi’s thought-world on the one hand, while further developing deep, informed critiques on its conservative/status-quoist dimensions on the other.

Transcendental member stiffness matrices for vibration (or buckling) arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretisation errors. Assembling them into the overall structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or critical load factors) are found with certainty using the Wittrick-Williams algorithm. This paper gives equations for the recently discovered member stiffness determinant, which equals the appropriately normalised FEM stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. Vibrating Bernoulli-Euler beams and vibrating, axially loaded Timoshenko members are covered, using a recent convenient notation for the latter, such that its stiffnesses clearly limit to the Bernoulli-Euler ones when axial force, shear rigidity and rotatory inertia are neglected. The present paper gives the first ever derivation of the Bemoulli-Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

Technology transfer between disciplines is an important but relatively infrequently occurring activity. This paper deals with aspects of the transfer of the Wittrick-Williams (W-W) algorithm, and in particular its powerful and exact multi-level substructuring capability, from its parent discipline of structural engineering to a mathematical area of current and intense interest. This area involves examining the eigenvalues of systems of differential equations connected together with tree topology. In the structural analogy, the problem is that of finding the natural frequencies of a tree of co-linear bars. It is shown: that trees with 10¹² or more bars, which represent second order Sturm-Liouville equations, can be analysed in almost negligibly small computer time and without ill-conditioning; that the existence and extremely high multiplicity of multiple eigenvalues can be predicted precisely from the structural analogy; that the fragmentation of the multiplicity due to members at one level of the tree no longer being identical to those at the other levels can be predicted and; related conclusions can be drawn when the bars are replaced by beams, which represent fourth order Sturm-Liouville equations.

We present results of the recent research on sparse graphs and finite structures in the context of contemporary combinatorics, graph theory, model theory and mathematical logic, complexity of algorithms and probability theory. The topics include: complexity of subgraph- and homomorphism- problems; model checking problems for first order formulas in special classes; property testing in sparse classes of structures. All these problems can be studied under the umbrella of classes of structures which are Nowhere Dense and in the context of Nowhere Dense – Somewhere Dense dichotomy. This dichotomy presents the classification of the general classes of structures which proves to be very robust and stable as it can be defined alternatively by most combinatorial extremal invariants as well as by algorithmic and logical terms. We give examples from logic, geometry and extremal graph theory. Finally we characterize the existence of all restricted dualities in terms of limit objects defined on the homomorphism order of graphs.