A new method for calculating three-particle interaction in the theory of modulus elasticity

We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G ₃ = O(3) ? P ₃. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: \(\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}\), where I _j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: \(I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)\).     

Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition

The complete potential energy of a crystal $E\left( {\vec r_{ik} } \right)$ is presented in the form of an expansion in irreducible interactions in clusters containing pairs, triplets, and quadruplets of atoms, situated on A2 lattice sites. The full set of invariants $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ , on which $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ can depend is found. Vectors $\vec r_{ik}$ are presented in the form of an expansion of the base of a Brave lattice. This allows us to present $I_j \left( {\vec r_{ik} } \right)$ in the form of integers (lattice sums) multiplied by τ ^m , where τ is half of an elementary cell rib, and m = const is determined by the model. The sum of the Lenard-Jones potential and the potentials of tri- and tetra-atomic interactions was chosen as the model potential. Within this model, elastic moduli of the second and third order were calculated for crystals with A2-type structure.     

On non-consensus motions of dynamical linear multiagent systems

The first-principle density functional theory (DFT) calculations were employed to investigate the electronic structures, magnetic properties and half-metallicity of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) Heusler alloys with \(\text {AlCu}_{2}\text {Mn}\)- and \(\text {CuHg}_{2}\text {Ti}\)-type structures within local density approximation and generalised gradient approximation for the exchange correlation potential. It was found that \(\text {CuHg}_{2}\text {Ti}\)-type structure in ferromagnetic state was energetically more favourable than \(\text {AlCu}_{2}\text {Mn}\)-type structure in all compounds except \(\text {Ti}_{2}\text {IrB}\) which was stable in \(\text {AlCu}_{2}\text {Mn}\)-type structure in non-magnetic state. \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) alloys in \(\text {CuHg}_{2}\text {Ti}\)-type structure were half-metallic ferromagnets at their equilibrium lattice constants. Half-metallic band gaps were respectively equal to 0.87, 0.79, 0.75, and 0.73 eV for \(\text {Ti}_{2}\text {IrB}\), \(\text {Ti}_{2}\text {IrAl}\), \(\text {Ti}_{2}\text {IrGa}\), and \(\text {Ti}_{2}\text {IrIn}\). The origin of half-metallicity was discussed for \(\text {Ti}_{2}\text {IrGa}\) using the energy band structure. The total magnetic moments of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) compounds in \(\text {CuHg}_{2}\text {Ti}\)-type structure were obtained as \(2\mu _{\mathrm{B}}\) per formula unit, which were in agreement with Slater–Pauling rule (\(M_{\mathrm{tot}} =Z_{\mathrm{tot}}-\)18). All the four compounds were half-metals in a wide range of lattice constants indicating that they may be suitable and promising materials for future spintronic applications.     

A Lax pair structure for the half-wave maps equation

We consider the half-wave maps equation

$$\begin{aligned} \partial _t \vec {S} = \vec {S} \wedge |\nabla | \vec {S}, \end{aligned}$$

where \(\vec {S}= \vec {S}(t,x)\) takes values on the two-dimensional unit sphere \(\mathbb {S}^2\) and \(x \in \mathbb {R}\) (real line case) or \(x \in \mathbb {T}\) (periodic case). This an energy-critical Hamiltonian evolution equation recently introduced in Lenzmann and Schikorra (2017, arXiv:1702.05995v2), Zhou and Stone (Phys Lett A 379:2817–2825, 2015) which formally arises as an effective evolution equation in the classical and continuum limit of Haldane–Shastry quantum spin chains. We prove that the half-wave maps equation admits a Lax pair and we discuss some analytic consequences of this finding. As a variant of our arguments, we also obtain a Lax pair for the half-wave maps equation with target \(\mathbb {H}^2\) (hyperbolic plane).

     

Discussion About the Magnetic Field Dimensionality,Invariant Axis Condition,and Coulomb Gauge to Solve the Grad-Shafranov Equation

We discuss the relationship between the Coulomb gauge, the existence of an invariant axis, and the dimensionality (2-D or 2\(\frac {1}{2}\)-D) of the magnetic field in a mathematical-physical formalism that leads us to the Grad-Shafranov (GS) equation. In the literature, we found that a 2-D magnetic structure is used as a prerequisite to derive the GS equation from the Vlasov equation. However, other consulted works are based on a 2\(\frac {1}{2}\)-D (two-and-a-half) magnetic structure as a prerequisite to derive the GS equation from the balance of forces between the pressure gradient and the magnetic force, respectively. We replaced the magnetic vector potential on Ampère’s equation and used the Coulomb gauge to obtain a system of three Poisson equations, one for each component. We also used the same procedure explained above, but without the Coulomb gauge. Comparing z-component in both equation systems, we concluded that there are two possible solutions. We suggest using a 2\(\frac {1}{2}\)-D magnetic field configuration instead of a 2-D, when working with kinetic theory or magnetostatic equilibrium to derive the GS equation. We clarified that there is no relationship between the Coulomb gauge and the magnetic field dimensionality. In this problem, the invariant axis condition is imposed, which means that \(\vec {\nabla }\cdot \vec {A}\) is independent of z, i.e., \(\vec {\nabla }\cdot \vec {A}\) could have any value in which an invariant axis is a sufficient condition to obtain the GS equation.     

Strange non-chaotic attractors in a state controlled-cellular neural network-based quasiperiodically forced MLC circuit

The adsorption energies, bond order, atomic charge, optical properties, and electrostatic potential of nitrogen molecules of armchair single-walled carbon nanotubes (SWCNTs) and nitrogen-doped single-walled carbon nanotubes (N-SWCNTs) were investigated using density functional theory (DFT). Our results show that adsorption of the \(\hbox {N}_{2}\) molecules on the external wall of a nanotube is more effective than on the internal wall in SWCNTs. The results show that \(\hbox {N}_{2}\) molecule(s) are weakly bonded to SWCNTs and N-SWCNTs through van der Waals-type interactions. The interaction of \(\hbox {N}_{2}\) molecules with SWCNTs and N-SWCNTs is physisorption as the adsorption energy and charge transfer are small, and adsorption distance is large. The electronic transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) (\(\hbox {H}\rightarrow \hbox {L}\)) have the maximum wavelength and the lowest oscillator strength. The potential sensor on the surface of pristine SWCNTs and N-SWCNTs for the adsorption of \(\hbox {N}_{2}\) molecule(s) is investigated. The N-loaded single-walled carbon nanotube is introduced as a better \(\hbox {N}_{2}\) molecule(s) detector when compared with SWCNTs.     

Search of the neutrino-less double beta decay of $$^{}$$Se into the excited states of $$^{}$$Kr with CUPID-0

The CUPID-0 experiment searches for double beta decay using cryogenic calorimeters with double (heat and light) read-out. The detector, consisting of 24 ZnSe crystals 95\(\%\) enriched in \(^{82}\)Se and two natural ZnSe crystals, started data-taking in 2017 at Laboratori Nazionali del Gran Sasso. We present the search for the neutrino-less double beta decay of \(^{82}\)Se into the 0\(_1^+\), 2\(_1^+\) and 2\(_2^+\) excited states of \(^{82}\)Kr with an exposure of 5.74 kg\(\cdot \)yr (2.24\(\times \)10\(^{25}\) emitters\(\cdot \)yr). We found no evidence of the decays and set the most stringent limits on the widths of these processes: \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{0_1^+}\))8.55\(\times \)10\(^{-24}\) yr\(^{-1}\), \(\varGamma \) (\(^{82}\) Se \(\rightarrow ^{82}\) Kr \(_{2_1^+}\))\(\,{<}\,6.25 \,{\times }\,10^{-24}\) yr\(^{-1}\), \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{2_2^+}\))8.25\(\times \)10\(^{-24}\) yr\(^{-1}\) (90\(\%\) credible interval).     

Strange quark star with Tolman IV background

In this paper, using the optical emission spectroscopy (OES) technique, the optical characteristics of a radiofrequency (RF) plasma jet are examined. The \(\hbox {Ar}/\hbox {O}_{2}\) mixture is taken as the operational gas and, the Ar percentage in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture is varied from 70% to 95%. Using the optical emission spectrum analysis of the RF plasma jet, the excitation temperature is determined based on the Boltzmann plot method. The electron density in the plasma medium of the RF plasma jet is obtained by the Stark broadening of the hydrogen Balmer \(H_{\beta }\). It is mostly seen that, the radiation intensity of Ar 4p\(\rightarrow \)4s transitions at higher argon contributions in \(\hbox {Ar}/\hbox {O}_{2}\) mixture is higher. It is found that, at higher Ar percentages, the emission intensities from atomic oxygen (O) are higher and, the line intensities from the argon atoms and ions including O atoms linearly increase. It is observed that the quenching of \(\hbox {Ar}^{*}\) with \(\hbox {O}_{2}\) results in higher O species with respect to \(\hbox {O}_{2}\) molecules. In addition, at higher percentages of Ar in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture, while the excitation temperature is decreased, the electron density is increased.     

Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets \(\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )\) are studied for negative admissible levels k, as are certain infinite-order simple current extensions \(\mathsf {B}_{k}\) of \(\mathsf {C}_{k}\). Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to \(\mathsf {C}_{k}\), irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-modules are obtained from those of \(\mathsf {L}_{k}(\mathfrak {sl}_{2})\). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible \(\mathsf {B}_{k}\)-modules. The irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the \(\mathsf {B}_{k}\) are \(C_2\)-cofinite vertex operator algebras.     

First-principle calculations of structural,electronic, optical,elastic and thermal properties of $$\hbox {MgXAs}_{2}$$ ($$\hbox {X}=\hbox {Si}, \hbox {Ge}$$X=Si,Ge) compounds

First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite \(\hbox {MgXAs}_{2}\) (\(\hbox {X}=\hbox {Si}, \hbox {Ge}\)) have been performed within the density functional theory (DFT) using the full-potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson (mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, \(C_{11}\), \(C_{12}\), \(C_{13}\), \(C_{33}\), \(C_{44}\) and \(C_{66 }\) are evaluated. The effects of temperature and pressure on some macroscopic properties of \(\hbox {MgSiAs}_{2}\) and \(\hbox {MgGeAs}_{2}\) are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.     

Photoreflectance spectroscopy of the chalcopyrite semiconductor <Emphasis Type="Bold">AgInS</Emphasis><Subscript>2</Subscript> for ordinary and extraordinary rays

Photoreflectance spectra have been measured on the chalcopyrite semiconductor silver indium disulfide (\(\hbox {AgInS}_{2}\)) for light polarization \({\varvec{E}}\) perpendicular (\({\varvec{E}} \bot {c}\)) and parallel to the c-axis (\({\varvec{E}} \vert \vert {c}\)) at temperature between 10 and 300 K. The measured photoreflectance spectra revealed distinct structures at 1.8–2.1 eV. The lowest bandgap energies \(E_{0A}\), \(E_{0B}\), and \(E_{0C}\) of \(\hbox {AgInS}_{2}\) show unusual temperature dependence at low temperatures (\(\le\)140 K). The \(E_{0\alpha }\) (\(\alpha =A, B, C\)) is found to increase with increasing temperature from 10 to \(\sim\)140 K and decreases with a further increase in temperature. This result has been successfully explained by taking into account the effects of thermal expansion and electron–phonon interaction. The spin–orbit and crystal-field splitting parameters of \(\hbox {AgInS}_{2}\) are determined to be \(\Delta _{{\mathrm{so}}}=38\) meV and \(\Delta _{{\mathrm{cr}}}=-168\) meV at T = 10 K, respectively, and are discussed from an aspect of the electronic energy band structure consequences. The temperature dependence of spin–orbit and crystal-field splitting parameters of \(\hbox {AgInS}_{2}\) was also presented.     

Nuclear suppression of the $$\phi $$ meson yields with large $$p_T$$pT at the RHIC and the LHC

We calculate \(\phi \) meson transverse momentum spectra in \(\mathrm{p}+\mathrm{p}\) collisions as well as their nuclear suppressions in central \(\mathrm{A}+\mathrm{A}\) collisions both at the RHIC and the LHC in LO and NLO with the QCD-improved parton model. We have included the parton energy loss effect in a hot/dense QCD medium with the effectively medium-modified \(\phi \) fragmentation functions in the higher-twist approach of jet quenching. The nuclear modification factors of the \(\phi \) meson in central \(\mathrm{Au}+\mathrm{Au}\) collisions at the RHIC and central \(\mathrm{Pb}+\mathrm{Pb}\) collisions at the LHC are provided, and nice agreement of our numerical results at NLO with the ALICE measurement is observed. Predictions of the yield ratios of neutral mesons such as \(\phi /\pi ^0\), \(\phi /\eta \) and \(\phi /\rho ^0\) at large \(p_T\) in relativistic heavy-ion collisions are also presented for the first time.     

Translation Invariant Extensions of Finite Volume Measures

We investigate the following questions: Given a measure \(\mu _\Lambda \) on configurations on a subset \(\Lambda \) of a lattice \(\mathbb {L}\), where a configuration is an element of \(\Omega ^\Lambda \) for some fixed set \(\Omega \), does there exist a measure \(\mu \) on configurations on all of \(\mathbb {L}\), invariant under some specified symmetry group of \(\mathbb {L}\), such that \(\mu _\Lambda \) is its marginal on configurations on \(\Lambda \)? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which \(\mathbb {L}=\mathbb {Z}^d\) and the symmetries are the translations. For the case in which \(\Lambda \) is an interval in \(\mathbb {Z}\) we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which \(\mathbb {L}\) is the Bethe lattice. On \(\mathbb {Z}\) we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When \(\Lambda \subset \mathbb {Z}\) is not an interval, or when \(\Lambda \subset \mathbb {Z}^d\) with \(d>1\), the LTI condition is necessary but not sufficient for extendibility. For \(\mathbb {Z}^d\) with \(d>1\), extendibility is in some sense undecidable.     

Quantum Electrodynamics of Atomic Resonances

A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass m, finitely many excited states and an electric dipole moment, \({\vec{d}_0 = -\lambda_{0} \vec{d}}\), where \({\| d^{i}\| = 1, i = 1, 2, 3,}\) and \({\lambda_0}\) is proportional to the elementary electric charge. The interaction of the atom with the radiation field is described with the help of the Ritz Hamiltonian, \({-\vec{d}_0 \cdot \vec{E}}\), where \({\vec{E}}\) is the electric field, cut off at large frequencies. A mathematical study of the Lamb shift, the decay channels and the life times of the excited states of the atom is presented. It is rigorously proven that these quantities are analytic functions of the momentum \({\vec{p}}\) of the atom and of the coupling constant \({\lambda_0}\), provided \({\vert\vec{p} \vert < mc}\) and \({\vert \Im \vec{p} \vert}\) and \({\vert \lambda_{0} \vert}\) are sufficiently small. The proof relies on a somewhat novel inductive construction involving a sequence of ‘smooth Feshbach–Schur maps’ applied to a complex dilatation of the original Hamiltonian, which yields an algorithm for the calculation of resonance energies that converges super-exponentially fast.     

One-pot synthesis of $$\upgamma $$-spiroiminolactones and $$\upgamma $$-dispiroiminolactones using $$\textit{N}{,}{} \textit{N}^{\prime }$$N,N′-disubstituted parabanic acid and thioparabanic acid derivatives

A direct entry and simple process for the synthesis of \(\upgamma \)-spiroiminolactones present in a large number of natural products has been developed. In the first step, the synthesis of parabanic acid derivatives was commenced from the reaction of \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted urea and thiourea with oxalyl chloride, then a three-component reaction was carried out with isocyanides, acetylenic esters, and \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted parabanic acid derivatives. The method allows the construction of a variety of \(\upgamma \)-spiroiminolactone structures in good to high yields starting from readily available precursors. It was found that in the case of \(\textit{N}{,}{} \textit{N}^{\prime }\)-diphenyl thioparabanic acid, additional products of \(\upgamma \)-dispiroiminolactones have been formed due to the higher electrophilicity of \(\upalpha \)-dicarbonyl groups. The structures were fully established using spectroscopic analysis NMR, IR, and Mass spectrometry. The crystal structure of \(\upgamma \)-dispiroiminolactone was confirmed from single-crystal X-ray diffraction study.     

Unbounded Trace Orbits of Thue–Morse Hamiltonian

It is well known that, an energy is in the spectrum of Fibonacci Hamiltonian if and only if the corresponding trace orbit is bounded. However, it is not known whether the same result holds for the Thue–Morse Hamiltonian. In this paper, we give a negative answer to this question. More precisely, we construct two subsets \(\Sigma _{II}\) and \(\Sigma _{III}\) of the spectrum of the Thue–Morse Hamiltonian, both of which are dense and uncountable, such that each energy in \(\Sigma _{II}\cup \Sigma _{III}\) corresponds to an unbounded trace orbit. Exact estimates on the norm of the transfer matrices are also obtained for these energies: for \(E\in \Sigma _{II}\cup \Sigma _{III}, \) the norms of the transfer matrices behave like

$$\begin{aligned} e^{c_1\gamma \sqrt{n}}\le \Vert T_{ n}(E)\Vert \le e^{c_2\gamma \sqrt{n}}. \end{aligned}$$

However, two types of energies are quite different in the sense that each energy in \(\Sigma _{II}\) is associated with a two-sided pseudo-localized state, while each energy in \(\Sigma _{III}\) is associated with a one-sided pseudo-localized state. The difference is also reflected by the local dimensions of the spectral measure: the local dimension is 0 for energies in \(\Sigma _{II}\) and is larger than 1 for energies in \(\Sigma _{III}.\) As a comparison, we mention another known countable dense subset \(\Sigma _I\). Each energy in \(\Sigma _I\) corresponds to an eventually constant trace map and the associated eigenvector is an extended state. In summary, the Thue–Morse Hamiltonian exhibits “mixed spectral nature”.

     

Fully constrained Majorana neutrino mass matrices using $$\varvec{\varSigma (72\times 3)}$$

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (\(\nu _2\)) columns, namely tri-chi-maximal mixing (\(\text {T}\chi \text {M}\)) and tri-phi-maximal mixing (\(\text {T}\phi \text {M}\)), were proposed. In 2012, it was shown that \(\text {T}\chi \text {M}\) with \(\chi =\pm \,\frac{\pi }{16}\) as well as \(\text {T}\phi \text {M}\) with \(\phi = \pm \,\frac{\pi }{16}\) leads to the solution, \(\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}\), consistent with the latest measurements of the reactor mixing angle, \(\theta _{13}\). To obtain \(\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}\) and \(\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}\), the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, \(m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}\). In this paper we construct a flavour model based on the discrete group \(\varSigma (72\times 3)\) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric \(3\times 3\) matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of \(\varSigma (72\times 3)\). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.     

Excited state mass spectra of doubly heavy $$\Xi $$ baryons

In this paper, the mass spectra are obtained for doubly heavy \(\Xi \) baryons, namely, \(\Xi _{cc}^{+}\), \(\Xi _{cc}^{++}\), \(\Xi _{bb}^{-}\), \(\Xi _{bb}^{0}\), \(\Xi _{bc}^{0}\) and \(\Xi _{bc}^{+}\). These baryons consist of two heavy quarks (cc, bb, and bc) with a light (d or u) quark. The ground, radial, and orbital states are calculated in the framework of the hypercentral constituent quark model with Coulomb plus linear potential. Our results are also compared with other predictions, thus, the average possible range of excited states masses of these \(\Xi \) baryons can be determined. The study of the Regge trajectories is performed in (n, \(M^{2}\)) and (J, \(M^{2}\)) planes and their slopes and intercepts are also determined. Lastly, the ground state magnetic moments of these doubly heavy baryons are also calculated.