Moment of inertia of superconductors

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount $m_e/(\pi r_c)$, with $m_e$ the bare electron mass and $r_c=e^2/m_e{c}^2$ the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia $m_e{(2{\lambda }_L)}^2$, with ${\lambda }_L$ the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting.     

Thermodynamic calculation of spin scaling functions

Critical phenomena theory centers on the scaled thermodynamic potential per spin $?(\beta ,h)=|t{|}^{p}Y(h|t{|}^{?q})$, with inverse temperature $\beta =1/T$, $h=?\beta H$, ordering field H, reduced temperature $t=t(\beta )$, critical exponents p and q, and function $Y(z)$ of $z=h|t{|}^{?q}$. I discuss calculating $Y(z)$ with the information geometry of thermodynamics. Scaled solutions are found to obtain with three admissible functions $t(\beta )$: 1) $t=e^{?J\beta }$, 2) $t={\beta }^{?1}$, and 3) $t={\beta }_C?\beta$, where J and ${\beta }_C$ are constants. For $p=q$, information geometry yields $Y(z)=\sqrt{1+z^2}$, consistent with the one-dimensional (1D) ferromagnetic Ising model.     

Topological states in the Hofstadter model on a honeycomb lattice

We provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux ϕ. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion U (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\mathrm{\Delta }$, the topological insulator state, which is determined by chiral gapless edge modes in the gap Δ, is destroyed.     

Multi-objective optimization of the cavitation generation unit structure of an advanced rotational hydrodynamic cavitation reactor

Hydrodynamic cavitation (HC) has been widely considered a promising technique for industrial-scale process intensifications. The effectiveness of HC is determined by the performance of hydrodynamic cavitation reactors (HCRs). The advanced rotational HCRs (ARHCRs) proposed recently have shown superior performance in various applications, while the research on the structural optimization is still absent. The present study, for the first time, identifies optimal structures of the cavitation generation units of a representative ARHCR by combining genetic algorithm (GA) and computational fluid dynamics, with the objectives of maximizing the total vapor volume, $V_{\mathit{vapor}}$ , and minimizing the total torque of the rotor wall, ${\overrightarrow{M}}_z$ . Four important geometrical factors, namely, diameter (D), interaction distance (s), height (h), and inclination angle (θ), were specified as the design variables. Two high-performance fitness functions for $V_{\mathit{vapor}}$ and ${\overrightarrow{M}}_z$ were established from a central composite design with 25 cases. After performing 10,001 simulations of GA, a Pareto front with 1630 non-dominated points was obtained. The results reveal that the values of s and θ of the Pareto front concentrated on their lower (i.e., 1.5 mm) and upper limits (i.e., 18.75°), respectively, while the values of D and h were scattered in their variation regions. In comparison to the original model, a representative global optimal point increased the $V_{\mathit{vapor}}$ by 156% and decreased the ${\overrightarrow{M}}_z$ by 14%. The corresponding improved mechanism was revealed by analyzing the flow field. The findings of this work can strongly support the fundamental understanding, design, and application of ARHCRs for process intensifications.     

A Family-nonuniversal U(1)′ Model for Excited Beryllium Decays

Excited beryllium has been observed to decay into electron-positron pairs with a $6.8\sigma$ anomaly. The process is properly explained by a 17 MeV proto-phobic vector boson. In present work, we consider a family-nonuniversal $U{\left(1\right)}^{\prime }$ that is populated by a $U{\left(1\right)}^{\prime }$ gauge boson $Z^{\prime }$ and a scalar field $S,$ charged under $U{\left(1\right)}^{\prime }$ and singlet under the Standard Model (SM) gauge symmetry. The SM chiral fermion and scalar fields are charged under $U{\left(1\right)}^{\prime }$ and we provide them to satisfy the anomaly-free conditions. The Cabibbo-Kobayashi-Maskawa (CKM) matrix is reproduced correctly by higher-dimension Yukawa interactions facilitated by $S$. The vector and axial-vector current couplings of the $Z^{\prime }$ boson to the first generation of fermions do satisfy all the bounds from the various experimental data. The $Z^{\prime }$ boson can have kinetic mixing with the hypercharge gauge boson and $S$ can directly couple to the SM-like Higgs field. The kinetic mixing of $Z^{\prime }$ with the hypercharge gauge boson, as we show by a detailed analysis, generates the observed beryllium anomaly. We find that beryllium anomaly can be properly explained by a MeV-scale sector with a minimal new field content. The minimal model we construct forms a framework in which various anomalous SM decays can be discussed.     

Electronic vacuum charge for an overcritical nucleus

A “cut-off” Coulomb potential taking into account the finite size of the nucleus is finite, and a solution of the Dirac equation can be constructed for any energy, both positive and negative. In the paper we develop an exact solution of the Dirac equation for a fixed value of the total momentum j for the whole spectrum of energies, which allows us to determine the vacuum charge and its spatial distribution. We consider nuclei with different charges Z, both $Z<Z_c$ and $Z>Z_c$, where $Z=Z_c$ is the “critical” charge, at which the energy of the lowest discrete state reaches the boundary of the lower continuum $\epsilon =?m{c}^2$. Polarization of vacuum is determined, and the vacuum charge for several values of Z is found. For an undercritical nuclear charge, $Z<Z_c$, the total vacuum charge appears to be zero, while for $Z>Z_c$, the vacuum gets rearranged, and the total vacuum charge becomes equal to $?2e$. The vacuum charge distribution for $j=1/2$ for both undercritical and overcritical nuclei is calculated.     

Molecular dynamics simulations on the effect of nanovoid on shock-induced phase transition in uranium nitride

The Angular-Dependent Potential (ADP) proposed by Tseplyaev et al. was used to study the structural behavior of uranium nitride (UN) under shock pressure by molecular dynamics (MD) simulations. Based on the calculations of shock velocity $U_S$ and particle velocity $U_P$, the results show that a pressure-induced phase transition of $\mathit{Fm}?3m\to R?3m$ structure in UN occurs at 35 GPa, and it agrees well with experimental results of 30–32 GPa. We also considered the effect of nanovoid on the phase transition of UN crystal from $Fm?3m$ to $R?3m$ structure. It is found that the pressure of phase transition decreases with the increasing nanovoid diameter. The phase transition takes place firstly around nanovoid, companied by the nanovoid collapsing, and then spreads to the void-free regions in the process of shock loading. Due to different stresses at different direction the spreading velocity of phase transition perpendicular to the direction of shock wave is observed to be far faster than the one parallel to the direction of shock wave.